Characterization of foam flow in horizontal pipes by using two-flow-regime concept

Chemical Engineering Science 66 (2011) 1536–1549

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Characterization of foam flow in horizontal pipes by using two-flow-regime concept R.N. Gajbhiye, S.I. Kam n Craft and Hawkins Department of Petroleum Engineering, Louisiana State University, Baton Rouge, LA 70803, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 April 2010 Received in revised form 7 December 2010 Accepted 10 December 2010 Available online 21 December 2010

Foam has been widely used in numerous scientific and engineering applications. Although foam has relatively low fluid density because of high gas content, it can exhibit a viscosity value enormously higher – often several orders of magnitude higher – than that of bulk gas or liquid phase. Since foam typically exists as a complex fluid system with internal gas bubbles and external liquid phase, understanding and characterizing its flow behavior is very challenging. The objective of this study is to investigate the characteristics of foam rheology in horizontal pipes in a wide range of experimental conditions—two different pipe materials (stainless steel and nylon pipes with about 0.5 in in outer diameter and 12 ft in length), three surfactant formulations (Cedepal FA-406, Stepanform-1050, and Aquet-944), and three surfactant concentrations (0.1, 0.5, and 5 wt%). The experimental data can be collected in terms of (i) pressure measurements at several positions along the pipes and (ii) visual analysis of bubble size and bubble-size distribution during the shear flow. The concept of ‘‘two foam-flow regimes’’ consisting of high-quality regime and low-quality regime is at the heart of interpreting the experimental outcome. The experimental results showed that there were two distinct high-quality and low-quality foam flow regimes which could be identified by both pressure responses and direct visual observations. The results further showed that the high-quality regime was characterized by unstable and oscillating pressure responses represented by the repetition of fine-textured foam and free gas (i.e., slug flow), while the lowquality regime was characterized by stable pressure responses represented by either the flow of finetextured foams (i.e., plug flow) or the flow of upper-layer foams and lower-layer liquid (i.e., segregated flow). These two regimes, separated by a locus of fng in the contour plot, were shown to have different sensitivities to the change in gas and liquid velocities: (1) foam rheology in the high-quality regime was dependent upon both gas and liquid velocities because the lengths of fine-textured-foam and free-gas sections were altered to adjust to the new flow conditions, and (2) foam rheology in the low-quality regime was primarily dependent upon gas velocity because of the development of fine-textured foams with increase in shear rates, and was relatively independent of liquid velocity because of lubricating effect and drainage effect. The implication of these experimental findings is discussed for applications such as foam-assisted underbalanced drilling processes and foam fracturing treatments in the petroleum industry. & 2010 Elsevier Ltd. All rights reserved.

Keywords: Foam Rheology Characterization Two flow regimes Underbalanced drilling Foam fracturing

1. Introduction Foam has been considered as an important and useful means in many engineering disciplines. When properly managed and designed, foam treatments can take great advantage of its high viscosity with low density, high solids-carrying capacity, and minimum filtrate and circulation losses. Many of these features are strongly desired in drilling and fracturing operations in petroleum industry, by transporting rock cuttings and proppants

n

Corresponding author. Tel.: + 1 225 578 5216; fax: + 1 225 578 6039. E-mail address: [email protected] (S.I. Kam).

0009-2509/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2010.12.012

effectively and minimizing the formation damage with reduced amount of aqueous phase (Bonilla and Shah, 2000; Schramm, 1994; Affonso et al., 2004; Capo et al., 2006). Surfactant foams are also popular in reservoir applications, not only in small-scale nearwellbore production enhancement but also in large-scale mobility control and sweep-efficiency improvement (Patton et al., 1983; Kovscek et al., 1995; Rossen et al., 1999; Lakatos et al., 2003; Li et al., 2008; Kam, 2008). Previous foam studies show that achieving and maintaining desired foam properties such as foam texture, foam viscosity, solid-carrying capability, and so on is often quite challenging, and furthermore the results at certain test conditions may not be easily translated into different conditions when it comes to up-scaling and down-scaling issues.

R.N. Gajbhiye, S.I. Kam / Chemical Engineering Science 66 (2011) 1536–1549

Foam is a dispersion of gas bubbles in a surfactant-laden liquid phase. Bulk-foam rheology in pipes is shown to be very complicated and strongly influenced by numerous parameters including temperature, pressure, foam quality (i.e., gas fraction), foam texture (i.e., bubble size), fluid–wall interactions, external liquidphase properties, and type and concentration of the surfactants (Heller and Kuntamukkula, 1987; Bonilla and Shah, 2000). Other additives such as guars, polymers, and gels are often formulated together to endow foams with better stability and higher viscosity (Reidenbach et al., 1986; Harris and Heath, 1996a, 1996b; Sani and Shah, 2001; Khade and Shah, 2004; Hutchins and Miller, 2005). The presence of solids often requires an additional level of complications for modeling bulk foam stability and rheology (Kam and Rossen, 1999, 2002; Kam et al., 2002). As observed by Patton et al. (1983), it is typical that foam viscosity can be of several orders of magnitude greater than the viscosity of external liquid phase. Efforts have been made to model the rheological properties of foams for decades, mostly using different types of fluid models. Many of those studies show that foam viscosity decreases with increasing shear rate, which is the conventional behavior of Ostwald-de Waele pseudo-plastic fluid (Raza and Marsden, 1967; David and Marsden, 1969; Sanghani and Ikoku, 1983). This allows foam rheology to be modeled by a two-parameter equation, well known as the power-law model (Despande and Barigou, 2000). Other studies such as Mitchell (1969), Blauer et al. (1974), and Calvert and Nezhati (1986) report a noticeable magnitude of yield stress and describe foam rheology using a yield stress and a plastic viscosity, so-called the Binghamplastic model. Putting these two models together, it is possible to come up with a general three-parameter model, known as the Hershel–Bulkley model, as suggested by Saintpere et al. (1999) from their foam study for underbalanced drilling. No matter which foam models are used, it is certain that foam viscosity is strongly affected by foam quality and texture. Previous experiments with increasing foam quality at a fixed total injection velocity show that there are two threshold values of foam quality (fg), fgth1 and fgth2, as shown in Fig. 1, which can distinguish different types of foam flow characteristics (David and Marsden, 1969; Blauer et al., 1974; Harris and Heath, 1996a, 1996b; Briceno and Joseph, 2003): (1) for fg ofgth1, apparent foam viscosity (mapp) does not change significantly but increases with foam quality (fg) gradually; (2) for fgth1 ofg ofgth2, the viscosity increases dramatically with foam quality, reaching its maximum at fg ¼ fgth2; and

