- Email: [email protected]
Different strategies of foam stabilization in the use of foam as a fracturing fluid
Journal Pre-proof Different strategies of foam stabilization in the use of foam as a fracturing fluid
Jun Zhou, P.G. Ranjith, W.A.M. Wanniarachchi PII:
S0001-8686(19)30321-5
DOI:
https://doi.org/10.1016/j.cis.2020.102104
Reference:
CIS 102104
To appear in:
Advances in Colloid and Interface Science
Revised date:
1 January 2020
Please cite this article as: J. Zhou, P.G. Ranjith and W.A.M. Wanniarachchi, Different strategies of foam stabilization in the use of foam as a fracturing fluid, Advances in Colloid and Interface Science(2020), https://doi.org/10.1016/j.cis.2020.102104
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier.
Journal Pre-proof Different Strategies of Foam Stabilization in the Use of Foam as a Fracturing Fluid Jun Zhou1 , P.G. Ranjith*1 , W.A.M. Wanniarachchi1 1
Department of Civil Engineering, Monash University, Building 60, Melbourne, Victoria,
3800, Australia. *Corresponding author:
oo f
Prof. Ranjith PG Deep Earth Energy Laboratory, Monash University, Building 60,
pr
Melbourne, Victoria, 3800, Australia. Phone/Fax: 61-3-9905 4982
Abstract
al
Pr
e-
E-mail: [email protected]
rn
An attractive alternative to mitigate the adverse effects of conventional water-based fluids on the efficiency of hydraulic fracturing is to inject foam-based fracking fluids into reservoirs.
Jo u
The efficiency of foaming fluids in subsurface applications largely depends on the stability and transportation of foam bubbles in harsh environments with high temperature, pressure and salinity, all of which inevitably lead to poor foam properties and thus limit fracturing efficiency. The aim of this paper is to elaborate popular strategies of foam stabilization under reservoir conditions. Specifically, this review first discusses three major mechanisms governing foam decay and summarizes recent progress in research on these phenomena. Since surfactants, polymers, nanoparticles and their composites are popular options for foam stabilization, their stabilizing effects, especially the synergies in composites, are also reviewed. In addition to reporting experimental results, the paper also reports recent advances in interfacial properties via molecular dynamical simulation, which provide new insights into gas/liquid interfacial properties under the influence of these popular additives at molecular scale. The results of both experiments and simulations indicate that foam additives play an
1
Journal Pre-proof essential role in foam stability and the synergic effects of surfactants and nanoparticles exhibit more favorable performance.
Keywords: Foam-based fracking fluids; foam stability; stabilizing mechanisms; synergistic effects;
Jo u
rn
al
Pr
e-
pr
oo f
molecular dynamic simulation
2
Journal Pre-proof Contents 1 INTRODUCTION .................................................................................................................. 5 2 MECHANISMS GOVERNING FOAM AGING................................................................... 6 2.1 LIQUID DRAINAGE IN AQUEOUS FOAM ............................................................................... 7 2.2 COARSENING IN AQUEOUS FOAM..................................................................................... 11 2.3 BUBBLE COALESCENCE IN AQUEOUS FOAM ...................................................................... 13
3 STRATEGIES OF FOAM STABILIZATION..................................................................... 14 3.1 SURFACTANT-STABILIZED FOAM ..................................................................................... 14 3.1.1 THERMALLY STABLE SURFACTANTS ...................................................................................................... 16
oo f
3.1.2 SYNERGISTIC EFFECT O F COMPOUND SURFACTANTS ......................................................................... 18
3.2 P OLYM ER-ENHANCED FOAM ........................................................................................... 23 3.2.1 MECHANISM................................................................................................................................................ 23
pr
3.2.2 RECENT PROGRESS IN POLYMER-ENHANCED FOAM........................................................................... 24
3.3 NANOPARTICLE-STABILIZED FOAM ................................................................................. 26
e-
3.3.1 MECHANISMS O F IN-SITU SURFACE ACTIVATIO N O F NP ................................................................... 26 3.3.2 SYNERGISTIC EFFECTS O F SURFACTANTS AND NANOPARTICLES..................................................... 28
Pr
4 MOLECULAR DYNAMIC SIMULATION OF FOAM STABILITY ............................... 31 4.1 SIMULATION METHODS ................................................................................................. 31 4.2 LITERATURE RES ULTS FROM MOLECULAR S IMULAT ION ............................................... 32
al
CONCLUSION ........................................................................................................................ 36
Jo u
Nomenclature
rn
REFERENCES ..................................................... ERROR! BOOKMARK NOT DEFINED.
AOS: Alpha olefin sulfonate
AOT: Bis-(2-ethylhexyl) sulfosuccinate sodium CTAB: Cetyltrimethylammonium bromide CTAC: Cetyltrimethylammonium chloride CB: Cetyl betaine CAPB: Cocoamidopropyldimethyl betaine (C12–14 tail) CHSB: Cocamidopropyl hydroxyl sulfobetaine
CMC: Critical micelle concentration DSB: Dodecyl sulfobetaine DDAPS: N-Dodecyl-N, N-dimethyl-3-ammonio-1-propanesulfonate DMDCS: Dimethyldichlorosilane EPS: Exopolysaccharide
3
Journal Pre-proof EAPB: Erucylamidopropyldimethyl betaine (C18 tail) HT: high temperature, HS: high salinity HPAM: Hydrolysis of partially hydrolyzed polyacrylamide LDEA: Lauryl diethanol amide NaSal: Sodium salicylate OAPB: Oleylamidopropyldimethyl betaine (C22 tail) OA-12: Lauryl dimethyl amine oxide OTAB: Octadecyltrimethylammonium Bromide SDS: Sodium dodecyl sulfate
oo f
SDBS: Sodium dodecylbenzene sulfonate TDS: Total dissolved solids
pr
TMHDA: N, N, N′, N′-tetramethyl-1, 6-hexanediamine) TX-100: Polyoxyethylene octyl phenyl ether
Jo u
rn
al
Pr
e-
PAM: Polyacrylamide
4
Journal Pre-proof
1 Introduction Hydraulic fracturing is an effective stimulation technique for the extraction of unconventional natural gas from ultra- low permeable reservoirs [1]. During the fracturing process, highly pressurized fluids are pumped into reservoirs to create fractures, and solid proppants are then added to the fracturing fluids in order to prevent cracks from closing again after pumping stops. In this case, the fracturing fluid is a crucial element in determining the long-term productivity of a fractured reservoir [2]. To our knowledge, the most widely- used fracking fluid is water, and its advantages and disadvantages are fully reviewed in [3]. Compared with water-based fluids, foam-based fracturing fluid has great advantages, including lower water
oo f
consumption, higher proppant-carrying capability, less formation damage and quicker flowback efficiency [4-6]. Therefore, foam-based fracturing fluid is an attractive alternative
pr
to conventional water- based fracturing fluids.
Nevertheless, there are some issues in the field application of foam-based fluids. One major
e-
challenge is how to maintain the long-term stability of foaming fluids during the fracturing process [7, 8]. Due to the inherent complexities of the two-phase fluid, injected foam in the
Pr
reservoir cannot remain stable until the fracking process finishes, and failure to maintain foam stability causes untimely distribution of proppants in fractures, leading to low fracture
al
conductivity. Three recognized mechanisms govern the foam decay process: liquid drainage,
rn
coarsening, and bubble coalescence [9]. To mediate these phenomena, various chemical additives are added to foaming solutions. Surfactants, commonly used as foaming agents,
Jo u
also limit coarsening and bubble coalescence by reducing the rate of gas diffusion and film thinning due to the presence of adsorbed surfactant
layers at the interface [10]. Some
polymers can also enhance foam stability by increasing the viscosity of the liquid phase and forming a chain network between films to constrain liquid drainage and coarsening [11, 12]. However, some vital factors limit the application of these chemical additives in the field. For example, most surfactants exhibit a high tendency for degradation or adsorption onto mineral surfaces under harsh reservoir conditions (e.g. the temperature may be up to 120 ℃, injecting pressure may be over 20 MPa and brine salinity is from 0.3 to 21 wt%) [13-15]. In the case of polymer, its residual concentration in the reservoir can reach 10-15 fold above the original rate, which potentially induces pore throat blockage and formation damage [16]. Recently, as nanoscience has developed, many researchers have reported that the addition of nanoparticles (NPs) to foaming solutions greatly improves the stability of foam, even at high temperatures and salinities [17-19]. Compared with surfactants or polymers, NPs are more stable and 5
Journal Pre-proof irreversibly aggregate at foam films because of their high desorption energy [20, 21]. Normally, surfactants are added to nanoparticle suspensions to improve NPs’ surface properties, and such synergy usually makes a foam more stable than that generated by the individual components [22, 23]. Moreover, the addition of polymers to surfactant-NP solutions can even improve foam stability further due to the presence of a supplementary steric repulsive force [24]. A large number of reviews concentrated on foam stability has been published in recent years. For example, Wang et al. [25] reported the mechanisms governing foam drainage and the effect of solid particles and several popular models concerning foam height, growth and
oo f
collapse. Yekeen et al. [26] reviewed experimental studies of NP-stabilized foams, focusing on their application in enhanced oil recovery. They discussed different experimental techniques used for studying foam properties and also proposed various parameters affecting
pr
foam stability and flow behavior in porous media. Despite these previous reviews, foam
e-
aging mechanisms have still not been fully reviewed. Furthermore, the application of special surfactants, such as zwitterionic surfactants, viscoelastic surfactants, and blended stabilizers,
Pr
greatly improves foam stability, but no attempt has been made to date to summarize these developments. Hence, the aim of the present paper is to review the major mechanisms
al
controlling the foam decay process and popular additives used for improving foam stability. The content is organized as follows: Section 2 mainly focuses on three major mechanisms
rn
governing foam aging, and strategies used for enhancing foam stability and their mechanisms
Jo u
are presented in Section 3. Section 4 introduces the application of molecular dynamic simulation to understand the effect of various stabilizers on the liquid/gas interface at a molecular scale.
2 Mechanisms governing foam aging Aqueous foam is a typical two-phase system, which can be defined as the dispersion of gas in a continuous liquid phase [27]. Fig. 1 presents the general structure of a foam, which is divided into two parts based on different liquid fractions: dry foam and wet foam. In dry foam, the gas bubbles are polyhedral and have well-defined edges, while in wet foam the bubbles are more spherical and stable [28]. Foam films (also named lamellae) are formed between two bubbles; plateau borders (PBs) are the interspace of any three approaching bubbles, and the junction of any four PBs is called a node [28, 29].
6
oo f
Journal Pre-proof
pr
Fig. 1 General structure of liquid foam: (a) foam column, (b) 3-D model of foam bubble, (c) 2-D model of foam bubble
e-
Foam is thermo-dynamically unstable, and spontaneously separates into gas and liquid phases once generated, and this instability significantly constrains the subsurface applications of
Pr
foaming fluids. Drainage, coarsening and coalescence are three major processes which occur during foam aging [30, 31], and it is noticeable that these phenomena are interdependent:
al
drainage is a major factor resulting in foam instability because it reduces the liquid content of the foam, which determines the thickness of the film [32]. Due to the reduction of film
rn
thickness, gas diffusion through films becomes easy, which causes large bubbles to become
Jo u
larger at the expense of small bubbles, eventually leading to the rupture of thinning films, and changes in bubble size distribution also increase the rate of liquid drainage in foams [33]. In the following sections these phenomena are discussed in detail.
2.1 Liquid drainage in aqueous foam Liquid drainage, which plays a dominant role in the foam destabilization process, refers to liquid flow through foam driven by gravity and capillary pressure while being resisted by viscous dissipation. More specifically, gravity results in the drainage of liquid from the network of PBs, while capillary pressure and viscous stress drain the liquid from films to PBs and may also induce liquid suction, especially at the bottom of the foam [34]. A multi-scale methodology has been constructed to understand liquid drainage in foam, which can be categorized into two major scales, as illustrated in Fig. 2. In macro-scale studies (at least several bubbles or bulk foam), researchers attempt to build a common drainage equation to describe the liquid flow process in at least several bubbles or bulk foam as well as the 7
Journal Pre-proof parameters that affect this process [35, 36]. However, in micro-scale studies, many efforts have been made to track liquid flow through a single elementary structure of foam, ignoring the interactions of the complex networks in the foam [37-40]. Since Anazadehsayed et al. [41] have already fully summarized the progress on foam drainage at a micro-scale, here we
e-
pr
oo f
provide an extensive review of recent progress in foam drainage at a macro-scale.
2.1.1 Theories of foam drainage
Pr
Fig. 2 Various research methods on foam drainage
al
To quantitatively analyze the foam drainage process, many efforts have been made to develop an easy dynamic model for foam drainage, and the earliest model of liquid drainage
rn
proposed by Leonard and Lemlich [42] assumed that flow dissipation occurs only in PB with
Jo u
finite surface viscosity. Based on their studies, several analytical models have been developed to improve the calculation of the average drainage rate and determine correlations between surface viscosity and flow velocity, which has been discussed in [30]. However, these models usually predict slower drainage rates than experimental data provide due to the initial assumption that PB plays a major role in drainage. Considering the significant hydrodynamic dissipation in the nodes, Koehler et al. [43] modified a PB-dominated model and assumed that PBs are mobile and nodes dominate dissipation, i.e. the so-called nodedominated drainage equation. Later, Cox et al. [44] proposed a generalized model coupling bubble size in time and space and extended this into two and three dimensions. The foam drainage equation is a typical nonlinear partial differential equation and later studies in this area have mainly concentrated on seeking solutions for foam drainage equations through experimental data fitting, analytical methods, and developments are summarized in Table 1. 8
numerical simulations.
Recent
Journal Pre-proof Table 1 Progress in development of foam drainage equation Source
Methods
Contributions
Helal and Mehanna [45]
Adomian decomposition method (semianalytic) and tanh method (analytic)
Mirmoradi et al. [46]
Variational iteration method
Khani [47]
Exp-function method
Darvishi and Khani [48]
Homotopy analysis method
Khan and Gondal [49]
Laplace decomposition method
He [50]
Semi-inverse method
Fadravi [51]
Homotopy analysis method
Khan and Wu [52]
Homotopy perturbation transform method
Fereidoon et al. [53]
Homotopy perturbation method
Lyiola et al. [54]
Generalised homotopy analysis method
Nikkar [55]
Variational iteration method-II
Md. Nur Alam [56]
Generalized (G’/G) expansion method
Gubes [57]
Reduced differential transform method
Somayeh Arbabi [58]
Haar wavelet method
Brito-Parada et al. [59]
Finite element method
Narsimhan [60]
Analytical method
Anazadehsayed et al. [61-63]
Computational fluid dynamics CFD
Shafiei et al. [64]
Experimental and analytical method
Obtain analytic solutions for foam drainage equation in dimensionless form:
A 2 A A A 0 t x 2 x
al
Pr
e-
pr
oo f
where, A, x and t is the cross section of a PB, location and time, respectively.
2-D model accurately resolves the dynamics of the wetting front in forced foam drainage. A model for drainage of foam film stabilized by particles 3-D model of flow through internal and external PB and node, films and transitional areas. A novel drainage model considering the impact of the concentration of surfactants, nanoparticles, and monovalent ions.
rn
Nevertheless, it is not clear if this drainage theory fully describes the foam drainage process.
Jo u
There remain large discrepancies between experiments and theoretical predictions, and one possible explanation for this disagreement is that liquid films also contribute to the drainage process by providing another region for liquid flow [65]. Sett et al. [66] developed a method for measuring the surface elasticity of vertical films suspended on a frame and found that the difference in surface tension between the upper and lower parts of the film induces Marangoni stress, which limits gravity-driven drainage to some extent. Other parameters, including the liquid content and container effects, have also attracted some attention. For example, Neethling et al. [67] extended a previous foam drainage model assuming low liquid content in the foam, and presented a new model to account for the contribution of both the plateau borders and vertices on liquid drainage over the whole range of liquid contents. SaintJalmes [68] proposed a generalized foam drainage equation which includes the effects of arbitrary container shape. Based on this model, Cox et al. [69] provided a more general solution, which not only accommodates the boundary conditions but also obtains a better
9
Journal Pre-proof approximation to the drained liquid content. In addition, Papara et al. [70] studied the effect of the container on wet foam drainage, including the diameter, wettability and shape of the walls. Recently, a multiscale model [71] was proposed to simulate the dynamics of evolving foams, including bubble rearrangement, thin film drainage and rupture, which provides some new insights in understanding how liquid drainage, bubble coarsening and coalescence influence one another on both local and global scales. 2.1.2 Macroscopic experiments on foam drainage Three major techniques are normally used in macro-scale experiments on liquid drainage based on different triggering mechanisms, including free drainage, forced drainage produced
oo f
by a continuous injection of liquid into the top of dry foam, and pulsed drainage using a finite pulse of liquid instead of continuous injection, which have been reviewed in detail by earlier studies [30, 36]. Recently, due to the application of other stabilizers, such as polymers and
pr
particles, the drainage process has become more complex. Previous researchers [72, 73]
e-
assumed that the liquid phase is Newtonian fluid, and while this is true for most surfactant foams, it is unreasonable when studying polymer-stabilized foams or those generated by high
Pr
surfactant concentrations. Unlike most surfactant solutions, polymeric solutions usually exhibit shear-thinning behavior, and the drainage rule of these foams is totally different,
al
being determined by the bulk viscosity of the liquid phase [74]. Recently, a mathematical model has been developed to describe free drainage in a polymer stabilized foam, in which
rn
the rheological parameters of the liquid phase are measured independently [75]. The model
Jo u
successfully predicts the equilibrium profile of the liquid volume fraction and shows that this volume is unrelated to the power law index of non-Newtonian liquid [75]. With the presence of particles in the foam, the drainage process becomes even more complicated, being dominated by the particle size and its volume fraction [76], and their effects can be divided into four regimes based on different conditions, as illustrated in Fig. 3. Wang and Nguyen [77] conducted forced drainage experiments to stud y liquid flow in foam in the presence of silica particles. Their results show that even a small amount (0.0932 g/L) of solid particles significantly limits drainage velocity by increasing the rigidity of the interfaces and the viscous losses in the PBs of the foams, which also induce a transition of the foam drainage regime from a node-dominated regime to a PB-dominated regime.
10
Journal Pre-proof
oo f
Fig. 3 Reduced viscous drag ( V 1 , reciprocal of reduced drainage velocity) of foam as a function of the confinement parameter (the ratio of particle size to size of passage in foam) at various particle volume fractions. (Modified from [76])
Another essential factor influencing the drainage process is bubble evolution in the foam, i.e.
pr
coarsening and coalescence. An early study showed that the foam aging process has three stages: liquid drainage initially dominates coarsening, then drainage and coarsening occur
e-
concurrently, and eventually coarsening prevails over drainage [78]. Such dominant
Pr
behaviors exhibit a relationship to the surfactant concentration. Lioumbas et al. [34] studied the interaction between foam free drainage and bubble size evolution when the surfactant concentration is below its critical micelle concentration (CMC). According to their results,
al
the maximum drainage rate decreases as the surfactant concentration increases. More
rn
importantly, at a relatively lower concentration, bubble size increases at an accelerating rate during the drainage process due to the superposition of coalescence to coarsening, which is
Jo u
totally different from previous studies, in which surfactant concentration is above CMC, and bubble coalescence is unlikely to occur at an early stage [78-80]. Interestingly, a recent paper [81] also proposes that the influence of bubble size on drainage varies at different time scale s when the surfactant concentration is relatively high (0.5~5.0 CMC): at the early stage (100~300s), since liquid drains out quickly and bubbles are still very small, bubble size seems have no effect on drainage. Overall, liquid drainage is relatively easy to monitor by tracking the liquid content in the foam. However, bubble size evolution, which involves two processes: coarsening and coalescence, is very hard to track from a macroscopic viewpoint, and more efforts have been made in this area using micro-scale experiments.
2.2 Coarsening in aqueous foam Bubble coarsening refers to gas diffusion through films due to a pressure difference, and large bubbles become larger while small ones tend to disappear. For dry foams, gas mainly
11
Journal Pre-proof diffuses through adjoining films and this process in two-dimensional foams is well described by the von Neumann-Mullins law [82, 83]: dAi (ni 6) dt 3
(1)
where, Ai is the bubble area, is the effective diffusion coefficient, and ni is the sides of a bubble. Fig. 4 shows that the rate of bubble growth depends only on their topology: foam bubbles with 6 sides remain stationary and those with 7 or more sides tend to grow, while bubbles with 5 or fewer sides tend to shrink [28].
Po
Po
n < 6, films are convex on average, and Pi > Po.
n = 6, films are straight on average, and Pi = Po.
Pi
n > 6, films are concave on average, and Pi < Po.
e-
pr
Po
o
Po
oo f P
Pi
Po
Pi
Po
Po
Po Po
Pr
Fig. 4 Schematic of evolution of a 2-D bubble with different sides , n represents the number of a bubble’s faces, Pi and Po represent the inner and outer pressure of a bubble, respectively (Modified from [28]).
For 3-D dry foam, however, the growth rate of a bubble is not exactly a function of its neighbors. In recent years, many researchers have tried to extend von Neumann’s law to
al
three-dimensional dry foam and many popular models based on Equation (1) have been
rn
proposed to describe the growth rate of 3-D dry foam, which has been briefly discussed in [84, 85]. In a wet foam which contains a large amount of liquid, the film areas are much
Jo u
smaller when PBs and vertices inflate with liquid [86]. Hence, the inter-bubble gas diffusion process is totally different from that in dry foam. Roth et al. [87] extended von Neumann’s law by incorporating the border-blocking effect and this model successfully offsets the discrepancies of von Neumann’s model for wet foams. Numerical simulations are also used for studying the self- similar growth of bubbles in wet foam [86-90]. As this is beyond the scope of the present paper, we do not discuss it further. To experimentally investigate the coarsening rate in foams, one basic premise is to constrain the influence of liquid drainage, and special set- ups, including the rotating cell [91], and diamagnetic levitation [92], are used for this purpose. More directly, some experiments have been conducted under microgravity [93, 94]. Various techniques have been developed to monitor the coarsening process, including multiple light scattering, magnetic resonance imaging, optical tomography, X-ray tomography, and observation of surface bubbles. The application of various stabilizers also has a significant effect on bubble coarsening. For 12
Journal Pre-proof example, tightly packed surfactant adsorption layers block gas diffusion through liquid films [95]. For nanoparticle-stabilized foam, aggregations of surfactant-NPs at bubble surfaces even exist with higher desorption energy and serve as an irreversible “armor” around the bubble, which greatly limits the coarsening and coalescence process [96].
2.3 Bubble coalescence in aqueous foam In addition to drainage and coarsening, bubble coalescence (i.e. the rupture of two neighboring
films; refer to Fig. 5) is also an essential process inducing foam aging.
Compared with the two former processes, the mechanism of coalescence is still poorly
Contacting
Squeezing & film thinning
Coalesce
Pr
Approaching
e-
pr
oo f
understood.
Fig. 5 Schematic diagram of two bubbles coalescing
Film thickness is an important parameter which determines the coalescence process, and is
al
closely related to the force conditions at the films [97]. Based on different thicknesses, the
rn
film is divided into two types: common black film (> 5 nm) and Newton black film (3~5 nm) [98]. As stated previously, foam drainage plays a dominant role in the initial foam aging
Jo u
process, and film thinning occurs due to the loss of liquid. However, when the liquid content in the foam is so limited that bubbles cannot rearrange, avalanches of coalescence then occur [99]. The film stability is governed by the in-situ force conditions which can be described by the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory: the electrostatic repulsive force that stabilizes film and van der Waals forces that destabilize film [100-102]. To explain stratification during film thinning, several kinds of
non-DLVO forces have also been
proposed, including oscillatory structural force considering the effect of particles [103, 104], and steric interaction due to the application of polymers [105]. The influence of these forces on film thinning and its stability has been reviewed in [106]. However, the film thinning process in foam is more complex due to the presence of surface active agents at the interface, the first of which is the so-called the Gibbs-Marangoni effect [107]. Fig. 6 shows the reaction of a liquid film to a surface disturbance; film thinning leads to an increase in the local surface area, resulting in a local surfactant concentration gradient 13
Journal Pre-proof from the intact area to the thinned region. This concentration gradient then drives a surfactant flow to provide a temporary restoring force to thin films, thus finally stabilizing the thinned film [108]. This is true for dilute pure surfactant foam, for foam-stabilized polymer or mixed surfactants; however, surface viscoelasticity (surface elasticity and surface viscosity) become more important [35]. As coherent surface adsorption layers form acting as an elastic membrane, most disturbances cannot easily rupture the film. The application of surfactantcompounded surfactants or polymers and their superior stabilizing effects is discussed in the following section.
oo f
Gas
pr
Gas
e-
Film repair
Gas
Film drainage
Gas
al
Pr
Marangoni effects Gas Surfactant gradient Film drainage
Film thinning
Marangoni flow
Gas
rn
Fig. 6 Schematic diagram of Gibbs -Marangoni effect (Modified from [108])
Jo u
3 Strategies of Foam Stabilization The thermodynamic instability of the foam is a major concern that affects effectiveness in practical application. Drainage, coarsening and coalescence are three major phenomena which are interdependent and interrelated and finally cause foam decay. In the previous section these decay mechanisms and possible factors influencing them have been fully reviewed, and in this section, three strategies are discussed to mitigate these processes and extend the lifetime of foam.
3.1 Surfactant-stabilized foam Surfactants are the most common foaming agents, and are normally classified into four types based on their head groups: anionic surfactants (positively charged), cationic surfactants (negatively charged), nonionic surfactants (uncharged) and zwitterionic surfactants (containing both positive charge and negative charge) [109]. A brief summary of the characteristics of different surfactants is presented in Table 3. Concerning the effectiveness of 14
Journal Pre-proof surfactants, it is well known that surfactants decrease surface tension at the gas/liquid interface, and CMC is an essential characteristic to evaluate its maximum dosage, above which the surface tension no longer decreases and surfactant micelles start to generate in the liquid [110], as shown in Fig.7.
Table 2 Comparison of different types of surfactant Common examples Properties Surfactants contain anionic Solubility highly dependent on temperature and easily head group, e.g. AOS, SDS. hydrolyses at HT & pH <4 [111]. Low adsorption to negatively-charged minerals [112]. Cationic Surfactants contain cationic High solubility and stability at HTHS [113]. head group, e.g. CTAB, Readily adsorb on rocks or minerals. DTAC. Nonionic Surfactants have no charged High adsorption to mineral surface [112]. head group, e.g. Ethoxylates High tendency to precipitate at HTHS (T > cloud point). Less sensitive to water hardness and salinity tolerance [114]. Zwitterionic Surfactants have both Potential to form wormlike micelles which exhibit higher cationic and anionic group, thermal stability [115]. e.g. Betaine salts. Relatively expensive. AOS: alpha olefin sulfonate, SDS: Sodiu m dodecyl sulfate, CTAB: Cetyltrimethylammoniu m bro mide, DTAC:
e-
pr
oo f
Type Anionic
Pr
Dodecyltrimethylammoniu m chloride, HT: high temperature, HS: high salinity.
Extensive studies on surfactant-stabilized foam have been conducted and the mechanisms of foam stabilization have attracted significant attention [116-119]. As stated in Section 2, liquid
al
drainage, coarsening and coalescence are three major aging phenomena, and one fundamental
rn
solution to stabilize foams is to constrain these three processes. For surfactants, the stabilizing mechanism can be summarized in two ways: (a) adsorbed surfactants at foam
Jo u
films improve the interfacial properties (e.g. surface elasticity, surface viscosity) which constrain bubble coarsening and coalescence; (b) self-assembly micelles in the solution decrease the drainage rate [115, 120-122]. Head
Gas
Tail
Surfactant
Surface tension
Liquid
CMC Surfactant concentration
Fig. 7 Schematic of surface tension change with increasing concentration and formation of micelles
15
Journal Pre-proof In field applications, the performance of a surfactant is highly dependent on reservoir conditions, such as temperature, pressure and salt concentration. Based on a previous study [109], most surfactants exhibit a high tendency to degrade or precipitate when the temperature is beyond 120 °C. In addition, the CMC of most surfactants is dependent on these external conditions [123-125]. As Fig. 8 shows, the CMC of ionic surfactants initially decreases with increasing temperature to a minimum and then sharply increases, especially over 120 °C [123]. Under relatively low pressure (< 50 MPa), CMC monotonic ally increases with increased pressure [124, 125]. In other words, to obtain optimum performance under reservoir conditions, the required quantity becomes larger, and thus increases the industrial
oo f
cost. Moreover, in such environments, surfactants, especially ionic surfactants, easily adsorb on the surface of reservoir rocks and minerals, which causes great surfactant loss and results in foam destabilization. Furthermore, the presence of divalent salts in reservoirs decreases the
0.28
8
AOS Empigen
Dow XS Varion
Dowfax Fluorad
e-
In 2.33% NaCl: In 2.1% TDS: 0.10
0.26
Pr
0.08
0.24
0.06 0.04
4
CMC (mM)
6
0.02
al
CMC (mM)
pr
solubility of surfactants and thus increases their loss [112, 126].
0.00 20
40
60
80
100
0.20
0 0
25
50
Jo u
rn
2
75
100
125
150
0.22
0.18
0.16 175
Temperature (℃ )
(a)
200
0
50
100
150
200
250
300
350
Pressure (MPa)
(b)
Fig. 8 Influence of temperature (a) and pressure (b) on CMC of surfactants. Surfactants used in (a), AOS: an anionic olefin sulfonate, Dowfax: an anionic alkyl aromatic sulfonate, Dow XS: a 50:50 blend of these two sulfonates. Three zwitterionic surfactants, Empigen: carboxyl-betaine, Varion: sulfobetaine, Fluorad: fluorinated sulfobetaine. Surfactant in (b) is TX100, a nonionic surfactant. (Data from [123, 124])
To mitigate the negative effects of traditional surfactants on the subsurface application of foam, several novel surfactants have been introduced or synthetized as foam stabilizers and show favorable performance in foam stabilization under high temperature, pressure and/or salinity conditions. In the following sections the focus is on recent advances in these special surfactants.
3.1.1 Thermally-stable surfactants (i) Effects of zwitterionic surfactants
16
Journal Pre-proof Zwitterionic (or amphoteric) surfactants are becoming popular in foam stabilization because they maintain foam stability over 100 ℃ [127, 128]. Their superior properties mainly depend on their special functional groups, including ethylene oxide units, ethoxy units and saturated/unsaturated tail groups. Hussain et al. [129] synthesized betaine zwitterionic surfactants by incorporating ethoxy units and their results showed that the surfactants generated exhibit high solubility and salt tolerance in formation water and seawater, and maintain thermal stability up to 280 °C. They also studied the effect of the hydrophobic tails of surfactants on their stability and solubility, and found that surfactants with unsaturated tails possess excellent long-range heat stability [130]. Many recent studies have reported that
oo f
the foam generated by zwitterionic surfactants exhibits superior properties under conditions similar to reservoirs, and a summary of the experiments and major findings of recent studies relating to these surfactants is shown in Table 3.
