Experimental determination of the dew point pressure for bulk and confined gas mixtures using an isochoric apparatus

Fluid Phase Equilibria 508 (2020) 112439

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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

Experimental determination of the dew point pressure for bulk and confined gas mixtures using an isochoric apparatus Shadi Salahshoor, Ph.D. Principal Reservoir Engineer, Gas Technology Institute *, Mashhad Fahes, Ph.D. Assistant Professor, University of Oklahoma University of Oklahoma, United States

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 July 2019 Received in revised form 16 December 2019 Accepted 18 December 2019 Available online xxx

A robust high precision experimental approach to determine the Dew Point Pressure (DPP) of the gas condensates in a nano-porous medium is presented in this study. Gas condensate reservoirs have been the center of attention for numerous numerical and experimental studies for decades. Therefore, accurate measurement of DPP is crucial in developing long-term production plans for these reservoirs. This paper presents for the first time a proof of concept for a procedure to study the effect of the pore size distribution on the degree and direction of the shift in the saturation pressure of hydrocarbon gas mixtures under confinement over a relevant range of pressures and temperatures. Isochoric method, an indirect high-precision way of phase transition point determination, is commonly used in other disciplines where a clear non-visual determination of phase transition of a fixed volume of fluid is needed. This study provides an insight into using this approach for determining DPP of gas mixtures inside and outside of the porous media. A semi-automated apparatus for measuring and monitoring equilibrium conditions along with fluid properties is designed based on the isochoric method. The apparatus provides constant volume, variable pressure (0e104 bar), and variable temperature (290e410 K) experimental conditions. Pressure and temperature measurements provide a way to detect the phase transition point along the constant-mole-constant-volume line based on the change in the slope of this line at the phase transition point. A packed bed of BaTiO3 nanoparticles, providing a homogenous porous medium with pores of 1e70 nm is used as a representative nano-scale porous medium. The synthesized porous medium is very helpful in uncoupling the effect of pore size from the effect of mineralogy on the observed deviations in behavior, providing a volume more than 1000 times larger than the typical nano channels. The result is a set of isochoric lines for bulk and confined sample, plotted on the mixture's corresponding phase envelope to demonstrate the change in the saturation pressure. Phase envelopes (P-T diagrams) of the same mixture using different equations of state are created and the accuracy of each of these equations of state in providing an estimate of the experimentally detected DPP is discussed. Many attempts in explaining the shift in saturation pressures of the reservoir fluid confined in the narrow pores of unconventional reservoirs compared to those of the bulk can be found in the literature. However, there are some contradictions between the predicted behavior using different mathematical approaches. Experimental data could be substantially helpful in both validating the models and improving the understanding of the fluid behavior in these formations. Contrary to what many published models proposed, our results show that confinement effect shifts the DPP towards higher values compared to the bulk for a fixed temperature in the retrograde region. Capillary condensation is identified as the main source of the deviations observed in the behavior of fluids inside the nanopores. We evaluated some published models, including those based on EoS modifications, by comparing those to the experimental results which provides a quantification of their accuracy in estimating saturation pressure values for the confined mixtures. © 2019 Elsevier B.V. All rights reserved.

Keywords: Phase behavior Equation of state Confinement effect Confined fluid Pore size effect Nano-pores Gas condensate Phase transition Dew point pressure Unconventional gas Experiment VLE Isochoric PVT

* Corresponding author. E-mail addresses: [email protected], [email protected] (S. Salahshoor), [email protected] (M. Fahes). https://doi.org/10.1016/j.fluid.2019.112439 0378-3812/© 2019 Elsevier B.V. All rights reserved.

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S. Salahshoor, M. Fahes / Fluid Phase Equilibria 508 (2020) 112439

1. Introduction The deliverability and productivity of gas condensate reservoirs highly depends on the accurate determination of the phase transition point in order to avoid liquid dropout in the reservoir or the near wellbore region. If drawdown pressure continues to increase, the pressure of the gas condensate will drop below the Dew Point Pressure (DPP) of the system inside the reservoir which decreases the productivity and causes condensate banking. Therefore, accurate yet less complicated methods of DPP determination are needed. Numerical methods and empirical correlations, including equations of state, require detailed analysis of the reservoir fluid to deliver the maximum accuracy. Even with proper characterization of the fluid, especially in the presence of C7þ plus fraction, there is no guarantee that the predicted DPP is accurate [1e4]. These methods are proven to be unsuccessful in capturing DPP of gas condensates especially in the near critical region [5e7]. Consequently, experimentally collected data from laboratory samples are needed for accurate determination of fluid phase behavior properties, specifically DPP [7e9]. Experimentally determined DPP of gas condensates is very accurate and reliable, however, most of these experimental processes are time consuming, costly, and only applicable for bulk fluids. Constant Volume Depletion (CVD) is the most widely used experiment in characterizing gas condensates to predict DPP. This test is basically a series of expansion of the fluid into the two-phase split, followed by disposing the gas at each stage under constant pressure. The volume of the cell remains constant at the end of each stage, and the first droplet of liquid formation is detected through a glass window to estimate DPP. The gas depletion process needs extra cautious and a very precise experimental design to avoid uncertainties in determining fluid properties [10]. Isothermal experiments are also not very accurate in DPP prediction because the isotherms become very flat near the critical region and the slightest error in pressure measurements would cause a dramatic error in coexisting volumes determination. It is also possible to obtain the DPP by visual detection of the appearance of the first liquid drop inside an experimental cell equipped with a chilling mirror. This process requires an industrial apparatus and relies on the precision of the visual detector and the cooling rate of the mirror [11]. Aside from conventional experimental methods which are widely used in PVT studies, there are quiet many experimental approaches for specific needs and conditions. The isochoric VLE method, whose appearance in literature dates to 1986, is one of the versatile, static, closed-cell methods for fluid two phase behavior studies over wide ranges of pressure and temperature. This method relies on identifying the change in slope of isochoric lines as they cross vapor-liquid phase boundaries [12]. Current developments in enhancing the technology and practices for improving gas condensate recovery from tight formations encouraged scholars to investigate the factors affecting complicated fluid behavior of these formations. The impact of adsorption, altered wettability, elevated capillary forces, and mineralogy on phase behavior of fluid confined in nanopores of tight formations has been studied by many researchers [13]). Phase behavior alterations as a result of confinement require very careful consideration and management to avoid possible irreversible losses in productivity. Some models show that confinement can result in a lower risk of condensation in retrograde fluids [14]; Okuno et al., 2018) while other models anticipate an increase in that risk with determining a higher DPP [15e20]. Experimental work in this area to validate these models has been very limited because, as discussed, most of the established experimental procedures are designed for bulk fluids separated from the porous medium. Experimental works in the presence of