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(3) for fg 4fgth2, foam viscosity declines rapidly with foam quality. Making a distinction between these three cases is primarily based on how actively bubbles interact and how stable foam films are during shear flow. Although foam rheology in presence of other chemical agents such as polymers and gels is much more complicated, it still seems to follow this basic trend reasonably well (Harris and Heath, 1996a, 1996b; Bonilla and Shah, 2000). The rheology of bulk foams can be even more complicated because: (i) foam mixture is not typically moving at the same velocity with the liquid accumulated at the bottom or at the wall of the flow conduit, and (ii) those bubbles within foam mixture may not be necessarily moving together as a single homogeneous phase. These additional complexities are reported by Briceno and Joseph (2003) and Peysson and Herzhaft (2008) using the concept of lubrication effect and drainage effect. Following two steady-state strong-foam regimes in porous media first observed by Osterloh and Jante (1992) and further developed by Alvarez et al. (2001), Rossen and Wang (1999), and Kam (2008). Bogdanovich et al. (2009) recently conducted flow experiments in 0.5-in and 1-in diameter pipes by using five different types of surfactants in order to investigate foam rheology in pipes, and proposed a new way to report and represent foam rheology in pipes by plotting the contours of resulting steady-state pressure drops as a function of both liquid and gas velocities on x and y axes. The contour plots exhibited two distinct regimes, so-called high-quality and low-quality regimes, separated by a threshold foam quality denoted by fng. They conjectured that the two different flow regimes based on the pressure measurements resulted from different flow patterns depending on foam quality and total velocity. The boundary between the high-quality and the low-quality regimes (fng) in their study in fact coincides with fgth2 in Fig. 1. In continuation with Bogdanovic et al. (2009), this study aims to investigate the rheological properties of foams in horizontal pipes within the context of two-flow-regime concept. Special emphases are placed on the visualization experiments which allow foam flow to be characterized by the visual images of foam texture and bubble size distribution in flow conduits during foam flow. The implications of the presence of two flow regimes in actual foam filed applications are also discussed in terms of the optimal design of foam-assisted underbalanced drilling processes and foam fracturing treatments.

2. Methods 2.1. Experimental set-up and materials

fgth2 Apparent foam viscosity, μapp

Low quality regime

High quality regime

An apparatus to inject nitrogen gas and surfactant solutions into a pipe was set up as schematically shown in Fig. 2. The surfactant solution with a pre-specified surfactant concentration stored in a

fgth1 Dramatic increase in μapp

Dramatic reduction in μapp

Moderate increase in μapp

Foam quality, fg (gas fraction) Fig. 1. A schematic showing changes in apparent foam viscosity (mapp) as a function of foam quality at fixed total injection velocity: (1) for fg o fgth1, foam viscosity gradually increases with foam quality; (2) for fgth1 ofg ofgth2, the viscosity increases dramatically with foam quality reaching its maximum at fg ¼fgth2; and (3) for fg 4 fgth2, foam viscosity declines rapidly with foam quality.

Fig. 2. Experimental set-up for foam flow in horizontal pipe in this study.

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beaker was pumped into the pipe by using Optos 3HM pump (Eldex, CA) which had the flow rate range of 0.04–80 cm3/min (or, 6.66  10  9–1.33  10  6 m3/s). A high-pressure (2500 psi) nitrogen gas cylinder supplied the gas phase, which was regulated by a 5850E Brooks mass flow controller (Brooks Instruments, PA). Predetermined gas and liquid surfactant flow rates were then applied and maintained until the flow was believed to reach a steady state. A visual cell was placed upstream of the pipe so that one could examine the mixture of gas and liquid before entering the pipe. A filter with 50- or 90-mm opening size was installed upstream of the visual cell in order to artificially create fine-textured foams for testing purpose if needed, but the filter was bypassed in all experiments reported here. Two different pipe materials were used in the experiments: one with stainless steel and the other with nylon. The stainless steel pipe was 11.94 ft (or, 3.63 m) in length and 0.36/0.5 in (or 0.0091/ 0.012 m) in inner/outer diameter, and the nylon pipe was 12.58 ft (or, 3.83 m) in length and 0.38/0.5 in (or 0.0096/0.012 m) in inner/ outer diameter. The nylon pipe was transparent so that one could see through the pipe to investigate flow patterns and bubble size distribution. Eight Omega pressure transducers (Omegadyne Inc., OH) were installed to measure the sectional pressure drops along the pipe. These pressure transducers, named port A–port H, were roughly equally spaced – about 20.47 in (or, 0.51 m) and 21 in (or, 0.53 m) apart from each other for stainless steel and nylon pipes, respectively – with the first one installed right after the inlet of the pipe, the last one installed right before the end of the pipe, and six others installed in between. The measured pressure data from the transducers were transmitted to the data gathering system on a real-time basis. The fluids were collected and disposed at the outlet of the pipe. For the experiments with a nylon pipe, the flow was photographed and videotaped near the outlet. The tubing upstream of the pipe was constituted with 1/8 and 1/4 in inner and outer diameters, respectively. Three different surfactants were used in the flow experiments— Cedepal FA-406 (Stepan, IL), Stepanform-1050 (Stepan, IL), and Aquet-944 (Baker Petrolite, TX). They were anionic surfactants typically used in drilling and fracturing applications in petroleum industry. 2.2. Procedure The flow experiments were carried out by following the steps described below: (1) Prepare a surfactant solution of desired formulation, concentration, and quantity. The concentration of surfactant solution in this study is expressed in percent of total weight (wt%). (2) Inject the surfactant solution first at a pre-specified value until the solution is produced at the outlet. (3) Inject nitrogen gas at a pre-specified value using a gas mass flow controller. (4) Make sure from the visual cell installed upstream of pipes that the mixture of gas and surfactant solutions flows into the pipe together as intended. (5) Activate the data acquisition system (this step can be placed before step 2), and continue to inject gas and surfactant solutions at pre-specified values until the pressure response reaches a steady state. For the range of injection velocities applied in this study, a steady state can be commonly achieved within several to ten minutes. Most of the experiments in this study were carried out at one fixed value of liquid velocity, either monotonically increasing or decreasing gas velocity step by step. The nominal liquid velocities