Surfactants
Experimental conditions T (℃) P (MPa) Salinity
Main findings
e-
Ref.
pr
Table 3 Recent experiments on foam stabilized by zwitterionic surfactants
[132]
Ammonyx® LMDO, PETROSTEP ® SB
98.9
[133]
CAPB OAPB EAPB
[134]
CHSB
-
22% TDS
Pr
~150
al
CB
22
-
Jo u
rn
[131]
~120
-
-
[135]
OAPB EDAB MACAT Ethoquad Triameen Aromax Ethomeen
20/50/9 0
-
-
[136]
DSB+EPS
50
-
-
17
1. CB is thermally stable at 135℃ for 30 days, and C/W foam is stabilized at temperatures up to 150 ℃. 2. Core flood test indicates that CB stabilize sC/W foam within 6 pore volumes of injection at 120 ℃. 1. All surfactants can generate foams under these conditions 2. Foam viscosity increases with surfactant concentration. 3. Injection quality is important for foam generation in some cases. 1. CO2 foam (quality: 0.99) is highly thermally stable (120 ℃) and also highly viscous (>100 cP). 2. Long carbon tail (C18 &C22 ) can generate viscoelastic wormlike micelles over a wide range of salinity and pH. 3. Apparent viscosities reached more than 120 cP with stabilities more than 30-fold over CAPB foam. 1. Excellent performance at temperature of 120 °C and salinity of 220 g/L and good longterm stability after aging for 60 days . 1. Any type of surfactants can generate viscoelastic solution. 2. Foam’s long-term stability is related to aqueous phase viscosity, and N2 foam have much higher apparent viscosity than CO2 . 3. Extremely high temperatures lead to less foam stability and lower apparent viscosity than lower temperatures. 1. EPS/DSB solution exhibits better foamability and foam stability than single DSB solution.
Journal Pre-proof
[137]
DDAPS
-
1. The effectiveness of salts in reducing the foam stability followed the sequence: AlCl3 > CaCl2 > NaCl 2. The foam collapse rate was reduced in the presence of salt. 3. The effectiveness of salts in reducing the zeta potential was in the sequence: AlCl3 > CaCl2 > NaCl.
0/10%/5 0%
-
(ii) Effects of viscoelastic surfactants Viscoelastic surfactants are those which generate wormlike micelles in foaming solutions when dissolved above their CMC and also possess viscosity-modifying properties, acting as small molecular polymers [138]. Foam generated by viscoelastic surfactants exhibits many
oo f
advantages: ultralow consumption of water, greatly increased viscosity and superior stability at high temperatures and pressures. Xue et al. [139] generated highly stable CO 2 foams with ultra- low water fractions (foam quality up to 98%) under high pressure. The foam was
pr
stabilized with a viscoelastic solution containing viscoelastic wormlike micelles formed by binary surfactants with added salts. The viscosity of these ultra-dry foams is 3-4 fold greater
e-
than traditional foams, and their stability is considerably enhanced due to the limited lamella
Pr
drainage rate as well as the coarsening rate. Alzobaidi et al. [133] proposed a different method to produce ultra-dry foam by mixing single zwitterionic surfactant with salts and these foams remain stable even at temperatures up to 120℃. In another study [135], these
al
researchers also reported that viscoelastic solutions can be produced by nonionic, cationic,
rn
and zwitterionic surfactants under ambient conditions. Their results show that a slight increase in temperature (from 25℃ to 50℃) leads to better foamability and stability due to the
Jo u
better interfacial activity of the surfactant. As expected, the viscosity of foam becomes lower with further increase in temperature (from 50 ℃ to 90℃). The capabilities of proppant transport and distribution of such kinds of foam have also been tested, and the results are favorable. Elhag et al. [140] attempted to compare the performance of foam stabilized by different viscoelastic surfactants. According to their results, compared with spherical micelles, entangled viscoelastic micelles in the liquid lamellae exhibit higher viscosity and stability. (iii) Role of gemini surfactants Unlike the surfactants discussed above, gemini surfactants normally consist of two head groups and a tail group linked by a spacer at or near the head groups. Previous studies have demonstrated that the foamability and foam stability of gemini surfactants mainly depend on the length of the spacers [141]. As their potential application in reservoir stimulation has been discussed in a recent review [142], it is not explored further here. 3.1.2 Synergistic effect of compound surfactants 18
Journal Pre-proof In addition to the application of thermally-stable surfactants, the synergisms of mixing conventional surfactants have also attracted the attention of researchers [143-145]. Some exhibit favorable performance in foam stabilization under high temperature, pressure and salinity conditions. In the research, the most commonly used compound surfactant system is a binary surfactant mixture, including three different mixing types: cationic/anionic surfactants [146-149], ionic/nonionic surfactants, and fluorocarbon/hydrocarbon surfactants (which show good performance in fire extinguishing [150], and are not discussed further here). The mechanisms of the synergisms among different surfactants are complex and depend on the structural properties of each component. For example, hydrogen bonding is dominant in
charged
atoms among surfactants,
and
oo f
the nonionic/anionic mixing system due to the presence of the -OH group and negatively electrostatic attractions are common
in
cationic/anionic mixing systems because of the high charge difference [151]. For some amino
pr
acid-based surfactant mixtures, the interactions also involve cationic-effects and -effects.
e-
Some other molecular interactions in surfactant systems include ion-dipole forces between ionic/nonionic hydrophilic groups, steric forces between bulky groups, and van der Waals
Pr
forces between hydrophobic groups [152]. Due to the presence of these complex interactions, compound surfactant systems significantly improve the properties of gas/liquid systems
al
compared with systems containing solely pure surfactants, such as enhancing interfacial activity, enlarging surfactant solubility in solutions, improving micelle structure and stability,
rn
and reducing the adsorption loss of surfactants onto mineral/rock surfaces. A summary of
Jo u
some selected literature on compound surfactants and their effects on interfacial properties is presented in Table 5.
Table 5 Summary of recent advances in compound surfactants and their effects on interfacial properties and micelle formation Compound surfactants Anionic/zwitterionic Cationic/anionic ionic/nonionic Anionic/nonionic Ionic/nonionic Anionic/nonionic gemini Cationic/nonionic gemini Ionic/nonionic Cationic/anionic Cationic/anionic
19
Experimental focus Synergism of surface properties, including surface tension, adsorption behavior, elasticity. Synergism of foam stability and its mechanisms. Foam behavior and surface tension Stability of mixed micelle. Drainage coefficient of foam films formed by mixed surfactants, and effect of mixture composition on it. Synergism of micelle formation and surface tension reduction efficiency. Effect of alkyl chain length on mixed micelle. Critical thickness of foam films formed by mixed surfactants, and influence of mixture composition on it. Competition adsorption of catanionic surfactant mixtures on quartz, and its effect on wettability of quartz surface. Improvement of mixed surfactant in oil/water interfacial properties, and factors affecting it: mixing ratio, surfactant type and alky chain length.
Reference [153] [121] [154] [155] [145] [156] [157] [144] [158] [159]
Journal Pre-proof
Ionic/nonionic/zwitterionic Cationic/anionic Cationic/anionic gemini Anionic/anionic Cationic/anionic Cationic/anionic
Cationic/anionic
Cationic/anionic Anionic/nonionic
Synergism of mixed surfactants on foam stability at high temperatures (over 100℃), pressures (over 10MPa) and salinities (over 100g/L). Stable foam generated by triple surfactant mixture. Foam drainage rate under high pH and temperature (15-25℃) Formation of wormlike micelles and its effect on viscosity. Molecular simulation of micelle formation. Synergism of surface properties and micelle formation Effect of mixed surfactants on foam stability in absence and presence of crude oil, and influence of brine water. Interfacial properties and foam stability in presence of oil Synergistic effects in enhancing surface properties and micelle formation. Adsorption process of mixed surfactants. Improvement in properties of quaternary ammonium surfactant with hydroxyethyl group when coupled with anionic surfactants, and effects of mixing fraction. Synergism of foaming efficiency in high salinity. Synergism of foam stability at high temperatures (up to 130 ℃, 2 MPa), and its mechanisms: hydrogen bonding and electrostatic force.
oo f
Anionic/ nonionic
[160] [143] [161] [162] [163] [164] [165]
[166] [167] [151]
pr
(i) Improvement in gas/liquid interfacial properties
e-
One well-known factor which affects foamability and foam stability is the surface tension of the solution, and surface or interfacial tension can be greatly decreased with the addition of
Pr
surfactants. For a compound surfactant system, stronger interactions between mixed surfactants cause the adsorbed surfactant to be packed more tightly at the interface, which leads to a further decrease in surface tension [158]. Fig. 9 shows the effect of cationic/anionic
al
surfactant mixtures on surface tension at the interface, and it is obvious that the surface
rn
tension of the mixed system is much lower than that of any pure surfactant, varying as a function of surfactant concentration, and the optimum occurs at the equimolar mixing ratio
Jo u
[162]. This phenomenon has also been reported for other cationic/anionic or ionic/nonionic mixing systems [168]. Due to the strong local interactions, mixed surfactants tend to be more tightly arranged at the interface, which confers a strong dilatational elasticity as well as a high disjoining pressure for approaching films, and the generated foam correspondingly tends to be extremely stable against coarsening and coalescence [121, 153, 169]. However, the stabilizing effects vary with the properties of the surfactants. For example, Li et al. [164] studied the effect of the length of the hydrocarbon chain on foam stabilized by compound surfactants and reported that the stabilizing effect reaches its peak when surfactants contain hydrophobic chains of similar lengths. Concerning foam stability at high temperature and pressure, Wang et al. [160] found that nonylphenol polyethoxylate surfactants exhibit good thermal resistance, which can be further enhanced by increasing the ethylene oxide groups. Furthermore, amine-based surfactants are able to maintain foam stability at high temperatures and pressures (over 80 ℃ and 10 MPa). Fig. 10 shows a comparison of the performance of 20
Journal Pre-proof compound surfactants and SDS alone in foam stabilization, and the half- life of foam
oo f
stabilized by mixtures is over 20 min. at 100 ℃ and 50g/L salinity [151].
pr
Fig. 9 Equilibrium surface tension of individual and equimolar mixed surfactant solutions . The insert graph shows that peak performance in terms of surface tension reduction occurs at the equimolar mixing ratio, where the total surfactant concentration is 4 ×10-6 mol/L. SGS12: a sulfonate Gemini surfactant, BQAS: a
280
8000
200
al
30
160
rn
20
0 50
60
70
80
Jo u
10
90
100
110
120
FCI (cm3·min)
40
Foam volume/Vmax (cm3)
50
Half-life (min)
15
LDEA/SDS, FCI SDS, FCI
Pr
LDEA/SDS, T0.5 SDS LDEA/SDS, Vmax 240 SDS
LDEA/SDS, u SDS
12
6000 9
4000 6
2000
3
120 0
130
Defoaming rate, u(cm3/min)
60
e-
bisquaternary ammonium salt. (Reproduced from [162])
140
Temperature (℃ )
(a)
0 50
60
70
80
90
100
110
120
130
140
Temperature (℃ )
(b)
Fig. 10 Co mparison of properties of LDEA/SDS foam (0.5 wt %:0.5 wt %) and SDS foam (1.0 wt%), conditions: 20000 mg/L brine water and 10.5 MPa. FCI is a general foam performance indicator, FCI = 0.75Vmax×T0.5 , and a larger FCI value means a better performance [151].
(ii) Improvement in micellar structure The formation of micelles in solutions greatly affects their viscosity, and a viscous liquid phase in the foam leads to a relatively low drainage rate, contributing to foam stability. The cooperative effects of compound surfactants also have a favorable influence on the formation of micelles in two ways: 1), the CMC of mixed systems is further decreased, as is clearly shown in Fig. 9, which means an earlier beginning of micelle formation with increasing surfactant concentration [152, 155, 170]; 2), the formation of mixed surfactant micelles is totally different from that of single surfactant micelles and the structure is more complicated 21
Journal Pre-proof and stable. Cui et al. [149] experimentally observed the formation of mixed micelles in ionic/nonionic as well as cationic/ionic surfactant solutions, and found that the formation is governed by the CMC of each component: as the total concentration increases, micelles of surfactant with lower CMC are generated first, then the other surfactant fuses, leading to mixed micelles. In addition, to evaluate the stability of micelles, the excess free energy of the surfactant is an effective indicator, which can be calculated by Equation (2) for binary surfactant systems, and the smaller the absolute value of Gex , the less stable the formed micelles.
oo f
Gex RT ( x1 ln f1 x2 ln f 2 )
(2)
where, R is the universal gas constant, T is the temperature, x 1 , x2 is the mole fraction of each surfactant, and f 1 , f 2 is the activity coefficient of each surfactant, written as fi e ( xi ) , and 2
pr
is the interaction parameter depending on the surfactant properties.
e-
Trawinska et al. [156, 157] conducted experiments to investigate the synergistic effects in micelle formation and surface tension in ionic/nonionic surfactant mixtures. According their
Pr
results, the free energy of micelles has more negative values for mixtures than for each component in all mixing systems. [161] reported the transition to shear-thinning behavior of solutions due to changes in the molar ratios of surfactants, and this was explained by the
al
formation of wormlike micelles and their morphologies observed from their simulation
rn
results, as shown in Fig. 11. In addition, several studies have reported switchable wormlike surfactant micelles triggered by CO 2 injection [171-173], According to [173], by injecting
Jo u
CO 2 into solutions, two amine groups of TMHDA (N,N,N ′ ,N ′ -tetramethyl-1, 6hexanediamine) are protonated into quaternary ammonium salt when mixed with sodium oleate (NaOA) at a molar ratio of 1:2, and eventually generate a pseudo-gemini surfactant due to the bridge of NaOA. Fig. 12 illustrates this process, and these pseudo-gemini surfactants can spontaneously form wormlike micelles, resulting in a sharp increase of viscosity. Interestingly, this process can be repeatedly triggered by CO 2 or N 2 injection, which has tremendous application potential in foam fracturing.
22
Journal Pre-proof
Viscosity, h (Pa·s)
102 101
10
0
10-1 10-2 10-3
Zero shear viscosity, h0 (Pa·s)
1000 COTAB(mM): 0 20 40 60 80 100 140 200
103
800
600
400
200
0 10-2
10-1
100
101
102
103
0
50
Shear rate (s-1)
100
150
200
OTAB Concentration (mM)
(a)
(b)
e-
pr
oo f
Fig. 11 Viscosity changes as a function of shear rate (a), and zero shear viscosity of solutions as the increase in OTAB (Octadecyltrimethylammoniu m Bromide) concentration and possible micelle morphology during evolution (Modified from[161]).
Protonation _
+
+ _
_
Pr
_
rn
al
Micelle formation
Jo u
Fig. 12 Illustration of protonation of amine groups induced by CO 2 and formation of switchable wormlike micelles (Modified from [173]).
3.2 Polymer-enhanced foam 3.2.1 Mechanism
As discussed previously, the liquid phase with high viscosity and surface elasticity is an effective way to enhance foam stability. For these cases, polymers (mainly polyelectrolytes) are also extensively used as foam stabilizers together with surfactants to improve foam stability by increasing the viscosity of foaming solutions [105]. Similar to surfactants, some low molecular polymers also adsorb at the interface and thus decrease the gas permeability of foam films [174]. Interactions among surfactants and polymers are mainly induced by electrostatic and hydrophobic forces, as illustrated in Fig. 13, which shows that polymer chains binding surfactants attach at the gas/liquid interface and some long chains act as a “bridge” between neighboring films.
23
Journal Pre-proof Liquid Liquid
Polymer chain chain Polymer
Gas
Surfactant Surfactant
Gas Gas
Plateau border board Plateau
Fig. 4 Schematic of interactions between polymer and surfactant in foam film
However, the function of interfacial complexes is questionable, as the effect of the polymer-
oo f
surfactant mixture on foam stability can also be attributed to the net charge of the film and the foam film’s stability is reduced to the isoelectric point (IEP) of the solution, followed by destabilization around the IEP, and becomes very stable above the IEP [175, 176]. According
pr
to Fauser et al. [177], when the total ionic strength of the film reaches its maximum, the synergistic adsorption of both surfactant and polymer at the interface is largest, leading to the
e-
most stable foam film.
Pr
3.2.2 Recent progress in polymer-enhanced foam
Synergistic interactions among surfactant-polymer mixtures indeed improve foam stability, and factors influencing such synergisms have also attracted the attention of researchers [178,
al
179]. For example, the contributions of surfactant and polymer to synergism differ, and foam
rn
stability is mainly controlled by the role of the surfactant while the effect of polymer type is minor [180]. Concerning surface activity, Goswami et al. [181] found that these interactions
Jo u
are composition-dependent, and the decrease in surface tension is dominated by polymers. Furthermore, opposite charges are not necessary for synergism [182], but they influence performance. For weak systems (uncharged polymer/ionic surfactants, or mixtures with the same charge), both foamability and stability are increased compared with surfactant only, due to the fast surfactant adsorption and strong steric repulsion of surface-active polymers. For strong systems (oppositely-charged mixtures), only foam stability can be strengthened relative to surfactant only because of the strong association of the surfactants and polymers, which slows the formation of the adsorption layer [182-184]. Considering the effects of surfactants or polymers themselves, Uhlig et al. [185] found rigid polymers in the mixture show better foam stability that flexible polymers. Pu et al. [186] observed that polymers with higher molecular weight exhibit better foam stabilization, which is further increased with polymer concentration. Schulze-Zachau et al. [187] reported that interfacial charge and
24
Journal Pre-proof surfactant binding efficiency are strongly dependent on the a lkyl chain length of the surfactants. The application of polymers in foam stabilization in reservoirs may be limited by reduced flowing properties in the reservoir due to the increased viscosity and polymers are usually degraded when the reservoir temperature is higher than 85℃ [188, 189]. Hence, some new insights into PEF have been published recently. Instead of using traditional polymers, Zhao et al. [188] studied the long-term stability of gel-enhanced foam by adding comb polymer gel to high-temperature reservoirs. Their results show that increased viscosity enhances the thickness and strength of foam films, which is also observed in the morphology of foams.
oo f
However, according to their flooding experiments, foams with such high viscosity also exhibit great plugging capacity in porous media, which may not be suitable for foam fracturing. Verma et al.[190] proposed a method to improve the rheology of PEF by adding
pr
bentonite, which achieves a similar proppant capacity while reducing the dose of polymer,
e-
and the foam remains thermally stable at temperatures up to 90 ℃. In this case, the formation damage caused by insoluble guar can be constrained, and this improves the flow behavior of
Pr
fracturing foam in low permeability reservoirs. Yin et al. [191] experimentally investigated the stability of regenerated cellulose (RC)-enhanced CO 2 foam under oilfield conditions and
al
its stabilization mechanisms and found that RC foam undergoes slower bubble coalescence and size increase in the first 30 min, showing the best stabilizing foam performance. This
rn
trend has been verified by their micro-experiments. As shown in Fig. 14, the presence of RC
for a long time. 1.6
1% SS163 1% SS163+1% RC 1% SS163+1% SiO2 NP 1% SS163+1% Al2O3 NP 1% SS163+HPAM
1.4 1.2
350 300
Diameter (mm)
Relative film thickness
Jo u
greatly strengthens the thickness of the liquid films, enabling foam stability to be maintained
1.0 0.8 0.6
250 200 150
0.4
100
0.2
50
0.0
1% SS163 1% SS163+1% RC 1% SS163+1% SiO2 NP 1% SS163+1% Al2O3 NP 1% SS163+HPAM
0 0
50
100
150
Time (min)
(a)
200
250
300
0
50
100
150
200
250
Time (min)
(b)
Fig. 5 Foam (a) film relative thickness and (b) diameter of bubbles changes during foam aging process (modified after Yin et al. 2018).
25
300
Journal Pre-proof
3.3 Nanoparticle-stabilized foam Because of certain inherent weaknesses of surfactants and polymers as stabilizers under harsh reservoir conditions, many efforts have been made to find other more appropriate alternatives. Nanoparticles (NPs) have gradually attracted attention for this purpose, and foam stabilized by such NPs, i.e. the so-called Pickering foam, exhibits superior performance even under extreme experimental conditions [192-195]. However, it is difficult to generate foams solely using NPs, but partially hydrophilic NPs are good foam stabilizers at the appropriate concentration. To achieve moderate hydrophilicity, one strategy is to utilize NP and surfactant mixtures and adjust the surface property of NPs by surfactant electrostatic
oo f
adsorption.
3.3.1 Mechanisms of in-situ surface activation of NPs
pr
With the addition of surfactants, a series of interactions between surfactants and NPs occur and thus improve the hydrophobicity of NPs. Generally, the mechanisms of this activation
e-
process are primarily controlled by the type of surfactant and the mixing ratio of the NP/surfactant. Previous experiments indicated that NPs can only be surface activated by
Pr
oppositely-charged surfactants and the adsorption of surfactants onto the surface of NPs is a cumulative process governed by many forces, including the electrostatic force, non-polar
al
interactions and hydrophobic interactions [196-199]. For different NPs, different types of
rn
surfactants are required to modify their surface properties due to their different surface electric potentials in solutions. Generally, silica NPs are negative in solutions and can be
Jo u
improved by cationic surfactants, while bare calcium carbonate NPs can be modified by anionic surfactants [197, 200]. Furthermore, the hydrocarbon chain length of surfactants may also influence modification performance, because surfactants with shorter chains are more soluble in water [201]. For example, Liu et al. [202] investigated the adsorption behavior of four surfactants with different hydrocarbon chain lengths and found that a longer chain length induces stronger hydrophobic interactions and hence greater surfactant adsorption, which leads to highly stable foam at a lower surfactant concentration. However, Cui et al. [197] reported that SDS is a more efficient surfactant for this surface activation than AOT (Bis-(2ethylhexyl) sulfosuccinate sodium) because AOT has double hydrocarbon chains, which leads to the formation of double adsorption layers on NPs due to hydrophobic interactions at a relatively low concentration. Recently, Wang et al. [203] modified silica NPs using different charged surfactants and the results showed that a better synergistic effect occurs
26
Journal Pre-proof between NPs and OA-12 (Lauryl dimethyl amine oxide) because of the opposite charge and shorter molecular chains. In addition to the utilization of suitable types of surfactant, the relative concentration of surfactant (also described as the mixing ratio) in foaming solutions also influences the surface activation of NPs [204]. Sonn et al. [205] studied the effects of silica NPs modified by 1.0 wt.% Dimethyldichlorosilane (DMDCS) on foam stability in the presence of extra DMDCS. In their experiments, they found that the presence of the extra DMDCS has a negative influence on the synergy between silica NP and surfactant, which causes a further increase in surface hydrophobicity and leads to the tendency for particles to move in the air in bubbles, so that
oo f
foams become unstable. However, when the concentration of DMDCS is over 0.025 wt%, these negative effects are offset due to the dominance of DMDCS in the liquid phase, and foam stability increases again. In an earlier study [116], researchers proposed that surfactant
pr
adsorption on the surface of particles is a two-stage process: from an initially disorganized
e-
monolayer to a closely-packed monolayer with some head- groups facing into the solution due to the π–π interactions. In Zhang et al.’s work [206], with increased AOT concentration, the
Pr
adsorption status of AOT on particle surfaces is divided into three regions, which are mainly controlled by the electrostatic forces and hydrophobic interactions. Sun et al. [207] proposed
al
four different adsorption behaviors of surfactants with increased surfactant concentration and indicated that modified NPs move to the gas/liquid interface when adsorbing a certain
rn
amount of surfactants, which therefore increases dilatational viscoelasticity. A recent study
Jo u
by Rad et al. [208] summarized the arrangement of NPs and surfactants at different mixing ratios. As shown in Fig. 15, as the concentration of NPs increases, the surfactant adsorption layer evolves, from a compactly bilayer initially, then to a bilayer/partial bilayer/monolayer, and then nearly all monolayer, and then monolayer/partial monolayer, and finally only partial monolayer. In stages (a) and (b), the particles have no affinity for the gas-water interface. When the particles become only partially covered by surfactant in stages (c) and (d), they can attach to the gas-water interface and reduce the surface tension.
27
Journal Pre-proof (a)
(b) Bubble
Bubble
(c)
(d) Bubble
oo f
Bubble
pr
Fig. 6 Position of surfactants and NPs in solution at different stages : in (a) NPs are covered by surfactant bilayer, and various surface coverage in (b) and partial coverage in (a) and (d) (Modified from [208])
e-
3.3.2 Synergistic effects of surfactants and nanoparticles
Pr
Foam stabilization with bare NPs does not allow a good level of performance, but synergistic interactions at the interface of NPs and surfactant lead to the generation of more stable foam in harsh environments [22, 23]. This synergy can potentially be used to maximize foam
al
transportation and fracture conductivity in reservoir stimulations. Previous studies have
rn
proposed many possible explanations for the mechanisms of foam stabilization by modified NPs but some of those arguments occur repeatedly [23, 26]. Like chemical surfactants, the
Jo u
adsorption of partially hydrophobic NPs at the bubble interface is the fundamental element in maintaining the long-term stability of foam, even under harsh conditions. Nevertheless, NPs show several distinct advantages over chemical surfactants: 1) higher desorption energy in the moderate surface hydrophilic state; 2) multiple arrangement at the bubble interface [209, 210] (i) High desorption energy The contact angle of NPs attached to gas/liquid interfaces is an essential parameter for the evaluation of their wettability by liquid, which assists particles to attach to the gas/liquid interface fully [211]. Compared with surfactant molecules, NPs are so large that they require greater energy to detach from the interface. The detachment energy (E) [212] of spherical particles can be calculated by E R 2 1 cos
28
2
(3)
Journal Pre-proof where, R is the radius of the particle, is the surface tension, and is the contact angle between the nanoparticle and water. Fig. 16 shows the arrangement of NPs with different contact angle at the surface. For hydrophilic NPs, as the surfactant concentration in the solution increases, the contact angle also increases due to the electrostatic adsorption of surfactant on the NPs’ surfaces [213]. Studies have found that the desorption energy reaches the maximum when the contact angle of NPs is close to 90° at an optimum concentration of surfactant [206, 214]. It is also revealed that long-term foam stabilization can be achieved if a high concentration of moderately hydrophobic NPs (contact angle about 60 to 70°) is used. According to Equation (3), the presence of surfactant also lowers this energy due to the
oo f
reduction of surface tension [215], but this effect is relatively inferior to the enhancement; as a result, there still exists a larger detachment energy of NPs which ensures foam stability.
Gas
Water
Water
Gas
Pr
Gas
(c)
pr
(b)
e-
(a)
(e)
Gas
rn
Water
al
(d)
Water
< 90°
Gas Water
90°
Jo u
Fig. 7 The distribution of nanoparticles with different contact angles at bubble interface; particles are irreversibly attached when (a) < 90° and (b) = 90°, wh ile particle residue exists on gas side when (c) > 90°. Bubble curvature also depends on contact angle, as shown in (d) and (e). (Reproduced from [35])
In addition, Wang et al. [203] found that NPs and surfactant play different roles in foam stabilization: surfactant decreases the surface tension of the liquid phase while NPs coated with surfactants increase the modulus of elasticity. Indeed, according to other experiments (refer to Fig. 17) [216], the size distribution of foam bubbles generated by surfactant-NP mixtures is more fine and uniform. The irreversible adsorption of the NP-surfactant layer at the bubble surface also increases dilatational viscoelasticity, restricts bubble coarsening and coalescence, and maintains the long-term stability of the foam [203, 217].
29
Journal Pre-proof
oo f
Fig. 17 Micro-morphology of foam bubbles as a function of time (Modified from [216]).
(ii) Arrangement of NPs at bubble interface
Due to the superior adsorption capacity of high surface-active NPs, they exist in the
pr
elemental structure of the foam in three ways (Fig. 18): (1) as a monolayer of bridging
e-
particles; (2) as a bilayer of closely packed particles; and (3) as a network of aggregating
Jo u
rn
al
Pr
particles [23, 218].
Fig. 18 Schematic of three arrangements of NPs at the interface [23].
The structure of NPs mainly depends on the concentration of NPs. At low concentrations, only a single layer of NPs forms at the liquid film, which produces sterically strong interfacial barriers that prevent foam coalescence and coarsening [24]. In addition, the bridging of partly hydrophilic NPs also plays an essential role in film drainage, which binds some water content after the initial drainage [23]. With the increase of NP concentration, the adsorbed layers are more likely to be composed of particle aggregation multilayers rather than monolayers because of the high particle coagulation [219]. These multilayers of particles in the films or PBs of the foam assist in constraining film thinning and thus maintaining film thickness. On the other hand, such structures largely prevent the direct contact of adjacent 30
Journal Pre-proof bubbles and can also act as barriers, reducing liquid drainage. Therefore, the foam generated by NP-surfactant mixtures exhibits long-term stability even under harsh conditions.
4 Molecular dynamic simulation of foam stability As discussed above, experimental investigation is a major method to evaluate the effects of various chemical additives on the stability of aqueous foam, but it can only provide the macroscale performance of the stabilizers. To fully understand the stabilizing mechanisms, both interfacial and bulk properties in the foam are necessary, including interactions among surfactant and water molecules. However, it is hard to obtain this knowledge through macroscale experiments. In recent years, molecular dynamic (MD) simulation has been used
oo f
to fill this gap. To obtain optimum stabilizers which maintain foam stability under reservoir conditions, it is necessary to screen many different types of potential chemicals. These are
pr
not only difficult to synthesize but the process is time-consuming and requires considerable resources. Through molecular dynamic simulation, surface tension reduction and micelle
e-
formation under various conditions can be easily monitored at a molecular scale, which provides a new way of filtering out suitable additives and then verifying their effects through
Pr
experiments. To our knowledge, to date there has been no summary of progress in this area, and a comprehensive review of recent progress in gas/liquid interfacial and bulk system
rn
4.1 Simulation methods
al
through MD is therefore provided as follows.
Foam is a complex gas/liquid mixture system and at molecular scale, we are more interested
Jo u
in the phenomenon as a liquid film, and foam is therefore usually simplified as a gas/liquid interface. Two popular methods are normally used for building such an interface: one method initially includes two surfactant adsorption monolayers distributed at both sides of a liquid layer filled with water molecules, counter ions and other soluble or suspended materials, as shown in Fig. 19 (a) [220-222]; the other model initially includes, from the top down, a vacuum layer, a surfactant adsorption monolayer, a liquid layer and an energy barrier to constrain molecules from travelling across the boundary (Fig. 19 (b)) [223]. Both methods can be used to study the effect of foaming agents on the stability of foam films, and each has advantages and disadvantages. For the former model, as the thickness of the liquid layer is large enough (>2 nm), the interactions between the two surfactant adsorption layers can be ignored [224]. The disadvantage is that it is very time-consuming due to the huge computational load. In contrast, the latter model requires less time, but the behavior of molecules near the confined layer is very complex. 31
Journal Pre-proof
Gas molecules or vacuum
Surfactant molecule Liquid film
Water molecules
Frozen molecules
(a)
(b) Fig. 19 Sketch of two simulation domain configurations
oo f
One major factor that affects the results of simulation is the force field, and commonly- used force fields include GROMOS [225], OPLS [226], CHARMM [227] and AMBER [228]. To
pr
simulate the self-assembly of surfactants or polymers at a larger temporal and spatial scale, some coarse- grained force fields have also been proposed, including the MARTINI force
e-
field [229] and the SPICA force field [230]. However, to date, no force field has been designed specifically for the simulation of surfactant behaviors at the interface, and this may
Pr
be one possible factor which causes discrepancies between simulations and experiments. 4.2 Research results of molecular simulation
al
Interfacial properties. As discussed above, molecular dynamic simulation of foam stability usually simplifies the foam as a liquid/gas interface and focuses on the properties of this
rn
interface. Interfacial tension is an essential parameter for describing the surface activating
Jo u
process, which is defined as the difference between the normal and lateral pressure of the whole system in molecular dynamic simulations. If z direction is normal to the gas/liquid interface, the relationship can be written as:
1 lz Pzz 0.5 Pxx Pyy dz n 0
(4)
where, Pxx, Pyy, Pzz are three principal components of the stress tensor, respectively, lz is the length of the simulation box along the z axis, and n is the number of interfaces in the system. For example, in Fig. 19 (a), as the system has two interfaces, n equals 2. The interfacial tension of water has been extensively studied, and simulation results mainly depend on the application of various water models. The advantages and disadvantages of different water models as well as the effects of temperature have been fully reviewed in recent papers [231, 232].