nano-pores are mostly based on the visual detection of the phase transition inside transparent nanochannels or the detection of the latent heat in calorimetry device [21e24]. Almost all these studies agreed that confinement in pores less than 100 nm has a significant impact on phase behavior regardless of the pore mineralogy. This effect is more pronounced in smaller pores down to below 10 nm where elevated intermolecular forced increase the levels of complexity of the models [25e30]. The isochoric experiment is an indirect method to identify phase transition points by detecting the changing slope of the isochoric line (pressure-temperature line for a fixed composition mixture inside a cell with a fixed volume). This method has not received much attention in petroleum engineering PVT studies, nevertheless, has been widely used in other disciplines to obtain the locus of phase envelope of fluid mixtures inside the fixed volume pressure cells. Such applications include supercritical chemical reactors that are used to achieve a homogeneous operation or provide a way for isothermal density measurements [31e34]. A typical isochoric apparatus is a closed cell made of temperature resistant material, equipped with a surrounding heat exchange, a temperature control/monitoring system, and a pressure control/ monitoring system. The sample is loaded into the isochoric cell at the initial desired condition to be a single-phase liquid or gas. The heat exchanger is used to lower or raise the temperature, and the pressure is monitored accordingly. After stabilization, pressure and temperature data are collected and analyzed. The P-T data are plotted and the change in the slope of the P-T line (Fig. 1&2), which happens at one point very close to the phase boundary, allows determination of bubble point or dew point pressures [33e35]. Potsch and Braeuer [12] introduced this method as a novel graphical way of determining DPP for gas condensates and drew the attention of petroleum industry scholars into a less complicated experimental method of detecting the phase transition point of gaseous mixtures. However, to the best of our knowledge, there has been no attempts at utilizing this method in petroleum engineering industry and research projects. Given the high demand for experimental data on the phase behavior of confined fluid [13], which requires conducting the experiment at a constant volume porous medium, it is time to pay close attention to this approach. We identify this approach as one of the most reliable ways to perform fluid phase behavior tests in the presence of porous media. In this work, the isochoric method is used to obtain the DPP of a known mixture of hydrocarbons under both bulk and confined conditions. Experimental results are compared with the data generated by a commercial simulator utilizing various equations of

Fig. 1. Isochoric approach for determining phase boundaries [35].

S. Salahshoor, M. Fahes / Fluid Phase Equilibria 508 (2020) 112439

3

Fig. 2. Two Phase diagram of a mixture and isochoric lines [34].

state. The developed experimental procedure can address the phase equilibrium and PVT behavior of pure to multicomponent systems and facilitates experimental DPP determination in a less complicated, more reliable way. A mixture of a lighter and a comparatively heavier hydrocarbon with the most visible deviation in the slope of the isochoric line inside the two-phase region compared to the single-phase one is chosen to be used as a proof of the concept then the work can be expanded to any other binary- or multicomponent-mixture of hydrocarbons. For this purpose, phase envelope creation and two-phase flash calculation for various binary hydrocarbon systems were performed in the simulator. The best composition complying with the pressure and temperature

tolerance of the experimental setup (104 bar and 422 K) to accommodate the phase transition point detection using the isochoric procedure, was an ethane-pentane mixture with molar composition of 70 mol% C2 and 30 mol% C5. Table 1 is the sample provenance table for the components used in this study including hydrocarbon gases and porous medium material. 2. Theory 2.1. Equations of state for bulk fluid The vapor-liquid phase boundary is commonly determined

Table 1 Sample provenance table. Product Name

Provider Purity

Product Specifications

Ethane

Airgas

99.99% O2 5 ppm

Pentane

Sigma Aldrich

99.0%

free acid (as CH3COOH) 0.005%

Barium Titanate Nano-powders

TPL, Inc.

99.5%

Appearance White powder

Other Components (mol/Mol Units) H2O Other Hydrocarbons 5 ppm 80 ppm Other Components (mol/Mol Units) non-volatile ppb fluorescence matter (quinine) at 254 nm 0.0005% 1 ppb Other Key Properties Melting point/ Relative density freezing point 1625  C 5.7 g/ml

Co/Co2 5 ppm

N2 10 ppm

ppb fluorescence (quinine) at 365 nm 1 ppb Solubility Insoluble in water/ Alkanes