were 0.017, 0.033, 0.050, and 0.067 ft/s (i.e., 20, 40, 60, and 80 cm3/min, or 3.3  10  7, 6.66  10  7, 10  10  7, and 1.33  10  6 m3/s, respectively) with gas velocity ranging from 0.082 to 3.590 ft/s (i.e., 100– 5,000 cm3/min, or 1.66  10  6–8.33  10  5 m3/s at standard conditions) for 0.36-in inner diameter stainless-steel pipes. 2.3. Data analysis The pressure data obtained from the experiments on a real-time basis can be time-averaged when the steady-state condition is reached. These pressure values are used to determine the sectional pressure drops, which then can be translated into the apparent foam viscosities (mapp). The contour plots can be constructed based on either the pressure drop or the apparent viscosity. For foam flow with gas and surfactant solutions injected together, the total flow rate (Qt) is simply the addition of gas flow rate (Qg) and liquid flow rate (Qw), i.e., Qt ¼ Qw þ Qg

ð1Þ

which is essentially the same as the following equation using the superficial velocities: ut ¼ uw þ ug

ð2Þ

where ut, uw and ug are the total, liquid, and gas superficial velocities, respectively. Note that the superficial velocity of phase j (uj) is defined as the flow rate of the phase (Qj) divided by the cross-sectional area (A) of the pipe, i.e., uj ¼Qj/A, where A¼(pd2)/4, with d being the inner diameter. The shear stress at the wall, if the flow conduit is cylindrical, can be expressed by   dDp ð3Þ tw ¼ 3 L where tw is the wall shear stress [lbf/ft2], Dp is the pressure drop [psi], and d and L are the diameter and length of the corresponding pipe segment [ft], respectively. The shear rate for the flow in pipe is given by   Q gw ¼ 39:216 3t , ð4Þ d where, gw is the wall shear rate [s  1], Qt is the total flow rate [gal/min], and d is the pipe inner diameter [in]. The apparent foam viscosity is then calculated as follows:   t mapp ¼ 47,880 w ð5Þ

gw

where mapp is the apparent foam viscosity [cp], tw is the shear stress [lbf/ft2], and gw is the wall shear rate [s  1]. 3. Results and discussions We first measured two basic fluid properties, density of surfactant solution and interfacial tension of air/surfactant system, as summarized in Table 1. Interfacial tension was measured by pendant drop method (Adamson, 1976) which analyzes the shape of liquid droplets. This information can be used to infer the critical micelle concentration (CMC) of each surfactant. Table 2 shows the list of 9 different series of experiments conducted in this study (Base case and Cases 1–8) which are described more in detail in the following sections. 3.1. Experiments in stainless-steel pipes (0.36/0.5 in ID/OD): base case and Cases 1–4 3.1.1. Base case In our preliminary surfactant-screening phase, a foam stability test in which the decay in bulk foam height is measured as a

R.N. Gajbhiye, S.I. Kam / Chemical Engineering Science 66 (2011) 1536–1549

Table 1 Density and surface tension of surfactant samples. Surfactant

Surfactant conc. (wt%)

Density (g/cm3)

Surface tension (dyne/cm)

Cedepal FA-406 Cedepal FA-406 Cedepal FA-406 Stepanform-1050 Stepanform-1050 Aquet-944 Aquet-944 Aquet-944

0.1 0.5 5 0.1 0.5 0.1 0.5 5

0.9963 0.9979 1.004 0.9977 0.9981 0.9979 0.9979 0.999

59.73 40.36 37.91 36.40 37.42 35.19 35.45 34.60

Table 2 Nine different cases examined in this study. Cases

Pipe size and material

Surfactant type and concentration

Base case 1 2 3 4 5 6 7 8

OD OD OD OD OD OD OD OD OD

Cedepal FA-406, 0.5 wt% Cedepal FA-406, 0.1 wt% Cedepal FA-406, 5.0 wt% Stepanform-1050, 0.5 wt% Stepanform-1050, 0.1 wt% Cedepal FA-406, 0.5 wt% Aquet-944, 5 wt% Aquet-944, 0.5 wt% Aquet-944, 0.1 wt%

0.5 in 0.5 in 0.5 in 0.5 in 0.5 in 0.5 in 0.5 in 0.5 in 0.5 in

stainless steel stainless steel stainless steel stainless steel stainless steel Nylon 6 transparent Nylon 6 transparent Nylon 6 transparent Nylon 6 transparent

function of time is performed for different types of surfactants available from a range of manufacturers. Stepan FA-406, among many, is selected as a base-case surfactant, because of its superior stability when the surfactant concentration of 0.5 wt%, a typical value in many field treatments, is tried. As shown in Fig. 3 with the base-case flow experiments (i.e., 0.5 wt% Stepan FA-406 surfactant), the pressure response is collected by changing superficial gas velocity (ug) step by step in all pressure ports from A–H at fixed superficial liquid velocities (uw). Figs. 3(a)–(d) show the results at four superficial liquid velocities such as 0.017 ft/s (0.0051 m/s), 0.033 ft/s (0.010 m/s), 0.050 ft/s (0.015 m/s), and 0.067 ft/s (0.020 m/s), corresponding to liquid flow rates of 20, 40, 60, and 80 cm3/min (or 3.3  10  7, 6.66  10  7, 10  10  7, and 1.33  10  6 m3/s, equivalently). For example, when the liquid velocity (uw) is at 0.017 ft/s (or, Qw ¼20 cm3/min) in Fig. 3(a), the experiment starts with gas velocity (ug) of 0.083 ft/s (or, Qg ¼100 cc/min) which essentially increases to 3.312 ft/s (or, Qg ¼4000 cc/min) step by step, and then reduce back down to 0.083 ft/s (or, Qg ¼100 cc/min) again. The steady-state pressure value increases dramatically until it reaches a maximum at the gas velocity of 1.243 ft/s (or, Qg ¼1500 cc/min), followed by a rapid reduction at higher gas velocity (or higher foam quality). The entire plot with two pressure humps seems symmetric and mirrorimaged, meaning that there is no hysteresis involved in this process. It should be mentioned that the pressure response at higher foam quality is relatively unstable and oscillating, and the pressure response at lower foam quality is relatively stable. This feature is explained more in visualization experiments later. These pressure data provided in Fig. 3(a)–(d) can be used to obtain the sectional pressure drops exerted by foams and be translated into the apparent foam viscosities. The pressure values measured at the first and last pressure ports (i.e., port A and port H) are not taken into consideration in the analysis due to possible inlet and outlet effects. As a result, the pressure drop between port B and port G (DpBG) is used for interpretation. (Note that the notation DpIJ represents the pressure difference between pressure ports I and J, therefore, DpBG ¼pB  pG.) After looking into the pressure data, we believe that DpBG truly