32
Journal Pre-proof As stated previously, most surfactants are able to significantly reduce surface tension at the interface, and this phenomenon can also be reproduced based on molecular simulations, although most focus on the oil/water interface [233-237]. Fig. 20 shows the effect of various surfactant types and surface concentrations on interfacial tension: before reaching CMC, the interfacial tension decreases as the surfactant numbers at the surface increase, and it remains stable when the number is beyond the CMC. The graph also shows that gemini surfactant exhibits better performance than the others, which may be due to its complex multiple polar heads [237]. 60
Anionic surfactant Nonionic surfactant Zwitterionic surfactant Gemini surfactant
oo f
40
pr
30
20
e-
Interfacial tension (mN/m)
50
0 0
20
40
Pr
10
60
80
100
120
140
160
180
Surfactant number
al
Fig. 20 Changes in interfacial tension as a function of surfactant number [237].
rn
In addition, the organization of surfactants at the interface also a ffects the interfacial properties, which depends on the surface concentration of surfactant. The tilt angle is an
Jo u
effective indicator to describe the orientation of surfactant molecules at the interface, w hich is the angle between the vector of the tail group and the normal direction of the interface. As shown in Fig. 21, with increased CTAB concentration, most CTABs tend to vertically insert into the water slab and the surfactant layers thicken, which is a result of the competition of van der Waals interactions (attraction between surfactants) and electrostatic interactions (repulsion) [238]. Meanwhile, due to the presence of the surfactant layer, the interface thickness also changes, which is defined as the distance falls from 90% to 10% of the bulk value, as illustrated in Fig. 22. In practice, the thickness is calculated as the average of t 1 and t 2 . In addition, for film stability, Yang et al [239, 240] proposed the concept of critical film thickness, which is the minimum thickness of the interface which remains intact. Based on this concept, they proposed a stability index (SI) for liquid film:
33
Journal Pre-proof SI
hc , w hc , w/ s hc , w
100%
(5)
where, hc,w is the critical film thickness without the surfactant and hc,w/s is the critical thickness of film stabilized by surfactant. 0.20
8
2 nm
Interaction parameter Af
0.15
Probability
CTAB concentration increase
0.10
Repulsion
4
0
Attration Attraction
0.05
-8
0.00 0
10
20
30
40
1.42 50
2.66
60
70
Simulation data Experimental data
3.51 80
-12
90
1.0
pr
-6 mol/m2)： C (×10-5
oo f
-4
2.0
3.0
4.0
Surfactant concentration (10-6 mol/m2)
Tail tilt angle (°)
(a)
(b)
Pr
e-
Fig. 21 CTAB at gas/liquid interface. (a) Surfactant tail tilt angles with different concentrations at the interface; the insert picture is the final configuration of CTAB corresponding to 1.42 ×10 −6 mol/m2 , 2.66 × 10−6 mol/m2 , and 3.51 × 10−6 mol/m2 (b) Local Frumkin interaction parameter Af as a function of surfactant surface concentration, AF = w22 RT , where w22 is the total pairwise interactions between surfactants (Modified from [238]). Chart Title
1.2
t1
al
t2
90%
rn
0.8 0.6 0.4
Jo u
Density (kg/m3)
1.0
0.2 0.0
10%
50
100
150
200 Z-axis (Å)
250
300
350
Fig. 22 Illustration of Gibbs interface thickness based on density profile of liquid phase
Another focus is the complex intermolecular interaction and its influence on interfacial properties. The self-diffusion coefficient is a parameter which indicates the motion of molecules at the interface. Normally, there are two different methods for calculating the selfdiffusion coefficient of water in molecular simulation: the mean-square displacement (MSD)based method and the velocity-auto-correlation function (VACF)-based method, and discussions of the diffusion coefficient of water under different simulation conditions can be found in [241]. With the addition of surfactant, the diffusion coefficient of water is limited due to the hydration reactions between the surfactant and water molecules, which is related to the head group of the surfactant [242]. The interaction between surfactants and polymers has 34
Journal Pre-proof also been reported frequently in research studies [220, 240, 243, 244]. For example, Wu et al. [220] investigated the effect of the concentration of PAM and the degree of HPAM on the stability of SDS foams by analyzing the density distribution of SDS head- groups, the radial distribution function (RDF) of hydration of SDS head- groups, and the MSD of hydrated water around the amide group. Gao et al. [243] studied the improvement by betaines of the stability of alkyl-polyoxyethylene carboxylate (AEC) foam. Their results showed that the presence of betaines constrains the repulsion between the head- groups of anionic surfactants, and the electrostatic structures become denser with the increasing concentration of betaine, which enhances the entry barrier and thus creates better foam stability. Moreover, the effect
oo f
of different salt ions in liquid phase on foam film stability at molecular level has also been fully reported in recent papers. For example, Li et al. [221] studied the different effects of Ca2+ and Mg2+ on the stability of foam, and their results showed that Mg2+ broadens the
pr
distribution thickness of surfactant head-groups and thus enhances foam stability, while the
e-
presence of Ca2+ causes the surfactant to aggregate more and destroys foam stability. Formation of micelles. The formation of micelles is also an important factor in the
Pr
evaluation of the performance of surfactants in bulk systems, and most molecular simulations on this topic are conducted using coarse-grained force field due to the considerable
al
computing costs. Transitions of morphologies of single or binary surfactant micelles ha ve been extensively studied and salt concentration and mixing ratio are two major influencing
rn
factors [245, 246]. Fig. 23 shows a typical transition of CTAC micelles: from sphere to worm,
Jo u
to branch, and to sphere again. This phenomenon is mainly due to the counter ions in solutions which form a salt bridge helping surfactants jump to approaching micelles [247]. For binary surfactant systems, the mixing ratio also affects the evolution of micelle morphology by producing different barrier heights for micelle fusion [161]. Yan et al. also found that charge neutralization occurs around the head group when the concentration of one type of surfactant increases, and this constrains the repulsive force based on DLVO theory, which makes micelle fusion easier [248]. The interactions between surfactants and polymers or nanoparticles during micelle formation have also attracted the attention of researchers. For example, Hu et al. [249] reported that micelle morphologies change from spherical to rod- like aggregations as the degree of hydrolysis of partially hydrolyzed polyacrylamide (HPAM) hydrolysis increases. Sambasivam et al. [250] studied the fusion of a single NP–surfactant complex with rod-like micelles and observed that the end-caps of micelles open up and bridge with the NP surface through a surfactant exchange process.
35
Journal Pre-proof The rheological properties of solutions are other important factors, which are mainly evaluated through shear viscosity in molecular simulations. For only surfactant solutions, bulk viscosity and surfactant solution have a linear relation with the presence of sphere micelles [251]. Dhakal et al. [252] observed an anomalous zero-shear viscosity variation of CTAC/NaSal solutions, apparently resulting from changes of micelle morphologies, fundamentally governed by the NaSal concentration. Yan et al. [248] indicated that solutions become shear-thinning with the transition from spherical micelles to wormlike micelles in catanionic surfactant solutions. The addition of nanoparticles to surfactant solutions also induces a transition from zero-shear viscosity to shear-thinning with the increase in shear rate,
(b)
(c)
(d)
Pr
(a)
e-
pr
oo f
and the transition point decreases as the NP volume fraction increases [253].
Conclusion
al
Fig. 23 Illustration of evolution of micelle mo rphologies with increased salt concentration: fro m sphere to worm, to branch, and to sphere again. The molar ratios of salt and surfactant are: (a) 0.00, (b) 0.67, (c) 1.33, (d) 2.00 (Modified from [247]).
rn
This review presents detailed information on three major strategies of foam stabilization,
Jo u
including the application of surfactants, polymers, nanoparticles and their compounds. Liquid drainage, coarsening, and bubble coalescence are three dominant processes governing foam destabilization. Past studies have indicated that these phenomena are interdependent and liquid drainage dominates at the earlier stage, while coarsening and coalescence become more significant later. All foam-stabilizing strategies are proposed to fundamentally retard these aging processes. In the research literature, surfactant is the additive most used to stabilize foam by improving the interfacial properties and forming micelles in the liquid phase. The results of laboratory experiments show that some thermally stable surfactants and compound surfactant mixtures exhibit better performance in foamability and foam stability. Polymer is another popular material used together with surfactants for enhancing foam stability, which constrain drainage mainly by increasing the viscosity of foaming solutions. Moreover, the synergy of surfactant and nanoparticle is reported to show best performance in foam stabilization, even under extreme reservoir conditions. This superiority mainly 36
Journal Pre-proof contributes to the favorable arrangement of surfactant/nanoparticle mixtures, as well as their high desorption energies. In addition to experimental investigations, the paper has also reviewed recent progress in interfacial phenomena based on molecular dynamic simulations, which provide new insights into interfacial properties and micelle formation under the influence of these popular foam stabilizers. References
Jo u
rn
al
Pr
e-
pr
oo f
[1] Denney D. Evaluating Implications of Hydraulic Fracturing in Shale-Gas Reservoirs. SPE-1108-G. 2009;61:53-4. [2] Ribeiro L, Sharma M. Fluid Selection for Energized Fracture Treatments. SPE Hydraulic Fracturing Technology Conference. The Woodlands, Texas, USA: Society of Petroleum Engineers; 2013. p. 11. [3] Wanniarachchi WAM, Ranjith PG, Perera MSA. Shale gas fracturing using foam-based fracturing fluid: a review. Environmental Earth Sciences. 2017;76:91. [4] Wanniarachchi WAM, Ranjith PG, Perera MSA, Lashin A, Al Arifi N, Li JC. Current opinions on foam-based hydro- fracturing in deep geological reservoirs. Geomechanics and Geophysics for Geo-Energy and Geo-Resources. 2015;1:121-34. [5] Wang J, Wang S, Lin W, Kang Z, You Q. Formula optimization and rheology study of clean fracturing fluid. Journal of Molecular Liquids. 2017;241:563-9. [6] Li C, Huang Y, Sun X, Gao R, Zeng F, Tontiwachwuthikul P, et al. Rheological properties study of foam fracturing fluid using CO 2 and surfactant. Chemical Engineering Science. 2017;170:720-30. [7] Wang G, Wang KL, Lu CJ. Advances of Researches on Improving the Stability of Foams by Nanoparticles. IOP Conference Series: Materials Science and Engineering. Vol. 242: IOP Publishing; 2017. p. 012020. [8] Nazari N, Tsau J-S, Barati R. CO 2 Foam Stability Improvement Using Polyelectrolyte Complex Nanoparticles Prepared in Produced Water. Energies. 2017;10:516. [9] Langevin D. Bubble coalescence in pure liquids and in surfactant solutio ns. Current Opinion in Colloid and Interface Science. 2015;20:92-7. [10] Angarska J, Stubenrauch C, Manev E. Drainage of foam films stabilized with mixtures of non- ionic surfactants. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2007;309:189-97. [11] Xue Z, Worthen A, Qajar A, Robert I, Bryant SL, Huh C, et al. Viscosity and stability of ultra- high internal phase CO 2-in-water foams stabilized with surfactants and nanoparticles with or without polyelectrolytes. J Colloid Interface Sci. 2016;461:383-95. [12] Xu K, Zhu P, Colon T, Huh C, Balhoff M. A Microfluidic Investigation of the Synergistic Effect of Nanoparticles and Surfactants in Macro-Emulsion-Based Enhanced Oil Recovery. SPE Journal. 2017;22:459-69. [13] Zhu T, Ogbe DO, Khataniar S. Improving the Foam Performance for Mobility Control and Improved Sweep Efficiency in Gas Flooding. Industrial & Engineering Chemistry Research. 2004;43:4413-21. [14] Worthen AJ, Bagaria HG, Chen Y, Bryant SL, Huh C, Johnston KP. Nanoparticlestabilized carbon dioxide-in-water foams with fine texture. J Colloid Interface Sci. 2013;391:142-51. [15] Yekeen N, Idris AK, Manan MA, Samin AM, Risal AR, Kun TX. Bulk and bubble-scale experimental studies of influence of nanoparticles on foam stability. Chinese Journal of Chemical Engineering. 2017;25:347-57. 37
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[16] Emrani AS, Nasr-El-Din HA. An experimental study of nanoparticle-polymer-stabilized CO 2 foam. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;524:17-27. [17] Cervantes Martinez A, Rio E, Delon G, Saint-Jalmes A, Langevin D, Binks BP. On the origin of the remarkable stability of aqueous foams stabilised by nanoparticles: link with microscopic surface properties. Soft Matter. 2008;4:1531. [18] Hunter TN, Pugh RJ, Franks GV, Jameson GJ. The role of particles in stabilising foams and emulsions. Advances in Colloid and Interface Science. 2008;137:57-81. [19] Zhang T, Espinosa D, Yoon Ky, Rahmani A, yu H, Manuel Caldelas F, et al. Engineered Nanoparticles as Harsh-Condition Emulsion and Foam Stabilizers and as Novel Sensors. Offshore Technology Conference. Houston, Texas, USA2011. p. 15. [20] Karakashev SI, Ozdemir O, Hampton MA, Nguyen AV. Formation and stability of foams stabilized by fine particles with similar size, contact angle and different shapes. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2011;382:132-8. [21] Worthen AJ, Bryant SL, Huh C, Johnston KP. Carbon dioxide-in-water foams stabilized with nanoparticles and surfactant acting in synergy. AIChE Journal. 2013;59:3490-501. [22] Nourafkan E, Asachi M, Hu Z, Gao H, Wen D. Synthesis of stable nanoparticles at harsh environment using the synergistic effect of surfactants blend. Journal of Industrial and Engineering Chemistry. 2018;64:390-401. [23] Singh R, Mohanty KK. Synergy between Nanoparticles and Surfactants in Stabilizing Foams for Oil Recovery. Energy & Fuels. 2015;29:467-79. [24] Kumar S, Mandal A. Investigation on stabilization of CO 2 foam by ionic and nonionic surfactants in presence of different additives for application in enhanced oil recovery. Applied Surface Science. 2017;420:9-20. [25] Wang J, Nguyen AV, Farrokhpay S. A critical review of the growth, drainage and collapse of foams. Advances in Colloid and Interface Science. 2016;228:55-70. [26] Yekeen N, Manan MA, Idris AK, Padmanabhan E, Junin R, Samin AM, et al. A comprehensive review of experimental studies of nanoparticles-stabilized foam for enhanced oil recovery. Journal of Petroleum Science and Engineering. 2018;164:43-74. [27] Schramm LL. Emulsions, foams, and suspensions: fundamentals and applications: John Wiley & Sons; 2006. [28] Isabelle C, Sylvie CA, Florence E, François G, Reinhard H, Olivier P, et al. Foams : structure and dynamics2013. [29] Pitois O, Fritz C, Vignes-Adler M. Liquid drainage through aqueous foam: study of the flow on the bubble scale. J Colloid Interface Sci. 2005;282:458-65. [30] Koehler SA, Hilgenfeldt S, Stone HA. A Generalized View of Foam Drainage: Experiment and Theory. Langmuir. 2000;16:6327-41. [31] Neethling SJ, Lee HT, Grassia P. The growth, drainage and breakdown of foams. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2005;263:184-96. [32] Kruglyakov PM, Karakashev SI, Nguyen AV, Vilkova NG. Foam drainage. Current Opinion in Colloid and Interface Science. 2008;13:163-70. [33] Babcsán N, Banhart J. Metal Foams: Towards High- Temperature Colloid Chemistry. In: Binks BP, Horozov TS, (editors). Colloidal Particles at Liquid Interfaces. Cambridge: Cambridge University Press; 2006. p. 445-500. [34] Lioumbas JS, Georgiou E, Kostoglou M, Karapantsios TD. Foam free drainage and bubbles size for surfactant concentrations below the CMC. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;487:92-103. [35] Pugh RJ. Bubble and Foam Chemistry. Cambridge: Cambridge University Press; 2016. [36] Sun Q, Tan L, Wang G. Liquid foam drainage: An overview. International Journal of Modern Physics B. 2008;22:2333-54. 38
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[37] Carrier V, Destouesse S, Colin A. Foam drainage: A film contribution? Physical Review E. 2002;65:061404. [38] Koehler SA, Hilgenfeldt S, Stone HA. Foam drainage on the microscale I. Modeling flow through single Plateau borders. J Colloid Interface Sci. 2004;276:420-38. [39] Koehler SA, Hilgenfeldt S, Weeks ER, Stone HA. Foam drainage on the microscale II. Imaging flow through single Plateau borders. J Colloid Interface Sci. 2004;276:439-49. [40] Nguyen AV. Liquid drainage in single plateau borders of foam. J Colloid Interface Sci. 2002;249:194-9. [41] Anazadehsayed A, Rezaee N, Naser J, Nguyen AV. A review of aqueous foam in microscale. Advances in Colloid and Interface Science. 2018;256:203-29. [42] Leonard RA, Lemlich R. A study of interstitial liquid flow in foam. Part I. Theoretical model and application to foam fractionation. AIChE Journal. 1965;11:18-25. [43] Koehler SA, Hilgenfeldt S, Stone HA. Liquid Flow through Aqueous Foams: The NodeDominated Foam Drainage Equation. Physical Review Letters. 1999;82:4232-5. [44] Cox SJ, Weaire D, Hutzler S, Murphy J, Phelan R, Verbist G. Applications and generalizations of the foam drainage equation. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 2000;456:2441-64. [45] Helal MA, Mehanna MS. The tanh method and Adomian decomposition method for solving the foam drainage equation. Applied Mathematics and Computation. 2007;190:599609. [46] Mirmoradi SH, Hosseinpour I, Barari A, Ghotbi AR. Analysis of foam drainage problem using variational iteration method. Advanced Studies in Theoretical Physics. 2009;3:283-92. [47] Khani F, Hamedi-Nezhad S, Darvishi MT, Ryu S-W. New solitary wave and periodic solutions of the foam drainage equation using the Exp- function method. Nonlinear Analysis: Real World Applications. 2009;10:1904-11. [48] Darvishi MT, Khani F. A series solution of the foam drainage equation. Computers & Mathematics with Applications. 2009;58:360-8. [49] Khan M, Gondal M. A new analytical solution of foam drainage equation by Laplace decomposition method. Journal of Advanced Research in Differential Equations. 2010;2:5364. [50] He J-H. Variational approach to foam drainage equation. Meccanica. 2011;46:1265-6. [51] Hosseini Fadravi H, Saberi Nik H, Buzhabadi R. Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives. International Journal of Differential Equations. 2011:Article ID 237045. [52] Khan Y, Wu Q. Homotopy perturbation transform method for nonlinear equations using He’s polynomials. Computers & Mathematics with Applications. 2011;61:1963-7. [53] Fereidoon A, Yaghoobi H, Davoudabadi M. Application of the Homotopy Perturbation Method for Solving the Foam Drainage Equation. International Journal of Differential Equations. 2011:Article ID: 864023. [54] Iyiola O, Mukiawa SE, Enyi C. Generalised homotopy analysis method (q-HAM) for solving foam drainage equation of time fractional type. Mathematics in Engineering, Science and Aerospace MESA. 2013;4:429-40. [55] Nikkar A. Assesment of New Analytical Method for Solving the Foam Drainage Equation. Chinese Journal of Mathematics. 2014:Article ID: 656039. [56] Alam MN. Exact solutions to the foam drainage equation by using the new generalized (G′/G)-expansion method. Results in Physics. 2015;5:168-77. [57] Gubes M, Keskin Y, Oturanc G. Numerical solution of time-dependent foam drainage equation (FDE). Computational Methods for Differential Equations. 2015;3:111-22. [58] Arbabi S, Nazari A, Darvishi MT. A semi-analytical solution of foam drainage equation by Haar wavelets method. Optik. 2016;127:5443-7. 39
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[59] Brito-Parada PR, Neethling SJ, Cilliers JJ. Modelling the behaviour of the wetting front in non-standard forced foam drainage scenarios. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2013;438:21-7. [60] Narsimhan G. Drainage of particle stabilized foam film. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;495:20-9. [61] Anazadehsayed A, Naser J. A combined CFD simulation of Plateau borders including films and transitional areas of liquid foams. Chemical Engineering Science. 2017;166:11-8. [62] Anazadehsayed A, Rezaee N, Naser J. Numerical modelling of flow through foam's node. J Colloid Interface Sci. 2017;504:485-91. [63] Anazadehsayed A, Rezaee N, Naser J. Exterior foam drainage and flow regime switch in the foams. J Colloid Interface Sci. 2018;511:440-6. [64] Shafiei Y, Ghazanfari MH, Seyyedsar SM. A study of liquid drainage rate from foam with population balance equation: impact of bubble evolution. Colloid and Polymer Science. 2018;296:1097-108. [65] Pitois O, Fritz C, Vignes-Adler M. Hydrodynamic resistance of a single foam channel. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2005;261:109-14. [66] Sett S, Sinha-Ray S, Yarin AL. Gravitational Drainage of Foam Films. Langmuir. 2013;29:4934-47. [67] Neethling S, Lee H, Cilliers J. A foam drainage equation generalized for all liquid contents. Journal of Physics: Condensed Matter. 2001;14:331. [68] Saint-Jalmes A, Vera MU, Durian DJ. Free drainage of aqueous foams: Container shape effects on capillarity and vertical gradients. Europhysics Letters (EPL). 2000;50:695-701. [69] Cox S, Weaire D. Comment on "Free drainage of aqueous foams: Container shape effects on capillarity and vertical gradients" by A. Saint-Jalmes et al. Europhysics Letters (EPL). 2001;55:445. [70] Papara M, Zabulis X, D. Karapantsios T. Container effects on the free drainage of wet foams. 2009;64:1404-15. [71] Saye RI, Sethian JA. Multiscale modelling of evolving foams. J Comput Phys. 2016;315:273-301. [72] Verbist G, Weaire D, Kraynik AM. The foam drainage equation. Journal of Physics: Condensed Matter. 1996;8:3715-31. [73] Jun S, Pelot DD, Yarin AL. Foam consolidation and drainage. Langmuir. 2012;28:532330. [74] Bureiko A, Trybala A, Huang J, Kovalchuk N, Starov V. Bulk and surface rheology of Aculyn™ 22 and Aculyn™ 33 polymeric solutions and kinetics of foam drainage. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2013;434:268-75. [75] Arjmandi- Tash O, Trybala A, Mahdi FM, Kovalchuk NM, Starov V. Foams built up by non-Newtonian polymeric solutions: Free drainage. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;521:112-20. [76] Haffner B, Khidas Y, Pitois O. The drainage of foamy granular suspensions. Journal of Colloid and Interface Science. 2015;458:200-8. [77] Wang J, Nguyen AV. Foam drainage in the presence of solid particles. Soft Matter. 2016;12:3004-12. [78] Magrabi SA, Dlugogorski BZ, Jameson GJ. Bubble size distribution and coarsening of aqueous foams. Chemical Engineering Science. 1999;54:4007-22. [79] Ganan-Calvo A, Fernandez J, Marquez Oliver A, Marquez M. Coarsening of monodisperse wet microfoams. Applied Physics Letters. 2004;84:4989-91. [80] Feitosa K, Durian D. Gas and liquid transport in steady-state aqueous foam. The European Physical Journal E. 2008;26:309-16.
40
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[81] Wang J, Cao Y, Li G, Li S, Wang Y, Ma Z, et al. Investigation on the Properties of Aqueous Foams Stabilized by Cetyltrimethylammonium Bromide in Terms of Free Drainage and Bubble Size. Journal of Surfactants and Detergents. 2019;22:855-63. [82] von Neumann J. Shape of Metal Grains. Metal Interfaces. 1952:108. [83] Mullins WW. Estimation of the geometrical rate constant in idealized three dimensional grain growth. Acta Metallurgica. 1989;37:2979-84. [84] MacPherson RD, Srolovitz DJ. The von Neumann relation generalized to coarsening of three-dimensional microstructures. Nature. 2007;446:1053-5. [85] Yadav V, Moelans N. Analysis of grain topology and volumetric growth rate relation in three-dimensional normal grain growth. Acta Materialia. 2018;156:275-86. [86] Schimming CD, Durian DJ. Border-crossing model for the diffusive coarsening of twodimensional and quasi-two-dimensional wet foams. Physical Review E. 2017;96:032805. [87] Roth AE, Jones CD, Durian DJ. Bubble statistics and coarsening dynamics for quasitwo-dimensional foams with increasing liquid content. Physical Review E. 2013;87:042304. [88] Lambert J, Mokso R, Cantat I, Cloetens P, Glazier JA, Graner F, et al. Coarsening Foams Robustly Reach a Self-Similar Growth Regime. Physical Review Letters. 2010;104:248304. [89] Thomas GL, Belmonte JM, Graner F, Glazier JA, de Almeida RMC. 3D simulations of wet foam coarsening evidence a self similar growth regime. Colloids and Surfaces A, Physicochemical and Engineering Aspects. 2015;473:109-14. [90] Khakalo K, Baumgarten K, Tighe BP, Puisto A. Coarsening and mechanics in the bubble model for wet foams. Physical Review E. 2018;98:012607. [91] Saint-Jalmes A. Physical chemistry in foam drainage and coarsening. Soft Matter. 2006;2:836-49. [92] Isert N, Maret G, Aegerter CM. Coarsening dynamics of three-dimensional levitated foams: From wet to dry. The European Physical Journal E. 2013;36:116-22. [93] Langevin D, Vignes-Adler M. Microgravity studies of aqueous wet foams. The European Physical Journal E. 2014;37:16. [94] Vandewalle N, Caps H, Delon G, Saint-Jalmes A, Rio E, Saulnier L, et al. Foam stability in microgravity. Journal of Physics: Conference Series. 2011;327:012024. [95] Tcholakova S, Mitrinova Z, Golemanov K, Denkov ND, Vethamuthu M, Ananthapadmanabhan KP. Control of Ostwald Ripening by Using Surfactants with High Surface Modulus. Langmuir. 2011;27:14807-19. [96] Lv Q, Li Z, Li B, Husein M, Shi D, Zhang C, et al. Wall slipping behavior of foam with nanoparticle-armored bubbles and its flow resistance factor in cracks. Scientific Reports. 2017;7:5063. [97] Klitzing Rv, Müller H-J. Film stability control. Current Opinion in Colloid & Interface Science. 2002;7:42-9. [98] Tarazona P, Martínez H, Chacón E, Bresme F. Newton black films as wetting systems. Physical Review B. 2012;85:085402. [99] Forel E, Dollet B, Langevin D, Rio E. Coalescence in Two-Dimensional Foams: A Purely Statistical Process Dependent on Film Area. Physical Review Letters. 2019;122:088002. [100] Derjaguin BV. Theory of stability of colloids and thin films: Consultants Bureau New York; 1989. [101] Verwey EJW. Theory of the stability of lyophobic colloids. The Journal of Physical Chemistry. 1947;51:631-6. [102] Derjaguin BV, Landau LD. Acta Physicochim. URSS. 1941;14:633. [103] Bergeron V, Radke CJ. Equilibrium measurements of oscillatory disjoining pressures in aqueous foam films. Langmuir. 1992;8:3020-6. 41
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[104] Bindal SK, Sethumadhavan G, Nikolov AD, Wasan DT. Foaming mechanisms in surfactant free particle suspensions. AIChE Journal. 2002;48:2307-14. [105] Gochev G. Thin liquid films stabilized by polymers and polymer/surfactant mixtures. Current Opinion in Colloid and Interface Science. 2015;20:115-23. [106] Ghosh P. Coalescence of bubbles in liquid. Bubble Science, Engineering & Technology. 2009;1:75-87. [107] Bikerman JJ. Foams. New York: Springer-Verlag; 1973. [108] Kawale D. Influence of dynamic surface tension on foams: Application in gas well deliquification [Master thesis]: Delft University of Technology; 2012. [109] Negin C, Ali S, Xie Q. Most common surfactants employed in chemical enhanced oil recovery. Petroleum. 2017;3:197-211. [110] Wikipedia contributors. Critical micelle concentration. Wikipedia, The Free Encyclopedia. [111] Levitt D, Jackson A, Heinson C, Britton LN, Malik T, Dwarakanath V, et al. Identification and Evaluation of High-Performance EOR Surfactants. SPE-152907-PA. 2009;12:243-53. [112] Xue Z, Panthi K, Fei Y, Johnston KP, Mohanty KK. CO 2-Soluble Ionic Surfactants and CO 2 Foams for High-Temperature and High-Salinity Sandstone Reservoirs. Energy & Fuels. 2015;29:5750-60. [113] Chen Y, Elhag AS, Poon BM, Cui L, Ma K, Liao SY, et al. Switchable Nonionic to Cationic Ethoxylated Amine Surfactants for CO 2 Enhanced Oil Recovery in HighTemperature, High-Salinity Carbonate Reservoirs. SPE Journal. 2014;19:249-59. [114] Rosen MJ, Kunjappu JT. Characteristic Features of Surfactants. Surfactants and Interfacial Phenomena2012. p. 1-38. [115] Da C, Elhag A, Jian G, Zhang L, Alzobaidi S, Zhang X, et al. CO2/Water Foams Stabilized with Cationic or Zwitterionic Surfactants at Temperatures up to 120 °C in High Salinity Brine. SPE Annual Technical Conference and Exhibition. Dallas, Texas, USA: Society of Petroleum Engineers; 2018. p. 14. [116] Hunter TN, Wanless EJ, Jameson GJ, Pugh RJ. Non- ionic surfactant interactions with hydrophobic nanoparticles: Impact on foam stability. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2009;347:81-9. [117] Jones SA, Laskaris G, Vincent-Bonnieu S, Farajzadeh R, Rossen WR. Effect of surfactant concentration on foam: From coreflood experiments to implicit-texture foammodel parameters. Journal of Industrial and Engineering Chemistry. 2016;37:268-76. [118] Yekeen N, Manan MA, Idris AK, Samin AM. Influence of surfactant and electrolyte concentrations on surfactant Adsorption and foaming characteristics. Journal of Petroleum Science and Engineering. 2017;149:612-22. [119] Golemanov K, Denkov ND, Tcholakova S, Vethamuthu M, Lips A. Surfactant Mixtures for Control of Bubble Surface Mobility in Foam Studies. Langmuir. 2008;24:995661. [120] Lee J, Nikolov A, Wasan D. Foam stability: The importance of film size and the micellar structuring phenomenon. The Canadian Journal of Chemical Engineering. 2014;92:2039-45. [121] Varade D, Carriere D, Arriaga LR, Fameau AL, Rio E, Langevin D, et al. On the origin of the stability of foams made from catanionic surfactant mixtures. Soft Matter. 2011;7:655770. [122] Bournival G, Du Z, Ata S, Jameson GJ. Foaming and gas dispersion properties of nonionic surfactants in the presence of an inorganic electrolyte. Chemical Engineering Science. 2014;116:536-46.