Incompatible materials

Molar Mass Strong oxidizing agents, 233.19 g/ Strong acids mol

4

S. Salahshoor, M. Fahes / Fluid Phase Equilibria 508 (2020) 112439

using equations of state to show what phases exist or co-exist at different pressure and temperature conditions. Equations of states fall into two main categories: cubic and non-cubic equations. Although non-cubic EoS describe the volumetric behavior of the pure substances, they are not good for complex hydrocarbon mixtures, especially in the critical region [36]. Most of the non-cubic models and equations of state are complex and necessitate knowing pure component constants or binary interaction factors [37]. Therefore, most commercial software use one of the cubic equations of state to build the phase envelope with practical accuracy. Peng-Robinson (PR) and SoaveeRedlicheKwong (SRK) equations of state are two of the widely used ones. Nasrifar et al. [38] compared 15 equations of state in terms of their accuracy in predicting natural gas dew points, including twoparameter EoSs of the RedlicheKwong (RK) and Peng-Robinson (PR) family. Three-parameter EoSs including Patel and Teja (PT & PTV), Guo and Du (GD), Mohsen-Nia- Modarress- Mansoori (MMM), and Schmidt and Wenzel (SW) were also investigated along with the four-parameter Trebble- Bishnoi- Salim (TBS) EoS. They found that for mixtures with a considerable amount of C7þ, the three-parameter equations of state are more accurate while for the mixtures with a considerable percentage of lighter hydrocarbons (C1eC7), the two-parameter ones are more accurate. They also proposed that for the lighter mixtures, the RK family (RK, SRK, and SSRK) provides the best prediction of DPP. Mørch et al. [9]. used a chilled mirror apparatus to measure the DPP for several synthetic hydrocarbon mixtures consisting of C1 to C5 fractions and compared the measured DPPs with the calculated ones from RKEoS. Their results show that SRK EoS gives the best estimation of experimental DPP; however, a significant deviation is observed between the experimental and calculated values when the pressure is increased to cricondenbar. In a similar study, Ahmed [39], examined eight different equations of state in terms of their accuracy in predicting the volumetric behavior of gas condensates. His work proved that SW-EoS is the most accurate one in predicting the volumetric behavior of such systems while PR, PT, and SW present the same accuracy in VLE calculations for the same system. Other scholars tried to overcome the uncertainties of equations of state application by developing new models and correlations [1e3,6]. Most of these theoretical studies agreed that the pseudo components and C7þ fractions are the source of errors in DPP prediction using EoS and correlations. However, our results demonstrate that even in the absence of C7þ fractions, application of equations of state is accompanied with a degree of uncertainty in determining DPP of hydrocarbon mixtures. In this work, PR- and SRK- EoS, two of the most promising methods introduced in the literature, are compared with the experimentally measured DPP of a binary mixture of ethane and pentane. This comparison demonstrates that SRK-EoS provides a better match to the experimentally measured DPP compared to the PR-EoS. Therefore, it supports the conclusion of the studies provided in the literature regarding the better accuracy of the RKfamily EoS in measuring DPP of gas condensates. The mathematics of these two equations of state are summarized below. Peng-Robinson Equation of State. This equation is a modification of the Van der Waals EoS, which was introduced by Peng and Robinson [40] as follows:


Pþ

 aðTÞ ðn  bÞ ¼ RT nðn þ bÞ þ bðn  bÞ

(1)

This equation improved the liquid density prediction but could not accurately describe the volumetric behavior around the critical point [36]. Density prediction is the weakness of almost all equations of state.

Soave-Redlich-Knowng Equation of State. Redlich and Kwong (RK) (1949) made an important modification to the attractive term (relating it to temperature) of the van der Waals EoS by proposing the following equation [36]:

2

3

6 6P þ 4

a T nðn þ bÞ 1 2

7 7ðn  bÞ ¼ RT 5

(2)

Later, Soave made a significant improvement to the RedlichKwong equation of state by replacing the temperature in the attraction term by a more general function a. Hence, the RedlichKwong EoS is written as:

P¼

RT aa  Vm  b Vm ðVm þ bÞ

(3)

Where, a ¼ T10:5 . Traditionally, a set of binary interaction coefficients were used to improve the volumetric prediction of hydrocarbon mixtures with equations of state. These interaction coefficients were replaced by corrections to the vapor pressure of pure components [41]. neloux et al. introduced volume correction parameter (volPe ume shift) to improve the volumetric prediction of SRK-EoS. The volume shift parameter does not change the vapor-liquid equilibrium calculations and the equilibrium ratio (Ki). It only improves the volumetric derivation from the original EoS for both vapor and liquid phase [42]. Jhaveri and Youngren [43] followed the procedure proposed by neloux et al. [42] to make the same volumetric improvement for Pe the PR-EoS. Their work was later extended by Whitson and Brule [44] for several pure components.

2.2. Equations of state for confined fluid As discussed in section 2.1, equations of state have been used for decades to describe the PVT behavior of reservoir fluids and are still actively used by the industry in different simulators to investigate reservoir fluid properties. However, most of the equations of state are proven to be inaccurate in calculating the reservoir fluid critical properties in tight formations due to the abundance of nanoscale pores resulting in perplexing phase behavior. Many scholars attempted to modify conventional equations of state to include the pore size effect on fluid properties in the original equations. A comprehensive review on these studies is provided elsewhere [13]. Nevertheless, most of these modifications demonstrate continuous reduction of the critical properties of the fluid with reducing the pore size. Therefore, constructed phase envelopes for the confined fluid using these modified equations with shifted critical properties present an upward shift in the DPP line of the phase envelope. This way, a higher saturation pressure at each temperature is expected for the confined condensate mixture compared to the bulk; while our experimental results illustrate the opposite behavior. Lowry and Piri [45]. discussed that the mineralogy of the pores has to be considered along with the pore size to evaluate the degree and direction of the shift in the critical properties of nanoconfined fluids compared to the bulk Liu et al. [46]. defined competitive adsorption of different components of the gas mixture as a controlling factor in the alteration of fluid phase behavior. Basically, competitive adsorption of different components to the pore walls can change the initial composition of the fluid mixture and the shift in the critical properties happens consequently. As stated by Jin and Firoozabadi [16]; direct use of equations of state, even with adjusting critical properties to account for

S. Salahshoor, M. Fahes / Fluid Phase Equilibria 508 (2020) 112439 Table 2 Properties of ethane and pentane (pure components).

Table 4 Key properties of Barium Titanate Nano-powders from TPL, Inc.

Component SRK Volume Shifta (cm3/gmol)

PR Volume Shifta (cm3/ g-mol)

Critical Pressurea (bar)

Critical Acentric Temperaturea Factora (K)

C2 C5

7.08 2.44

48.8 33.7

305.4 469.7

3.78 7.55

0.099 0.251

a Values taken from: Ahmed, T. 2010. Chapter 15 - Vapor-Liquid Phase Equilibria. In: AHMED, T. (ed.) Reservoir Engineering Handbook (Fourth Edition). Boston: Gulf Professional Publishing.

