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The effect of inclination angles on foam rheology in pipes
Journal of Petroleum Science and Engineering 86–87 (2012) 246–256
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Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
The effect of inclination angles on foam rheology in pipes R.N. Gajbhiye, S.I. Kam ⁎ Craft and Hawkins Department of Petroleum Engineering, Louisiana State University, Patrick F. Taylor Hall, Rm 3521, Baton Rouge, LA 70803, USA
a r t i c l e
i n f o
Article history: Received 14 December 2010 Accepted 14 March 2012 Available online 1 April 2012 Keywords: foams bubbles flow in pipes two flow regimes foam underbalanced drilling liquid unloading foam fracturing
a b s t r a c t Foams are regarded as a versatile means in many industrial applications due to its high viscosity and low density. Recent experimental studies in horizontal pipes show the existence of two flow regimes: the highquality regime exhibits a repetition of fine-textured foams and free gas sections (i.e. “slug flow” pattern) with fluctuating pressure responses; and the low-quality regime exhibits stable foams (either “plug flow” pattern with homogenous foams, or “segregated flow” pattern with upper foam layer and lower liquid layer) with stable pressure responses. In continuation with these previous studies, this study investigates the effects of inclination angles on foam rheology in pipes within the context of two-flow-regime concept. The results showed that foam rheology was not significantly altered as long as the slug flow or plug flow pattern was formed because of a viscous-force dominant environment. However, if flow conditions fell within the segregated flow pattern, foam rheology was governed by the gravitational force rather than the viscous force, and therefore the flow characteristics were sensitive to inclination angles. These findings were supported by visual observations as well as pressure responses. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Foam has been actively applied to numerous operations in oil and gas industry. Examples include underbalanced drilling, hydraulic fracturing, cementing, wellbore solid removal, and liquid unloading (Bonilla and Shah, 2000; David and Marsden, 1969; Herzhaft et al., 2005; Schramm, 1994) in which fine-textured foam exhibits desired properties by increasing apparent viscosity and interfacial area between gas and liquid. The size and shape of flow conduits may vary significantly depending on applications, from the case of flow through slits with an opening gap of less than a few inches in fracturing treatments, to the case of flow in pipes and annuli with an opening size of more than several inches in liquid unloading and drilling processes. The nature of foam flow also varies significantly — some with considerable amounts of solids and chemical additives (Kam and Rossen, 1999; Kam et al., 2002); and others with a wide range of well geometries (Capo et al., 2006). The direction of foam flow is an important parameter because a well trajectory often consists of vertical, inclined and horizontal segments (e.g. directional and horizontal drilling), the flow of interest can be either upward or downward (e.g. downward foam flow into the drilling pipe followed by upward foam flow along the annulus), and the efficiency of solid transport is inclination-dependent (e.g.
⁎ Corresponding author. Tel.: + 1 225 578 5216. E-mail address: [email protected] (S.I. Kam). 0920-4105/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2012.03.002
cutting transport in horizontal/inclined wells and upward movement of foamed cement slurry). Foam flow in pipe has been extensively investigated in many decades as shown by some early studies of Sibree (1934), Grove et al. (1951), and Mitchell (1969) which focus on foam rheology as a function of injection foam quality (i.e., the volume ratio of gas to total fluid injected). A comprehensive summary on foam flow in pipes is also available in Okpobiri and Ikoku (1986), Heller and Kuntamukkula (1987), and Deshpande and Barigou (2000). As pointed out by Deshpande and Barigou (2000), most foam flow studies consider certain inclination angles to meet their needs. As a result, there exist a limited number of experimental studies available showing how foam rheology changes as a function of inclination angle by keeping other test conditions identical. An example of such studies is given by Capo et al. (2006) which specifically examined the effect of inclination angle on the efficiency of cutting transport, by carrying out the experiments in a range of solid concentrations. They carried out experiments on a 90 ft long flow loop with an 8-inch inner-diameter transparent casing and a 4.4 inch outer-diameter drill pipe. Their study showed that the cutting transport efficiency at 45° inclination was better than those at 55° and 65° inclination for 70% foam quality, and lower foam quality (70%) performed better than higher foam quality (80%). Martins et al. (2001) experimentally examined the performance of foams in hole cleaning within horizontal (0°) and inclined (45° and 75°) well geometries. The hole cleaning performance was poor in the inclined wells (45° and 75°) as compared to the horizontal well. The results at 45° were very similar to 75° inclination though. The
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Fig. 1. Steady-state pressure contours showing two flow regimes for foam flow in pipe (Bogdanovic et al. 2009).