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represents the pressure response of the entire system, because the injected foams adjust its texture quite rapidly to reach the steady-state texture and the same texture and flow patterns are typically maintained within the length scale of the pipes in this study, as observed in the pressure measurements and visual images. Fig. 4(a) summarizes the values of DpBG shown in Fig. 3(a)–(d) in a wide range of gas and liquid velocities as a function of adjusted superficial gas velocity (ug,adj), that is, the superficial gas velocity (ug) adjusted at the average pressure within the pipe (i.e., (pB +pG)/2). At each given liquid velocity, there is a pair of DpBG values reported—one outbound (i.e., increasing gas velocity) symbolized by filled marks and the other inbound (i.e., decreasing gas velocity) symbolized by open marks. The same DpBG plot is constructed as a function of foam quality in Fig. 4(b). Fig. 4(a) and (b) show that: (1) there is a threshold value of gas velocity (ug) or foam quality (fg) below which the pressure drop (DpBG) monotonically increases with increasing ug or fg, and above which the pressure drop (DpBG) monotonically decreases with increasing ug or fg, and (2) the magnitude of pressure drop (DpBG) increases as total velocity (ut) increases at the same foam quality. It is of paramount importance in many applications to estimate or predict the value of fng, which is, the fg at which the peak in pressure drop (DpBG) takes place. Note that the results in Fig. 4(b) shows that the value of fng decreases with increasing liquid velocity, which is further discussed with pressure contours in later sections. The pressure data in Fig. 4(a) and (b) can be converted into apparent foam viscosity, shear stress, and shear rate by using Eqs. (3)–(5) as shown in Fig. 5: Fig. 5(a) with the shear stress (tw) as a function of the wall shear rate (gw), and Fig. 5(b) with the apparent viscosity (mapp) as a function of the wall shear rate (gw) or foam quality (fg). These pressure data and calculated apparent viscosity values can be plotted in a form of contours as shown in Fig. 6(a) and (b), respectively, with liquid velocity on x axis and gas velocity on y axis. The boxed numbers in Fig. 6(a) are the measured pressure drop in [psi] from DpBG over 8.58-ft distance between pressure ports B and G, and the boxed numbers in Fig. 6(b) are the corresponding apparent viscosity in [cp]. As shown by Figs. 3–5, the fng at which the peak in DpBG or mapp occurs splits the entire domain into two pieces so-called high-quality regime and low-quality regime. These contour plots show that: (1) in the low-quality regime, DpBG and mapp are relatively independent of liquid velocity but sensitive to gas velocity, exhibiting the contours almost horizontal, and (2) in the high-quality regime, DpBG and mapp decrease with gas velocity at fixed liquid velocity, exhibiting the contours with finite slopes. These two distinct regimes are caused by different foam-flow characteristics and patterns, which are further explained in the later visual experiment section. As pointed out in Fig. 4(b), fng is not a constant. Rather, the locus bends concavely as liquid velocity increases. One may wonder why the response in terms of mapp somewhat different from that in terms of DpBG, by comparing Figs. 4(b) and 5(b), or Fig. 6(a) and (b). It is because of the finite number of the data points obtained from the experiments. The shape of these plots would be identical, if an infinite number of pressure data points were available.

3.1.2. Effect of surfactant concentrations (Cases 1 and 2) Flow experiments similar to the base case are repeated at two other surfactant concentrations such as 0.1 and 5 wt%, referred to as Cases 1 and 2, respectively. Other conditions are kept identical to the base case by using 0.5-inch OD stainless-steel pipe at the same four liquid velocities (uw) such as 0.017 ft/s (0.0051 m/s), 0.033 ft/s (0.010 m/s), 0.050 ft/s (0.015 m/s), and 0.067 ft/s (0.020 m/s), corresponding to liquid flow rates of 20, 40, 60, and 80 cm3/min (or 3.3  10  7, 6.66  10  7, 10  10  7, and 1.33  10  6 m3/s,

R.N. Gajbhiye, S.I. Kam / Chemical Engineering Science 66 (2011) 1536–1549

a

Base Case (SS pipe, 0.5"OD, FA-406, 0.5 weight% concentration) 11.7

Press A Press B Press C Press D Press E Press F Press G Press H

Pressure (psi)

9.7 7.7 5.7

c

Base Case (SS pipe, 0.5" OD, FA-406, 0.5 weight% concentration) 29.7

19.7 14.7

3.7

9.7

1.7

4.7

-0.3

-0.3 Time (sec) Base Case (SS pipe, 0.5" OD, FA-406, 0.5 weight% concentration)

29.7

Press A Press B Press C Press D Press E Press F Press G Press H

24.7

Pressure (psi)

Time (sec)

19.7 14.7

d

Base Case (SS pipe, 0.5" OD, FA-406, 0.5 weight% concentration) 29.7

19.7 14.7

9.7

9.7

4.7

4.7

-0.3

-0.3 Time (sec)

Press A Press B Press C Press D Press E Press F Press G Press H

24.7

Pressure (psi)

b

Press A Press B Press C Press D Press E Press F Press G Press H

24.7

Pressure (psi)

1540

Time (sec)

Fig. 3. Pressure response of base case (0.5 wt% FA-406, 0.36/0.5 in ID/OD stainless-steel pipe) at fixed liquid injection rate of (a) 20 cm3/min, (b) 40 cm3/min, (c) 60 cm3/min, and (d) 80 cm3/min. Gas injection rate was first raised from 100 to 4000 cm3/min step by step, and then reduced back to 100 cm3/min. Note that the injection flow rate of 100 cm3/min corresponds to the superficial velocity of 0.083 ft/s or 0.0253 m/s.