PR-EoS SRK-EoS

Mixture: 69.96 mol% C2 and 30.04 mol% C5 Critical Temperature (K)

Critical Pressure (bar)

387.66 389.47

66.94 67.40

confinement, is not accurate for nanopores, especially pores less than 10 nm Salahshoor and Fahes [47]. presented the deficiency of the correlations proposed for critical properties shift in capturing the extent of the change in P-T behavior of pure fluids under confinement. The correlation for critical properties shift proposed by Sun et al. [48] is based on a molecular simulation proven to be the best estimate of pure fluid isochoric behavior under confinement in the absence of adsorbed gas layer. The same correlation is used in this work to adjust the critical properties of ethane and pentane for the average pore sizes of 20 nm in diameter. Details of this correlation are provided below:

DTc ¼

 1:13637 Dp TcB  TcP ¼ 1:2 TcB sLJ

Appearance

White powder

Melting point/freezing point Relative density Solubility Incompatible materials Molar Mass

1625  C 5.7 g/ml Insoluble in water/Alkanes Strong oxidizing agents, Strong acids 233.19 g/mol

DPc ¼

Table 3 Properties of ethane and pentane mixtures. Equation of State

5

(4)

PcB  PcP ¼ 1:5 PcB



Dp

0:625

sLJ

(5)

Where, sLJ is the Lennard-Jones potential parameter for the confined fluid, TcB and PcB are the critical properties of the bulk fluid, and TcP and PcP are the critical properties of the confined fluid. The equation of state with shifted critical properties using correlations 4 and 5, is compared to our experimental results showing the deficiency of this method. 2.3. Vapor-liquid equilibrium (VLE) Another widely-used modification of EoS for confined fluids is based on adjusting VLE calculations to include the effect of the existing capillary pressure in nanopores into the original calculations [14,46,49,50]. Conventionally, the first step in VLE studies is defining the equilibrium ratio (Ki ¼ yxii ). In a multi-component system, the equilibrium ratio is defined as the ratio of the mole fraction of a component in gas phase (yi ) to the mole fraction of that component in liquid phase (xi ) [51]. The difference between VLE calculations for confined fluids compared to the bulk fluids is that for a bulk fluid, surface tension (interfacial tension between liquid-vapor, solid-liquid, or solidvapor) does not depend on the curvature. In other words, it is the same as planar values. For the confined fluid, this effect is

Fig. 3. Phase envelop (generated by both PR- and SRK- EoS) and mathematically constructed isochoric line for the mixture of 69.96 mol % C2 and 30.04 mol % C5.

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S. Salahshoor, M. Fahes / Fluid Phase Equilibria 508 (2020) 112439

considerable and in the derivation of the equilibrium conditions, the effect of curved interface (curvature effect) needs to be taken into account. Zuo et al. [52] developed a model to incorporate the effect of capillary pressure into phase envelope and saturation pressure predictions for fluid mixtures using EoS. This study shows that the presence of capillary pressure causes a decrease in the bubble point pressure of the confined fluid compared to the bulk and an increase in the dew point pressure with reducing the pore size. This theory is based on adapting Young-Laplace equation (Eq. (6)) into the capillary pressure models, where q is the contact angle between the pore wall and the wetting phase. This equation can be used to calculate saturation pressures (bubble points and dew points pressures at each temperature) and consequently to build the two-phase envelope from the bubble- and dew-point lines.

dPG ¼ dPL þ

2s cos q r

(6)

In the present work, we utilize the isochoric experiment to examine pressure-temperature (PT) relationship along an isochoric line for a binary hydrocarbon mixture under both confinement and bulk conditions. This experiment is used as a proof of concept for the application of this technique in identifying changes in fluid properties of different hydrocarbon mixtures in the presence of a porous medium. Experimental results are compared with the results of some of the widely-used correlations for confined fluids in nanopores proposed in the literature, including shift in critical properties and modifications of VLE calculations. Test results demonstrate that when a fluid mixture is confined in less than 100 nm pore spaces, the DPP of the fluid is shifted towards a lower pressure at a constant temperature compared to the bulk in the

retrograde region. Several scholars confirmed this behavior through modeling works [14,16]. 3. Experiment 3.1. Experimental design and methodology In order to mathematically construct an isochoric line for a specified composition using an EoS, values for the vapor phase zfactor, vapor phase volume percent, and vapor phase mole percent at each temperature and pressure are obtained from flash calculation. Both flash calculations and the two-phase envelopes are generated by the simulator for the desired mixture. The total volume of the system is set to a constant value as in the isochoric test the total volume remains constant even though the volume of each phase can change. Note that calculations for the isochoric line are independent of volume, and the volume of the system can easily be updated based on different experimental conditions. Initial pressure and initial temperature are then identified on the P-T diagram in a way that the system is in a single gaseous phase away from the critical point. The real gas equation (compressibility EoS) is employed next to get the total number of moles for the system according to the desired condition and based on flash calculation data, as follows:

PV ¼ ZnRT

(7)

Consequently,

n¼

PV zRT

(8)

This equation, for only the gas phase and from flash calculation,

Fig. 4. Schematic representation of the experimental apparatus for isochoric experiment.

S. Salahshoor, M. Fahes / Fluid Phase Equilibria 508 (2020) 112439

7

Fig. 5. Schematic of the experimental apparatus [47].

3.2. Materials

can be re-written as:

Pvg ¼ RT zng

(9)

Once a range of interest for pressure and temperature is deterPv mined, zngg is calculated for each pressure value at a fixed temperature. This process is repeated for all temperature values and as a Pv result, a plot of zngg versus pressure is generated to determine the pressure value corresponding to each temperature step (the presPv sure at which RT is equal to zngg ). The locus of phase boundary for a binary mixture of 70 mol% ethane and 30 mol% pentane is constructed using both PR- and SRK EoS. Volume shift parameters are adjusted in the simulator for ethane and pentane in both EoS to eliminate volumetric deficiency [41]. Table 2 summarizes the properties of pure ethane and pentane used in simulations and Table 3 summarizes the properties of the ethane-pentane mixture. The design system for our case was a 70/30 mol percent of C2/C5. However, this was modified to 69.96/30.04 mol percent to match the exact chemical composition that was loaded into the experimental cell. As shown in Fig. 3, at the temperature of 386 K, the phase transition point, based on the discrete change in the isochoric line slope shows a higher DPP (62.9 bar) compared to the one calculated by PR-EoS (61.2 bar) and a lower DPP compared to the calculated value using SRK-EoS (64.4 bar). Experimental validations of these results are presented in the next section.