results showed that an increase in total rate as well as a reduction in gas fraction (or foam quality) generally resulted in improved holecleaning performance, and this effect was more pronounced when the inclination angle was 0° (or horizontal). They also proposed a model to predict hole cleaning while under-balanced or near-balanced drilling conditions in horizontal wells as a function of foam quality and mixture Reynolds number. Osunde and Kuru (2006) investigated the mechanisms of cutting transport during drilling processes in inclined wells by performing 1D numerical modeling and transient simulation studies. Their model was constructed based on the assumption that foam behaved as a power-law fluid. The model could predict the optimum foam flow rate (liquid and gas) which maximized the cutting transport efficiency at a given inclination angle. Their model was validated by using data from Capo et al. (2006) with an error range from 4.65% to 21.65%. The study by Guo et al. (2003a,b) provides initial efforts to calculate bottomhole pressure when drilling with foam in a deviated
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hole using analytical models. Their model was similar to the model by Okpobiri and Ikoku (1986) but neglected solid friction factor of cuttings, which resulted in lower bottomhole pressure prediction. This model accounted for the frictional and hydrostatic pressure components in vertical and inclined wellbores, and was validated using bottomhole data from two wells drilled with stable foams in Parana basin, Brazil, where 12-1/4″ hole section was drilled with nitrogen foam for the depth from 152 to 1300 m. A study by Saintpere et al. (2000) evaluated the hole cleaning capability of foams in terms of dimensionless parameters such as Herschel–Bulkley number (Hb, the ratio of yield stress to viscous stress), specific volume expansion ratio (Ns, the ratio of foam volume to the specific volume of the base fluid) and shear thinning index (n) at different inclination angles (0–90°). The results showed that Hb and Ns had a strong correlation with hole-cleaning efficiency. The study of Chen et al. (2009) with polymer-thickened foams examined the effect of inclination on foam properties such as foam quality, density, and velocity showing the profiles of pressure, foam quality, velocity and density at different inclination angles. Addition of polymers increased the viscosity and density of foam, and caused a change in pressure profile and foam quality. The change in foam quality due to the compression of gas phase ranged from 77% to 67% for the vertical well, from 84% to 75% for the directional well (45° inclination angle), and from 86% to 77% for the horizontal well. They noticed that the foam properties in vertical wells changed more dramatically than inclined and horizontal wells. Recently Bogdanovic et al. (2009) came up with a two-flowregime concept to describe the steady-state pressure response during foam flow in pipes as shown in Fig. 1. Gajbhiye and Kam (2011) confirmed the findings by using visual observations as shown in Fig. 2: the high-quality regime (i.e., the regime above the threshold value of foam quality (fg⁎)) is characterized by the fluctuating pressure response with a repetition of fine-textured foam and free gas (i.e., slug flow); on the other hand, the low-quality regime (i.e., the regime below the threshold value of foam quality (fg⁎)) is characterized
Fig. 2. Characterization of foam flow in horizontal pipes by using two-flow regime concept (Gajbhiye and Kam, 2011).