equivalently). The overall pressure responses at different surfactant concentrations are comparable with those in Fig. 3 of the base case: the trend shows that, at fixed liquid velocity, the pressure increases monotonically with increasing gas velocity up to fng, then decreases monotonically with increasing gas velocity beyond that. Fig. 7(a) and (b) show the contours of pressure response and apparent viscosity, respectively, when 0.1 wt% FA-406 surfactant solution is applied in Case 1. Note that these figures can be contrasted with Fig. 6(a) and (b) of the base case. The results show that the peak in pressure drop between ports B and G (DpBG) and the peak in resulting apparent viscosity (mapp) take place at lower foam quality. The overall magnitudes of DpBG and mapp are also lower than those of the base case. Fig. 8(a) and (b), which can be compared with Fig. 7(a) and (b), show the pressure and apparent viscosity with 5 wt% FA-406 surfactant solution in Case 2. The peaks in DpBG and mapp translate towards higher foam quality, and their magnitudes are higher compared with 0.1 or 0.5 wt% FA-406 in Case 1 or the base case. By putting the contours of 0.1, 0.5, and 5 wt% concentrations together, it can be noticed that an increase in surfactant concentration improves foam stability to make the measured pressure drop higher. As a result, the transition from low-quality to high-quality regime (i.e., fng) occurs at higher foam quality as surfactant concentration increases. In all three concentrations, the curves connecting fng values are concave in the contour plots, meaning that the transition from low-quality to high-quality regime takes place at lower foam quality as liquid velocity increases. It can be generally said that the high-quality regime expands (or the low-quality regime contracts) as foam becomes less stable with lower surfactant concentration, which is similar to what Alvarez et al. (2001) observed.

3.1.3. Effect of surfactant formulations (Cases 3 and 4) The same flow experiments, called Case 3 and Case 4, are carried out by using another anionic surfactant, Stepanform-1050 (Stepan, IL), at two different concentrations of 0.5 and 0.1 wt%, respectively. Laboratory foam stability tests show that the stability of Stepanform-1050 is comparable with that of FA-406 at the same surfactant concentrations. Fig. 9(a) and (b) show the contours of pressure and apparent viscosity of Case 3 with 0.5 wt% Stepanform-1050 surfactant solution. Note that these figures can be contrasted with Fig. 6(a) and (b) in which the same concentration of FA-406 is used. Likewise, Fig. 10(a) and (b) show the results of Case 4 with 0.1 wt% Stepanform-1050 surfactant, which can be contrasted with Fig. 7(a) and (b). As expected from the bulk foam stability tests, the peak values of DpBG and mapp, together with fng at which these peaks take place, are similar. 3.2. Experiments in transparent nylon pipes (0.38 in ID and 0.5 in OD): Cases 5–8 In order to characterize foam flow in pipe visually, the same experiments can be repeated in a see-through transparent pipe made of Nylon 6 (McMaster, GA). Note that the dimension of the nylon pipe is roughly the same as that of the stainless steel pipe. 3.2.1. Flow experiments with FA-406 (Case 5) Fig. 11(a) and (b) show the contours of pressure and apparent viscosity in Case 5 with 0.5 wt% FA-406 in a nylon pipe, which can be contrasted with those in a stainless steel pipe (cf., Fig. 6(a) and (b)). Although the magnitudes of DpBG and mapp are slightly larger

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τw, [lbf/ft2]

ΔPBG, (PB - PG), [ psi ]

R.N. Gajbhiye, S.I. Kam / Chemical Engineering Science 66 (2011) 1536–1549

γw, [sec-1]

μapp, [cp]

ΔPBG, (PB - PG), [ psi ]

ug (adjusted), [ft/sec]

γw, [sec-1] Foam quality

Foam quality Fig. 4. Base case pressure response as a function of (a) gas velocity and (b) foam quality at four different liquid velocities (0.5 wt% FA-406, 0.36/0.5 in ID/OD stainless-steel pipe).

with the nylon pipe, the results in these two different types of pipes are comparable.

3.2.2. Flow experiments with Aquet-944 surfactants (Cases 6–8) Another anionic surfactant, Aquet-944 (Baker Petrolite, TX), is tried for flow experiments in the nylon pipe: Fig. 12(a) and (b) are the results for 5 wt% in Case 6; Fig. 13(a) and (b) are the results for 0.5 wt% in Case 7; and Fig. 14(a) and (b) are the results for 0.1 wt% Aquet-944 surfactants. The effect of surfactant concentration discussed in earlier sections is still applicable: (1) the steady-state pressure drop and the apparent viscosity increase with increasing surfactant concentration; and (2) the transition from low-quality regime to high-quality regime takes place at lower foam quality as surfactant concentration decreases, which causes growing highquality regime (or shrinking low-quality regime, equivalently) with decreasing surfactant concentration.

3.3. Visual observations from nylon pipe experiments (0.38 in ID and 0.5 in OD) The visual analyses using the transparent nylon pipe are conducted with FA-406 (0.5 wt% as in Case 5) and Aquet-944 (0.5 wt% in Case 7 and 0.1 wt% in Case 8). The flow characteristics such as bubble size and bubble size distribution provide the basis for the characterization of foam flow. The observation through the transparent nylon pipe can be made anywhere from the inlet to the outlet, but the photos and movies are taken at about 1 ft upstream of the outlet, where the foam texture is believed to be fully matured and developed.

Fig. 5. Base case (a) shear stress as a function of shear rate and (b) foam viscosity as a function of foam quality and shear rate at four different liquid velocities (0.5 wt% FA406, 0.36/0.5 in ID/OD stainless-steel pipe).