Barium Titanite (BaTiO3) nanoparticles (99.5% purity based on vendor's MSDS- outlined in Table 4), 400 nm in diameter, are used to synthesize a nanoscale porous media. Barium Titanite is insoluble in both water and alkanes and is highly hydrophilic which makes it a great candidate to decouple the effect of mineralogy and wettability from the pore size effect on the hydrocarbon phase behavior. Ultra-high purity (99.99%) ethane from Airgas and HPLC grade (99%) pentane from Sigma Aldrich are used in this work as hydrocarbon components. 3.3. Experimental apparatus and procedure The isochoric experiment is conducted in two different stages. The first stage is for the bulk fluid and the second stage is for the confined fluid undergoing the isochoric test along with a reference bulk fluid sample. 3.3.1. Isochoric experiment for bulk fluid Two PVT cells similar to the conventional PVT cells but with more capacities (1 L in volume) are built using stainless steel accumulators. One of these accumulators is the actual PVT cell which holds the fluid mixture through the isochoric process and the other one is used as a loading chamber to combine components and transfer them into the main PVT cell. The entire apparatus, including PVT cell, is vacuumed for a period of 4 h prior to the experiment to assure purity of the loaded mixture. Commercial stainless still quarter turn plug valves (316 SS) are used to isolate

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S. Salahshoor, M. Fahes / Fluid Phase Equilibria 508 (2020) 112439

Fig. 6. a (left): BaTiO3 powders; particles with nominal diameter of 400 nm. b (right): Synthetized porous media; BaTiO3 powders (400 nm) after packing process.

different parts of the system, including the PVT cell from the loading chamber. Both of these stainless-steel cells are equipped with a piston whose position can be controlled by injecting a fluid (PG1 oil or water) using Isco 500D syringe pumps connected at the bottom of the cells. The major advantages of syringe pumps are the ability for continuous injection of the fluid under constant rate or constant pressure along with the high precision. A schematic of this experimental setup for the bulk fluid system is shown in Fig. 4. During the isochoric experiment, the volume of the system remains constant (cell acts as a control volume that can only exchange thermal energy with its environment) and the molar mass of the mixture inside the cell is also fixed. Pressure data are collected using pressure transducers (that converts measured pressure into an electrical signal). A data acquisition system (DAQNI 9205) is used to record, monitor, and store data. LabVIEW program provides an automated acquisition and control system for the two 345 bar pressure transducers (S-series Swagelok) connected to the cells and the computer. Pressure transducers are directly connected to the main PVT cells from the top connections, thus, they are in direct contact with the fluid sample and send real-time pressure values to the computer. Temperature is controlled by a heating chamber (VWR® Gravity Convection Ovens, 6.2 cu.ft., 120V) that provides a wide range of temperature values, transfers heat to the accumulators, and keeps the temperature constant at the pre-defined value throughout each stage of the test. Pressure data are recorded every tenth of a second till an equilibrium condition is stablished, then the temperature is reduced step-wise to collect corresponding pressure values for all other temperature values that are a part of the experimental design. The main purpose of this stage of the experiment with bulk fluid is to collect the data for the bulk phase and compare it with the SRK- and PR-EoS to determine the most accurate EoS for the rest of the study. Results are outlined in section 4.1. 3.3.2. Isochoric experiment for bulk and confined fluid The only difference between this stage of the test with the previous stage (shown in Fig. 4) is the presence of the porous medium inside the accumulator 2. Therefore, the fluid inside accumulator 1 is the bulk system and the fluid inside accumulator 2 is confined. Schematic of the designed isochoric apparatus for this study is presented in Fig. 5. The nanoscale porous medium is synthesized in the form of a solid cylindrical block (Fig. 6) from BaTio3 powders using soil compaction packing approach [47,53]. The efficiency of our experiments relies on how good of a packing these particles can provide us. Two common methods for packing particles in the form of a well-packed solid disc or column are: dry packing, and wet or slurry packing. Particles that cannot be dry-packed as they get clumpy or

Fig. 7a. SEM picture of the synthetized porous media; BaTiO3 powders (400 nm) after packing process, showing the pores and particles.

they are too delicate to be mechanically pressurized to get wellpacked, must be suspended in a liquid and introduced to their cell as a slurry. Once they are suspended in a liquid, they can be transferred and packed to the medium using a high-pressure pump. Then the stationary phase (solid particles) and the suspension liquid are homogenized, and liquid is removed with compatible methods and procedures to leave the packed solid particles behind. The particles we used (BaTiO3 powders) are mechanically stable which made them a great candidate for dry packing. There are different dry packing methods in the literature, a modified version of soil compaction method (applying downward force to compress the particles) using static force is developed for packing the needed porous media using BaTiO3 particles in our experiment. The SEM picture of the packing in shown in Fig. 7a which confirms that particles are between 300 and 400 nm in diameter. The pore size distribution is also calculated by processing the SEM image and results represented in the graph in Fig. 7b. The experiment starts by vacuuming the entire system, including both accumulators, porous medium and all connection, for a period of 10 h to eliminate any possible impurity. After vacuuming, isolation valve (valve 3) is closed which isolates the porous medium from the bulk experimental cell. A binary mixture of 70 mol% ethane and 30 mol% pentane is loaded into a Acc. 1 using a third accumulator as the loading chamber to inject required amount of each component to get the specified composition at the

Fig. 7b. Pore size distribution of the sample based on SEM image, showing pores of 1e70 nm with majority of the pores between 20 and 30 nm.