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PRV L A
B
C
Pressure Gauge
Angle Finder
D
E
F
G
H
Pressure Transducers
Visual Cell
Pumps Gas Flow Controller
Surfactant Solution
N i t r o g e n
Foam Disposal Data Acquisition
Fig. 3. A schematic of the experimental set-up which can accommodate inclination angle from 0° to 90° in both upward and downward directions.
by the stable pressure response with either plug flow with finetextured homogeneous foams, or segregated flow between upper foam layer and lower liquid layer. In continuation with Bogdanovic et al. (2009) and Gajbhiye and Kam (2011), this study investigates the effect of inclination angles on foam rheology in pipe. Our aim is to present how foam rheology is affected by different inclination angles comprehensively when other experimental conditions are kept identical. The use of (i) two flow regimes with pressure and apparent-viscosity contours and (ii) visualization efforts with bubble size distributions lies in the heart of this study.
2. Methodology 2.1. Experimental set-up The experimental set-up is schematically shown in Fig. 3 followed by the actual photo in Fig. 4. The flowrate of nitrogen gas from the cylinder was controlled by a 5850E Brooks mass flow controller (Brooks Instruments, PA; maximum rate of 5000 cm 3/min), whereas the flowrate of liquid phase was controlled by a liquid injection pump (Optos 3HM Eldex, CA; maximum rate of 80 cm 3/min). The gas and liquid were co-injected at pre-determined rates until a steady-state
Pressure Transducers Magnetic compass
Data Acquisition
Flow Visual Movie System
Nitrogen Cylinder
Fig. 4. Laboratory set-up for the experiments.
Foam Outlet
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was achieved which typically took 5 to 10 min. A visual cell was placed before the pipe inlet to ensure the formation of fine-textured foams, if needed. The pipe made of Nylon 6 (McMaster-Carr, GA) was installed on a wooden arm which could be adjusted to any inclination angles (i.e., from 0° to 90°, with the flow either upward or downward) with the help of a magnetic compass angle finder attached at the center of the arm. Eight pressure transducers (Omegadyne, Inc. OH) were installed to measure the sectional pressure drops along the pipe. The transducers were equally spaced, about 21 in. (or, 0.53 m) apart from each other. The eight pressure transducers, named A through H, were installed with transducer A at the immediate entry of the pipe and with pressure transducer H just before the exit. The fluid at the outlet was collected in a large bucket. Movies were taken at the section between pressure
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transducers C and D, for the analysis of bubble size and bubble size distribution. Cedepal FA-406, an anionic surfactant popularly used in drilling operations, was supplied by Stepan Company (Northfield, IL), and a concentration of 0.5 wt.% – typically applied in the field – was selected in this study. Five inclination angles were selected in this study: upward (45° and 90°), downward (45° and 90°), and horizontal directions. 2.2. Procedure Once the inclination angle of interest is determined, a series of flow experiments were carried out at four different liquid injection
Fig. 5. (A). Pressure response of the Base Case (Inclination 0°) at pressure ports A through H with liquid injection rate 20 cm3/min (6 × 10 7 cm3/min = 1 m3/s; 1 psi = 6.9 × 103 Pa). (B). Pressure response of the Base Case (Inclination 0°) at pressure ports A through H with liquid injection rate 40 cm3/min (6 × 10 7 cm3/min = 1 m3/s; 1 psi = 6.9 × 103 Pa). (C). Pressure response of the Base Case (Inclination 0°) at pressure ports A through H with liquid injection rate 60 cm3/min (6 × 107 cm3/min = 1 m3/s; 1 psi = 6.9 × 103 Pa). (D). Pressure response of the Base Case (Inclination 0°) at pressure ports A through H with liquid injection rate 80 cm 3/min (6 × 107 cm3/min = 1 m3/s; 1 psi = 6.9 × 103 Pa).