42
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[123] Stasiuk ENB, Schramm LL. The Temperature Dependence of the Critical Micelle Concentrations of Foam-Forming Surfactants. Journal of Colloid and Interface Science. 1996;178:324-33. [124] Hara K, Kuwabara H, Kajimoto O, Bhattacharyya K. Effect of pressure on the critical micelle concentration of neutral surfactant using fluorescence probe method. Journal of Photochemistry and Photobiology A: Chemistry. 1999;124:159-62. [125] Lesemann M, Thirumoorthy K, Kim YJ, Jonas J, Paulaitis ME. Pressure Dependence of the Critical Micelle Concentration of a Nonionic Surfactant in Water Studied by 1H-NMR. Langmuir. 1998;14:5339-41. [126] Xue Z, Foster E, Wang Y, Nayak S, Cheng V, Ngo VW, et al. Effect of Grafted Copolymer Composition on Iron Oxide Nanoparticle Stability and Transport in Porous Media at High Salinity. Energy & Fuels. 2014;28:3655-65. [127] Kumar A, Mandal A. Characterization of rock-fluid and fluid-fluid interactions in presence of a family of synthesized zwitterionic surfactants for application in enhanced oil recovery. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2018;549:112. [128] Zhao L, Li A, Chen K, Tang J, Fu S. Development and evaluation of foaming agents for high salinity tolerance. Journal of Petroleum Science and Engineering. 2012;81:18-23. [129] Hussain SMS, Fogang LT, Kamal MS. Synthesis and performance evaluation of betaine type zwitterionic surfactants containing different degrees of ethoxylation. Journal of Molecular Structure. 2018;1173:983-9. [130] Shakil Hussain SM, Kamal MS, Fogang LT. Effect of internal olefin on the properties of betaine-type zwitterionic surfactants for enhanced oil recovery. Journal of Molecular Liquids. 2018;266:43-50. [131] Da C, Alzobaidi S, Jian G, Zhang L, Biswal SL, Hirasaki GJ, et al. Carbon dioxide/water foams stabilized with a zwitterionic surfactant at temperatures up to 150 °C in high salinity brine. Journal of Petroleum Science and Engineering. 2018;166:880-90. [132] AlYousif Z, Kokal S, Alabdulwahab A, Gizzatov A. CO 2-Foam Rheology: Effect of Surfactant Concentration, Shear Rate and Injection Quality. SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition. Dammam, Saudi Arabia: Society of Petroleum Engineers; 2018. p. 12. [133] Alzobaidi S, Da C, Tran V, Prodanović M, Johnston KP. High temperature ultralow water content carbon dioxide- in-water foam stabilized with viscoelastic zwitterionic surfactants. Journal of Colloid and Interface Science. 2017;488:79-91. [134] Sun L, Wei P, Pu W, Wang B, Wu Y, Tan T. The oil recovery enhancement by nitrogen foam in high- temperature and high-salinity environments. Journal of Petroleum Science and Engineering. 2016;147:485-94. [135] Alzobaidi S, Lotfollahi M, Lu C, Bloom M, Zhang X, Prodanovic M, et al. Identification and Evaluation of Viscoelastic Surfactants Including Smart Viscoelastic Systems for Generation and Stabilization of Ultra-Dry N 2 and CO 2 Foam for Fracturing Fluids and Proppant Transport. Proceedings of the 6th Unconventional Resources Technology Conference2018. p. 16. [136] Deng Q, Li H, Li C, Lv W, Li Y. Enhancement of foamability and foam stability induced by interactions between a hyperbranched exopolysaccharide and a zwitterionic surfactant dodecyl sulfobetaine. RSC Advances. 2015;5:61868-75. [137] Varade SR, Ghosh P. Foaming in aqueous solutions of zwitterionic surfactant: Effects of oil and salts. Journal of Dispersion Science and Technology. 2017;38:1770-84. [138] Santvoort Jv, Golombok M. Viscoelastic surfactants for diversion control in oil recovery. Journal of Petroleum Science and Engineering. 2015;135:671-7.
43
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[139] Xue Z, Worthen AJ, Da C, Qajar A, Ketchum IR, Alzobaidi S, et al. Ultradry Carbon Dioxide-in-Water Foams with Viscoelastic Aqueous Phases. Langmuir. 2016;32:28-37. [140] Elhag AS, Da C, Chen Y, Mukherjee N, Noguera JA, Alzobaidi S, et al. Viscoelastic diamine surfactant for stable carbon dioxide/water foams over a wide range in salinity and temperature. J Colloid Interface Sci. 2018;522:151-62. [141] Kuliszewska E, Brecker L. Gemini Surfactants Foam Formation Ability and Foam Stability Depends on Spacer Length. Journal of Surfactants and Detergents. 2014;17:951-7. [142] Kamal MS. A Review of Gemini Surfactants: Potential Application in Enhanced Oil Recovery. Journal of Surfactants and Detergents. 2016;19:223-36. [143] Marinova KG, Naydenova KT, Basheva ES, Bauer F, Tropsch J, Franke J. New surfactant mixtures for fine foams with slowed drainage. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;523:54-61. [144] Ivanova DS, Angarska JK, Manev ED, Tachev KD. Critical thickness of foam films stabilized by nonionic or ionic surfactants and their mixtures. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;519:34-45. [145] Angarska JK, Ivanova DS, Manev ED. Drainage of foam films stabilized by nonionic, ionic surfactants and their mixtures. Colloids and Surface s A: Physicochemical and Engineering Aspects. 2015;481:87-99. [146] Jiang N, Sheng Y, Li C, Lu S. Surface activity, foam properties and aggregation behavior of mixtures of short-chain fluorocarbon and hydrocarbon surfactants. Journal of Molecular Liquids. 2018;268:249-55. [147] Wang C, Fang H, Gong Q, Xu Z, Liu Z, Zhang L, et al. Roles of Catanionic Surfactant Mixtures on the Stability of Foams in the Presence of Oil. Energy & Fuels. 2016;30:6355-64. [148] Kanokkarn P, Shiina T, Santikunaporn M, Chavadej S. Equilibrium and dynamic surface tension in relation to diffusivity and foaming properties: Effects of surfactant type and structure. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;524:135-42. [149] Cui X, Jiang Y, Yang C, Lu X, Chen H, Mao S, et al. Mechanism of the Mixed Surfactant Micelle Formation. The Journal of Physical Chemistry B. 2010;114:7808-16. [150] Ananth R, Snow AW, Hinnant KM, Giles SL, Farley JP. Synergisms between Siloxane-polyoxyethylene and Alkyl Polyglycoside Surfactants in Foam Stability and Pool Fire Extinction. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2019;579:123686. [151] Zhang P, Bai G, Cui G, Zhang L, Peng X, Pei S, et al. Enhanced CO 2 foam based on amide and amine surfactants and synergistically coupled with sodium dodecyl sulfate at high temperature and high pressure. Journal of Petroleum Science and Engineering. 2019;179:26675. [152] Negm NA, Sabagh AME. Interaction between cationic and conventional nonionic surfactants in the mixed micelle and monolayer formed in aqueous medium. Química Nova. 2011;34:1007-13. [153] Danov KD, Kralchevska SD, Kralchevsky PA, Ananthapadmanabhan KP, Lips A. Mixed Solutions of Anionic and Zwitterionic Surfactant (Betaine): Surface-Tension Isotherms, Adsorption, and Relaxation Kinetics. Langmuir. 2004;20:5445-53. [154] Bera A, Ojha K, Mandal A. Synergistic Effect of Mixed Surfactant Systems on Foam Behavior and Surface Tension. Journal of Surfactants and Detergents. 2013;16:621-30. [155] Poša M. Mixed micelles of binary surfactant mixtures Tween 40 – Na-3,12-dioxo-5βcholanate and Tween 80 – Na-3,12-dioxo-5β-cholanate and their thermodynamic description and characterization. Chemical Engineering Research and Design. 2014;92:2826-39. [156] Trawiſska A, Hallmann E, MĿdrzycka K. The effect of alkyl chain length on synergistic effects in micellization and surface tension reduction in nonionic gemini (S-10) 44
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
and anionic surfactants mixtures. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;506:114-26. [157] Trawińska A, Hallmann E, Mędrzycka K. Synergistic effects in micellization and surface tension reduction in nonionic gemini S-10 and cationic RTAB surfactants mixtures. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;488:162-72. [158] Wang C, Cao X-L, Guo L-L, Xu Z-C, Zhang L, Gong Q-T, et al. Effect of adsorption of catanionic surfactant mixtures on wettability of quartz surface. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;509:564-73. [159] Wang C, Cao X- L, Guo L-L, Xu Z-C, Zhang L, Gong Q-T, et al. Effect of molecular structure of catanionic surfactant mixtures on their interfacial properties. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;509:601-12. [160] Wang Y, Zhang Y, Liu Y, Zhang L, Ren S, Lu J, et al. The stability study of CO 2 foams at high pressure and high temperature. Journal of Petroleum Science and Engineering. 2017;154:234-43. [161] Wang P, Tan J, Pei S, Wang J, Zhang Y, Sun X, et al. Dual effects of cationic surfactant on the wormlike micelle formation of catanionic surfactants mixtures: An experiment and simulation study. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;529:95-101. [162] Li Y, Lai L, Mei P, Zhang W-X, Li Y-H, Cheng L, et al. Surface properties and solubility enhancement of Gemini/conventional surfactant mixtures based on sulfonate Gemini surfactant. Journal of Molecular Liquids. 2019;276:488-96. [163] Almobarky M, AlYousef Z, Schechter D. Enhancing the Foam Stab ility Using Surfactants Mixtures. SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition. Dammam, Saudi Arabia: Society of Petroleum Engineers; 2018. p. 13. [164] Wang C, Zhao L, Xu B-c, Cao X-l, Guo L- l, Zhang L, et al. Effect of dynamic interfacial dilational properties on the foam stability of catanionic surfactant mixtures in the presence of oil. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2018;541:78-86. [165] Li S-J, Lai L, Mei P, Li Y, Cheng L, Ren Z-H, et al. Equilibrium and dynamic surface properties of cationic/anionic surfactant mixtures based on bisquaternary ammonium salt. Journal of Molecular Liquids. 2018;254:248-54. [166] Li J, Li Y, Song Y, Wang Z, Zhang Q. Properties of quaternary ammonium surfactant with hydroxyethyl group and anionic surfactant mixed systems. Journal of Molecular Liquids. 2018;271:373-9. [167] Agneta M, Zhaomin L, Chao Z, Gerald G. Investigating synergism and antagonism of binary mixed surfactants for foam efficiency optimization in high salinity. Journal of Petroleum Science and Engineering. 2019;175:489-94. [168] Fauser H, Uhlig M, Miller R, Klitzing Rv. Surface Adsorption of Oppositely Charged SDS:C12TAB Mixtures and the Relation to Foam Film Formation and Stability. The Journal of Physical Chemistry B. 2015;119:12877-86. [169] Stocco A, Carriere D, Cottat M, Langevin D. Interfacial Behavior of Catanionic Surfactants. Langmuir. 2010;26:10663-9. [170] Hosseini H, Tsau JS, Shafer-Peltier K, Marshall C, Ye Q, Barati Ghahfarokhi R. Experimental and Mechanistic Study of Stabilized Dry CO 2 Foam Using Polyelectrolyte Complex Nanoparticles Compatible with Produced Water To Improve Hydraulic Fracturing Performance. Industrial & Engineering Chemistry Research. 2019;58:9431-49. [171] Su X, Cunningham MF, Jessop PG. Switchable viscosity triggered by CO 2 using smart worm-like micelles. Chemical Communications. 2013;49:2655-7. [172] Liu D, Suo Y, Tan J, Lu H. CO 2 -Switchable microemulsion based on a pseudogemini surfactant. Soft Matter. 2017;13:3783-8. 45
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[173] Wang J, Huang Z, Zheng C, Lu H. CO 2 /N2-switchable viscoelastic fluids based on a pseudogemini surfactant system. Journal of Dispersion Science and Technology. 2017;38:1705-10. [174] Shah V, Bharatiya B, Shukla AD, Mukherjee T, Shah DO. Adsorption of nonionic Brij and Tween surfactants at PTFE-water and air-water interfaces: Investigations on wetting, dispersion stability, foaming and drug solubilization. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;508:159-66. [175] Kristen N, Simulescu V, Vüllings A, Laschewsky A, Miller R, von Klitzing R. No Charge Reversal at Foam Film Surfaces after Addition of Oppositely Charged Polyelectrolytes? The Journal of Physical Chemistry B. 2009;113:7986-90. [176] Kristen-Hochrein N, Laschewsky A, Miller R, von Klitzing R. Stability of Foam Films of Oppositely Charged Polyelectrolyte/Surfactant Mixtures: Effect of Isoelectric Point. The Journal of Physical Chemistry B. 2011;115:14475-83. [177] Fauser H, von Klitzing R, Campbell RA. Surface adsorption of oppositely charged C14TAB-PAMPS mixtures at the air/water interface and the impact on foam film stability. J Phys Chem B. 2015;119:348-58. [178] Khristov K, Petkova H, Alexandrova L, Nedyalkov M, Platikanov D, Exerowa D, et al. Foam, emulsion and wetting films stabilized by polyoxyalkylated diethylenetriamine (DETA) polymeric surfactants. Advances in Colloid and Interface Science. 2011;168:105-13. [179] Xu C, Wang D, Wang H, Hu J, Zhu X, Zhang Y. Effect of partially hydrolyzed polyacrylamide on the solution and foam properties of sodium alcohol ether sulfate. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2018;556:51-60. [180] Kristen N, Vüllings A, Laschewsky A, Miller R, von Klitzing R. Foam Films from Oppositely Charged Polyelectolyte/Surfactant Mixtures: Effect of Polyelectrolyte and Surfactant Hydrophobicity on Film Stability. Langmuir. 2010;26:9321-7. [181] Goswami A, Hassan PA, Bhagwat SS. Static and dynamic surface tension behaviour of a triblock copolymer and a non ionic surfactant mixture. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;484:190-6. [182] Petkova R, Tcholakova S, Denkov ND. Foaming and foam stability for mixed polymersurfactant solutions: Effects of surfactant type and polymer charge. Langmuir. 2012;28:49965009. [183] Petkova R, Tcholakova S, Denkov ND. Role of polymer–surfactant interactions in foams: Effects of pH and surfactant head group for cationic polyvinylamine and anionic surfactants. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2013;438:174-85. [184] Bureiko A, Trybala A, Kovalchuk N, Starov V. Current applications of foams formed from mixed surfactant-polymer solutions. Adv Colloid Interface Sci. 2015;222:670-7. [185] Uhlig M, Miller R, Klitzing Rv. Surface adsorption of sulfonated poly(phenylene sulfone)/C14TAB mixtures and its correlation with foam film stability. Physical Chemistry Chemical Physics. 2016;18:18414-23. [186] Pu W, Wei P, Sun L, Wang S. Stability, CO2 sensitivity, oil tolerance and disp lacement efficiency of polymer enhanced foam. RSC Advances. 2017;7:6251-8. [187] Schulze- Zachau F, Braunschweig B. CnTAB/polystyrene sulfonate mixtures at air– water interfaces: effects of alkyl chain length on surface activity and charging state. Physical Chemistry Chemical Physics. 2019;21:7847-56. [188] Zhao G, Dai C, Zhang Y, Chen A, Yan Z, Zhao M. Enhanced foam stability by adding comb polymer gel for in-depth profile control in high temperature reservoirs. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;482:115-24. [189] Dupas A, Henaut I, Rousseau D, Poulain P, Tabary R, Argillier J-F, et al. Impact of polymer mechanical degradation on shear and extensional viscosities: toward better 46
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
injectivity forecasts in polymer flooding operations. SPE International Symposium on Oilfield Chemistry: Society of Petroleum Engineers; 2013. p. 11. [190] Verma A, Chauhan G, Ojha K. Synergistic effects of polymer and bentonite clay on rheology and thermal stability of foam fluid developed for hydra ulic fracturing. Asia-Pacific Journal of Chemical Engineering. 2017;12:872-83. [191] Yin X, Kang W, Song S, Huang Z, Hou X, Yang H. Stabilization mechanism of CO2 foam reinforced by regenerated cellulose. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2018;555:754-64. [192] Binks BP, Horozov TS. Aqueous foams stabilized solely by silica nanoparticles. Angew Chem Int Ed Engl. 2005;44:3722-5. [193] Blute I, Pugh RJ, van de Pas J, Callaghan I. Silica nanoparticle sols. 1. Surface chemical characterization and evaluation of the foam generation (foamability). Journal of Colloid and Interface Science. 2007;313:645-55. [194] Khalil M, Jan BM, Tong CW, Berawi MA. Advanced nanomaterials in oil and gas industry: design, application and challenges. Applied Energy. 2017;191:287-310. [195] Li S, Qiao C, Li Z, Wanambwa S. Properties of Carbon Dioxide Foam Stabilized by Hydrophilic Nanoparticles and Hexadecyltrimethylammonium Bromide. Energy & Fuels.31:1478-88. [196] Liu Q, Zhang S, Sun D, Xu J. Aqueous foams stabilized by hexylamine- modified Laponite particles. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2009;338:40-6. [197] Cui ZG, Cui YZ, Cui CF, Chen Z, Binks BP. Aqueous foams stabilized by in situ surface activation of CaCO 3 nanoparticles via adsorption of anionic surfactant. Langmuir. 2010;26:12567-74. [198] Kumar S, Aswal VK, Kohlbrecher J. Size-Dependent Interaction of Silica Nanoparticles with Different Surfactants in Aqueous Solution. Langmuir. 2012;28:9288-97. [199] Zhang R, Somasundaran P. Advances in adsorption of surfactants and their mixtures at solid/solution interfaces. Advances in Colloid and Interface Science. 2006;123-126:213-29. [200] Veyskarami M, Ghazanfari MH. Synergistic effect of like and opposite charged nanoparticle and surfactant on foam stability and mobility in the absence and presence of hydrocarbon: A comparative study. Journal of Petroleum Science and Engineering. 2018;166:433-44. [201] Singh R, Mohanty KK. Foams Stabilized by In-Situ Surface-Activated Nanoparticles in Bulk and Porous Media. SPE Journal. 2016;21:121-30. [202] Liu Q, Zhang S, Sun D, Xu J. Foams stabilized by Laponite nanoparticles and alkylammonium bromides with different alkyl chain lengths. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2010;355:151-7. [203] Wang P, You Q, Han L, Deng W, Liu Y, Fang J, et al. Experimental Study on the Stabilization Mechanisms of CO 2 Foams by Hydrophilic Silica Nanoparticles. Energy & Fuels. 2018;32:3709-15. [204] Binks BP, Kirkland M, Rodrigues JA. Origin of stabilisation of aqueous foams in nanoparticle-surfactant mixtures. Soft Matter. 2008;4:2373-82. [205] Sonn JS, Lee JY, Jo SH, Yoon I-H, Jung C-H, Lim JC. Effect of surface modification of silica nanoparticles by silane coupling agent on decontamination foam stability. Annals of Nuclear Energy. 2018;114:11-8. [206] Zhang C, Li Z, Sun Q, Wang P, Wang S, Liu W. CO 2 foam properties and the stabilizing mechanism of sodium bis(2-ethylhexyl)sulfosuccinate and hydrophobic nanoparticle mixtures. Soft Matter. 2016;12:946-56.
47
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[207] Sun Q, Li Z, Wang J, Li S, Li B, Jiang L, et al. Aqueous foam stabilized by partially hydrophobic nanoparticles in the presence of surfactant. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;471:54-64. [208] Doroudian Rad M, Telmadarreie A, Xu L, Dong M, Bryant SL. Insight on Methane Foam Stability and Texture via Adsorption of Surfactants on Oppositely Charged Nanoparticles. Langmuir. 2018;34:14274-85. [209] Whitby CP, Fornasiero D, Ralston J. Effect of oil soluble surfactant in emulsions stabilised by clay particles. Journal of Colloid and Interface Science. 2008;323:410-9. [210] Carn F, Colin A, Pitois O, Vignes-Adler M, Backov R. Foam drainage in the presence of nanoparticle-surfactant mixtures. Langmuir. 2009;25:7847-56. [211] Eftekhari AA, Krastev R, Farajzadeh R. Foam Stabilized by Fly Ash Nanoparticles for Enhancing Oil Recovery. Industrial & Engineering Chemistry Research. 2015;54:12482-91. [212] B. P. Binks, T. S. Horozov, L. Bergström, J. C. Fernández-Toledano, A. Moncho-Jordá, F. Martínez-López, et al. Colloidal Particles at Liquid Interfaces. Cambridge: Cambridge University Press; 2006. [213] Yang W, Wang T, Fan Z. Highly Stable Foam Stabilized by Alumina Nanoparticles for EOR: Effects of Sodium Cumenesulfonate and Electrolyte Concentrations. Energy & Fuels. 2017;31:9016-25. [214] Emrani AS, Nasr-El-Din HA. Stabilizing CO 2 foam by Use of nanoparticles. SPE Journal. 2017;22:494-504. [215] Singh R, Gupta A, Mohanty KK, Huh C, Lee D, Cho H. Fly Ash NanoparticleStabilized CO 2 -in-Water Foams for Gas Mobility Control Applications. SPE Annual Technical Conference and Exhibition. Houston, Texas, USA: Society of Petroleum Engineers; 2015. p. 13. [216] Lv Q, Li Z, Li B, Li S, Sun Q. Study of Nanoparticle–Surfactant-Stabilized Foam as a Fracturing Fluid. Industrial & Engineering Chemistry Research. 2015;54:9468-77. [217] Wu Y, Fang S, Zhang K, Zhao M, Jiao B, Dai C. Stability Mechanism of Nitrogen Foam in Porous Media with Silica Nanoparticles Modified by Cationic Surfactants. Langmuir. 2018;34:8015-23. [218] Horozov TS. Foams and foam films stabilised by solid particles. Current Opinion in Colloid & Interface Science. 2008;13:134-40. [219] Verma A, Chauhan G, Baruah PP, Ojha K. Morphology, Rheolo gy, and Kinetics of Nanosilica Stabilized Gelled Foam Fluid for Hydraulic Fracturing Application. Industrial & Engineering Chemistry Research. 2018;57:13449-62. [220] Wu G, Zhu Q, Yuan C, Wang H, Li C, Sun S, et al. Molecular dynamics simulation of the influence of polyacrylamide on the stability of sodium dodecyl sulfate foam. Chemical Engineering Science. 2017;166:313-9. [221] Li C, Zhang T, Ji X, Wang Z, Sun S, Hu S. Effect of Ca 2+ /Mg 2+ on the stability of the foam system stabilized by an anionic surfactant: A molecular dynamics study. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;489:423-32. [222] Chen M, Lu X, Liu X, Hou Q, Zhu Y, Zhou H. Temperature-Dependent Phase Transition and Desorption Free Energy of Sodium Dodecyl Sulfate at the Water/Vapor Interface: Approaches from Molecular Dynamics Simulations. Langmuir. 2014;30:10600-7. [223] Wang H, Wang Z, Lv Q, Li C, Du Z, Sun S, et al. Mechanism of Foam Film Destruction Induced by Emulsified Oil: A Coarse- Grained Simulation Study. The Journal of Physical Chemistry C. 2018;122:26438-46. [224] Boecker J, Schlenkrich M, Bopp P, Brickmann J. Molecular dynamics simulation of a n-hexadecyltrimethylammonium chloride monolayer. The Journal of Physical Chemistry. 1992;96:9915-22.
48
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[225] Gunsteren WFv, Berendsen HJC. Groningen Molecular Simulation (GROMOS) Library Manual. Biomos, Groningen, The Netherlands; 1987. p. 1-221. [226] L. Jorgensen W, Tirado-Rives J. The OPLS potential functions for proteins. Energy minimizations for crystals of cyclic peptides and crambin. 1988;110:1657-66. [227] Vanommeslaeghe K, Hatcher E, Acharya C, Kundu S, Zhong S, Shim J, et al. CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields. J Comput Chem. 2010;31:671-90. [228] Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, et al. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. Journal of the American Chemical Society. 1995;117:5179-97. [229] Marrink SJ, Risselada HJ, Yefimov S, Tieleman DP, de Vries AH. The MARTINI Force Field: Coarse Grained Model for Biomolecular Simulations. The Journal of Physical Chemistry B. 2007;111:7812-24. [230] Shinoda W, DeVane R, Klein ML. Coarse-grained molecular modeling of non- ionic surfactant self-assembly. Soft Matter. 2008;4:2454-62. [231] Ghoufi A, Malfreyt P, Tildesley DJ. Computer modelling of the surface tension of the gas-liquid and liquid- liquid interface. Chem Soc Rev. 2016;45:1387-409. [232] Ghoufi A, Malfreyt P. Calculation of the surface tension of water: 40 years of molecular simulations. Molecular Simulation. 2019;45:295-303. [233] Deguillard E, Pannacci N, Creton B, Rousseau B. Interfacial tension in oil–water– surfactant systems: On the role of intra-molecular forces on interfacial tension values using DPD simulations. The Journal of Chemical Physics. 2013;138:144102. [234] Posocco P, Perazzo A, Preziosi V, Laurini E, Pricl S, Guido S. Interfacial tension of oil/water emulsions with mixed non- ionic surfactants: comparison between experiments and molecular simulations. RSC Advances. 2016;6:4723-9. [235] Xue C, Qu G, Han Y, Li S, Gao X, Ding W. Molecular Dynamics Simulations of Sulfobetaine-Type Zwitterionic Surfactant at the Decane/Water Interface AU - Xue, Chunlong. Journal of Dispersion Science and Technology. 2016;37:1480-5. [236] Liu Z-Y, Wang C, Zhou H, Wang Y, Zhang L, Zhang L, et al. Characterizing the impact of surfactant structure on interfacial tension: a molec ular dynamics study. Journal of Molecular Modeling. 2017;23:112. [237] Shi P, Zhang H, Lin L, Song C, Chen Q, Li Z. Molecular dynamics simulation of four typical surfactants at oil/water interface. Journal of Dispersion Science and Technology. 2018;39:1258-65. [238] Yazhgur P, Vierros S, Hannoy D, Sammalkorpi M, Salonen A. Surfactant Interactions and Organization at the Gas-Water Interface (CTAB with Added Salt). Langmuir. 2018;34:1855-64. [239] Yang W, Wu R, Kong B, Zhang X, Yang X. Molecular Dynamics Simulations of Film Rupture in Water/Surfactant Systems. The Journal of Physical Chemistry B. 2009;113:83328. [240] Sun Y, Li Y, Li C, Zhang D, Cao X, Song X, et al. Molecular array behavior and synergistic effect of sodium alcohol ether sulphate and carboxyl betaine/sulfobetaine in foam film under high salt conditions. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;480:138-48. [241] Tsimpanogiannis IN, Moultos OA, Franco LFM, Spera MBdM, Erdős M, Economou IG. Self-diffusion coefficient of bulk and confined water: a critical review of classical molecular simulation studies. Molecular Simulation. 2019;45:425-53. [242] Wu G, Yuan C, Ji X, Wang H, Sun S, Hu S. Effects of head type on the stability of gemini surfactant foam by molecular dynamics simulation. Chemical Physics Letters. 2017;682:122-7. 49
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[243] Gao F, Liu G, Yuan S. The effect of betaine on the foam stability: Molecular simulation. Applied Surface Science. 2017;407:156-61. [244] Yang W, Yang X. Molecular Dynamics Study of the Foam Stability of a Mixed Surfactant/Water System with and without Calcium Ions. The Journal of Physical Chemistry B. 2011;115:4645-53. [245] Pires JM, Moura AFd, Freitas LCG. Investigating the spontaneous formation of SDS micelle in aqueous solution using a coarse-grained force field. Química Nova. 2012;35:97881. [246] Wang S, Larson RG. Coarse-Grained Molecular Dynamics Simulation of SelfAssembly and Surface Adsorption of Ionic Surfactants Using an Implicit Water Model. Langmuir. 2015;31:1262-71. [247] Wang P, Pei S, Wang M, Yan Y, Sun X, Zhang J. Study on the transformation from linear to branched wormlike micelles: An insight from molecular dynamics simulation. Journal of Colloid and Interface Science. 2017;494:47-53. [248] Yan Z, Dai C, Zhao M, Sun Y. Rheological characterizations and molecular dynamics simulations of self-assembly in an anionic/cationic surfactant mixture. Soft Matter. 2016;12:6058-66. [249] Hu S, Zhu Q, Wang P, Wang H, Li C, Sun S. Effect of HPAM hydrolysis degree on catanionic mixtures of DTAB/HPAM: A coarse-grained molecular dynamic simulation. Computational Materials Science. 2018;153:134-40. [250] Sambasivam A, Sangwai AV, Sureshkumar R. Self-Assembly of Nanoparticle– Surfactant Complexes with Rodlike Micelles: A Molecular Dynamics Study. Langmuir. 2016;32:1214-9. [251] Ruiz-Morales Y, Romero-Martinez A. Coarse-Grain Molecular Dynamics Simulations To Investigate the Bulk Viscosity and Critical Micelle Concentration of the Ionic Surfactant Sodium Dodecyl Sulfate (SDS) in Aqueous Solution. J Phys Chem B. 2018;122:3931-43. [252] Dhakal S, Sureshkumar R. Topology, length scales, and energetics of surfactant micelles. The Journal of Chemical Physics. 2015;143:024905. [253] Sambasivam A, Dhakal S, Sureshkumar R. Structure and rheology of self-assembled aqueous suspensions of nanoparticles and wormlike micelles. Molecular Simulation. 2018;44:485-93.
50
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
Conflict of Interests We declare that there is no conflict of interests.
51
Journal Pre-proof Graphical Abstract Configuration of various stabilizers at a film Liquid film
Gas
Major process
Aging
Drainage
Surfactant stabilized film
Foam stabilizers
Stabilizing
Surfactant
Coarsening
Polymer
Coalescence
Nanoparticle
Aqueous foam
Surfactant micelle
Polymer chain
Bare nanoparticle
Surface activated nanoparticle
Jo u
rn
al
Pr
e-
Surfactant
pr
oo f
Polymer stabilized film
52
Nanoparticle stabilized film
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
Highlights 1. Three major mechanisms including drainage, coarsening and coarsening govern the decay of the aqueous foam. 2. The application of surfactant, polymer and nanoparticle can greatly enhance the stability of foam. 3 the compounded system of these additives make it more favorable for foam life even under severe reservoir conditions. 4. Molecular dynamical simulation of the foaming additives provides novel insights into their effects on interfacial or bulk properties.