S. Salahshoor, M. Fahes / Fluid Phase Equilibria 508 (2020) 112439 Table 5 Experimental values for the isochoric data at equilibrium for a mixture of 69.96 mol% C2- 30.04 mol% C5 at the listed temperaturea and pressure with standard uncertainty of u(P). Temperature (K) 323.15 343.15 353.15 363.15 368.15 378.15 383.15 388.15 393.15 397.15 401.15 405.15 412.15 a

± ± ± ± ± ± ± ± ± ± ± ± ±

1 1 1 1 1 1 1 1 1 1 1 1 1

Pressure (bar) 30.6000 39.2300 43.0700 47.3700 49.5900 53.9700 56.3900 58.4000 61.1600 63.2200 65.5200 67.8400 72.3900

± ± ± ± ± ± ± ± ± ± ± ± ±

0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863

u(P) (bar) 0.0002 0.0001 0.0000 0.0001 0.0002 0.0001 0.0002 0.0002 0.0002 0.0001 0.0001 0.0001 0.0002

Standard uncertainty (u) for the temperatures is u(T) ¼ 0.1 K.

required initial pressure based on the simulation results [54]. Once fluid is loaded to the bulk test accumulator (Acc. 1), the temperature of the air bath is increased to 423.15 K in order to get the fluid mixture into the single-phase gas region. Once thermal and mechanical equilibrium is established (identify by pressure stabilization recorded through data acquisition unit), the isolation valve is opened to let the fluid expand into the porous medium. Temperature remains constant and pressure is monitored continuously to achieve stabilization. Once system is stabilized, the isolation valve is closed to separate the bulk space from the confined one. From there, isochoric test is started by reducing the temperature of the air bath stepwise and recording the corresponding stabilized pressure on both sides (bulk and confined) through two identical pressure transducers. Upon getting to the minimum temperature (363.15 K), the temperature is increased with the same increment to get back to the starting point (423.15 K)

9

while stabilized corresponding pressure is recorded at each step. This process is repeated three times (providing 6 pressure measurement at each temperature) to confirm the reproducibility of the data and minimize possible associated human/measurement errors. Reported pressure value is the arithmetic mean of the 6 recorded values with a maximum standard deviation of 0.1930 bar. Data are plotted on top of the phase envelope for the experimented mixture with the specified composition to illustrate the alteration of saturation pressure (dew point in this specific test) inside nanoscale pore sizes of a tight formation compared to the bulk. 3.3.3. Data processing & experimental uncertainty During the isochoric experiment the mass and volume of the system remains constant (the system is a control volume that can only exchange energy with the environment). Possible expansions of the stainless-steel parts at the experimental range of temperature is ignorable. Prior to the experiment, volumes of each section of the setup are measured using gas compressibility equation for the pure gas (helium) filling the system. This gas is pressurized through fluid injection using syringe pump to the bottom of Acc. 1 which is equipped with a piston isolating the bottom portion from the top. Pressure is recorded by 345 bar pressure transducers with voltage range of 0e5 V connected to a data acquisition system (DAQ) which records, monitors, and stores the data Human machine interface (HMI) provides automated data acquisition and control system. Data are sampled every tenth of a second for pressure measurements during all stages of the experiment. Temperature is controlled by a heating chamber capable of holding the temperature constant at the predefined value during each stage of the test with an accuracy of ±0.1 K. Calibration of a variable against a standard value does not eliminate the system error entirely. Calibration errors are usually associated with three sources; the standard value itself, the calibration instrument or system, or the calibration process. In this

Fig. 8. Phase envelop (both SRK- and PR-EoS) and predicted isochoric using compressibility EoS along with the isochoric experimental results for determining the dew point pressures of the mixture of 69.96 mol% C2 and 30.04 mol% C5.

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Fig. 9. Repeatability of the isochoric experiment for the mixture of 69.96 mol% C2 & 30.04 mol% C5.

work, pressure transducers are calibrated using the dead weight tester (DWT), a pressure producing and pressure measuring device used to calibrate pressure gauges. Calibration process was performed with extra cautious and DWT was in good condition. Therefore, we safely assume calibration errors to be zero. After calibration of pressure transducers using DWT, an error percentage of 0.025% of the span limit was obtained which is equal to 0.0863 bar of absolute error.Data-Acquisition (DAQ) errors are errors arising during acquiring data. These errors include system and instrument errors that are not already accounted in calibration; such as unknown changes to the measurement system conditions, sensor installation, sensor failure, etc. These errors are eliminated by calibrating pressure transducers first with DWT and then through DAQ settings in Labview program. Curve-fittings and correlation of data may cause data-reduction errors in test results. Truncation errors, interpolation errors, and assumed models and functional relationships errors also fall into this category. To minimize this category of errors, equilibrium pressures are recorded every tenth of a second for a period of at least 8 h. Each reported pressure data is therefore the arithmetic average of 288000 continuous readings with the maximum standard deviation of 0.1077 bar. 4. Results and analysis 4.1. Bulk fluid experiment The general procedure followed in this work for DPP determination using the isochoric apparatus is to start from single-phase gas mixture at equilibrium and reduce the temperature stepwise while the equilibrium pressure is recorded at each temperature step. The result of each test is a set of pressure and temperature points plotted on a P-T diagram. The phase transition point is detected through identification of the change in the slope of the linear regression line connecting experimental data in the gas phase from the two-phase region. These experimental data points for a bulk mixture of 69.96 mol% C2- 30.04 mol% C5 are reported in

Table 5. In Fig. 8, these data are plotted along with the simulated isochoric line and phase envelops of the same mixture simulated by PR- and SRK- equation of state to compare the experimentally identified DPP with the simulation results. Based on these experimental results, the saturation pressure for a mixture of 69.96 mol% C2 and 30.04 mol% n-C5 at the temperature of 397.08 K is 63.3 bar; and the saturation pressure for this mixture at the same temperature is equal to 63.5 bar from the simulation results of the isochoric process. If we consider the simulation value as our reference value (assuming that the obtained Z-factors from the flash calculation are accurate enough) and the experimental value as the measured one, the relative accuracy of the experimental measurement can be calculated as:

e¼

jMeasured value  True value ðReference valueÞj  100 True value ðReference valueÞ (10)

e¼

j63:5  63:3j  100 ¼ 0:31% 63:5

(11)

As calculation shows, the difference between the experimentally measured value and the simulation driven one is almost 0.3% which approves the acceptable accuracy of the experiment. This small difference might be due to some experimental uncertainties

Table 6 Predicted and measured saturation pressures (DPPs) for a mixture of 69.96 mol% C2 & 30.04 mol% n-C5 at T ¼ 397.08 Ka Measuring Method

Value (bar)

SRK-EoS Z-factor (compressibility) EoS Experimentb PR- EoS

63.23 63.50 63.3100 ± 0.0863 56.65

a b

Standard uncertainty (u) for the temperatures are u(T) ¼ 0.1 K. Standard uncertainty (u) for the pressures are u(P) ¼ 0.0002 bar.