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Fig. 5 (continued).
rates (such as Qw = 20, 40, 60, and 80 cm 3/min), with each series progressively changing gas rates (Qg) from 200 to 5000 cm 3/min then back to 200 cm 3/min step by step. The procedure given below further explains the steps in detail. 1. Adjust the pipe to a required inclination angle by using the angle finder and inject surfactant solution at a pre-specified value. 2. If the injected surfactant solution comes out at the outlet, start to inject the nitrogen gas at low injection rate. 3. Ensure that the gas and liquid phases flow together from the visual cell installed upstream of pipe. If foam flow is observed, bypass the visual cell. 4. Activate the data acquisition system and continue to co-inject the gas and liquid phases at pre-determined rates until a steady state is obtained. When a sufficient amount of data is collected, vary the gas injection rates until a series of gas rates are tested. Typically
gas injection rates (Qg) of 200, 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, and 5000 cm 3/min were tried in an increasing order first, followed by a decreasing order. 5. Continue the experiments at different liquid rates, repeating all previous steps, with typical liquid injection rates (Qw) of 20, 40, 60, and 80 cm 3/min. Note that steps 1 through 5 allow the construction of one contour plot (more in the result section). 6. Repeat steps 1 through 5 at different angles to examine the impact of inclination angles. It should be noted that, for the given pipe inner diameter (d) of 0.38 in. (or, the cross-sectional area (A) of 0.113 in. 2), the nominal liquid velocities tested (uw) were 0.014, 0.029, 0.044, and 0.059 ft/s (or, 3.33 × 10− 7, 6.66 × 10− 7, 10 × 10 − 7, 1.33 × 10− 6 m/s) corresponding to the liquid rates (Qw) of 20, 40, 60, 80 cm3/min respectively, and the nominal gas velocities tested (ug) were from 0.149 to 3.73 ft/s (or
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Fig. 6. The steady-state pressure drops over 8.52 ft. pipe length at various gas rates, or the steady-state shear stress at various shear rates at fixed liquid velocity (Base Case with Inclination angle 0°) (6 × 107 cm3/min = 1 m3/s; 1 psi = 6.9 × 103 Pa; 1 lbf/ft2 = 4.882 kgf/m2; 1 ft = 0.3048 m).
0.0455 to 1.139 m/s) at standard condition corresponding to the gas rates (Qg) 200 to 5000 cm3/min (or 3.33 × 10− 6 to 8.33 × 10 − 5 m 3/s). 2.3. Data analysis
τ μ app ¼ 47; 880 w ; γw
For a flow in pipe, the shear stress at the wall is given by dΔP ; τw ¼ 3 L
ð1Þ
where τw is the wall shear stress [lbf/ft 2], ΔP is the pressure drop [psi], and d and L are the inner diameter [in] and the length of corresponding pipe segments [ft]. The shear rate for the flow in pipe is given by Q γ w ¼ 39:216 3t ; d
where, γw 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 below:
ð2Þ
ð3Þ
where μapp is the apparent foam viscosity [cp], τw is the shear stress [lbf/ft 2], and γw is the wall shear rate [s − 1]. 3. Results and discussions We investigate five different inclination angles: horizontal (i.e., inclination angle = 0°), 45° upward, 90° upward, 45° downward, and 90° downward, which are named Base Case, Case 1, Case 2, Case 3, and Case 4, respectively. Other than the inclination angles varied, all other experimental conditions are kept the same, including 0.5 wt.% Cedepal FA-406 and 0.36/0.5-inches ID/OD Nylon-6 pipes.
Fig. 7. The steady-state pressure drops over 8.52 ft. pipe length at various foam qualities or apparent foam viscosity at various shear rates (Base Case with Inclination angle 0°). (1 psi = 6.9 × 103 Pa; 1 cp = 10− 3 kg/(m s); 1 ft = 0.3048 m).
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Fig. 8. Pressure and apparent-viscosity contours for Base Case: (A) pressure values in psi over 8.52 ft length and (B) apparent-viscosity in cp calculated from pressure data. (1 psi = 6.9 × 103 Pa; 1 cp = 10− 3 kg/(m s); 1 ft = 0.3048 m).