53
Jun Zhou, P.G. Ranjith, W.A.M. Wanniarachchi PII:
S0001-8686(19)30321-5
DOI:
https://doi.org/10.1016/j.cis.2020.102104
Reference:
CIS 102104
To appear in:
Advances in Colloid and Interface Science
Revised date:
1 January 2020
Please cite this article as: J. Zhou, P.G. Ranjith and W.A.M. Wanniarachchi, Different strategies of foam stabilization in the use of foam as a fracturing fluid, Advances in Colloid and Interface Science(2020), https://doi.org/10.1016/j.cis.2020.102104
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier.
Journal Pre-proof Different Strategies of Foam Stabilization in the Use of Foam as a Fracturing Fluid Jun Zhou1 , P.G. Ranjith*1 , W.A.M. Wanniarachchi1 1
Department of Civil Engineering, Monash University, Building 60, Melbourne, Victoria,
3800, Australia. *Corresponding author:
oo f
Prof. Ranjith PG Deep Earth Energy Laboratory, Monash University, Building 60,
pr
Melbourne, Victoria, 3800, Australia. Phone/Fax: 61-3-9905 4982
Abstract
al
Pr
e-
E-mail: [email protected]
rn
An attractive alternative to mitigate the adverse effects of conventional water-based fluids on the efficiency of hydraulic fracturing is to inject foam-based fracking fluids into reservoirs.
Jo u
The efficiency of foaming fluids in subsurface applications largely depends on the stability and transportation of foam bubbles in harsh environments with high temperature, pressure and salinity, all of which inevitably lead to poor foam properties and thus limit fracturing efficiency. The aim of this paper is to elaborate popular strategies of foam stabilization under reservoir conditions. Specifically, this review first discusses three major mechanisms governing foam decay and summarizes recent progress in research on these phenomena. Since surfactants, polymers, nanoparticles and their composites are popular options for foam stabilization, their stabilizing effects, especially the synergies in composites, are also reviewed. In addition to reporting experimental results, the paper also reports recent advances in interfacial properties via molecular dynamical simulation, which provide new insights into gas/liquid interfacial properties under the influence of these popular additives at molecular scale. The results of both experiments and simulations indicate that foam additives play an
1
Journal Pre-proof essential role in foam stability and the synergic effects of surfactants and nanoparticles exhibit more favorable performance.
Keywords: Foam-based fracking fluids; foam stability; stabilizing mechanisms; synergistic effects;
Jo u
rn
al
Pr
e-
pr
oo f
molecular dynamic simulation
2
Journal Pre-proof Contents 1 INTRODUCTION .................................................................................................................. 5 2 MECHANISMS GOVERNING FOAM AGING................................................................... 6 2.1 LIQUID DRAINAGE IN AQUEOUS FOAM ............................................................................... 7 2.2 COARSENING IN AQUEOUS FOAM..................................................................................... 11 2.3 BUBBLE COALESCENCE IN AQUEOUS FOAM ...................................................................... 13
3 STRATEGIES OF FOAM STABILIZATION..................................................................... 14 3.1 SURFACTANT-STABILIZED FOAM ..................................................................................... 14 3.1.1 THERMALLY STABLE SURFACTANTS ...................................................................................................... 16
oo f
3.1.2 SYNERGISTIC EFFECT O F COMPOUND SURFACTANTS ......................................................................... 18
3.2 P OLYM ER-ENHANCED FOAM ........................................................................................... 23 3.2.1 MECHANISM................................................................................................................................................ 23
pr
3.2.2 RECENT PROGRESS IN POLYMER-ENHANCED FOAM........................................................................... 24
3.3 NANOPARTICLE-STABILIZED FOAM ................................................................................. 26
e-
3.3.1 MECHANISMS O F IN-SITU SURFACE ACTIVATIO N O F NP ................................................................... 26 3.3.2 SYNERGISTIC EFFECTS O F SURFACTANTS AND NANOPARTICLES..................................................... 28
Pr
4 MOLECULAR DYNAMIC SIMULATION OF FOAM STABILITY ............................... 31 4.1 SIMULATION METHODS ................................................................................................. 31 4.2 LITERATURE RES ULTS FROM MOLECULAR S IMULAT ION ............................................... 32
al
CONCLUSION ........................................................................................................................ 36
Jo u
Nomenclature
rn
REFERENCES ..................................................... ERROR! BOOKMARK NOT DEFINED.
AOS: Alpha olefin sulfonate
AOT: Bis-(2-ethylhexyl) sulfosuccinate sodium CTAB: Cetyltrimethylammonium bromide CTAC: Cetyltrimethylammonium chloride CB: Cetyl betaine CAPB: Cocoamidopropyldimethyl betaine (C12–14 tail) CHSB: Cocamidopropyl hydroxyl sulfobetaine
CMC: Critical micelle concentration DSB: Dodecyl sulfobetaine DDAPS: N-Dodecyl-N, N-dimethyl-3-ammonio-1-propanesulfonate DMDCS: Dimethyldichlorosilane EPS: Exopolysaccharide
3
Journal Pre-proof EAPB: Erucylamidopropyldimethyl betaine (C18 tail) HT: high temperature, HS: high salinity HPAM: Hydrolysis of partially hydrolyzed polyacrylamide LDEA: Lauryl diethanol amide NaSal: Sodium salicylate OAPB: Oleylamidopropyldimethyl betaine (C22 tail) OA-12: Lauryl dimethyl amine oxide OTAB: Octadecyltrimethylammonium Bromide SDS: Sodium dodecyl sulfate
oo f
SDBS: Sodium dodecylbenzene sulfonate TDS: Total dissolved solids
pr
TMHDA: N, N, N′, N′-tetramethyl-1, 6-hexanediamine) TX-100: Polyoxyethylene octyl phenyl ether
Jo u
rn
al
Pr
e-
PAM: Polyacrylamide
4
Journal Pre-proof
1 Introduction Hydraulic fracturing is an effective stimulation technique for the extraction of unconventional natural gas from ultra- low permeable reservoirs [1]. During the fracturing process, highly pressurized fluids are pumped into reservoirs to create fractures, and solid proppants are then added to the fracturing fluids in order to prevent cracks from closing again after pumping stops. In this case, the fracturing fluid is a crucial element in determining the long-term productivity of a fractured reservoir [2]. To our knowledge, the most widely- used fracking fluid is water, and its advantages and disadvantages are fully reviewed in [3]. Compared with water-based fluids, foam-based fracturing fluid has great advantages, including lower water
oo f
consumption, higher proppant-carrying capability, less formation damage and quicker flowback efficiency [4-6]. Therefore, foam-based fracturing fluid is an attractive alternative
pr
to conventional water- based fracturing fluids.
Nevertheless, there are some issues in the field application of foam-based fluids. One major
e-
challenge is how to maintain the long-term stability of foaming fluids during the fracturing process [7, 8]. Due to the inherent complexities of the two-phase fluid, injected foam in the
Pr
reservoir cannot remain stable until the fracking process finishes, and failure to maintain foam stability causes untimely distribution of proppants in fractures, leading to low fracture
al
conductivity. Three recognized mechanisms govern the foam decay process: liquid drainage,
rn
coarsening, and bubble coalescence [9]. To mediate these phenomena, various chemical additives are added to foaming solutions. Surfactants, commonly used as foaming agents,
Jo u
also limit coarsening and bubble coalescence by reducing the rate of gas diffusion and film thinning due to the presence of adsorbed surfactant
layers at the interface [10]. Some
polymers can also enhance foam stability by increasing the viscosity of the liquid phase and forming a chain network between films to constrain liquid drainage and coarsening [11, 12]. However, some vital factors limit the application of these chemical additives in the field. For example, most surfactants exhibit a high tendency for degradation or adsorption onto mineral surfaces under harsh reservoir conditions (e.g. the temperature may be up to 120 ℃, injecting pressure may be over 20 MPa and brine salinity is from 0.3 to 21 wt%) [13-15]. In the case of polymer, its residual concentration in the reservoir can reach 10-15 fold above the original rate, which potentially induces pore throat blockage and formation damage [16]. Recently, as nanoscience has developed, many researchers have reported that the addition of nanoparticles (NPs) to foaming solutions greatly improves the stability of foam, even at high temperatures and salinities [17-19]. Compared with surfactants or polymers, NPs are more stable and 5
Journal Pre-proof irreversibly aggregate at foam films because of their high desorption energy [20, 21]. Normally, surfactants are added to nanoparticle suspensions to improve NPs’ surface properties, and such synergy usually makes a foam more stable than that generated by the individual components [22, 23]. Moreover, the addition of polymers to surfactant-NP solutions can even improve foam stability further due to the presence of a supplementary steric repulsive force [24]. A large number of reviews concentrated on foam stability has been published in recent years. For example, Wang et al. [25] reported the mechanisms governing foam drainage and the effect of solid particles and several popular models concerning foam height, growth and
oo f
collapse. Yekeen et al. [26] reviewed experimental studies of NP-stabilized foams, focusing on their application in enhanced oil recovery. They discussed different experimental techniques used for studying foam properties and also proposed various parameters affecting
pr
foam stability and flow behavior in porous media. Despite these previous reviews, foam
e-
aging mechanisms have still not been fully reviewed. Furthermore, the application of special surfactants, such as zwitterionic surfactants, viscoelastic surfactants, and blended stabilizers,
Pr
greatly improves foam stability, but no attempt has been made to date to summarize these developments. Hence, the aim of the present paper is to review the major mechanisms
al
controlling the foam decay process and popular additives used for improving foam stability. The content is organized as follows: Section 2 mainly focuses on three major mechanisms
rn
governing foam aging, and strategies used for enhancing foam stability and their mechanisms
Jo u
are presented in Section 3. Section 4 introduces the application of molecular dynamic simulation to understand the effect of various stabilizers on the liquid/gas interface at a molecular scale.
2 Mechanisms governing foam aging Aqueous foam is a typical two-phase system, which can be defined as the dispersion of gas in a continuous liquid phase [27]. Fig. 1 presents the general structure of a foam, which is divided into two parts based on different liquid fractions: dry foam and wet foam. In dry foam, the gas bubbles are polyhedral and have well-defined edges, while in wet foam the bubbles are more spherical and stable [28]. Foam films (also named lamellae) are formed between two bubbles; plateau borders (PBs) are the interspace of any three approaching bubbles, and the junction of any four PBs is called a node [28, 29].
6
oo f
Journal Pre-proof
pr
Fig. 1 General structure of liquid foam: (a) foam column, (b) 3-D model of foam bubble, (c) 2-D model of foam bubble
e-
Foam is thermo-dynamically unstable, and spontaneously separates into gas and liquid phases once generated, and this instability significantly constrains the subsurface applications of
Pr
foaming fluids. Drainage, coarsening and coalescence are three major processes which occur during foam aging [30, 31], and it is noticeable that these phenomena are interdependent:
al
drainage is a major factor resulting in foam instability because it reduces the liquid content of the foam, which determines the thickness of the film [32]. Due to the reduction of film
rn
thickness, gas diffusion through films becomes easy, which causes large bubbles to become
Jo u
larger at the expense of small bubbles, eventually leading to the rupture of thinning films, and changes in bubble size distribution also increase the rate of liquid drainage in foams [33]. In the following sections these phenomena are discussed in detail.
2.1 Liquid drainage in aqueous foam Liquid drainage, which plays a dominant role in the foam destabilization process, refers to liquid flow through foam driven by gravity and capillary pressure while being resisted by viscous dissipation. More specifically, gravity results in the drainage of liquid from the network of PBs, while capillary pressure and viscous stress drain the liquid from films to PBs and may also induce liquid suction, especially at the bottom of the foam [34]. A multi-scale methodology has been constructed to understand liquid drainage in foam, which can be categorized into two major scales, as illustrated in Fig. 2. In macro-scale studies (at least several bubbles or bulk foam), researchers attempt to build a common drainage equation to describe the liquid flow process in at least several bubbles or bulk foam as well as the 7
Journal Pre-proof parameters that affect this process [35, 36]. However, in micro-scale studies, many efforts have been made to track liquid flow through a single elementary structure of foam, ignoring the interactions of the complex networks in the foam [37-40]. Since Anazadehsayed et al. [41] have already fully summarized the progress on foam drainage at a micro-scale, here we
e-
pr
oo f
provide an extensive review of recent progress in foam drainage at a macro-scale.
2.1.1 Theories of foam drainage
Pr
Fig. 2 Various research methods on foam drainage
al
To quantitatively analyze the foam drainage process, many efforts have been made to develop an easy dynamic model for foam drainage, and the earliest model of liquid drainage
rn
proposed by Leonard and Lemlich [42] assumed that flow dissipation occurs only in PB with
Jo u
finite surface viscosity. Based on their studies, several analytical models have been developed to improve the calculation of the average drainage rate and determine correlations between surface viscosity and flow velocity, which has been discussed in [30]. However, these models usually predict slower drainage rates than experimental data provide due to the initial assumption that PB plays a major role in drainage. Considering the significant hydrodynamic dissipation in the nodes, Koehler et al. [43] modified a PB-dominated model and assumed that PBs are mobile and nodes dominate dissipation, i.e. the so-called nodedominated drainage equation. Later, Cox et al. [44] proposed a generalized model coupling bubble size in time and space and extended this into two and three dimensions. The foam drainage equation is a typical nonlinear partial differential equation and later studies in this area have mainly concentrated on seeking solutions for foam drainage equations through experimental data fitting, analytical methods, and developments are summarized in Table 1. 8
numerical simulations.
Recent
Journal Pre-proof Table 1 Progress in development of foam drainage equation Source
Methods
Contributions
Helal and Mehanna [45]
Adomian decomposition method (semianalytic) and tanh method (analytic)
Mirmoradi et al. [46]
Variational iteration method
Khani [47]
Exp-function method
Darvishi and Khani [48]
Homotopy analysis method
Khan and Gondal [49]
Laplace decomposition method
He [50]
Semi-inverse method
Fadravi [51]
Homotopy analysis method
Khan and Wu [52]
Homotopy perturbation transform method
Fereidoon et al. [53]
Homotopy perturbation method
Lyiola et al. [54]
Generalised homotopy analysis method
Nikkar [55]
Variational iteration method-II
Md. Nur Alam [56]
Generalized (G’/G) expansion method
Gubes [57]
Reduced differential transform method
Somayeh Arbabi [58]
Haar wavelet method
Brito-Parada et al. [59]
Finite element method
Narsimhan [60]
Analytical method
Anazadehsayed et al. [61-63]
Computational fluid dynamics CFD
Shafiei et al. [64]
Experimental and analytical method
Obtain analytic solutions for foam drainage equation in dimensionless form:
A 2 A A A 0 t x 2 x
al
Pr
e-
pr
oo f
where, A, x and t is the cross section of a PB, location and time, respectively.
2-D model accurately resolves the dynamics of the wetting front in forced foam drainage. A model for drainage of foam film stabilized by particles 3-D model of flow through internal and external PB and node, films and transitional areas. A novel drainage model considering the impact of the concentration of surfactants, nanoparticles, and monovalent ions.
rn
Nevertheless, it is not clear if this drainage theory fully describes the foam drainage process.
Jo u
There remain large discrepancies between experiments and theoretical predictions, and one possible explanation for this disagreement is that liquid films also contribute to the drainage process by providing another region for liquid flow [65]. Sett et al. [66] developed a method for measuring the surface elasticity of vertical films suspended on a frame and found that the difference in surface tension between the upper and lower parts of the film induces Marangoni stress, which limits gravity-driven drainage to some extent. Other parameters, including the liquid content and container effects, have also attracted some attention. For example, Neethling et al. [67] extended a previous foam drainage model assuming low liquid content in the foam, and presented a new model to account for the contribution of both the plateau borders and vertices on liquid drainage over the whole range of liquid contents. SaintJalmes [68] proposed a generalized foam drainage equation which includes the effects of arbitrary container shape. Based on this model, Cox et al. [69] provided a more general solution, which not only accommodates the boundary conditions but also obtains a better
9
Journal Pre-proof approximation to the drained liquid content. In addition, Papara et al. [70] studied the effect of the container on wet foam drainage, including the diameter, wettability and shape of the walls. Recently, a multiscale model [71] was proposed to simulate the dynamics of evolving foams, including bubble rearrangement, thin film drainage and rupture, which provides some new insights in understanding how liquid drainage, bubble coarsening and coalescence influence one another on both local and global scales. 2.1.2 Macroscopic experiments on foam drainage Three major techniques are normally used in macro-scale experiments on liquid drainage based on different triggering mechanisms, including free drainage, forced drainage produced
oo f
by a continuous injection of liquid into the top of dry foam, and pulsed drainage using a finite pulse of liquid instead of continuous injection, which have been reviewed in detail by earlier studies [30, 36]. Recently, due to the application of other stabilizers, such as polymers and
pr
particles, the drainage process has become more complex. Previous researchers [72, 73]
e-
assumed that the liquid phase is Newtonian fluid, and while this is true for most surfactant foams, it is unreasonable when studying polymer-stabilized foams or those generated by high
Pr
surfactant concentrations. Unlike most surfactant solutions, polymeric solutions usually exhibit shear-thinning behavior, and the drainage rule of these foams is totally different,
al
being determined by the bulk viscosity of the liquid phase [74]. Recently, a mathematical model has been developed to describe free drainage in a polymer stabilized foam, in which
rn
the rheological parameters of the liquid phase are measured independently [75]. The model
Jo u
successfully predicts the equilibrium profile of the liquid volume fraction and shows that this volume is unrelated to the power law index of non-Newtonian liquid [75]. With the presence of particles in the foam, the drainage process becomes even more complicated, being dominated by the particle size and its volume fraction [76], and their effects can be divided into four regimes based on different conditions, as illustrated in Fig. 3. Wang and Nguyen [77] conducted forced drainage experiments to stud y liquid flow in foam in the presence of silica particles. Their results show that even a small amount (0.0932 g/L) of solid particles significantly limits drainage velocity by increasing the rigidity of the interfaces and the viscous losses in the PBs of the foams, which also induce a transition of the foam drainage regime from a node-dominated regime to a PB-dominated regime.
10
Journal Pre-proof
oo f
Fig. 3 Reduced viscous drag ( V 1 , reciprocal of reduced drainage velocity) of foam as a function of the confinement parameter (the ratio of particle size to size of passage in foam) at various particle volume fractions. (Modified from [76])
Another essential factor influencing the drainage process is bubble evolution in the foam, i.e.
pr
coarsening and coalescence. An early study showed that the foam aging process has three stages: liquid drainage initially dominates coarsening, then drainage and coarsening occur
e-
concurrently, and eventually coarsening prevails over drainage [78]. Such dominant
Pr
behaviors exhibit a relationship to the surfactant concentration. Lioumbas et al. [34] studied the interaction between foam free drainage and bubble size evolution when the surfactant concentration is below its critical micelle concentration (CMC). According to their results,
al
the maximum drainage rate decreases as the surfactant concentration increases. More
rn
importantly, at a relatively lower concentration, bubble size increases at an accelerating rate during the drainage process due to the superposition of coalescence to coarsening, which is
Jo u
totally different from previous studies, in which surfactant concentration is above CMC, and bubble coalescence is unlikely to occur at an early stage [78-80]. Interestingly, a recent paper [81] also proposes that the influence of bubble size on drainage varies at different time scale s when the surfactant concentration is relatively high (0.5~5.0 CMC): at the early stage (100~300s), since liquid drains out quickly and bubbles are still very small, bubble size seems have no effect on drainage. Overall, liquid drainage is relatively easy to monitor by tracking the liquid content in the foam. However, bubble size evolution, which involves two processes: coarsening and coalescence, is very hard to track from a macroscopic viewpoint, and more efforts have been made in this area using micro-scale experiments.
2.2 Coarsening in aqueous foam Bubble coarsening refers to gas diffusion through films due to a pressure difference, and large bubbles become larger while small ones tend to disappear. For dry foams, gas mainly
11
Journal Pre-proof diffuses through adjoining films and this process in two-dimensional foams is well described by the von Neumann-Mullins law [82, 83]: dAi (ni 6) dt 3
(1)
where, Ai is the bubble area, is the effective diffusion coefficient, and ni is the sides of a bubble. Fig. 4 shows that the rate of bubble growth depends only on their topology: foam bubbles with 6 sides remain stationary and those with 7 or more sides tend to grow, while bubbles with 5 or fewer sides tend to shrink [28].
Po
Po
n < 6, films are convex on average, and Pi > Po.
n = 6, films are straight on average, and Pi = Po.
Pi
n > 6, films are concave on average, and Pi < Po.
e-
pr
Po
o
Po
oo f P
Pi
Po
Pi
Po
Po
Po Po
Pr
Fig. 4 Schematic of evolution of a 2-D bubble with different sides , n represents the number of a bubble’s faces, Pi and Po represent the inner and outer pressure of a bubble, respectively (Modified from [28]).
For 3-D dry foam, however, the growth rate of a bubble is not exactly a function of its neighbors. In recent years, many researchers have tried to extend von Neumann’s law to
al
three-dimensional dry foam and many popular models based on Equation (1) have been
rn
proposed to describe the growth rate of 3-D dry foam, which has been briefly discussed in [84, 85]. In a wet foam which contains a large amount of liquid, the film areas are much
Jo u
smaller when PBs and vertices inflate with liquid [86]. Hence, the inter-bubble gas diffusion process is totally different from that in dry foam. Roth et al. [87] extended von Neumann’s law by incorporating the border-blocking effect and this model successfully offsets the discrepancies of von Neumann’s model for wet foams. Numerical simulations are also used for studying the self- similar growth of bubbles in wet foam [86-90]. As this is beyond the scope of the present paper, we do not discuss it further. To experimentally investigate the coarsening rate in foams, one basic premise is to constrain the influence of liquid drainage, and special set- ups, including the rotating cell [91], and diamagnetic levitation [92], are used for this purpose. More directly, some experiments have been conducted under microgravity [93, 94]. Various techniques have been developed to monitor the coarsening process, including multiple light scattering, magnetic resonance imaging, optical tomography, X-ray tomography, and observation of surface bubbles. The application of various stabilizers also has a significant effect on bubble coarsening. For 12
Journal Pre-proof example, tightly packed surfactant adsorption layers block gas diffusion through liquid films [95]. For nanoparticle-stabilized foam, aggregations of surfactant-NPs at bubble surfaces even exist with higher desorption energy and serve as an irreversible “armor” around the bubble, which greatly limits the coarsening and coalescence process [96].
2.3 Bubble coalescence in aqueous foam In addition to drainage and coarsening, bubble coalescence (i.e. the rupture of two neighboring
films; refer to Fig. 5) is also an essential process inducing foam aging.
Compared with the two former processes, the mechanism of coalescence is still poorly
Contacting
Squeezing & film thinning
Coalesce
Pr
Approaching
e-
pr
oo f
understood.
Fig. 5 Schematic diagram of two bubbles coalescing
Film thickness is an important parameter which determines the coalescence process, and is
al
closely related to the force conditions at the films [97]. Based on different thicknesses, the
rn
film is divided into two types: common black film (> 5 nm) and Newton black film (3~5 nm) [98]. As stated previously, foam drainage plays a dominant role in the initial foam aging
Jo u
process, and film thinning occurs due to the loss of liquid. However, when the liquid content in the foam is so limited that bubbles cannot rearrange, avalanches of coalescence then occur [99]. The film stability is governed by the in-situ force conditions which can be described by the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory: the electrostatic repulsive force that stabilizes film and van der Waals forces that destabilize film [100-102]. To explain stratification during film thinning, several kinds of
non-DLVO forces have also been
proposed, including oscillatory structural force considering the effect of particles [103, 104], and steric interaction due to the application of polymers [105]. The influence of these forces on film thinning and its stability has been reviewed in [106]. However, the film thinning process in foam is more complex due to the presence of surface active agents at the interface, the first of which is the so-called the Gibbs-Marangoni effect [107]. Fig. 6 shows the reaction of a liquid film to a surface disturbance; film thinning leads to an increase in the local surface area, resulting in a local surfactant concentration gradient 13
Journal Pre-proof from the intact area to the thinned region. This concentration gradient then drives a surfactant flow to provide a temporary restoring force to thin films, thus finally stabilizing the thinned film [108]. This is true for dilute pure surfactant foam, for foam-stabilized polymer or mixed surfactants; however, surface viscoelasticity (surface elasticity and surface viscosity) become more important [35]. As coherent surface adsorption layers form acting as an elastic membrane, most disturbances cannot easily rupture the film. The application of surfactantcompounded surfactants or polymers and their superior stabilizing effects is discussed in the following section.
oo f
Gas
pr
Gas
e-
Film repair
Gas
Film drainage
Gas
al
Pr
Marangoni effects Gas Surfactant gradient Film drainage
Film thinning
Marangoni flow
Gas
rn
Fig. 6 Schematic diagram of Gibbs -Marangoni effect (Modified from [108])
Jo u
3 Strategies of Foam Stabilization The thermodynamic instability of the foam is a major concern that affects effectiveness in practical application. Drainage, coarsening and coalescence are three major phenomena which are interdependent and interrelated and finally cause foam decay. In the previous section these decay mechanisms and possible factors influencing them have been fully reviewed, and in this section, three strategies are discussed to mitigate these processes and extend the lifetime of foam.
3.1 Surfactant-stabilized foam Surfactants are the most common foaming agents, and are normally classified into four types based on their head groups: anionic surfactants (positively charged), cationic surfactants (negatively charged), nonionic surfactants (uncharged) and zwitterionic surfactants (containing both positive charge and negative charge) [109]. A brief summary of the characteristics of different surfactants is presented in Table 3. Concerning the effectiveness of 14
Journal Pre-proof surfactants, it is well known that surfactants decrease surface tension at the gas/liquid interface, and CMC is an essential characteristic to evaluate its maximum dosage, above which the surface tension no longer decreases and surfactant micelles start to generate in the liquid [110], as shown in Fig.7.
Table 2 Comparison of different types of surfactant Common examples Properties Surfactants contain anionic Solubility highly dependent on temperature and easily head group, e.g. AOS, SDS. hydrolyses at HT & pH <4 [111]. Low adsorption to negatively-charged minerals [112]. Cationic Surfactants contain cationic High solubility and stability at HTHS [113]. head group, e.g. CTAB, Readily adsorb on rocks or minerals. DTAC. Nonionic Surfactants have no charged High adsorption to mineral surface [112]. head group, e.g. Ethoxylates High tendency to precipitate at HTHS (T > cloud point). Less sensitive to water hardness and salinity tolerance [114]. Zwitterionic Surfactants have both Potential to form wormlike micelles which exhibit higher cationic and anionic group, thermal stability [115]. e.g. Betaine salts. Relatively expensive. AOS: alpha olefin sulfonate, SDS: Sodiu m dodecyl sulfate, CTAB: Cetyltrimethylammoniu m bro mide, DTAC:
e-
pr
oo f
Type Anionic
Pr
Dodecyltrimethylammoniu m chloride, HT: high temperature, HS: high salinity.
Extensive studies on surfactant-stabilized foam have been conducted and the mechanisms of foam stabilization have attracted significant attention [116-119]. As stated in Section 2, liquid
al
drainage, coarsening and coalescence are three major aging phenomena, and one fundamental
rn
solution to stabilize foams is to constrain these three processes. For surfactants, the stabilizing mechanism can be summarized in two ways: (a) adsorbed surfactants at foam
Jo u
films improve the interfacial properties (e.g. surface elasticity, surface viscosity) which constrain bubble coarsening and coalescence; (b) self-assembly micelles in the solution decrease the drainage rate [115, 120-122]. Head
Gas
Tail
Surfactant
Surface tension
Liquid
CMC Surfactant concentration
Fig. 7 Schematic of surface tension change with increasing concentration and formation of micelles
15
Journal Pre-proof In field applications, the performance of a surfactant is highly dependent on reservoir conditions, such as temperature, pressure and salt concentration. Based on a previous study [109], most surfactants exhibit a high tendency to degrade or precipitate when the temperature is beyond 120 °C. In addition, the CMC of most surfactants is dependent on these external conditions [123-125]. As Fig. 8 shows, the CMC of ionic surfactants initially decreases with increasing temperature to a minimum and then sharply increases, especially over 120 °C [123]. Under relatively low pressure (< 50 MPa), CMC monotonic ally increases with increased pressure [124, 125]. In other words, to obtain optimum performance under reservoir conditions, the required quantity becomes larger, and thus increases the industrial
oo f
cost. Moreover, in such environments, surfactants, especially ionic surfactants, easily adsorb on the surface of reservoir rocks and minerals, which causes great surfactant loss and results in foam destabilization. Furthermore, the presence of divalent salts in reservoirs decreases the
0.28
8
AOS Empigen
Dow XS Varion
Dowfax Fluorad
e-
In 2.33% NaCl: In 2.1% TDS: 0.10
0.26
Pr
0.08
0.24
0.06 0.04
4
CMC (mM)
6
0.02
al
CMC (mM)
pr
solubility of surfactants and thus increases their loss [112, 126].
0.00 20
40
60
80
100
0.20
0 0
25
50
Jo u
rn
2
75
100
125
150
0.22
0.18
0.16 175
Temperature (℃ )
(a)
200
0
50
100
150
200
250
300
350
Pressure (MPa)
(b)
Fig. 8 Influence of temperature (a) and pressure (b) on CMC of surfactants. Surfactants used in (a), AOS: an anionic olefin sulfonate, Dowfax: an anionic alkyl aromatic sulfonate, Dow XS: a 50:50 blend of these two sulfonates. Three zwitterionic surfactants, Empigen: carboxyl-betaine, Varion: sulfobetaine, Fluorad: fluorinated sulfobetaine. Surfactant in (b) is TX100, a nonionic surfactant. (Data from [123, 124])
To mitigate the negative effects of traditional surfactants on the subsurface application of foam, several novel surfactants have been introduced or synthetized as foam stabilizers and show favorable performance in foam stabilization under high temperature, pressure and/or salinity conditions. In the following sections the focus is on recent advances in these special surfactants.
3.1.1 Thermally-stable surfactants (i) Effects of zwitterionic surfactants
16
Journal Pre-proof Zwitterionic (or amphoteric) surfactants are becoming popular in foam stabilization because they maintain foam stability over 100 ℃ [127, 128]. Their superior properties mainly depend on their special functional groups, including ethylene oxide units, ethoxy units and saturated/unsaturated tail groups. Hussain et al. [129] synthesized betaine zwitterionic surfactants by incorporating ethoxy units and their results showed that the surfactants generated exhibit high solubility and salt tolerance in formation water and seawater, and maintain thermal stability up to 280 °C. They also studied the effect of the hydrophobic tails of surfactants on their stability and solubility, and found that surfactants with unsaturated tails possess excellent long-range heat stability [130]. Many recent studies have reported that
oo f
the foam generated by zwitterionic surfactants exhibits superior properties under conditions similar to reservoirs, and a summary of the experiments and major findings of recent studies relating to these surfactants is shown in Table 3.