S. Salahshoor, M. Fahes / Fluid Phase Equilibria 508 (2020) 112439

including component impurities (pentane used in this experiment is  99% purity from Sigma Aldrich and ethane is 99.99% purity from Airgas), weighting errors (the scale accuracy is 0.01 g) or loading process errors (since pentane is highly volatile). To assure that experimental data are free of random errors and are precisely reproducible, the repeatability of the entire experiment is examined. After finishing the data collection by experimenting, right upon getting back to the ambient condition under equilibrium, the entire process is repeated. This time, the lowest temperature step (343.15 K) is set as the start point and temperature is raised stepwise to the maximum value (412.15 K). In Fig. 9, the results of this round of experiment are plotted on top one the previous results presented in Fig. 8 as a proof the repeatability of the experiment. As shown in Fig. 9, collected data in the second round of the isochoric experiment (presented as “backward” on the figure because on the contrary to the first experiment, it started from the lowest temperature step and continued to the highest one) with the same sample in the bulk phase illustrates a good agreement with the first round of isochoric experiment. The difference between the values measured during the second-round and the ones measured in the first-round ranges between 0.03 and 0.3 bar which brings it to less than 0.3% error. It should be noted that getting back to the initial pressure value under the maximum temperature condition means the system contains the same number of moles and the same composition as the beginning of the test, which is a proof of mass balance throughout the experiment. These proof-of-concept results and investigations provide confidence in the method as well as the system built for experimental purposes. The congruency of the collected experimental data with the calculated results, besides the reproducibility of the data through different runs of the experiment, are indications of the reasonable accuracy of the system in determining the phase transition point. Having said that, follows is an investigation into the accuracy of the calculated saturation pressure using equations of

11

state compared to the measured saturation pressure from the isochoric experiment. As discussed in the theory section, most of the theoretical literature agrees that the RK- EoS family is more accurate in predicting the DPP of gas condensates compared to the rest of the equations of state, while PR-EoS is mostly accurate for the mixtures with significant amount of C7þ. Here, the analysis of the predicted DPPs from these two equations of state for the same composition used in the experimental work is provided. Relevant data are summarized in Table 6. Considering experimental value as our reference (or as the most accurate estimation), the accuracy of the equations of state using equation (7) can be evaluated as below:

e¼

j63:23  63:31j  100 ¼ 0:126% 63:31

e¼

j56:65  63:31j  100 ¼ 10:52% 63:31

SRK  EoS

PR  EoS

(12)

(13)

Therefore, it is evident that although the SRK- and the PR- EoS show the same accuracy in the non-retrograde region and are almost equally precise in predicting bubble point pressure (Fig. 10), there is a big difference in their prediction of DPP in the retrograde region (Fig. 11). PR-EoS presents an almost 10% underestimation of DPP compared to the experimental value, while SRK-EoS shows less than 0.2% underestimation. Based on these results, the value predicted by SRK is more congruent with the experimental value compared to the Z-factor equation.

4.2. Confined fluid experiment Experimental results of the isochoric test for a binary mixture of 70 mol% ethane and 30 mol% pentane are provided in Table 7. These results are plotted on the generated phase envelope for

Fig. 10. Comparison between the SRK- and PR- EoS in the retrograde vs non-retrograde region for the mixture of 69.96 mol% C2 & 30.04 mol% C5.

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Fig. 11. Comparison between the compressibility-, SRK-, and PR- EoS vs experimental data in the retrograde region for the mixture of 69.96 mol% C2 & 30.04 mol% C5.

the same mixture to show the saturation pressure (point of the slope change) for both bulk and confined fluid on top of the phase boundary and illustrate the direction of the shift (Fig. 12). As shown in Fig. 12, detected saturation pressure (from the change of slope in the linear regression of data) for the bulk fluid is 62.05 ± 0.08 bar at the temperature of 398.15 ± 1 K which clearly matches the boundary of the phase envelope at that specific temperature. However, the change of the slope happens at the pressure of 64.88 ± 0.08 bar and temperature of 4.3.15 ± 1 K for the confined fluid. This is presented in Fig. 13 in more details by magnifying the region of interest in Fig. 12. 5. Discussions Observation of the break in the slope of isochoric line for the fluid in the confined space at a higher temperature and pressure compared to the bulk is an evidence of condensation occurrence with a smaller pressure & temperature drop than what is normally expected for the bulk fluid mixture. In other words, condensation is nanopores can happen while the pressure and temperature are still above the dew point of the bulk fluid calculated using equations of state. Phase envelope of the confined binary mixture of C2eC5 is generated using shifted critical properties calculated by equations (1) and (2). In Fig. 14, by adjusting critical properties of the components for pore diameters of 1000, 500, 400, 100, 40, and 20 nm, phase envelopes are generated for C2eC5 mixture. As shown in this figure, the phase envelope gets smaller and smaller by reducing the pore diameter and moves towards the bulk for pore sizes around 1 mm. Other proposed correlations for critical properties shift available in the literature are similar in term of predicting the direction of the change and are slightly different in estimating the extent of the shift [17,19,20,29,55]. Experimentally determined dew point pressure, however, approve that the direct application of the equations of state, even by modifying correlations, are not accurate.

Scholars believe that formation of an adsorption layer around the pore walls is the dominant cause of condensation of fluid in nanopores at a higher pressures and temperatures compared to the bulk. Preferential adsorption of some components compared to the others affects the density distribution of the fluid inside the nanopores which shifts the phase envelope towards a different composition or different critical properties. For inorganic pores, capillary condensation provides the same effect by accelerating the formation of a higher density layer around the pore walls due to the elevated fluid molecules-pore wall interactions. Many substances are mechanically and adhesively very sensitive to the presence of even traces of “condensable” vapors; “vapors whose liquids form a small contact angle with the surface”. Once the first meniscus is formed, it will result in increased van der Waals interaction between vapor phase molecules inside the space of a capillary. Therefore, this process proceeds to a multilayer adsorption from vapor to the solid pore wall [56]. This phenomenon is known as capillary condensation; it occurs due to the strong pore wall fluid molecule interactions in tiny pore spaces and can lead to the point that the entire pore space is filled with condensed liquid above the