3.1. Base Case (Inclination 0°) Fig. 5(A) through (D) show the base-case experiments at the liquid injection rate (Qw) of 20, 40, 60 and 80 cm3/min. In each experiment, the gas injection rate (Qg) varies from 200 to 5000 cm3/min step by step, first in an increasing order followed by a decreasing order. The results of sectional pressure drops from transducers A through H show a few interesting behaviors: (1) the plots are in general symmetric, meaning that there is no hysteresis involved with the change in gas flow rates; (2) there is a threshold value of gas flow rate, below which the steady-state sectional pressure drop increases with gas rate, but above which the steady-state sectional pressure drop decreases with gas rate, as well demonstrated in Fig. 5(A) and (B); and (3) the pressure data collected during the experiments look relatively stable below the threshold gas flow rate and relatively scattered above the threshold gas flow rate. These effects described in (2) and (3) are consistent with previous observations made by Gajbhiye and Kam (2011) in their horizontal-flow experiments (e.g. Fig. 2) in which the high-quality regime is characterized by alternating free gas and fine-textured foams (called “slug flow pattern”) and the low-quality regime is characterized by either finetextured homogeneous foam flow (called “plug flow pattern”) or segregated layered flow between foams and liquid (called “segregated flow pattern”).
Fig. 9. Pressure and apparent-viscosity contours for Case 1 (Inclination 45° upward): (A) pressure values in psi over 8.52 ft length and (B) apparent-viscosity in cp calculated from pressure data. (1 psi = 6.9 × 103 Pa; 1 cp= 10− 3 kg/(m s); 1 ft= 0.3048 m).
The steady-state pressure values read from Fig. 5(A) through (D) can be used to construct a plot of pressure drop (ΔP) vs. gas rate (Qg) (or, shear stress (τw) vs. shear rate (γw)) as shown in Fig. 6, and a plot of pressure drop (ΔP) vs. foam quality (fg) (or, apparent foam viscosity (μapp) vs. shear rate (γw)) as shown in Fig. 7. These plots can be drawn in a form of pressure or apparent viscosity contours as shown in Fig. 8. These figures clearly indicate that there exist two very distinct foam flow regimes which are separated by the threshold foam quality values, fg*. It should be noted that the pressure-drop values reported here are from pressure transducers B though G because of possible entry and exit effect, and the gas rates in Figs. 6 and 8 are values adjusted at the average pressure within the pipe (i.e., (pB + pG)/2). 3.1.1. Effect of inclination on two flow regimes (Case 1 through Case 4) Similar flow experiments are conducted at different inclination angles. They are named Case 1 through Case 4 for 45° upward, 90° upward, 45° downward, and 90° downward, respectively, of which the steady-state pressure drops and apparent foam viscosities are presented as shown in Figs. 9 through 12. The results from these figures show that the overall shape of pressure and viscosity contours are not noticeably affected by inclination angles. A closer look at the contour plots in Figs. 9 through 12 shows that the maximum apparent viscosity values are
A Superficial gas velocity (adjusted), ug[ft/sec]
A Contour values
Measured values
fg*
Superficial gas velocity (adjusted), ug[ft/sec]
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Calculated values
fg*
Superficial liquid velocity, uw[ft/sec] Fig. 10. Pressure and apparent-viscosity contours for Case 2 (Inclination 90° upward): (A) pressure values in psi over 8.52 ft length and (B) apparent-viscosity in cp calculated from pressure data. (1 psi = 6.9 × 103 Pa; 1 cp= 10− 3 kg/(m s); 1 ft = 0.3048 m).
around 300 cp, which indicates that the whole process is dominated by viscous force rather than gravitational force once fine-textured foams are formed. This implies that for foam rheology to be strongly affected by inclination angle, the region of interest should be where the apparent foam viscosity is relatively low. This in turn implies that the objective of this study is more relevant to the lower foam quality region in the low-quality regime, especially near or below the transition from segregated flow to plug flow pattern, which is discussed more in the following section.