Surfactants
Experimental conditions T (℃) P (MPa) Salinity
Main findings
e-
Ref.
pr
Table 3 Recent experiments on foam stabilized by zwitterionic surfactants
[132]
Ammonyx® LMDO, PETROSTEP ® SB
98.9
[133]
CAPB OAPB EAPB
[134]
CHSB
-
22% TDS
Pr
~150
al
CB
22
-
Jo u
rn
[131]
~120
-
-
[135]
OAPB EDAB MACAT Ethoquad Triameen Aromax Ethomeen
20/50/9 0
-
-
[136]
DSB+EPS
50
-
-
17
1. CB is thermally stable at 135℃ for 30 days, and C/W foam is stabilized at temperatures up to 150 ℃. 2. Core flood test indicates that CB stabilize sC/W foam within 6 pore volumes of injection at 120 ℃. 1. All surfactants can generate foams under these conditions 2. Foam viscosity increases with surfactant concentration. 3. Injection quality is important for foam generation in some cases. 1. CO2 foam (quality: 0.99) is highly thermally stable (120 ℃) and also highly viscous (>100 cP). 2. Long carbon tail (C18 &C22 ) can generate viscoelastic wormlike micelles over a wide range of salinity and pH. 3. Apparent viscosities reached more than 120 cP with stabilities more than 30-fold over CAPB foam. 1. Excellent performance at temperature of 120 °C and salinity of 220 g/L and good longterm stability after aging for 60 days . 1. Any type of surfactants can generate viscoelastic solution. 2. Foam’s long-term stability is related to aqueous phase viscosity, and N2 foam have much higher apparent viscosity than CO2 . 3. Extremely high temperatures lead to less foam stability and lower apparent viscosity than lower temperatures. 1. EPS/DSB solution exhibits better foamability and foam stability than single DSB solution.
Journal Pre-proof
[137]
DDAPS
-
1. The effectiveness of salts in reducing the foam stability followed the sequence: AlCl3 > CaCl2 > NaCl 2. The foam collapse rate was reduced in the presence of salt. 3. The effectiveness of salts in reducing the zeta potential was in the sequence: AlCl3 > CaCl2 > NaCl.
0/10%/5 0%
-
(ii) Effects of viscoelastic surfactants Viscoelastic surfactants are those which generate wormlike micelles in foaming solutions when dissolved above their CMC and also possess viscosity-modifying properties, acting as small molecular polymers [138]. Foam generated by viscoelastic surfactants exhibits many
oo f
advantages: ultralow consumption of water, greatly increased viscosity and superior stability at high temperatures and pressures. Xue et al. [139] generated highly stable CO 2 foams with ultra- low water fractions (foam quality up to 98%) under high pressure. The foam was
pr
stabilized with a viscoelastic solution containing viscoelastic wormlike micelles formed by binary surfactants with added salts. The viscosity of these ultra-dry foams is 3-4 fold greater
e-
than traditional foams, and their stability is considerably enhanced due to the limited lamella
Pr
drainage rate as well as the coarsening rate. Alzobaidi et al. [133] proposed a different method to produce ultra-dry foam by mixing single zwitterionic surfactant with salts and these foams remain stable even at temperatures up to 120℃. In another study [135], these
al
researchers also reported that viscoelastic solutions can be produced by nonionic, cationic,
rn
and zwitterionic surfactants under ambient conditions. Their results show that a slight increase in temperature (from 25℃ to 50℃) leads to better foamability and stability due to the
Jo u
better interfacial activity of the surfactant. As expected, the viscosity of foam becomes lower with further increase in temperature (from 50 ℃ to 90℃). The capabilities of proppant transport and distribution of such kinds of foam have also been tested, and the results are favorable. Elhag et al. [140] attempted to compare the performance of foam stabilized by different viscoelastic surfactants. According to their results, compared with spherical micelles, entangled viscoelastic micelles in the liquid lamellae exhibit higher viscosity and stability. (iii) Role of gemini surfactants Unlike the surfactants discussed above, gemini surfactants normally consist of two head groups and a tail group linked by a spacer at or near the head groups. Previous studies have demonstrated that the foamability and foam stability of gemini surfactants mainly depend on the length of the spacers [141]. As their potential application in reservoir stimulation has been discussed in a recent review [142], it is not explored further here. 3.1.2 Synergistic effect of compound surfactants 18
Journal Pre-proof In addition to the application of thermally-stable surfactants, the synergisms of mixing conventional surfactants have also attracted the attention of researchers [143-145]. Some exhibit favorable performance in foam stabilization under high temperature, pressure and salinity conditions. In the research, the most commonly used compound surfactant system is a binary surfactant mixture, including three different mixing types: cationic/anionic surfactants [146-149], ionic/nonionic surfactants, and fluorocarbon/hydrocarbon surfactants (which show good performance in fire extinguishing [150], and are not discussed further here). The mechanisms of the synergisms among different surfactants are complex and depend on the structural properties of each component. For example, hydrogen bonding is dominant in
charged
atoms among surfactants,
and
oo f
the nonionic/anionic mixing system due to the presence of the -OH group and negatively electrostatic attractions are common
in
cationic/anionic mixing systems because of the high charge difference [151]. For some amino
pr
acid-based surfactant mixtures, the interactions also involve cationic-effects and -effects.
e-
Some other molecular interactions in surfactant systems include ion-dipole forces between ionic/nonionic hydrophilic groups, steric forces between bulky groups, and van der Waals
Pr
forces between hydrophobic groups [152]. Due to the presence of these complex interactions, compound surfactant systems significantly improve the properties of gas/liquid systems
al
compared with systems containing solely pure surfactants, such as enhancing interfacial activity, enlarging surfactant solubility in solutions, improving micelle structure and stability,
rn
and reducing the adsorption loss of surfactants onto mineral/rock surfaces. A summary of
Jo u
some selected literature on compound surfactants and their effects on interfacial properties is presented in Table 5.
Table 5 Summary of recent advances in compound surfactants and their effects on interfacial properties and micelle formation Compound surfactants Anionic/zwitterionic Cationic/anionic ionic/nonionic Anionic/nonionic Ionic/nonionic Anionic/nonionic gemini Cationic/nonionic gemini Ionic/nonionic Cationic/anionic Cationic/anionic
19
Experimental focus Synergism of surface properties, including surface tension, adsorption behavior, elasticity. Synergism of foam stability and its mechanisms. Foam behavior and surface tension Stability of mixed micelle. Drainage coefficient of foam films formed by mixed surfactants, and effect of mixture composition on it. Synergism of micelle formation and surface tension reduction efficiency. Effect of alkyl chain length on mixed micelle. Critical thickness of foam films formed by mixed surfactants, and influence of mixture composition on it. Competition adsorption of catanionic surfactant mixtures on quartz, and its effect on wettability of quartz surface. Improvement of mixed surfactant in oil/water interfacial properties, and factors affecting it: mixing ratio, surfactant type and alky chain length.
Reference [153] [121] [154] [155] [145] [156] [157] [144] [158] [159]
Journal Pre-proof
Ionic/nonionic/zwitterionic Cationic/anionic Cationic/anionic gemini Anionic/anionic Cationic/anionic Cationic/anionic
Cationic/anionic
Cationic/anionic Anionic/nonionic
Synergism of mixed surfactants on foam stability at high temperatures (over 100℃), pressures (over 10MPa) and salinities (over 100g/L). Stable foam generated by triple surfactant mixture. Foam drainage rate under high pH and temperature (15-25℃) Formation of wormlike micelles and its effect on viscosity. Molecular simulation of micelle formation. Synergism of surface properties and micelle formation Effect of mixed surfactants on foam stability in absence and presence of crude oil, and influence of brine water. Interfacial properties and foam stability in presence of oil Synergistic effects in enhancing surface properties and micelle formation. Adsorption process of mixed surfactants. Improvement in properties of quaternary ammonium surfactant with hydroxyethyl group when coupled with anionic surfactants, and effects of mixing fraction. Synergism of foaming efficiency in high salinity. Synergism of foam stability at high temperatures (up to 130 ℃, 2 MPa), and its mechanisms: hydrogen bonding and electrostatic force.
oo f
Anionic/ nonionic
[160] [143] [161] [162] [163] [164] [165]
[166] [167] [151]
pr
(i) Improvement in gas/liquid interfacial properties
e-
One well-known factor which affects foamability and foam stability is the surface tension of the solution, and surface or interfacial tension can be greatly decreased with the addition of
Pr
surfactants. For a compound surfactant system, stronger interactions between mixed surfactants cause the adsorbed surfactant to be packed more tightly at the interface, which leads to a further decrease in surface tension [158]. Fig. 9 shows the effect of cationic/anionic
al
surfactant mixtures on surface tension at the interface, and it is obvious that the surface
rn
tension of the mixed system is much lower than that of any pure surfactant, varying as a function of surfactant concentration, and the optimum occurs at the equimolar mixing ratio
Jo u
[162]. This phenomenon has also been reported for other cationic/anionic or ionic/nonionic mixing systems [168]. Due to the strong local interactions, mixed surfactants tend to be more tightly arranged at the interface, which confers a strong dilatational elasticity as well as a high disjoining pressure for approaching films, and the generated foam correspondingly tends to be extremely stable against coarsening and coalescence [121, 153, 169]. However, the stabilizing effects vary with the properties of the surfactants. For example, Li et al. [164] studied the effect of the length of the hydrocarbon chain on foam stabilized by compound surfactants and reported that the stabilizing effect reaches its peak when surfactants contain hydrophobic chains of similar lengths. Concerning foam stability at high temperature and pressure, Wang et al. [160] found that nonylphenol polyethoxylate surfactants exhibit good thermal resistance, which can be further enhanced by increasing the ethylene oxide groups. Furthermore, amine-based surfactants are able to maintain foam stability at high temperatures and pressures (over 80 ℃ and 10 MPa). Fig. 10 shows a comparison of the performance of 20
Journal Pre-proof compound surfactants and SDS alone in foam stabilization, and the half- life of foam
oo f
stabilized by mixtures is over 20 min. at 100 ℃ and 50g/L salinity [151].
pr
Fig. 9 Equilibrium surface tension of individual and equimolar mixed surfactant solutions . The insert graph shows that peak performance in terms of surface tension reduction occurs at the equimolar mixing ratio, where the total surfactant concentration is 4 ×10-6 mol/L. SGS12: a sulfonate Gemini surfactant, BQAS: a
280
8000
200
al
30
160
rn
20
0 50
60
70
80
Jo u
10
90
100
110
120
FCI (cm3·min)
40
Foam volume/Vmax (cm3)
50
Half-life (min)
15
LDEA/SDS, FCI SDS, FCI
Pr
LDEA/SDS, T0.5 SDS LDEA/SDS, Vmax 240 SDS
LDEA/SDS, u SDS
12
6000 9
4000 6
2000
3
120 0
130
Defoaming rate, u(cm3/min)
60
e-
bisquaternary ammonium salt. (Reproduced from [162])
140
Temperature (℃ )
(a)
0 50
60
70
80
90
100
110
120
130
140
Temperature (℃ )
(b)
Fig. 10 Co mparison of properties of LDEA/SDS foam (0.5 wt %:0.5 wt %) and SDS foam (1.0 wt%), conditions: 20000 mg/L brine water and 10.5 MPa. FCI is a general foam performance indicator, FCI = 0.75Vmax×T0.5 , and a larger FCI value means a better performance [151].
(ii) Improvement in micellar structure The formation of micelles in solutions greatly affects their viscosity, and a viscous liquid phase in the foam leads to a relatively low drainage rate, contributing to foam stability. The cooperative effects of compound surfactants also have a favorable influence on the formation of micelles in two ways: 1), the CMC of mixed systems is further decreased, as is clearly shown in Fig. 9, which means an earlier beginning of micelle formation with increasing surfactant concentration [152, 155, 170]; 2), the formation of mixed surfactant micelles is totally different from that of single surfactant micelles and the structure is more complicated 21
Journal Pre-proof and stable. Cui et al. [149] experimentally observed the formation of mixed micelles in ionic/nonionic as well as cationic/ionic surfactant solutions, and found that the formation is governed by the CMC of each component: as the total concentration increases, micelles of surfactant with lower CMC are generated first, then the other surfactant fuses, leading to mixed micelles. In addition, to evaluate the stability of micelles, the excess free energy of the surfactant is an effective indicator, which can be calculated by Equation (2) for binary surfactant systems, and the smaller the absolute value of Gex , the less stable the formed micelles.
oo f
Gex RT ( x1 ln f1 x2 ln f 2 )
(2)
where, R is the universal gas constant, T is the temperature, x 1 , x2 is the mole fraction of each surfactant, and f 1 , f 2 is the activity coefficient of each surfactant, written as fi e ( xi ) , and 2
pr
is the interaction parameter depending on the surfactant properties.
e-
Trawinska et al. [156, 157] conducted experiments to investigate the synergistic effects in micelle formation and surface tension in ionic/nonionic surfactant mixtures. According their
Pr
results, the free energy of micelles has more negative values for mixtures than for each component in all mixing systems. [161] reported the transition to shear-thinning behavior of solutions due to changes in the molar ratios of surfactants, and this was explained by the
al
formation of wormlike micelles and their morphologies observed from their simulation
rn
results, as shown in Fig. 11. In addition, several studies have reported switchable wormlike surfactant micelles triggered by CO 2 injection [171-173], According to [173], by injecting
Jo u
CO 2 into solutions, two amine groups of TMHDA (N,N,N ′ ,N ′ -tetramethyl-1, 6hexanediamine) are protonated into quaternary ammonium salt when mixed with sodium oleate (NaOA) at a molar ratio of 1:2, and eventually generate a pseudo-gemini surfactant due to the bridge of NaOA. Fig. 12 illustrates this process, and these pseudo-gemini surfactants can spontaneously form wormlike micelles, resulting in a sharp increase of viscosity. Interestingly, this process can be repeatedly triggered by CO 2 or N 2 injection, which has tremendous application potential in foam fracturing.
22
Journal Pre-proof
Viscosity, h (Pa·s)
102 101
10
0
10-1 10-2 10-3
Zero shear viscosity, h0 (Pa·s)
1000 COTAB(mM): 0 20 40 60 80 100 140 200
103
800
600
400
200
0 10-2
10-1
100
101
102
103
0
50
Shear rate (s-1)
100
150
200
OTAB Concentration (mM)
(a)
(b)
e-
pr
oo f
Fig. 11 Viscosity changes as a function of shear rate (a), and zero shear viscosity of solutions as the increase in OTAB (Octadecyltrimethylammoniu m Bromide) concentration and possible micelle morphology during evolution (Modified from[161]).
Protonation _
+
+ _
_
Pr
_
rn
al
Micelle formation
Jo u
Fig. 12 Illustration of protonation of amine groups induced by CO 2 and formation of switchable wormlike micelles (Modified from [173]).
3.2 Polymer-enhanced foam 3.2.1 Mechanism
As discussed previously, the liquid phase with high viscosity and surface elasticity is an effective way to enhance foam stability. For these cases, polymers (mainly polyelectrolytes) are also extensively used as foam stabilizers together with surfactants to improve foam stability by increasing the viscosity of foaming solutions [105]. Similar to surfactants, some low molecular polymers also adsorb at the interface and thus decrease the gas permeability of foam films [174]. Interactions among surfactants and polymers are mainly induced by electrostatic and hydrophobic forces, as illustrated in Fig. 13, which shows that polymer chains binding surfactants attach at the gas/liquid interface and some long chains act as a “bridge” between neighboring films.
23
Journal Pre-proof Liquid Liquid
Polymer chain chain Polymer
Gas
Surfactant Surfactant
Gas Gas
Plateau border board Plateau
Fig. 4 Schematic of interactions between polymer and surfactant in foam film
However, the function of interfacial complexes is questionable, as the effect of the polymer-
oo f
surfactant mixture on foam stability can also be attributed to the net charge of the film and the foam film’s stability is reduced to the isoelectric point (IEP) of the solution, followed by destabilization around the IEP, and becomes very stable above the IEP [175, 176]. According
pr
to Fauser et al. [177], when the total ionic strength of the film reaches its maximum, the synergistic adsorption of both surfactant and polymer at the interface is largest, leading to the
e-
most stable foam film.
Pr
3.2.2 Recent progress in polymer-enhanced foam
Synergistic interactions among surfactant-polymer mixtures indeed improve foam stability, and factors influencing such synergisms have also attracted the attention of researchers [178,
al
179]. For example, the contributions of surfactant and polymer to synergism differ, and foam
rn
stability is mainly controlled by the role of the surfactant while the effect of polymer type is minor [180]. Concerning surface activity, Goswami et al. [181] found that these interactions
Jo u
are composition-dependent, and the decrease in surface tension is dominated by polymers. Furthermore, opposite charges are not necessary for synergism [182], but they influence performance. For weak systems (uncharged polymer/ionic surfactants, or mixtures with the same charge), both foamability and stability are increased compared with surfactant only, due to the fast surfactant adsorption and strong steric repulsion of surface-active polymers. For strong systems (oppositely-charged mixtures), only foam stability can be strengthened relative to surfactant only because of the strong association of the surfactants and polymers, which slows the formation of the adsorption layer [182-184]. Considering the effects of surfactants or polymers themselves, Uhlig et al. [185] found rigid polymers in the mixture show better foam stability that flexible polymers. Pu et al. [186] observed that polymers with higher molecular weight exhibit better foam stabilization, which is further increased with polymer concentration. Schulze-Zachau et al. [187] reported that interfacial charge and
24
Journal Pre-proof surfactant binding efficiency are strongly dependent on the a lkyl chain length of the surfactants. The application of polymers in foam stabilization in reservoirs may be limited by reduced flowing properties in the reservoir due to the increased viscosity and polymers are usually degraded when the reservoir temperature is higher than 85℃ [188, 189]. Hence, some new insights into PEF have been published recently. Instead of using traditional polymers, Zhao et al. [188] studied the long-term stability of gel-enhanced foam by adding comb polymer gel to high-temperature reservoirs. Their results show that increased viscosity enhances the thickness and strength of foam films, which is also observed in the morphology of foams.
oo f
However, according to their flooding experiments, foams with such high viscosity also exhibit great plugging capacity in porous media, which may not be suitable for foam fracturing. Verma et al.[190] proposed a method to improve the rheology of PEF by adding
pr
bentonite, which achieves a similar proppant capacity while reducing the dose of polymer,
e-
and the foam remains thermally stable at temperatures up to 90 ℃. In this case, the formation damage caused by insoluble guar can be constrained, and this improves the flow behavior of
Pr
fracturing foam in low permeability reservoirs. Yin et al. [191] experimentally investigated the stability of regenerated cellulose (RC)-enhanced CO 2 foam under oilfield conditions and
al
its stabilization mechanisms and found that RC foam undergoes slower bubble coalescence and size increase in the first 30 min, showing the best stabilizing foam performance. This
rn
trend has been verified by their micro-experiments. As shown in Fig. 14, the presence of RC
for a long time. 1.6
1% SS163 1% SS163+1% RC 1% SS163+1% SiO2 NP 1% SS163+1% Al2O3 NP 1% SS163+HPAM
1.4 1.2
350 300
Diameter (mm)
Relative film thickness
Jo u
greatly strengthens the thickness of the liquid films, enabling foam stability to be maintained
1.0 0.8 0.6
250 200 150
0.4
100
0.2
50
0.0
1% SS163 1% SS163+1% RC 1% SS163+1% SiO2 NP 1% SS163+1% Al2O3 NP 1% SS163+HPAM
0 0
50
100
150
Time (min)
(a)
200
250
300
0
50
100
150
200
250
Time (min)
(b)
Fig. 5 Foam (a) film relative thickness and (b) diameter of bubbles changes during foam aging process (modified after Yin et al. 2018).
25
300
Journal Pre-proof
3.3 Nanoparticle-stabilized foam Because of certain inherent weaknesses of surfactants and polymers as stabilizers under harsh reservoir conditions, many efforts have been made to find other more appropriate alternatives. Nanoparticles (NPs) have gradually attracted attention for this purpose, and foam stabilized by such NPs, i.e. the so-called Pickering foam, exhibits superior performance even under extreme experimental conditions [192-195]. However, it is difficult to generate foams solely using NPs, but partially hydrophilic NPs are good foam stabilizers at the appropriate concentration. To achieve moderate hydrophilicity, one strategy is to utilize NP and surfactant mixtures and adjust the surface property of NPs by surfactant electrostatic
oo f
adsorption.
3.3.1 Mechanisms of in-situ surface activation of NPs
pr
With the addition of surfactants, a series of interactions between surfactants and NPs occur and thus improve the hydrophobicity of NPs. Generally, the mechanisms of this activation
e-
process are primarily controlled by the type of surfactant and the mixing ratio of the NP/surfactant. Previous experiments indicated that NPs can only be surface activated by
Pr
oppositely-charged surfactants and the adsorption of surfactants onto the surface of NPs is a cumulative process governed by many forces, including the electrostatic force, non-polar
al
interactions and hydrophobic interactions [196-199]. For different NPs, different types of
rn
surfactants are required to modify their surface properties due to their different surface electric potentials in solutions. Generally, silica NPs are negative in solutions and can be
Jo u
improved by cationic surfactants, while bare calcium carbonate NPs can be modified by anionic surfactants [197, 200]. Furthermore, the hydrocarbon chain length of surfactants may also influence modification performance, because surfactants with shorter chains are more soluble in water [201]. For example, Liu et al. [202] investigated the adsorption behavior of four surfactants with different hydrocarbon chain lengths and found that a longer chain length induces stronger hydrophobic interactions and hence greater surfactant adsorption, which leads to highly stable foam at a lower surfactant concentration. However, Cui et al. [197] reported that SDS is a more efficient surfactant for this surface activation than AOT (Bis-(2ethylhexyl) sulfosuccinate sodium) because AOT has double hydrocarbon chains, which leads to the formation of double adsorption layers on NPs due to hydrophobic interactions at a relatively low concentration. Recently, Wang et al. [203] modified silica NPs using different charged surfactants and the results showed that a better synergistic effect occurs
26
Journal Pre-proof between NPs and OA-12 (Lauryl dimethyl amine oxide) because of the opposite charge and shorter molecular chains. In addition to the utilization of suitable types of surfactant, the relative concentration of surfactant (also described as the mixing ratio) in foaming solutions also influences the surface activation of NPs [204]. Sonn et al. [205] studied the effects of silica NPs modified by 1.0 wt.% Dimethyldichlorosilane (DMDCS) on foam stability in the presence of extra DMDCS. In their experiments, they found that the presence of the extra DMDCS has a negative influence on the synergy between silica NP and surfactant, which causes a further increase in surface hydrophobicity and leads to the tendency for particles to move in the air in bubbles, so that
oo f
foams become unstable. However, when the concentration of DMDCS is over 0.025 wt%, these negative effects are offset due to the dominance of DMDCS in the liquid phase, and foam stability increases again. In an earlier study [116], researchers proposed that surfactant
pr
adsorption on the surface of particles is a two-stage process: from an initially disorganized
e-
monolayer to a closely-packed monolayer with some head- groups facing into the solution due to the π–π interactions. In Zhang et al.’s work [206], with increased AOT concentration, the
Pr
adsorption status of AOT on particle surfaces is divided into three regions, which are mainly controlled by the electrostatic forces and hydrophobic interactions. Sun et al. [207] proposed
al
four different adsorption behaviors of surfactants with increased surfactant concentration and indicated that modified NPs move to the gas/liquid interface when adsorbing a certain
rn
amount of surfactants, which therefore increases dilatational viscoelasticity. A recent study
Jo u
by Rad et al. [208] summarized the arrangement of NPs and surfactants at different mixing ratios. As shown in Fig. 15, as the concentration of NPs increases, the surfactant adsorption layer evolves, from a compactly bilayer initially, then to a bilayer/partial bilayer/monolayer, and then nearly all monolayer, and then monolayer/partial monolayer, and finally only partial monolayer. In stages (a) and (b), the particles have no affinity for the gas-water interface. When the particles become only partially covered by surfactant in stages (c) and (d), they can attach to the gas-water interface and reduce the surface tension.
27
Journal Pre-proof (a)
(b) Bubble
Bubble
(c)
(d) Bubble
oo f
Bubble
pr
Fig. 6 Position of surfactants and NPs in solution at different stages : in (a) NPs are covered by surfactant bilayer, and various surface coverage in (b) and partial coverage in (a) and (d) (Modified from [208])
e-
3.3.2 Synergistic effects of surfactants and nanoparticles
Pr
Foam stabilization with bare NPs does not allow a good level of performance, but synergistic interactions at the interface of NPs and surfactant lead to the generation of more stable foam in harsh environments [22, 23]. This synergy can potentially be used to maximize foam
al
transportation and fracture conductivity in reservoir stimulations. Previous studies have
rn
proposed many possible explanations for the mechanisms of foam stabilization by modified NPs but some of those arguments occur repeatedly [23, 26]. Like chemical surfactants, the
Jo u
adsorption of partially hydrophobic NPs at the bubble interface is the fundamental element in maintaining the long-term stability of foam, even under harsh conditions. Nevertheless, NPs show several distinct advantages over chemical surfactants: 1) higher desorption energy in the moderate surface hydrophilic state; 2) multiple arrangement at the bubble interface [209, 210] (i) High desorption energy The contact angle of NPs attached to gas/liquid interfaces is an essential parameter for the evaluation of their wettability by liquid, which assists particles to attach to the gas/liquid interface fully [211]. Compared with surfactant molecules, NPs are so large that they require greater energy to detach from the interface. The detachment energy (E) [212] of spherical particles can be calculated by E R 2 1 cos
28
2
(3)
Journal Pre-proof where, R is the radius of the particle, is the surface tension, and is the contact angle between the nanoparticle and water. Fig. 16 shows the arrangement of NPs with different contact angle at the surface. For hydrophilic NPs, as the surfactant concentration in the solution increases, the contact angle also increases due to the electrostatic adsorption of surfactant on the NPs’ surfaces [213]. Studies have found that the desorption energy reaches the maximum when the contact angle of NPs is close to 90° at an optimum concentration of surfactant [206, 214]. It is also revealed that long-term foam stabilization can be achieved if a high concentration of moderately hydrophobic NPs (contact angle about 60 to 70°) is used. According to Equation (3), the presence of surfactant also lowers this energy due to the
oo f
reduction of surface tension [215], but this effect is relatively inferior to the enhancement; as a result, there still exists a larger detachment energy of NPs which ensures foam stability.
Gas
Water
Water
Gas
Pr
Gas
(c)
pr
(b)
e-
(a)
(e)
Gas
rn
Water
al
(d)
Water
< 90°
Gas Water
90°
Jo u
Fig. 7 The distribution of nanoparticles with different contact angles at bubble interface; particles are irreversibly attached when (a) < 90° and (b) = 90°, wh ile particle residue exists on gas side when (c) > 90°. Bubble curvature also depends on contact angle, as shown in (d) and (e). (Reproduced from [35])
In addition, Wang et al. [203] found that NPs and surfactant play different roles in foam stabilization: surfactant decreases the surface tension of the liquid phase while NPs coated with surfactants increase the modulus of elasticity. Indeed, according to other experiments (refer to Fig. 17) [216], the size distribution of foam bubbles generated by surfactant-NP mixtures is more fine and uniform. The irreversible adsorption of the NP-surfactant layer at the bubble surface also increases dilatational viscoelasticity, restricts bubble coarsening and coalescence, and maintains the long-term stability of the foam [203, 217].
29
Journal Pre-proof
oo f
Fig. 17 Micro-morphology of foam bubbles as a function of time (Modified from [216]).
(ii) Arrangement of NPs at bubble interface
Due to the superior adsorption capacity of high surface-active NPs, they exist in the
pr
elemental structure of the foam in three ways (Fig. 18): (1) as a monolayer of bridging
e-
particles; (2) as a bilayer of closely packed particles; and (3) as a network of aggregating
Jo u
rn
al
Pr
particles [23, 218].
Fig. 18 Schematic of three arrangements of NPs at the interface [23].
The structure of NPs mainly depends on the concentration of NPs. At low concentrations, only a single layer of NPs forms at the liquid film, which produces sterically strong interfacial barriers that prevent foam coalescence and coarsening [24]. In addition, the bridging of partly hydrophilic NPs also plays an essential role in film drainage, which binds some water content after the initial drainage [23]. With the increase of NP concentration, the adsorbed layers are more likely to be composed of particle aggregation multilayers rather than monolayers because of the high particle coagulation [219]. These multilayers of particles in the films or PBs of the foam assist in constraining film thinning and thus maintaining film thickness. On the other hand, such structures largely prevent the direct contact of adjacent 30
Journal Pre-proof bubbles and can also act as barriers, reducing liquid drainage. Therefore, the foam generated by NP-surfactant mixtures exhibits long-term stability even under harsh conditions.
4 Molecular dynamic simulation of foam stability As discussed above, experimental investigation is a major method to evaluate the effects of various chemical additives on the stability of aqueous foam, but it can only provide the macroscale performance of the stabilizers. To fully understand the stabilizing mechanisms, both interfacial and bulk properties in the foam are necessary, including interactions among surfactant and water molecules. However, it is hard to obtain this knowledge through macroscale experiments. In recent years, molecular dynamic (MD) simulation has been used
oo f
to fill this gap. To obtain optimum stabilizers which maintain foam stability under reservoir conditions, it is necessary to screen many different types of potential chemicals. These are
pr
not only difficult to synthesize but the process is time-consuming and requires considerable resources. Through molecular dynamic simulation, surface tension reduction and micelle
e-
formation under various conditions can be easily monitored at a molecular scale, which provides a new way of filtering out suitable additives and then verifying their effects through
Pr
experiments. To our knowledge, to date there has been no summary of progress in this area, and a comprehensive review of recent progress in gas/liquid interfacial and bulk system
rn
4.1 Simulation methods
al
through MD is therefore provided as follows.
Foam is a complex gas/liquid mixture system and at molecular scale, we are more interested
Jo u
in the phenomenon as a liquid film, and foam is therefore usually simplified as a gas/liquid interface. Two popular methods are normally used for building such an interface: one method initially includes two surfactant adsorption monolayers distributed at both sides of a liquid layer filled with water molecules, counter ions and other soluble or suspended materials, as shown in Fig. 19 (a) [220-222]; the other model initially includes, from the top down, a vacuum layer, a surfactant adsorption monolayer, a liquid layer and an energy barrier to constrain molecules from travelling across the boundary (Fig. 19 (b)) [223]. Both methods can be used to study the effect of foaming agents on the stability of foam films, and each has advantages and disadvantages. For the former model, as the thickness of the liquid layer is large enough (>2 nm), the interactions between the two surfactant adsorption layers can be ignored [224]. The disadvantage is that it is very time-consuming due to the huge computational load. In contrast, the latter model requires less time, but the behavior of molecules near the confined layer is very complex. 31
Journal Pre-proof
Gas molecules or vacuum
Surfactant molecule Liquid film
Water molecules
Frozen molecules
(a)
(b) Fig. 19 Sketch of two simulation domain configurations
oo f
One major factor that affects the results of simulation is the force field, and commonly- used force fields include GROMOS [225], OPLS [226], CHARMM [227] and AMBER [228]. To
pr
simulate the self-assembly of surfactants or polymers at a larger temporal and spatial scale, some coarse- grained force fields have also been proposed, including the MARTINI force
e-
field [229] and the SPICA force field [230]. However, to date, no force field has been designed specifically for the simulation of surfactant behaviors at the interface, and this may
Pr
be one possible factor which causes discrepancies between simulations and experiments. 4.2 Research results of molecular simulation
al
Interfacial properties. As discussed above, molecular dynamic simulation of foam stability usually simplifies the foam as a liquid/gas interface and focuses on the properties of this
rn
interface. Interfacial tension is an essential parameter for describing the surface activating
Jo u
process, which is defined as the difference between the normal and lateral pressure of the whole system in molecular dynamic simulations. If z direction is normal to the gas/liquid interface, the relationship can be written as:
1 lz Pzz 0.5 Pxx Pyy dz n 0
(4)
where, Pxx, Pyy, Pzz are three principal components of the stress tensor, respectively, lz is the length of the simulation box along the z axis, and n is the number of interfaces in the system. For example, in Fig. 19 (a), as the system has two interfaces, n equals 2. The interfacial tension of water has been extensively studied, and simulation results mainly depend on the application of various water models. The advantages and disadvantages of different water models as well as the effects of temperature have been fully reviewed in recent papers [231, 232].