Fig. 15 shows the results with 0.5 wt% FA-406 surfactant in a wide range of gas and liquid velocities (cf. Fig. 11). There are a few important characteristics to be noted: (1) the high-quality regime exhibits the pattern of slug flow in which fine-textured-foam sections and free-gas sections repeat and alternate each other. This alternating nature of slug flow is reflected by oscillating pressure measurements as shown in earlier figures (cf. Fig. 3) (Note that the free-gas section may sometimes look like a gas phase with large bubbles (or, very coarse foam), and in that case the slug flow consists of a repetition of a fine-textured-foam section followed by a coarse-textured-foam section); (2) the low-quality regime exhibits two different patterns—(i) a plug flow of homogeneous foams when fg is relatively high and (ii) a segregated flow in which the liquid phase is accumulated and flows in the lower section of the pipe and the foam flows in the upper section of the pipe when fg is relatively low. Gas bubbles and liquid migrate roughly at the same velocity forming a plug flow in the former, while bubbles and liquids are segregated with the upper foam layer traveling slower than the lower liquid layer in the latter. In both cases, the pressure response was relatively stable without showing the oscillations in pressure (cf. Fig. 3); and (3) the fng values that split the entire domain into two regimes roughly correspond to the transition between the plug flow in the low-quality regime and the slug flow in the highquality regime. This explains why the maximum pressure gradient or the maximum apparent viscosity occurs near fng. In order to better understand the behavior of slug flow in the highquality regime, further experiments are performed with injection conditions within the high-quality regime only. Fig. 16(a) and (b) show the analysis in terms of the sizes of free-gas section and finetextured-foam section, respectively. Again, note that the term ‘‘free gas’’ in the high-quality regime represents a state in which no bubbles, or

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Fig. 6. (a) Pressure contours and (b) apparent viscosity contours of Base Case with liquid velocity on x axis and gas velocity on y axis (0.5 wt% FA-406, 0.36/0.5 in ID/OD stainless-steel pipe). Pressure drops are in [psi] and viscosities are in [cp].

Fig. 7. (a) Pressure contours and (b) apparent viscosity contours of Case 1 with liquid velocity on x axis and gas velocity on y axis (0.1 wt% FA-406, 0.36/0.5 in ID/OD stainless-steel pipe). Pressure drops are in [psi] and viscosities are in [cp].

very coarse-textured foams, are present. Fig. 16(a) shows that: (1) an increase in liquid velocity at the same gas velocity causes the size of free-gas section to decrease, and (2) an increase in gas velocity at the same liquid velocity causes the size of free-gas section to increase. This implies that any change in injection conditions which leads to drier foams (or, higher foam quality) stretches the size of free-gas section. Similarly, Fig. 16(b) shows that: (1) an increase in liquid velocity at the same gas velocity causes the size of fine-textured-foam section to increase, and (2) an increase in gas velocity at the same liquid velocity causes the size of fine-textured-foam section to decrease. This implies that any change in injection conditions which leads to drier foams (or, higher foam quality) reduces the size of fine-textured-foam section. It can be inferred that at extremely dry flow conditions, the fine-textured-foam section ultimately disappears leaving only free gas flow, which is consistent with mist flow that other experimental studies observed (Martins et al., 2001). A visualization experiment similar to Fig. 15 is repeated with Aquet-944 at 0.5 and 0.1 wt% concentrations (cf. Cases 7 and 8,

respectively). Although the results are not shown here, the general responses are in good agreement with those observed in Fig. 15 with 0.5 wt% FA-406. The results of visual experiments in Figs. 15 and 16 can be summarized as shown by the schematic figure in Fig. 17. Two regimes are separated by the locus of fng above which free gas and fine-textured foam alternate each other, and below which homogeneous foams flow by forming either plug flow or segregated flow. The low-quality regime can be roughly subdivided into four sections depending on total injection velocity and foam quality: (1) relatively high total velocity and high foam quality (the region denoted by ‘‘(A)’’) in which the mixture forms plug flow of fine-textured foams; (2) relatively high total velocity and low foam quality (the region denoted by ‘‘(B)’’) in which the mixture forms segregated flow of fine-textured foams and underlying liquid; (3) relatively low total velocity and high foam quality (the region denoted by ‘‘(C)’’) in which the mixture forms plug flow of foams but with less finer texture than foams in region (A); and (4) relatively low total velocity and low foam quality (the region denoted by ‘‘(D)’’) in

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Fig. 8. (a) Pressure contours and (b) apparent viscosity contours of Case 2 with liquid velocity on x axis and gas velocity on y axis (5 wt% FA-406, 0.36/0.5 in ID/OD stainless-steel pipe). Pressure drops are in [psi] and viscosities are in [cp].

which the mixture forms segregated flow again, the foams in the upper layer with less finer texture than foams in region (B). The distinction between the two regions of high total velocity ((A) and (B)) and low total velocity ((C) and (D)) (i.e., (A) vs. (C), or (B) vs, (D)) can be described by the change in bubble size as a function of injection velocity. At fixed foam quality, there is a threshold value of total velocity below which the texture becomes finer with increasing total velocity, and above which foam texture does not change significantly. The distinction between the two regions of plug flow ((A) and (C)) and segregated flow ((B) and (D)) (i.e., (A) vs. (B), or (C) vs, (D)) can be described by using the observation of effluent history, which is, gas and liquid fractions at the effluent are roughly the same as injection fractions during plug flow, while liquid fraction at the effluent is much higher than injection liquid fraction during segregated flow. The fact that the steady-state pressure drop in the low-quality regime is

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Fig. 9. (a) Pressure contours and (b) apparent viscosity contours of Case 3 with liquid velocity on x axis and gas velocity on y axis (0.5 wt% Stepanform-1050, 0.36/ 0.5 in ID/OD stainless-steel pipe). Pressure drops are in [psi] and viscosities are in [cp].

insensitive to liquid velocity (or, the pressure contours are relatively horizontal in the low-quality regime, equivalently) can be explained by ‘‘lubricating effect’’ or ‘‘drainage effect’’ (Weissman and Clavert, 1967; Joseph et al., 1999; Briceno and Joseph, 2003)—in case of plug flow, the increase in liquid velocity causes foam films to be thickening, which in turn reduces the friction between bubbles or the friction between bubbles and walls without affecting the pressure drop significantly (i.e., lubricating effect); on the other hand, in case of segregated flow, the increase in liquid velocity causes the level of liquid accumulated at the bottom to move upward, which results in the increase of liquid fraction trapped in pipe without affecting the pressure drop significantly (i.e., drainage effect). Further about the drainage effect in segregated flow, it is observed that the thickness of the lower liquid layer increases with increasing liquid velocity at fixed gas velocity, as sketched in

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Fig. 10. (a) Pressure contours and (b) apparent viscosity contours of Case 4 with liquid velocity on x axis and gas velocity on y axis (0.1 wt% Stepanform-1050, 0.36/ 0.5 in ID/OD stainless-steel pipe). Pressure drops are in [psi] and viscosities are in [cp].