Table 7 Isochoric experimental data for 70 mol% C2-30 mol% C5 at variable listed temperaturesa and pressures. Confined Space Temperature (K)

423.15 413.15 403.15 398.15 393.15 383.15 373.15 363.15 a

± ± ± ± ± ± ± ±

1 1 1 1 1 1 1 1

Pressure (bar) 76.8800 71.9100 66.8800 64.8100 62.7400 58.9500 55.1600 51.2300

± ± ± ± ± ± ± ±

0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863

Bulk Space u(P) (bar)

Pressure (bar)

0.0002 0.0002 0.0002 0.0002 0.0001 0.0001 0.0002 0.0002

76.8800 70.6700 64.8800 62.0500 59.8500 55.8500 51.7100 47.5700

± ± ± ± ± ± ± ±

0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863 0.0863

Standard uncertainties (u) for temperatures are u(T) ¼ 0.1 K.

u(P) (bar) 0.0002 0.0002 0.0002 0.0001 0.0002 0.0002 0.0001 0.0002

S. Salahshoor, M. Fahes / Fluid Phase Equilibria 508 (2020) 112439

13

Fig. 12. Comparison between the isochoric P-T line for the confined mixture of 70 mol% C2-30 mol% C5 and the bulk mixture of the same composition.

saturation pressure of the vapor, Psat. Li and Firoozabadi [57]. proposed that phase change due to capillary condensation could occur beyond the cricondentherm in nano-pores even when the bulk fluid is still in single phase. Several mathematical approaches are provided in the literature to account for inhomogeneous density distributions of confined fluids. In terms of modifying equations of state, two popular approaches are modification of the critical properties (Fig. 14) and modification of VLE calculations (Fig. 15) to account for the capillary pressure (curvature effect) in nano-pores. Fig. 15 illustrates the shifted phase envelope for the same mixture (70 mol% ethane and

30 mol% pentane) using VLE calculations modification (using equation (6)). As shown in the figure, this approach shows a good agreement with the extent and direction of the shift of the experimentally detected phase transition point for the confined fluid. 6. Conclusions This study outlines a comprehensive procedure to evaluate the DPP of a gas-condensate system using the isochoric approach (fixed-volume fixed-composition conditions). The design part of the experiment utilizes commercial software, where a novel

Fig. 13. Identifying the change of slope in the isochoric line for bulk and confined fluid mixture (70 mol% C2-30 mol% C5) to determine the phase transition point.

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Fig. 14. Continuous shrinkage of the envelope for a mixture of 70 mol% C2-30 mol% C5 in bulk and confined spaces as a result pore size reduction.

procedure to perform the required calculations is also defined. The proposed method is experimentally verified using a mixture of ethane and pentane. The study also provides a comparison between experimentally detected values and mathematically simulated ones using different equations of state. This comparison of EoS predicted values with the experimental ones, approves the conclusion of earlier theoretical studies in identifying the RK-family as the most accurate equations of state in predicting dew point pressure of gascondensates, especially in the near-critical and retrograde region.

Isochoric experiment is one the most convenient approaches to evaluate fluid phase behavior in the presence of a nanoscale porous medium indirectly. High pressure high temperature resistance of the system alleviates providing reservoir condition for the fluid sample and conducting simultaneous experiments under both confined and bulk conditions assures identical experimental condition for both fluid samples and minimizes experimental errors. Constant volume nature of this experiment along with the possibility of isolating the fluid confined in porous medium from the

Fig. 15. Original phase envelope and modified envelopes using VLE modifications versus experimentally measured isochoric lines.

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bulk fluid are other advantages of this method. The experimental data comparing behavior of pure gases in a decent range of pressures and temperatures for both bulk and confined condition prove that there is change in the properties and behavior of fluid caused by the porous media and pore size effect. Most of the published models in the literature agreed on the effect of confinement on fluid behavior. However, there are discrepancies in measuring the extent of this effect for various gases and different pore sizes using these correlations or models. This study delivers experimental pressure measurements for pure gases (both hydrocarbon and non-hydrocarbon) undergoing the same heating process to evaluate present models and correlations in terms of their accuracy in capturing the level of the change in the behavior of confined fluid. Results show that for the gas mixtures, condensation is nanopores can happen while the pressure and temperature are still above the dew point of the bulk fluid calculated using equations of state. In other words, the locus of the phase envelope for a confined gas condensate system expands over a wider range of pressures and temperatures compared to the locus of the phase envelope of the same system in bulk condition. This disapproves the theory of the reduction of critical properties as a result of pore size reduction, concluded from EoS modifications models. However, this experimental outcome is in agreement with the theorical modified VLE models available in the literature. This work proposes a new methodology that can be used to analyze the phase behavior of different gas and oil mixtures towards achieving an all-inclusive model or correlation to be used for PVT studies in unconventional reservoirs. The effect of nanoconfinement on fluid phase behavior and its long-term impact on reservoir characteristics and production profiles needs further investigations. In order to compare and evaluate available theories and mathematical models with their contradictory predictions of fluid behavior in a systematic way, more experimental work in this area is required. Contribution This work shares the results of Dr. Shadi Salahshoor’s PhD dissertation that was completed under supervision of Dr. Mashhad Fahes (PhD committee’s chair). Declaration of competing interest This work presents the results of the PhD dissertation completed by Dr. Shadi Salahshoor, published in May 2019 at the University of Oklahoma. Parts of this work have been presented in two technical sessions at the SPE conference/meeting over the past two years, once accepted, the release of copyright from SPE will be submitted. This paper a comprehensive collection of all the results and conclusions. We believe that this work will help many scholars to use the proposed methodology to expand this study in the future. Acknowledgement The authors would like to acknowledge Mewbourne School of Geological and Petroleum Engineering for their support to this work. Nomenclature P V T

q

Pressure, bar Volume, cc Temperature, K Contact angle between wetting phase and surface

DPP PG PL Pc Tc Dp

s r

sLJ

15

Dew Point Pressure, bar Vapor pressure Liquid Pressure Critical pressure, bar Critical temperature, K Average pore diameter, nm Interfacial tension Average pore throat radius, nm Lennard-Jones potential parameter

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