32
Journal Pre-proof As stated previously, most surfactants are able to significantly reduce surface tension at the interface, and this phenomenon can also be reproduced based on molecular simulations, although most focus on the oil/water interface [233-237]. Fig. 20 shows the effect of various surfactant types and surface concentrations on interfacial tension: before reaching CMC, the interfacial tension decreases as the surfactant numbers at the surface increase, and it remains stable when the number is beyond the CMC. The graph also shows that gemini surfactant exhibits better performance than the others, which may be due to its complex multiple polar heads [237]. 60
Anionic surfactant Nonionic surfactant Zwitterionic surfactant Gemini surfactant
oo f
40
pr
30
20
e-
Interfacial tension (mN/m)
50
0 0
20
40
Pr
10
60
80
100
120
140
160
180
Surfactant number
al
Fig. 20 Changes in interfacial tension as a function of surfactant number [237].
rn
In addition, the organization of surfactants at the interface also a ffects the interfacial properties, which depends on the surface concentration of surfactant. The tilt angle is an
Jo u
effective indicator to describe the orientation of surfactant molecules at the interface, w hich is the angle between the vector of the tail group and the normal direction of the interface. As shown in Fig. 21, with increased CTAB concentration, most CTABs tend to vertically insert into the water slab and the surfactant layers thicken, which is a result of the competition of van der Waals interactions (attraction between surfactants) and electrostatic interactions (repulsion) [238]. Meanwhile, due to the presence of the surfactant layer, the interface thickness also changes, which is defined as the distance falls from 90% to 10% of the bulk value, as illustrated in Fig. 22. In practice, the thickness is calculated as the average of t 1 and t 2 . In addition, for film stability, Yang et al [239, 240] proposed the concept of critical film thickness, which is the minimum thickness of the interface which remains intact. Based on this concept, they proposed a stability index (SI) for liquid film:
33
Journal Pre-proof SI
hc , w hc , w/ s hc , w
100%
(5)
where, hc,w is the critical film thickness without the surfactant and hc,w/s is the critical thickness of film stabilized by surfactant. 0.20
8
2 nm
Interaction parameter Af
0.15
Probability
CTAB concentration increase
0.10
Repulsion
4
0
Attration Attraction
0.05
-8
0.00 0
10
20
30
40
1.42 50
2.66
60
70
Simulation data Experimental data
3.51 80
-12
90
1.0
pr
-6 mol/m2)： C (×10-5
oo f
-4
2.0
3.0
4.0
Surfactant concentration (10-6 mol/m2)
Tail tilt angle (°)
(a)
(b)
Pr
e-
Fig. 21 CTAB at gas/liquid interface. (a) Surfactant tail tilt angles with different concentrations at the interface; the insert picture is the final configuration of CTAB corresponding to 1.42 ×10 −6 mol/m2 , 2.66 × 10−6 mol/m2 , and 3.51 × 10−6 mol/m2 (b) Local Frumkin interaction parameter Af as a function of surfactant surface concentration, AF = w22 RT , where w22 is the total pairwise interactions between surfactants (Modified from [238]). Chart Title
1.2
t1
al
t2
90%
rn
0.8 0.6 0.4
Jo u
Density (kg/m3)
1.0
0.2 0.0
10%
50
100
150
200 Z-axis (Å)
250
300
350
Fig. 22 Illustration of Gibbs interface thickness based on density profile of liquid phase
Another focus is the complex intermolecular interaction and its influence on interfacial properties. The self-diffusion coefficient is a parameter which indicates the motion of molecules at the interface. Normally, there are two different methods for calculating the selfdiffusion coefficient of water in molecular simulation: the mean-square displacement (MSD)based method and the velocity-auto-correlation function (VACF)-based method, and discussions of the diffusion coefficient of water under different simulation conditions can be found in [241]. With the addition of surfactant, the diffusion coefficient of water is limited due to the hydration reactions between the surfactant and water molecules, which is related to the head group of the surfactant [242]. The interaction between surfactants and polymers has 34
Journal Pre-proof also been reported frequently in research studies [220, 240, 243, 244]. For example, Wu et al. [220] investigated the effect of the concentration of PAM and the degree of HPAM on the stability of SDS foams by analyzing the density distribution of SDS head- groups, the radial distribution function (RDF) of hydration of SDS head- groups, and the MSD of hydrated water around the amide group. Gao et al. [243] studied the improvement by betaines of the stability of alkyl-polyoxyethylene carboxylate (AEC) foam. Their results showed that the presence of betaines constrains the repulsion between the head- groups of anionic surfactants, and the electrostatic structures become denser with the increasing concentration of betaine, which enhances the entry barrier and thus creates better foam stability. Moreover, the effect
oo f
of different salt ions in liquid phase on foam film stability at molecular level has also been fully reported in recent papers. For example, Li et al. [221] studied the different effects of Ca2+ and Mg2+ on the stability of foam, and their results showed that Mg2+ broadens the
pr
distribution thickness of surfactant head-groups and thus enhances foam stability, while the
e-
presence of Ca2+ causes the surfactant to aggregate more and destroys foam stability. Formation of micelles. The formation of micelles is also an important factor in the
Pr
evaluation of the performance of surfactants in bulk systems, and most molecular simulations on this topic are conducted using coarse-grained force field due to the considerable
al
computing costs. Transitions of morphologies of single or binary surfactant micelles ha ve been extensively studied and salt concentration and mixing ratio are two major influencing
rn
factors [245, 246]. Fig. 23 shows a typical transition of CTAC micelles: from sphere to worm,
Jo u
to branch, and to sphere again. This phenomenon is mainly due to the counter ions in solutions which form a salt bridge helping surfactants jump to approaching micelles [247]. For binary surfactant systems, the mixing ratio also affects the evolution of micelle morphology by producing different barrier heights for micelle fusion [161]. Yan et al. also found that charge neutralization occurs around the head group when the concentration of one type of surfactant increases, and this constrains the repulsive force based on DLVO theory, which makes micelle fusion easier [248]. The interactions between surfactants and polymers or nanoparticles during micelle formation have also attracted the attention of researchers. For example, Hu et al. [249] reported that micelle morphologies change from spherical to rod- like aggregations as the degree of hydrolysis of partially hydrolyzed polyacrylamide (HPAM) hydrolysis increases. Sambasivam et al. [250] studied the fusion of a single NP–surfactant complex with rod-like micelles and observed that the end-caps of micelles open up and bridge with the NP surface through a surfactant exchange process.
35
Journal Pre-proof The rheological properties of solutions are other important factors, which are mainly evaluated through shear viscosity in molecular simulations. For only surfactant solutions, bulk viscosity and surfactant solution have a linear relation with the presence of sphere micelles [251]. Dhakal et al. [252] observed an anomalous zero-shear viscosity variation of CTAC/NaSal solutions, apparently resulting from changes of micelle morphologies, fundamentally governed by the NaSal concentration. Yan et al. [248] indicated that solutions become shear-thinning with the transition from spherical micelles to wormlike micelles in catanionic surfactant solutions. The addition of nanoparticles to surfactant solutions also induces a transition from zero-shear viscosity to shear-thinning with the increase in shear rate,
(b)
(c)
(d)
Pr
(a)
e-
pr
oo f
and the transition point decreases as the NP volume fraction increases [253].
Conclusion
al
Fig. 23 Illustration of evolution of micelle mo rphologies with increased salt concentration: fro m sphere to worm, to branch, and to sphere again. The molar ratios of salt and surfactant are: (a) 0.00, (b) 0.67, (c) 1.33, (d) 2.00 (Modified from [247]).
rn
This review presents detailed information on three major strategies of foam stabilization,
Jo u
including the application of surfactants, polymers, nanoparticles and their compounds. Liquid drainage, coarsening, and bubble coalescence are three dominant processes governing foam destabilization. Past studies have indicated that these phenomena are interdependent and liquid drainage dominates at the earlier stage, while coarsening and coalescence become more significant later. All foam-stabilizing strategies are proposed to fundamentally retard these aging processes. In the research literature, surfactant is the additive most used to stabilize foam by improving the interfacial properties and forming micelles in the liquid phase. The results of laboratory experiments show that some thermally stable surfactants and compound surfactant mixtures exhibit better performance in foamability and foam stability. Polymer is another popular material used together with surfactants for enhancing foam stability, which constrain drainage mainly by increasing the viscosity of foaming solutions. Moreover, the synergy of surfactant and nanoparticle is reported to show best performance in foam stabilization, even under extreme reservoir conditions. This superiority mainly 36
Journal Pre-proof contributes to the favorable arrangement of surfactant/nanoparticle mixtures, as well as their high desorption energies. In addition to experimental investigations, the paper has also reviewed recent progress in interfacial phenomena based on molecular dynamic simulations, which provide new insights into interfacial properties and micelle formation under the influence of these popular foam stabilizers. References
Jo u
rn
al
Pr
e-
pr
oo f
[1] Denney D. Evaluating Implications of Hydraulic Fracturing in Shale-Gas Reservoirs. SPE-1108-G. 2009;61:53-4. [2] Ribeiro L, Sharma M. Fluid Selection for Energized Fracture Treatments. SPE Hydraulic Fracturing Technology Conference. The Woodlands, Texas, USA: Society of Petroleum Engineers; 2013. p. 11. [3] Wanniarachchi WAM, Ranjith PG, Perera MSA. Shale gas fracturing using foam-based fracturing fluid: a review. Environmental Earth Sciences. 2017;76:91. [4] Wanniarachchi WAM, Ranjith PG, Perera MSA, Lashin A, Al Arifi N, Li JC. Current opinions on foam-based hydro- fracturing in deep geological reservoirs. Geomechanics and Geophysics for Geo-Energy and Geo-Resources. 2015;1:121-34. [5] Wang J, Wang S, Lin W, Kang Z, You Q. Formula optimization and rheology study of clean fracturing fluid. Journal of Molecular Liquids. 2017;241:563-9. [6] Li C, Huang Y, Sun X, Gao R, Zeng F, Tontiwachwuthikul P, et al. Rheological properties study of foam fracturing fluid using CO 2 and surfactant. Chemical Engineering Science. 2017;170:720-30. [7] Wang G, Wang KL, Lu CJ. Advances of Researches on Improving the Stability of Foams by Nanoparticles. IOP Conference Series: Materials Science and Engineering. Vol. 242: IOP Publishing; 2017. p. 012020. [8] Nazari N, Tsau J-S, Barati R. CO 2 Foam Stability Improvement Using Polyelectrolyte Complex Nanoparticles Prepared in Produced Water. Energies. 2017;10:516. [9] Langevin D. Bubble coalescence in pure liquids and in surfactant solutio ns. Current Opinion in Colloid and Interface Science. 2015;20:92-7. [10] Angarska J, Stubenrauch C, Manev E. Drainage of foam films stabilized with mixtures of non- ionic surfactants. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2007;309:189-97. [11] Xue Z, Worthen A, Qajar A, Robert I, Bryant SL, Huh C, et al. Viscosity and stability of ultra- high internal phase CO 2-in-water foams stabilized with surfactants and nanoparticles with or without polyelectrolytes. J Colloid Interface Sci. 2016;461:383-95. [12] Xu K, Zhu P, Colon T, Huh C, Balhoff M. A Microfluidic Investigation of the Synergistic Effect of Nanoparticles and Surfactants in Macro-Emulsion-Based Enhanced Oil Recovery. SPE Journal. 2017;22:459-69. [13] Zhu T, Ogbe DO, Khataniar S. Improving the Foam Performance for Mobility Control and Improved Sweep Efficiency in Gas Flooding. Industrial & Engineering Chemistry Research. 2004;43:4413-21. [14] Worthen AJ, Bagaria HG, Chen Y, Bryant SL, Huh C, Johnston KP. Nanoparticlestabilized carbon dioxide-in-water foams with fine texture. J Colloid Interface Sci. 2013;391:142-51. [15] Yekeen N, Idris AK, Manan MA, Samin AM, Risal AR, Kun TX. Bulk and bubble-scale experimental studies of influence of nanoparticles on foam stability. Chinese Journal of Chemical Engineering. 2017;25:347-57. 37
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[16] Emrani AS, Nasr-El-Din HA. An experimental study of nanoparticle-polymer-stabilized CO 2 foam. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;524:17-27. [17] Cervantes Martinez A, Rio E, Delon G, Saint-Jalmes A, Langevin D, Binks BP. On the origin of the remarkable stability of aqueous foams stabilised by nanoparticles: link with microscopic surface properties. Soft Matter. 2008;4:1531. [18] Hunter TN, Pugh RJ, Franks GV, Jameson GJ. The role of particles in stabilising foams and emulsions. Advances in Colloid and Interface Science. 2008;137:57-81. [19] Zhang T, Espinosa D, Yoon Ky, Rahmani A, yu H, Manuel Caldelas F, et al. Engineered Nanoparticles as Harsh-Condition Emulsion and Foam Stabilizers and as Novel Sensors. Offshore Technology Conference. Houston, Texas, USA2011. p. 15. [20] Karakashev SI, Ozdemir O, Hampton MA, Nguyen AV. Formation and stability of foams stabilized by fine particles with similar size, contact angle and different shapes. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2011;382:132-8. [21] Worthen AJ, Bryant SL, Huh C, Johnston KP. Carbon dioxide-in-water foams stabilized with nanoparticles and surfactant acting in synergy. AIChE Journal. 2013;59:3490-501. [22] Nourafkan E, Asachi M, Hu Z, Gao H, Wen D. Synthesis of stable nanoparticles at harsh environment using the synergistic effect of surfactants blend. Journal of Industrial and Engineering Chemistry. 2018;64:390-401. [23] Singh R, Mohanty KK. Synergy between Nanoparticles and Surfactants in Stabilizing Foams for Oil Recovery. Energy & Fuels. 2015;29:467-79. [24] Kumar S, Mandal A. Investigation on stabilization of CO 2 foam by ionic and nonionic surfactants in presence of different additives for application in enhanced oil recovery. Applied Surface Science. 2017;420:9-20. [25] Wang J, Nguyen AV, Farrokhpay S. A critical review of the growth, drainage and collapse of foams. Advances in Colloid and Interface Science. 2016;228:55-70. [26] Yekeen N, Manan MA, Idris AK, Padmanabhan E, Junin R, Samin AM, et al. A comprehensive review of experimental studies of nanoparticles-stabilized foam for enhanced oil recovery. Journal of Petroleum Science and Engineering. 2018;164:43-74. [27] Schramm LL. Emulsions, foams, and suspensions: fundamentals and applications: John Wiley & Sons; 2006. [28] Isabelle C, Sylvie CA, Florence E, François G, Reinhard H, Olivier P, et al. Foams : structure and dynamics2013. [29] Pitois O, Fritz C, Vignes-Adler M. Liquid drainage through aqueous foam: study of the flow on the bubble scale. J Colloid Interface Sci. 2005;282:458-65. [30] Koehler SA, Hilgenfeldt S, Stone HA. A Generalized View of Foam Drainage: Experiment and Theory. Langmuir. 2000;16:6327-41. [31] Neethling SJ, Lee HT, Grassia P. The growth, drainage and breakdown of foams. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2005;263:184-96. [32] Kruglyakov PM, Karakashev SI, Nguyen AV, Vilkova NG. Foam drainage. Current Opinion in Colloid and Interface Science. 2008;13:163-70. [33] Babcsán N, Banhart J. Metal Foams: Towards High- Temperature Colloid Chemistry. In: Binks BP, Horozov TS, (editors). Colloidal Particles at Liquid Interfaces. Cambridge: Cambridge University Press; 2006. p. 445-500. [34] Lioumbas JS, Georgiou E, Kostoglou M, Karapantsios TD. Foam free drainage and bubbles size for surfactant concentrations below the CMC. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;487:92-103. [35] Pugh RJ. Bubble and Foam Chemistry. Cambridge: Cambridge University Press; 2016. [36] Sun Q, Tan L, Wang G. Liquid foam drainage: An overview. International Journal of Modern Physics B. 2008;22:2333-54. 38
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[37] Carrier V, Destouesse S, Colin A. Foam drainage: A film contribution? Physical Review E. 2002;65:061404. [38] Koehler SA, Hilgenfeldt S, Stone HA. Foam drainage on the microscale I. Modeling flow through single Plateau borders. J Colloid Interface Sci. 2004;276:420-38. [39] Koehler SA, Hilgenfeldt S, Weeks ER, Stone HA. Foam drainage on the microscale II. Imaging flow through single Plateau borders. J Colloid Interface Sci. 2004;276:439-49. [40] Nguyen AV. Liquid drainage in single plateau borders of foam. J Colloid Interface Sci. 2002;249:194-9. [41] Anazadehsayed A, Rezaee N, Naser J, Nguyen AV. A review of aqueous foam in microscale. Advances in Colloid and Interface Science. 2018;256:203-29. [42] Leonard RA, Lemlich R. A study of interstitial liquid flow in foam. Part I. Theoretical model and application to foam fractionation. AIChE Journal. 1965;11:18-25. [43] Koehler SA, Hilgenfeldt S, Stone HA. Liquid Flow through Aqueous Foams: The NodeDominated Foam Drainage Equation. Physical Review Letters. 1999;82:4232-5. [44] Cox SJ, Weaire D, Hutzler S, Murphy J, Phelan R, Verbist G. Applications and generalizations of the foam drainage equation. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 2000;456:2441-64. [45] Helal MA, Mehanna MS. The tanh method and Adomian decomposition method for solving the foam drainage equation. Applied Mathematics and Computation. 2007;190:599609. [46] Mirmoradi SH, Hosseinpour I, Barari A, Ghotbi AR. Analysis of foam drainage problem using variational iteration method. Advanced Studies in Theoretical Physics. 2009;3:283-92. [47] Khani F, Hamedi-Nezhad S, Darvishi MT, Ryu S-W. New solitary wave and periodic solutions of the foam drainage equation using the Exp- function method. Nonlinear Analysis: Real World Applications. 2009;10:1904-11. [48] Darvishi MT, Khani F. A series solution of the foam drainage equation. Computers & Mathematics with Applications. 2009;58:360-8. [49] Khan M, Gondal M. A new analytical solution of foam drainage equation by Laplace decomposition method. Journal of Advanced Research in Differential Equations. 2010;2:5364. [50] He J-H. Variational approach to foam drainage equation. Meccanica. 2011;46:1265-6. [51] Hosseini Fadravi H, Saberi Nik H, Buzhabadi R. Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives. International Journal of Differential Equations. 2011:Article ID 237045. [52] Khan Y, Wu Q. Homotopy perturbation transform method for nonlinear equations using He’s polynomials. Computers & Mathematics with Applications. 2011;61:1963-7. [53] Fereidoon A, Yaghoobi H, Davoudabadi M. Application of the Homotopy Perturbation Method for Solving the Foam Drainage Equation. International Journal of Differential Equations. 2011:Article ID: 864023. [54] Iyiola O, Mukiawa SE, Enyi C. Generalised homotopy analysis method (q-HAM) for solving foam drainage equation of time fractional type. Mathematics in Engineering, Science and Aerospace MESA. 2013;4:429-40. [55] Nikkar A. Assesment of New Analytical Method for Solving the Foam Drainage Equation. Chinese Journal of Mathematics. 2014:Article ID: 656039. [56] Alam MN. Exact solutions to the foam drainage equation by using the new generalized (G′/G)-expansion method. Results in Physics. 2015;5:168-77. [57] Gubes M, Keskin Y, Oturanc G. Numerical solution of time-dependent foam drainage equation (FDE). Computational Methods for Differential Equations. 2015;3:111-22. [58] Arbabi S, Nazari A, Darvishi MT. A semi-analytical solution of foam drainage equation by Haar wavelets method. Optik. 2016;127:5443-7. 39
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[59] Brito-Parada PR, Neethling SJ, Cilliers JJ. Modelling the behaviour of the wetting front in non-standard forced foam drainage scenarios. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2013;438:21-7. [60] Narsimhan G. Drainage of particle stabilized foam film. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;495:20-9. [61] Anazadehsayed A, Naser J. A combined CFD simulation of Plateau borders including films and transitional areas of liquid foams. Chemical Engineering Science. 2017;166:11-8. [62] Anazadehsayed A, Rezaee N, Naser J. Numerical modelling of flow through foam's node. J Colloid Interface Sci. 2017;504:485-91. [63] Anazadehsayed A, Rezaee N, Naser J. Exterior foam drainage and flow regime switch in the foams. J Colloid Interface Sci. 2018;511:440-6. [64] Shafiei Y, Ghazanfari MH, Seyyedsar SM. A study of liquid drainage rate from foam with population balance equation: impact of bubble evolution. Colloid and Polymer Science. 2018;296:1097-108. [65] Pitois O, Fritz C, Vignes-Adler M. Hydrodynamic resistance of a single foam channel. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2005;261:109-14. [66] Sett S, Sinha-Ray S, Yarin AL. Gravitational Drainage of Foam Films. Langmuir. 2013;29:4934-47. [67] Neethling S, Lee H, Cilliers J. A foam drainage equation generalized for all liquid contents. Journal of Physics: Condensed Matter. 2001;14:331. [68] Saint-Jalmes A, Vera MU, Durian DJ. Free drainage of aqueous foams: Container shape effects on capillarity and vertical gradients. Europhysics Letters (EPL). 2000;50:695-701. [69] Cox S, Weaire D. Comment on "Free drainage of aqueous foams: Container shape effects on capillarity and vertical gradients" by A. Saint-Jalmes et al. Europhysics Letters (EPL). 2001;55:445. [70] Papara M, Zabulis X, D. Karapantsios T. Container effects on the free drainage of wet foams. 2009;64:1404-15. [71] Saye RI, Sethian JA. Multiscale modelling of evolving foams. J Comput Phys. 2016;315:273-301. [72] Verbist G, Weaire D, Kraynik AM. The foam drainage equation. Journal of Physics: Condensed Matter. 1996;8:3715-31. [73] Jun S, Pelot DD, Yarin AL. Foam consolidation and drainage. Langmuir. 2012;28:532330. [74] Bureiko A, Trybala A, Huang J, Kovalchuk N, Starov V. Bulk and surface rheology of Aculyn™ 22 and Aculyn™ 33 polymeric solutions and kinetics of foam drainage. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2013;434:268-75. [75] Arjmandi- Tash O, Trybala A, Mahdi FM, Kovalchuk NM, Starov V. Foams built up by non-Newtonian polymeric solutions: Free drainage. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;521:112-20. [76] Haffner B, Khidas Y, Pitois O. The drainage of foamy granular suspensions. Journal of Colloid and Interface Science. 2015;458:200-8. [77] Wang J, Nguyen AV. Foam drainage in the presence of solid particles. Soft Matter. 2016;12:3004-12. [78] Magrabi SA, Dlugogorski BZ, Jameson GJ. Bubble size distribution and coarsening of aqueous foams. Chemical Engineering Science. 1999;54:4007-22. [79] Ganan-Calvo A, Fernandez J, Marquez Oliver A, Marquez M. Coarsening of monodisperse wet microfoams. Applied Physics Letters. 2004;84:4989-91. [80] Feitosa K, Durian D. Gas and liquid transport in steady-state aqueous foam. The European Physical Journal E. 2008;26:309-16.
40
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[81] Wang J, Cao Y, Li G, Li S, Wang Y, Ma Z, et al. Investigation on the Properties of Aqueous Foams Stabilized by Cetyltrimethylammonium Bromide in Terms of Free Drainage and Bubble Size. Journal of Surfactants and Detergents. 2019;22:855-63. [82] von Neumann J. Shape of Metal Grains. Metal Interfaces. 1952:108. [83] Mullins WW. Estimation of the geometrical rate constant in idealized three dimensional grain growth. Acta Metallurgica. 1989;37:2979-84. [84] MacPherson RD, Srolovitz DJ. The von Neumann relation generalized to coarsening of three-dimensional microstructures. Nature. 2007;446:1053-5. [85] Yadav V, Moelans N. Analysis of grain topology and volumetric growth rate relation in three-dimensional normal grain growth. Acta Materialia. 2018;156:275-86. [86] Schimming CD, Durian DJ. Border-crossing model for the diffusive coarsening of twodimensional and quasi-two-dimensional wet foams. Physical Review E. 2017;96:032805. [87] Roth AE, Jones CD, Durian DJ. Bubble statistics and coarsening dynamics for quasitwo-dimensional foams with increasing liquid content. Physical Review E. 2013;87:042304. [88] Lambert J, Mokso R, Cantat I, Cloetens P, Glazier JA, Graner F, et al. Coarsening Foams Robustly Reach a Self-Similar Growth Regime. Physical Review Letters. 2010;104:248304. [89] Thomas GL, Belmonte JM, Graner F, Glazier JA, de Almeida RMC. 3D simulations of wet foam coarsening evidence a self similar growth regime. Colloids and Surfaces A, Physicochemical and Engineering Aspects. 2015;473:109-14. [90] Khakalo K, Baumgarten K, Tighe BP, Puisto A. Coarsening and mechanics in the bubble model for wet foams. Physical Review E. 2018;98:012607. [91] Saint-Jalmes A. Physical chemistry in foam drainage and coarsening. Soft Matter. 2006;2:836-49. [92] Isert N, Maret G, Aegerter CM. Coarsening dynamics of three-dimensional levitated foams: From wet to dry. The European Physical Journal E. 2013;36:116-22. [93] Langevin D, Vignes-Adler M. Microgravity studies of aqueous wet foams. The European Physical Journal E. 2014;37:16. [94] Vandewalle N, Caps H, Delon G, Saint-Jalmes A, Rio E, Saulnier L, et al. Foam stability in microgravity. Journal of Physics: Conference Series. 2011;327:012024. [95] Tcholakova S, Mitrinova Z, Golemanov K, Denkov ND, Vethamuthu M, Ananthapadmanabhan KP. Control of Ostwald Ripening by Using Surfactants with High Surface Modulus. Langmuir. 2011;27:14807-19. [96] Lv Q, Li Z, Li B, Husein M, Shi D, Zhang C, et al. Wall slipping behavior of foam with nanoparticle-armored bubbles and its flow resistance factor in cracks. Scientific Reports. 2017;7:5063. [97] Klitzing Rv, Müller H-J. Film stability control. Current Opinion in Colloid & Interface Science. 2002;7:42-9. [98] Tarazona P, Martínez H, Chacón E, Bresme F. Newton black films as wetting systems. Physical Review B. 2012;85:085402. [99] Forel E, Dollet B, Langevin D, Rio E. Coalescence in Two-Dimensional Foams: A Purely Statistical Process Dependent on Film Area. Physical Review Letters. 2019;122:088002. [100] Derjaguin BV. Theory of stability of colloids and thin films: Consultants Bureau New York; 1989. [101] Verwey EJW. Theory of the stability of lyophobic colloids. The Journal of Physical Chemistry. 1947;51:631-6. [102] Derjaguin BV, Landau LD. Acta Physicochim. URSS. 1941;14:633. [103] Bergeron V, Radke CJ. Equilibrium measurements of oscillatory disjoining pressures in aqueous foam films. Langmuir. 1992;8:3020-6. 41
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[104] Bindal SK, Sethumadhavan G, Nikolov AD, Wasan DT. Foaming mechanisms in surfactant free particle suspensions. AIChE Journal. 2002;48:2307-14. [105] Gochev G. Thin liquid films stabilized by polymers and polymer/surfactant mixtures. Current Opinion in Colloid and Interface Science. 2015;20:115-23. [106] Ghosh P. Coalescence of bubbles in liquid. Bubble Science, Engineering & Technology. 2009;1:75-87. [107] Bikerman JJ. Foams. New York: Springer-Verlag; 1973. [108] Kawale D. Influence of dynamic surface tension on foams: Application in gas well deliquification [Master thesis]: Delft University of Technology; 2012. [109] Negin C, Ali S, Xie Q. Most common surfactants employed in chemical enhanced oil recovery. Petroleum. 2017;3:197-211. [110] Wikipedia contributors. Critical micelle concentration. Wikipedia, The Free Encyclopedia. [111] Levitt D, Jackson A, Heinson C, Britton LN, Malik T, Dwarakanath V, et al. Identification and Evaluation of High-Performance EOR Surfactants. SPE-152907-PA. 2009;12:243-53. [112] Xue Z, Panthi K, Fei Y, Johnston KP, Mohanty KK. CO 2-Soluble Ionic Surfactants and CO 2 Foams for High-Temperature and High-Salinity Sandstone Reservoirs. Energy & Fuels. 2015;29:5750-60. [113] Chen Y, Elhag AS, Poon BM, Cui L, Ma K, Liao SY, et al. Switchable Nonionic to Cationic Ethoxylated Amine Surfactants for CO 2 Enhanced Oil Recovery in HighTemperature, High-Salinity Carbonate Reservoirs. SPE Journal. 2014;19:249-59. [114] Rosen MJ, Kunjappu JT. Characteristic Features of Surfactants. Surfactants and Interfacial Phenomena2012. p. 1-38. [115] Da C, Elhag A, Jian G, Zhang L, Alzobaidi S, Zhang X, et al. CO2/Water Foams Stabilized with Cationic or Zwitterionic Surfactants at Temperatures up to 120 °C in High Salinity Brine. SPE Annual Technical Conference and Exhibition. Dallas, Texas, USA: Society of Petroleum Engineers; 2018. p. 14. [116] Hunter TN, Wanless EJ, Jameson GJ, Pugh RJ. Non- ionic surfactant interactions with hydrophobic nanoparticles: Impact on foam stability. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2009;347:81-9. [117] Jones SA, Laskaris G, Vincent-Bonnieu S, Farajzadeh R, Rossen WR. Effect of surfactant concentration on foam: From coreflood experiments to implicit-texture foammodel parameters. Journal of Industrial and Engineering Chemistry. 2016;37:268-76. [118] Yekeen N, Manan MA, Idris AK, Samin AM. Influence of surfactant and electrolyte concentrations on surfactant Adsorption and foaming characteristics. Journal of Petroleum Science and Engineering. 2017;149:612-22. [119] Golemanov K, Denkov ND, Tcholakova S, Vethamuthu M, Lips A. Surfactant Mixtures for Control of Bubble Surface Mobility in Foam Studies. Langmuir. 2008;24:995661. [120] Lee J, Nikolov A, Wasan D. Foam stability: The importance of film size and the micellar structuring phenomenon. The Canadian Journal of Chemical Engineering. 2014;92:2039-45. [121] Varade D, Carriere D, Arriaga LR, Fameau AL, Rio E, Langevin D, et al. On the origin of the stability of foams made from catanionic surfactant mixtures. Soft Matter. 2011;7:655770. [122] Bournival G, Du Z, Ata S, Jameson GJ. Foaming and gas dispersion properties of nonionic surfactants in the presence of an inorganic electrolyte. Chemical Engineering Science. 2014;116:536-46.