the three figures at the bottom of Fig. 17. In contrast, an increase in gas velocity at fixed liquid velocity leads to the reduction in the thickness of the lower liquid layer, ultimately getting rid of liquid layer accumulated at the bottom of the pipe beyond a certain value of gas velocity. The fraction of gas and liquid phases accumulated in the pipe is constantly changing depending on injection quality and total injection velocity (and thus foam texture), which is very similar to the relative permeability effect that describes why the low-quality regime of strong foams in porous media is relatively insensitive to liquid velocity as investigated by Rossen and Wang (1999) and implied by others (Osterloh and Jante, 1992; Alvarez et al., 2001; Dholkawala et al., 2007; Kam, 2008). Fig. 17 also explains why the two regimes have different sensitivity to gas and liquid velocities. As shown in the contour plots, the contours in the high-quality regime have finite slopes because an increase in

Fig. 11. (a) Pressure contours and (b) apparent viscosity contours of Case 5 with liquid velocity on x axis and gas velocity on y axis (0.5 wt% FA-406, 0.38/0.5 in ID/OD nylon pipe). Pressure drops are in [psi] and viscosities are in [cp].

liquid velocity (which results in increasing fine-textured-foam section) can be compensated by an increase in gas velocity (which results in increasing free-gas section). Put it differently, any change in injection conditions which makes foams drier is expected to elongate the freegas section, causing a reduction in pressure drop, while any change in injection conditions which makes foams wetter is expected to elongate the fine-textured-foam section, causing an increase in the pressure drop.

3.4. Implications in field applications Fig. 18 depicts how this two-flow-regime concept can improve modeling and simulation of foam-assisted underbalanced drilling operations in which the process experiences a significant change in pressure and temperature in addition to the influx of foreign fluids into the wellbore. For example, during foam flow inside drill pipe

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Fig. 12. (a) Pressure contours and (b) apparent viscosity contours of Case 6 with liquid velocity on x axis and gas velocity on y axis (5 wt% Aquet-944, 0.38/0.5 in ID/ OD nylon pipe). Pressure drops are in [psi] and viscosities are in [cp].

and within annulus, gas phase expands and shrinks considerably, forcing flow conditions to move across the fng boundary between the two regimes. In addition, intrusion of formation fluids can play a significant role too: formation brine may dilute surfactant solution by reducing surfactant concentration; reservoir oils entering bottom hole can destabilize foam mixture, and reduce effective foam viscosity and solid carrying capability; and gas influx may increase gas fraction of the mixture along the annulus. All these events tend to shift the locus of fng downward, increasing the possibility of the system moving into the high-quality regime. Also the fact that the locus of fng is curved concavely means that it is easier to obtain the high-quality regime as liquid velocity increases, which is obviously a factor to be considered in field applications. Fig. 18 also provides good insights into applications such as foam fracturing treatments in which maximizing the capability of solid transport is a key to the process. Because it is the interface between gas and liquid which effectively captures and mobilizes

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Fig. 13. (a) Pressure contours and (b) apparent viscosity contours of Case 7 with liquid velocity on x axis and gas velocity on y axis (0.5 wt% Aquet-944, 0.38/0.5 in ID/ OD nylon pipe). Pressure drops are in [psi] and viscosities are in [cp].

solids, the optimum injection condition should be maintained such that the flow of foam mixture stays within the plug-flow region (cf., Fig. 17) in which solid-transport efficiency is maximized by fine-textured foams. It is believed that this optimum condition can be pre-determined from laboratory flow experiments similar to those shown in this study prior to actual field treatments. Any deviation from the plug-flow region is expected to undermine the ability of foams as a solid carrier. How to implement two-flow regime concept developed in this study is obviously a very fieldspecific and application-specific task which we leave as future study.

3.5. Discussions on foams in porous media vs. foams in pipes Although the concept of two steady-state flow regimes is originated from foam studies in porous media, this study reveals

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Slug flow pattern

Qg (cc/min)

4000

Highquality regime

2000

500

Lowquality regime

100 Plug or Segregated flow pattern 20

40

60

Qw (cc/min) Fig. 15. Results from Case 5 visualization analysis near the outlet (i.e., about 1 ft upstream from the outlet) for 0.5 wt% FA-406 surfactant in a wide range of gas and liquid velocities.

Qg (cc/min)

2000

1000

20 Fig. 14. (a) Pressure contours and (b) apparent viscosity contours of Case 8 with liquid velocity on x axis and gas velocity on y axis (0.1 wt% Aquet-944, 0.38/0.5 in ID/ OD nylon pipe).Pressure drops are in [psi] and viscosities are in [cp].

2000 Qg (cc/min)

that foam rheological properties in pipe should not be viewed as an extension of those in porous media. Here is why, if a few major distinctions are taken as examples: (1) foam in porous media deals with tiny pore sizes in which capillary pressure is dominant, gravity is negligible, and the flow is mostly laminar, while foam in pipe deals with large conduit sizes in which capillary pressure is negligible, gravity is dominant, and the flow can be either laminar or turbulent; (2) the mechanisms of lamella creation and coalescence are different—for foam in porous media, mechanisms such as mobilization and division, snap off, and limiting capillary pressure (or, limiting water saturation) play a significant role, but for foam in pipe, high shear stress near the wall, pipe roughness, mechanical stability of foam films, film thickness at the wall for slip conditions, and bubble-to-bubble and bubble-to-wall interactions are important factors; and (3) the way the phases are distributed in the system is very different—for foam in porous media, the wetting liquid phase is pressed into tiny pores by the non-wetting gas phase (flowing together with foam films) present in the relatively large

40 Qw (cc/min)

1000

20

40 Qw (cc/min)

Fig. 16. Effect of gas and liquid injection velocities on the size of (a) free-gas section and (b) fine-textured-foam section in the high-quality regime.

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foam in pipes consists of two different flow patterns such as segregated flow and plug flow, with foam texture depending on total velocity, while foam in porous media shows foam texture almost unaltered near its maximum value; and (3) foam in porous media shows fng locus convex (i.e., bending up) because foam rheology in the low-quality regime is highly shear-thinning, while foam in pipes shows fng locus concave (i.e., bending down) because foam rheology in the low-quality regime is shear-thickening as observed in this study.

4. Conclusions This experimental study on foam flow in horizontal pipes can be summarized with the following major conclusions.

Fig. 17. A schematic of characterization of foam flow in horizontal pipes based on foam texture and flow pattern.

Fig. 18. A schematic showing the implication of two-flow regime on underbalanced drilling processes.

pores, while for foam in pipe, the distribution of gas and liquid is significantly affected by flow directions (i.e., upward vs. downward), inclination angles, and flow patterns (e.g., segregated flow, bubbly flow, slug flow, plug flow, annular flow, mist flow, and so on). In line with these characteristics, it should be noted that the main contribution of this study is not the fact that foam in pipes exhibits two flow regimes, but why it exhibits two flow regimes. One may recall from previous studies on foam in porous media that the high-quality regime is governed by limiting capillary pressure, and the low-quality regime is governed by mobilization of fine textured bubbles in porous media, which in turn is equivalent to relative permeability effect. How come foam flow in pipes – without such concepts as limiting capillary pressure and relative permeability – can still show two flow regimes? What are the mechanisms which force foam flow in pipes to follow two flow regimes? These are the major questions answered in this study, especially with the help of visualization study in the nylon pipes. Although contour plots in both cases of foams in porous media and foams in pipes make the same appearance of two flow regimes, they are very different by nature in that: (1) for the high-quality regime, foam in porous media shows almost vertical pressure contours due to limiting capillary pressure, whereas foam in pipe shows contours with finite slopes; (2) for the low-quality regime,

1. The presence of two-flow regimes observed and conjectured by the pressure data in the previous study was identified and confirmed by visualization experiments in this study: the highquality regime with a relatively higher gas fraction (i.e., fg 4fng) was characterized by fine-textured foams alternating with free gas (or, very coarse-textured foams if not), exhibiting slug flow; and the low-quality regime with a relatively lower gas fraction (i.e., fg ofng) was characterized by a stable flow of homogeneous foams, exhibiting either segregated or plug flow. The two regimes could be mapped out in a form of contour plot by using the resulting steady-state pressure drops or apparent foam viscosities. The boundary between the two flow regimes was expressed by a concave locus of fng which is affected by different experimental conditions related to foam stability. 2. For foams in the high-quality regime, the alternation of finetextured foams with free gas led to inherently unstable and oscillating pressure responses. Visualization experiments further demonstrated that within the high-quality regime: (i) an increase in gas velocity at the same liquid velocity elongated the size of free-gas section and reduced the size of fine-textured-foam section, leading to lower steady-state pressure drop, and (2) an increase in liquid velocity at the same gas velocity elongated the size of fine-texturedfoam section and shortened the size of free-gas section, leading to higher steady-state pressure drop. This implies that any change which makes the flow drier in the high-quality regime has longer free-gas section and shorter fine-textured-foam section, eventually resulting in lower pressure drop. 3. For foams in the low-quality regime, the uniform and homogeneous nature of foam flow led to stable pressure responses. In general, plug flow was observed at higher total velocities, whereas segregated flow was observed at lower total velocities. It was visualized from the experiments that: (i) in segregated flow, as total injection velocity increased, foam texture became finer and the upper foam layer grew thicker, essentially forming plug flow, and (ii) in plug flow, there was a threshold value of total injection velocity below which foam texture became finer with increasing velocity, and above which foam texture did not change noticeably. The lower liquid layer and the upper foam layer traveled at different velocities during segregated flow, typically with liquid production rate prevailing over gas production rate at the effluent, whereas bulky homogeneous foams flowed all together during plug flow with a thin liquid layer at the wall. 4. As shown in the contour plots, a monotonic increase in gas velocity at fixed liquid velocity resulted in increasing steadystate pressure drop in the low-quality regime (i.e., fg up to fng), but decreasing steady-state pressure drop in the high-quality regime (i.e., fg beyond fng). This transition around fng based on the pressure data was consistent with that based on the visualization experiments, which is, the velocity condition at which the maximum pressure gradient occurred roughly coincided with

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the velocity condition at which the free-gas section started to appear near fng. The texture of foam slug in the high-quality regime was comparable to the texture of fully developed foams in the plug-flow region in the low-quality regime, however. 5. Experimental results showed that fng that separated two flow regimes was not a fixed value. Rather, the magnitude of fng was sensitive to the experimental conditions which affected foam stability. It was observed that a reduction in surfactant concentration and/or the use of a poor foamer lowered fng, and resulted in stretching the high-quality regime and contracting the low-quality regime. When fine-textured foams are obtained, foam texture at low surfactant concentrations or with poor foamers is typically coarser than that at high surfactant concentrations or with good foamers. 6. Visualization experiments describe why the pressure contours in the two flow regimes have different slopes, or why the steadystate pressure drops have different sensitivity to gas or liquid velocities: (i) in the case of low-quality regime, the pressure contours are almost horizontal because an additional amount of liquid injected is consumed to increase the cross-sectional area open to liquid phase if segregated flow, or to thicken foam films between bubbles or between bubbles and pipe wall, if plug flow (which is consistent with drainage effect and lubricating effect, respectively). On the other hand, the pressure contours are sensitive to gas velocity, because an increase in gas velocity results in increasing shear stress to make bubble size smaller, and drier foams tend to have higher level of frictions between bubbles during shear flow; and (ii) in the case of high-quality regime, the pressure contours have finite slopes reflecting the fact that the steady-state pressure drop is influenced by both gas and liquid velocities. Any changes that cause the size of finetextured-foam section longer and the size of free-gas section shorter (i.e., by increasing liquid velocity or decreasing gas velocity) make the steady-state pressure drop higher.

Nomenclature A d L p Qg Qt Qw ug ug,adj ut uw

mapp gw tw Dp DpBG

cross-sectional area of a pipe (ft2) inner diameter of a pipe (in) length of a pipe (ft) pressure (psi) gas rate (gal/min) total flow rate (gal/min) liquid rate (gal/min) superficial gas velocity (ft/s) superficial gas velocity adjusted at elevated pressure (ft/s) total superficial liquid velocity (ft/s) superficial liquid velocity (ft/s) apparent viscosity (cp) the wall shear rate (s  1) wall shear stress (lbf/ft2) pressure drop (psi) pressure drop between transducer B and G (psi)

Acknowledgements We would like to express special thanks to Chevron Inc., Rural Research Institute, and Keller professorship for the financial support. Additional appreciation is reserved for our industry partners, especially Stepan and Baker Petrolite, who provided us with surfactant samples tested in this study.

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