42
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[123] Stasiuk ENB, Schramm LL. The Temperature Dependence of the Critical Micelle Concentrations of Foam-Forming Surfactants. Journal of Colloid and Interface Science. 1996;178:324-33. [124] Hara K, Kuwabara H, Kajimoto O, Bhattacharyya K. Effect of pressure on the critical micelle concentration of neutral surfactant using fluorescence probe method. Journal of Photochemistry and Photobiology A: Chemistry. 1999;124:159-62. [125] Lesemann M, Thirumoorthy K, Kim YJ, Jonas J, Paulaitis ME. Pressure Dependence of the Critical Micelle Concentration of a Nonionic Surfactant in Water Studied by 1H-NMR. Langmuir. 1998;14:5339-41. [126] Xue Z, Foster E, Wang Y, Nayak S, Cheng V, Ngo VW, et al. Effect of Grafted Copolymer Composition on Iron Oxide Nanoparticle Stability and Transport in Porous Media at High Salinity. Energy & Fuels. 2014;28:3655-65. [127] Kumar A, Mandal A. Characterization of rock-fluid and fluid-fluid interactions in presence of a family of synthesized zwitterionic surfactants for application in enhanced oil recovery. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2018;549:112. [128] Zhao L, Li A, Chen K, Tang J, Fu S. Development and evaluation of foaming agents for high salinity tolerance. Journal of Petroleum Science and Engineering. 2012;81:18-23. [129] Hussain SMS, Fogang LT, Kamal MS. Synthesis and performance evaluation of betaine type zwitterionic surfactants containing different degrees of ethoxylation. Journal of Molecular Structure. 2018;1173:983-9. [130] Shakil Hussain SM, Kamal MS, Fogang LT. Effect of internal olefin on the properties of betaine-type zwitterionic surfactants for enhanced oil recovery. Journal of Molecular Liquids. 2018;266:43-50. [131] Da C, Alzobaidi S, Jian G, Zhang L, Biswal SL, Hirasaki GJ, et al. Carbon dioxide/water foams stabilized with a zwitterionic surfactant at temperatures up to 150 °C in high salinity brine. Journal of Petroleum Science and Engineering. 2018;166:880-90. [132] AlYousif Z, Kokal S, Alabdulwahab A, Gizzatov A. CO 2-Foam Rheology: Effect of Surfactant Concentration, Shear Rate and Injection Quality. SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition. Dammam, Saudi Arabia: Society of Petroleum Engineers; 2018. p. 12. [133] Alzobaidi S, Da C, Tran V, Prodanović M, Johnston KP. High temperature ultralow water content carbon dioxide- in-water foam stabilized with viscoelastic zwitterionic surfactants. Journal of Colloid and Interface Science. 2017;488:79-91. [134] Sun L, Wei P, Pu W, Wang B, Wu Y, Tan T. The oil recovery enhancement by nitrogen foam in high- temperature and high-salinity environments. Journal of Petroleum Science and Engineering. 2016;147:485-94. [135] Alzobaidi S, Lotfollahi M, Lu C, Bloom M, Zhang X, Prodanovic M, et al. Identification and Evaluation of Viscoelastic Surfactants Including Smart Viscoelastic Systems for Generation and Stabilization of Ultra-Dry N 2 and CO 2 Foam for Fracturing Fluids and Proppant Transport. Proceedings of the 6th Unconventional Resources Technology Conference2018. p. 16. [136] Deng Q, Li H, Li C, Lv W, Li Y. Enhancement of foamability and foam stability induced by interactions between a hyperbranched exopolysaccharide and a zwitterionic surfactant dodecyl sulfobetaine. RSC Advances. 2015;5:61868-75. [137] Varade SR, Ghosh P. Foaming in aqueous solutions of zwitterionic surfactant: Effects of oil and salts. Journal of Dispersion Science and Technology. 2017;38:1770-84. [138] Santvoort Jv, Golombok M. Viscoelastic surfactants for diversion control in oil recovery. Journal of Petroleum Science and Engineering. 2015;135:671-7.
43
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[139] Xue Z, Worthen AJ, Da C, Qajar A, Ketchum IR, Alzobaidi S, et al. Ultradry Carbon Dioxide-in-Water Foams with Viscoelastic Aqueous Phases. Langmuir. 2016;32:28-37. [140] Elhag AS, Da C, Chen Y, Mukherjee N, Noguera JA, Alzobaidi S, et al. Viscoelastic diamine surfactant for stable carbon dioxide/water foams over a wide range in salinity and temperature. J Colloid Interface Sci. 2018;522:151-62. [141] Kuliszewska E, Brecker L. Gemini Surfactants Foam Formation Ability and Foam Stability Depends on Spacer Length. Journal of Surfactants and Detergents. 2014;17:951-7. [142] Kamal MS. A Review of Gemini Surfactants: Potential Application in Enhanced Oil Recovery. Journal of Surfactants and Detergents. 2016;19:223-36. [143] Marinova KG, Naydenova KT, Basheva ES, Bauer F, Tropsch J, Franke J. New surfactant mixtures for fine foams with slowed drainage. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;523:54-61. [144] Ivanova DS, Angarska JK, Manev ED, Tachev KD. Critical thickness of foam films stabilized by nonionic or ionic surfactants and their mixtures. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;519:34-45. [145] Angarska JK, Ivanova DS, Manev ED. Drainage of foam films stabilized by nonionic, ionic surfactants and their mixtures. Colloids and Surface s A: Physicochemical and Engineering Aspects. 2015;481:87-99. [146] Jiang N, Sheng Y, Li C, Lu S. Surface activity, foam properties and aggregation behavior of mixtures of short-chain fluorocarbon and hydrocarbon surfactants. Journal of Molecular Liquids. 2018;268:249-55. [147] Wang C, Fang H, Gong Q, Xu Z, Liu Z, Zhang L, et al. Roles of Catanionic Surfactant Mixtures on the Stability of Foams in the Presence of Oil. Energy & Fuels. 2016;30:6355-64. [148] Kanokkarn P, Shiina T, Santikunaporn M, Chavadej S. Equilibrium and dynamic surface tension in relation to diffusivity and foaming properties: Effects of surfactant type and structure. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;524:135-42. [149] Cui X, Jiang Y, Yang C, Lu X, Chen H, Mao S, et al. Mechanism of the Mixed Surfactant Micelle Formation. The Journal of Physical Chemistry B. 2010;114:7808-16. [150] Ananth R, Snow AW, Hinnant KM, Giles SL, Farley JP. Synergisms between Siloxane-polyoxyethylene and Alkyl Polyglycoside Surfactants in Foam Stability and Pool Fire Extinction. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2019;579:123686. [151] Zhang P, Bai G, Cui G, Zhang L, Peng X, Pei S, et al. Enhanced CO 2 foam based on amide and amine surfactants and synergistically coupled with sodium dodecyl sulfate at high temperature and high pressure. Journal of Petroleum Science and Engineering. 2019;179:26675. [152] Negm NA, Sabagh AME. Interaction between cationic and conventional nonionic surfactants in the mixed micelle and monolayer formed in aqueous medium. Química Nova. 2011;34:1007-13. [153] Danov KD, Kralchevska SD, Kralchevsky PA, Ananthapadmanabhan KP, Lips A. Mixed Solutions of Anionic and Zwitterionic Surfactant (Betaine): Surface-Tension Isotherms, Adsorption, and Relaxation Kinetics. Langmuir. 2004;20:5445-53. [154] Bera A, Ojha K, Mandal A. Synergistic Effect of Mixed Surfactant Systems on Foam Behavior and Surface Tension. Journal of Surfactants and Detergents. 2013;16:621-30. [155] Poša M. Mixed micelles of binary surfactant mixtures Tween 40 – Na-3,12-dioxo-5βcholanate and Tween 80 – Na-3,12-dioxo-5β-cholanate and their thermodynamic description and characterization. Chemical Engineering Research and Design. 2014;92:2826-39. [156] Trawiſska A, Hallmann E, MĿdrzycka K. The effect of alkyl chain length on synergistic effects in micellization and surface tension reduction in nonionic gemini (S-10) 44
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
and anionic surfactants mixtures. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;506:114-26. [157] Trawińska A, Hallmann E, Mędrzycka K. Synergistic effects in micellization and surface tension reduction in nonionic gemini S-10 and cationic RTAB surfactants mixtures. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;488:162-72. [158] Wang C, Cao X-L, Guo L-L, Xu Z-C, Zhang L, Gong Q-T, et al. Effect of adsorption of catanionic surfactant mixtures on wettability of quartz surface. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;509:564-73. [159] Wang C, Cao X- L, Guo L-L, Xu Z-C, Zhang L, Gong Q-T, et al. Effect of molecular structure of catanionic surfactant mixtures on their interfacial properties. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;509:601-12. [160] Wang Y, Zhang Y, Liu Y, Zhang L, Ren S, Lu J, et al. The stability study of CO 2 foams at high pressure and high temperature. Journal of Petroleum Science and Engineering. 2017;154:234-43. [161] Wang P, Tan J, Pei S, Wang J, Zhang Y, Sun X, et al. Dual effects of cationic surfactant on the wormlike micelle formation of catanionic surfactants mixtures: An experiment and simulation study. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2017;529:95-101. [162] Li Y, Lai L, Mei P, Zhang W-X, Li Y-H, Cheng L, et al. Surface properties and solubility enhancement of Gemini/conventional surfactant mixtures based on sulfonate Gemini surfactant. Journal of Molecular Liquids. 2019;276:488-96. [163] Almobarky M, AlYousef Z, Schechter D. Enhancing the Foam Stab ility Using Surfactants Mixtures. SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition. Dammam, Saudi Arabia: Society of Petroleum Engineers; 2018. p. 13. [164] Wang C, Zhao L, Xu B-c, Cao X-l, Guo L- l, Zhang L, et al. Effect of dynamic interfacial dilational properties on the foam stability of catanionic surfactant mixtures in the presence of oil. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2018;541:78-86. [165] Li S-J, Lai L, Mei P, Li Y, Cheng L, Ren Z-H, et al. Equilibrium and dynamic surface properties of cationic/anionic surfactant mixtures based on bisquaternary ammonium salt. Journal of Molecular Liquids. 2018;254:248-54. [166] Li J, Li Y, Song Y, Wang Z, Zhang Q. Properties of quaternary ammonium surfactant with hydroxyethyl group and anionic surfactant mixed systems. Journal of Molecular Liquids. 2018;271:373-9. [167] Agneta M, Zhaomin L, Chao Z, Gerald G. Investigating synergism and antagonism of binary mixed surfactants for foam efficiency optimization in high salinity. Journal of Petroleum Science and Engineering. 2019;175:489-94. [168] Fauser H, Uhlig M, Miller R, Klitzing Rv. Surface Adsorption of Oppositely Charged SDS:C12TAB Mixtures and the Relation to Foam Film Formation and Stability. The Journal of Physical Chemistry B. 2015;119:12877-86. [169] Stocco A, Carriere D, Cottat M, Langevin D. Interfacial Behavior of Catanionic Surfactants. Langmuir. 2010;26:10663-9. [170] Hosseini H, Tsau JS, Shafer-Peltier K, Marshall C, Ye Q, Barati Ghahfarokhi R. Experimental and Mechanistic Study of Stabilized Dry CO 2 Foam Using Polyelectrolyte Complex Nanoparticles Compatible with Produced Water To Improve Hydraulic Fracturing Performance. Industrial & Engineering Chemistry Research. 2019;58:9431-49. [171] Su X, Cunningham MF, Jessop PG. Switchable viscosity triggered by CO 2 using smart worm-like micelles. Chemical Communications. 2013;49:2655-7. [172] Liu D, Suo Y, Tan J, Lu H. CO 2 -Switchable microemulsion based on a pseudogemini surfactant. Soft Matter. 2017;13:3783-8. 45
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[173] Wang J, Huang Z, Zheng C, Lu H. CO 2 /N2-switchable viscoelastic fluids based on a pseudogemini surfactant system. Journal of Dispersion Science and Technology. 2017;38:1705-10. [174] Shah V, Bharatiya B, Shukla AD, Mukherjee T, Shah DO. Adsorption of nonionic Brij and Tween surfactants at PTFE-water and air-water interfaces: Investigations on wetting, dispersion stability, foaming and drug solubilization. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;508:159-66. [175] Kristen N, Simulescu V, Vüllings A, Laschewsky A, Miller R, von Klitzing R. No Charge Reversal at Foam Film Surfaces after Addition of Oppositely Charged Polyelectrolytes? The Journal of Physical Chemistry B. 2009;113:7986-90. [176] Kristen-Hochrein N, Laschewsky A, Miller R, von Klitzing R. Stability of Foam Films of Oppositely Charged Polyelectrolyte/Surfactant Mixtures: Effect of Isoelectric Point. The Journal of Physical Chemistry B. 2011;115:14475-83. [177] Fauser H, von Klitzing R, Campbell RA. Surface adsorption of oppositely charged C14TAB-PAMPS mixtures at the air/water interface and the impact on foam film stability. J Phys Chem B. 2015;119:348-58. [178] Khristov K, Petkova H, Alexandrova L, Nedyalkov M, Platikanov D, Exerowa D, et al. Foam, emulsion and wetting films stabilized by polyoxyalkylated diethylenetriamine (DETA) polymeric surfactants. Advances in Colloid and Interface Science. 2011;168:105-13. [179] Xu C, Wang D, Wang H, Hu J, Zhu X, Zhang Y. Effect of partially hydrolyzed polyacrylamide on the solution and foam properties of sodium alcohol ether sulfate. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2018;556:51-60. [180] Kristen N, Vüllings A, Laschewsky A, Miller R, von Klitzing R. Foam Films from Oppositely Charged Polyelectolyte/Surfactant Mixtures: Effect of Polyelectrolyte and Surfactant Hydrophobicity on Film Stability. Langmuir. 2010;26:9321-7. [181] Goswami A, Hassan PA, Bhagwat SS. Static and dynamic surface tension behaviour of a triblock copolymer and a non ionic surfactant mixture. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;484:190-6. [182] Petkova R, Tcholakova S, Denkov ND. Foaming and foam stability for mixed polymersurfactant solutions: Effects of surfactant type and polymer charge. Langmuir. 2012;28:49965009. [183] Petkova R, Tcholakova S, Denkov ND. Role of polymer–surfactant interactions in foams: Effects of pH and surfactant head group for cationic polyvinylamine and anionic surfactants. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2013;438:174-85. [184] Bureiko A, Trybala A, Kovalchuk N, Starov V. Current applications of foams formed from mixed surfactant-polymer solutions. Adv Colloid Interface Sci. 2015;222:670-7. [185] Uhlig M, Miller R, Klitzing Rv. Surface adsorption of sulfonated poly(phenylene sulfone)/C14TAB mixtures and its correlation with foam film stability. Physical Chemistry Chemical Physics. 2016;18:18414-23. [186] Pu W, Wei P, Sun L, Wang S. Stability, CO2 sensitivity, oil tolerance and disp lacement efficiency of polymer enhanced foam. RSC Advances. 2017;7:6251-8. [187] Schulze- Zachau F, Braunschweig B. CnTAB/polystyrene sulfonate mixtures at air– water interfaces: effects of alkyl chain length on surface activity and charging state. Physical Chemistry Chemical Physics. 2019;21:7847-56. [188] Zhao G, Dai C, Zhang Y, Chen A, Yan Z, Zhao M. Enhanced foam stability by adding comb polymer gel for in-depth profile control in high temperature reservoirs. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;482:115-24. [189] Dupas A, Henaut I, Rousseau D, Poulain P, Tabary R, Argillier J-F, et al. Impact of polymer mechanical degradation on shear and extensional viscosities: toward better 46
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
injectivity forecasts in polymer flooding operations. SPE International Symposium on Oilfield Chemistry: Society of Petroleum Engineers; 2013. p. 11. [190] Verma A, Chauhan G, Ojha K. Synergistic effects of polymer and bentonite clay on rheology and thermal stability of foam fluid developed for hydra ulic fracturing. Asia-Pacific Journal of Chemical Engineering. 2017;12:872-83. [191] Yin X, Kang W, Song S, Huang Z, Hou X, Yang H. Stabilization mechanism of CO2 foam reinforced by regenerated cellulose. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2018;555:754-64. [192] Binks BP, Horozov TS. Aqueous foams stabilized solely by silica nanoparticles. Angew Chem Int Ed Engl. 2005;44:3722-5. [193] Blute I, Pugh RJ, van de Pas J, Callaghan I. Silica nanoparticle sols. 1. Surface chemical characterization and evaluation of the foam generation (foamability). Journal of Colloid and Interface Science. 2007;313:645-55. [194] Khalil M, Jan BM, Tong CW, Berawi MA. Advanced nanomaterials in oil and gas industry: design, application and challenges. Applied Energy. 2017;191:287-310. [195] Li S, Qiao C, Li Z, Wanambwa S. Properties of Carbon Dioxide Foam Stabilized by Hydrophilic Nanoparticles and Hexadecyltrimethylammonium Bromide. Energy & Fuels.31:1478-88. [196] Liu Q, Zhang S, Sun D, Xu J. Aqueous foams stabilized by hexylamine- modified Laponite particles. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2009;338:40-6. [197] Cui ZG, Cui YZ, Cui CF, Chen Z, Binks BP. Aqueous foams stabilized by in situ surface activation of CaCO 3 nanoparticles via adsorption of anionic surfactant. Langmuir. 2010;26:12567-74. [198] Kumar S, Aswal VK, Kohlbrecher J. Size-Dependent Interaction of Silica Nanoparticles with Different Surfactants in Aqueous Solution. Langmuir. 2012;28:9288-97. [199] Zhang R, Somasundaran P. Advances in adsorption of surfactants and their mixtures at solid/solution interfaces. Advances in Colloid and Interface Science. 2006;123-126:213-29. [200] Veyskarami M, Ghazanfari MH. Synergistic effect of like and opposite charged nanoparticle and surfactant on foam stability and mobility in the absence and presence of hydrocarbon: A comparative study. Journal of Petroleum Science and Engineering. 2018;166:433-44. [201] Singh R, Mohanty KK. Foams Stabilized by In-Situ Surface-Activated Nanoparticles in Bulk and Porous Media. SPE Journal. 2016;21:121-30. [202] Liu Q, Zhang S, Sun D, Xu J. Foams stabilized by Laponite nanoparticles and alkylammonium bromides with different alkyl chain lengths. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2010;355:151-7. [203] Wang P, You Q, Han L, Deng W, Liu Y, Fang J, et al. Experimental Study on the Stabilization Mechanisms of CO 2 Foams by Hydrophilic Silica Nanoparticles. Energy & Fuels. 2018;32:3709-15. [204] Binks BP, Kirkland M, Rodrigues JA. Origin of stabilisation of aqueous foams in nanoparticle-surfactant mixtures. Soft Matter. 2008;4:2373-82. [205] Sonn JS, Lee JY, Jo SH, Yoon I-H, Jung C-H, Lim JC. Effect of surface modification of silica nanoparticles by silane coupling agent on decontamination foam stability. Annals of Nuclear Energy. 2018;114:11-8. [206] Zhang C, Li Z, Sun Q, Wang P, Wang S, Liu W. CO 2 foam properties and the stabilizing mechanism of sodium bis(2-ethylhexyl)sulfosuccinate and hydrophobic nanoparticle mixtures. Soft Matter. 2016;12:946-56.
47
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[207] Sun Q, Li Z, Wang J, Li S, Li B, Jiang L, et al. Aqueous foam stabilized by partially hydrophobic nanoparticles in the presence of surfactant. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;471:54-64. [208] Doroudian Rad M, Telmadarreie A, Xu L, Dong M, Bryant SL. Insight on Methane Foam Stability and Texture via Adsorption of Surfactants on Oppositely Charged Nanoparticles. Langmuir. 2018;34:14274-85. [209] Whitby CP, Fornasiero D, Ralston J. Effect of oil soluble surfactant in emulsions stabilised by clay particles. Journal of Colloid and Interface Science. 2008;323:410-9. [210] Carn F, Colin A, Pitois O, Vignes-Adler M, Backov R. Foam drainage in the presence of nanoparticle-surfactant mixtures. Langmuir. 2009;25:7847-56. [211] Eftekhari AA, Krastev R, Farajzadeh R. Foam Stabilized by Fly Ash Nanoparticles for Enhancing Oil Recovery. Industrial & Engineering Chemistry Research. 2015;54:12482-91. [212] B. P. Binks, T. S. Horozov, L. Bergström, J. C. Fernández-Toledano, A. Moncho-Jordá, F. Martínez-López, et al. Colloidal Particles at Liquid Interfaces. Cambridge: Cambridge University Press; 2006. [213] Yang W, Wang T, Fan Z. Highly Stable Foam Stabilized by Alumina Nanoparticles for EOR: Effects of Sodium Cumenesulfonate and Electrolyte Concentrations. Energy & Fuels. 2017;31:9016-25. [214] Emrani AS, Nasr-El-Din HA. Stabilizing CO 2 foam by Use of nanoparticles. SPE Journal. 2017;22:494-504. [215] Singh R, Gupta A, Mohanty KK, Huh C, Lee D, Cho H. Fly Ash NanoparticleStabilized CO 2 -in-Water Foams for Gas Mobility Control Applications. SPE Annual Technical Conference and Exhibition. Houston, Texas, USA: Society of Petroleum Engineers; 2015. p. 13. [216] Lv Q, Li Z, Li B, Li S, Sun Q. Study of Nanoparticle–Surfactant-Stabilized Foam as a Fracturing Fluid. Industrial & Engineering Chemistry Research. 2015;54:9468-77. [217] Wu Y, Fang S, Zhang K, Zhao M, Jiao B, Dai C. Stability Mechanism of Nitrogen Foam in Porous Media with Silica Nanoparticles Modified by Cationic Surfactants. Langmuir. 2018;34:8015-23. [218] Horozov TS. Foams and foam films stabilised by solid particles. Current Opinion in Colloid & Interface Science. 2008;13:134-40. [219] Verma A, Chauhan G, Baruah PP, Ojha K. Morphology, Rheolo gy, and Kinetics of Nanosilica Stabilized Gelled Foam Fluid for Hydraulic Fracturing Application. Industrial & Engineering Chemistry Research. 2018;57:13449-62. [220] Wu G, Zhu Q, Yuan C, Wang H, Li C, Sun S, et al. Molecular dynamics simulation of the influence of polyacrylamide on the stability of sodium dodecyl sulfate foam. Chemical Engineering Science. 2017;166:313-9. [221] Li C, Zhang T, Ji X, Wang Z, Sun S, Hu S. Effect of Ca 2+ /Mg 2+ on the stability of the foam system stabilized by an anionic surfactant: A molecular dynamics study. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2016;489:423-32. [222] Chen M, Lu X, Liu X, Hou Q, Zhu Y, Zhou H. Temperature-Dependent Phase Transition and Desorption Free Energy of Sodium Dodecyl Sulfate at the Water/Vapor Interface: Approaches from Molecular Dynamics Simulations. Langmuir. 2014;30:10600-7. [223] Wang H, Wang Z, Lv Q, Li C, Du Z, Sun S, et al. Mechanism of Foam Film Destruction Induced by Emulsified Oil: A Coarse- Grained Simulation Study. The Journal of Physical Chemistry C. 2018;122:26438-46. [224] Boecker J, Schlenkrich M, Bopp P, Brickmann J. Molecular dynamics simulation of a n-hexadecyltrimethylammonium chloride monolayer. The Journal of Physical Chemistry. 1992;96:9915-22.
48
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[225] Gunsteren WFv, Berendsen HJC. Groningen Molecular Simulation (GROMOS) Library Manual. Biomos, Groningen, The Netherlands; 1987. p. 1-221. [226] L. Jorgensen W, Tirado-Rives J. The OPLS potential functions for proteins. Energy minimizations for crystals of cyclic peptides and crambin. 1988;110:1657-66. [227] Vanommeslaeghe K, Hatcher E, Acharya C, Kundu S, Zhong S, Shim J, et al. CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields. J Comput Chem. 2010;31:671-90. [228] Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, et al. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. Journal of the American Chemical Society. 1995;117:5179-97. [229] Marrink SJ, Risselada HJ, Yefimov S, Tieleman DP, de Vries AH. The MARTINI Force Field: Coarse Grained Model for Biomolecular Simulations. The Journal of Physical Chemistry B. 2007;111:7812-24. [230] Shinoda W, DeVane R, Klein ML. Coarse-grained molecular modeling of non- ionic surfactant self-assembly. Soft Matter. 2008;4:2454-62. [231] Ghoufi A, Malfreyt P, Tildesley DJ. Computer modelling of the surface tension of the gas-liquid and liquid- liquid interface. Chem Soc Rev. 2016;45:1387-409. [232] Ghoufi A, Malfreyt P. Calculation of the surface tension of water: 40 years of molecular simulations. Molecular Simulation. 2019;45:295-303. [233] Deguillard E, Pannacci N, Creton B, Rousseau B. Interfacial tension in oil–water– surfactant systems: On the role of intra-molecular forces on interfacial tension values using DPD simulations. The Journal of Chemical Physics. 2013;138:144102. [234] Posocco P, Perazzo A, Preziosi V, Laurini E, Pricl S, Guido S. Interfacial tension of oil/water emulsions with mixed non- ionic surfactants: comparison between experiments and molecular simulations. RSC Advances. 2016;6:4723-9. [235] Xue C, Qu G, Han Y, Li S, Gao X, Ding W. Molecular Dynamics Simulations of Sulfobetaine-Type Zwitterionic Surfactant at the Decane/Water Interface AU - Xue, Chunlong. Journal of Dispersion Science and Technology. 2016;37:1480-5. [236] Liu Z-Y, Wang C, Zhou H, Wang Y, Zhang L, Zhang L, et al. Characterizing the impact of surfactant structure on interfacial tension: a molec ular dynamics study. Journal of Molecular Modeling. 2017;23:112. [237] Shi P, Zhang H, Lin L, Song C, Chen Q, Li Z. Molecular dynamics simulation of four typical surfactants at oil/water interface. Journal of Dispersion Science and Technology. 2018;39:1258-65. [238] Yazhgur P, Vierros S, Hannoy D, Sammalkorpi M, Salonen A. Surfactant Interactions and Organization at the Gas-Water Interface (CTAB with Added Salt). Langmuir. 2018;34:1855-64. [239] Yang W, Wu R, Kong B, Zhang X, Yang X. Molecular Dynamics Simulations of Film Rupture in Water/Surfactant Systems. The Journal of Physical Chemistry B. 2009;113:83328. [240] Sun Y, Li Y, Li C, Zhang D, Cao X, Song X, et al. Molecular array behavior and synergistic effect of sodium alcohol ether sulphate and carboxyl betaine/sulfobetaine in foam film under high salt conditions. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;480:138-48. [241] Tsimpanogiannis IN, Moultos OA, Franco LFM, Spera MBdM, Erdős M, Economou IG. Self-diffusion coefficient of bulk and confined water: a critical review of classical molecular simulation studies. Molecular Simulation. 2019;45:425-53. [242] Wu G, Yuan C, Ji X, Wang H, Sun S, Hu S. Effects of head type on the stability of gemini surfactant foam by molecular dynamics simulation. Chemical Physics Letters. 2017;682:122-7. 49
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
[243] Gao F, Liu G, Yuan S. The effect of betaine on the foam stability: Molecular simulation. Applied Surface Science. 2017;407:156-61. [244] Yang W, Yang X. Molecular Dynamics Study of the Foam Stability of a Mixed Surfactant/Water System with and without Calcium Ions. The Journal of Physical Chemistry B. 2011;115:4645-53. [245] Pires JM, Moura AFd, Freitas LCG. Investigating the spontaneous formation of SDS micelle in aqueous solution using a coarse-grained force field. Química Nova. 2012;35:97881. [246] Wang S, Larson RG. Coarse-Grained Molecular Dynamics Simulation of SelfAssembly and Surface Adsorption of Ionic Surfactants Using an Implicit Water Model. Langmuir. 2015;31:1262-71. [247] Wang P, Pei S, Wang M, Yan Y, Sun X, Zhang J. Study on the transformation from linear to branched wormlike micelles: An insight from molecular dynamics simulation. Journal of Colloid and Interface Science. 2017;494:47-53. [248] Yan Z, Dai C, Zhao M, Sun Y. Rheological characterizations and molecular dynamics simulations of self-assembly in an anionic/cationic surfactant mixture. Soft Matter. 2016;12:6058-66. [249] Hu S, Zhu Q, Wang P, Wang H, Li C, Sun S. Effect of HPAM hydrolysis degree on catanionic mixtures of DTAB/HPAM: A coarse-grained molecular dynamic simulation. Computational Materials Science. 2018;153:134-40. [250] Sambasivam A, Sangwai AV, Sureshkumar R. Self-Assembly of Nanoparticle– Surfactant Complexes with Rodlike Micelles: A Molecular Dynamics Study. Langmuir. 2016;32:1214-9. [251] Ruiz-Morales Y, Romero-Martinez A. Coarse-Grain Molecular Dynamics Simulations To Investigate the Bulk Viscosity and Critical Micelle Concentration of the Ionic Surfactant Sodium Dodecyl Sulfate (SDS) in Aqueous Solution. J Phys Chem B. 2018;122:3931-43. [252] Dhakal S, Sureshkumar R. Topology, length scales, and energetics of surfactant micelles. The Journal of Chemical Physics. 2015;143:024905. [253] Sambasivam A, Dhakal S, Sureshkumar R. Structure and rheology of self-assembled aqueous suspensions of nanoparticles and wormlike micelles. Molecular Simulation. 2018;44:485-93.
50
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
Conflict of Interests We declare that there is no conflict of interests.
51
Journal Pre-proof Graphical Abstract Configuration of various stabilizers at a film Liquid film
Gas
Major process
Aging
Drainage
Surfactant stabilized film
Foam stabilizers
Stabilizing
Surfactant
Coarsening
Polymer
Coalescence
Nanoparticle
Aqueous foam
Surfactant micelle
Polymer chain
Bare nanoparticle
Surface activated nanoparticle
Jo u
rn
al
Pr
e-
Surfactant
pr
oo f
Polymer stabilized film
52
Nanoparticle stabilized film
Journal Pre-proof
Jo u
rn
al
Pr
e-
pr
oo f
Highlights 1. Three major mechanisms including drainage, coarsening and coarsening govern the decay of the aqueous foam. 2. The application of surfactant, polymer and nanoparticle can greatly enhance the stability of foam. 3 the compounded system of these additives make it more favorable for foam life even under severe reservoir conditions. 4. Molecular dynamical simulation of the foaming additives provides novel insights into their effects on interfacial or bulk properties.
53