3.2. Transition from segregated to plug flow pattern (Case 5) A series of experiments are followed in order to observe the pattern of foam flow in pipes. The results are shown in Figs. 13, 14, and 15 for horizontal, 45° upward and 45° downward experiments, respectively. As visualized by Gajbhiye and Kam (2011) from their flow experiments in horizontal pipes, three different flow patterns are also observed in our horizontal flow experiments: slug flow pattern in the high-quality regime where the pressure contours have some finite slopes (cf. Figs. 8 through 12); and either plug flow pattern or segregated flow pattern in the low-quality regime where the pressure contours are relatively flat (cf. Figs. 8 through 12).
Superficial gas velocity (adjusted), ug[ft/sec]
Superficial gas velocity (adjusted), ug[ft/sec]
B Contour values
Contour values Measured values
fg*
Superficial liquid velocity, uw[ft/sec]
Superficial liquid velocity, uw[ft/sec]
B
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Contour values
Calculated values
fg*
Superficial liquid velocity, uw[ft/sec] Fig. 11. Pressure and apparent-viscosity contours for Case 3 (Inclination 45° downward): (A) pressure values in psi over 8.52 ft length and (B) apparent-viscosity in cp calculated from pressure data. (1 psi = 6.9 × 103 Pa; 1 cp= 10− 3 kg/(m s); 1 ft= 0.3048 m).
The same visualization experiments are shown in Figs. 14 and 15 at 45° upward and 45° downward inclination angles. There are a few important aspects observed which should be noted as follows: (1) the three flow patterns observed in horizontal flow (i.e., slug, plug, and segregated flows) are still present in a wide range of inclination angles (all the way from 90° upward to 90° downward, although results are shown only for 45° upward and 45° downward); (2) for upward flow (e.g. Fig. 14), if the flow condition falls within the segregated flow pattern in the horizontal flow, the system repeats two states of (a) the layered flow of foam and liquid, both flowing together upward and (b) the upper foam layer flowing upward but the lower liquid layer flowing downward (the downward motion of liquid is accompanied by the accumulation of liquid at a certain location first, then as the liquid moving downward due to gravity is taken up by the following rising foams, the liquid either moves together with the foams as a distinct layer or merges into next-following foams helping create fine-textured foams); and (3) for downward flow (e.g. Fig. 15), if the flow condition falls within the segregated flow pattern in the horizontal flow, the lower liquid layer runs faster and the upper foam layer runs more slowly as the inclination becomes steeper (because of the liquid running faster, the liquid layer is thinner during downward flow compared to that during horizontal flow). These observations in upward and downward flow directions show that the formation of fine-textured foams, which is required for
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A
Superficial gas velocity (adjusted),ug[ft/sec]
254
Qg (cc/min)
Contour values
Slug flow pattern High-
Measured values
quality
2000
regime
fg* 500
Lowquality regime
200
B
Superficial gas velocity (adjusted),ug[ft/sec]
Superficial liquid velocity, uw[ft/sec]
Plug or Segregated flow pattern
Contour values
40
20
Qw(cc/min)
Calculated values
fg*
Superficial liquid velocity, uw[ft/sec] Fig. 12. Pressure and apparent-viscosity contours for Case 4 (Inclination 90° downward): (A) pressure values in psi over 8.52 ft length and (B) apparent-viscosity in cp calculated from pressure data. (1 psi = 6.9 × 103 Pa; 1 cp = 10− 3 kg/(m s); 1 ft = 0.3048 m).
Fig. 14. Flow patterns observed in Case 1 (Inclination 45° upward) (6 × 107 cm3/ min = 1 m3/s).
the transition from segregated flow pattern to plug flow pattern, is more favored for upward flow due to the relatively higher liquid fraction caused by sporadic downward flow of accumulated liquid, but less favored for downward flow due to the relatively lower liquid fraction caused by rapid downward liquid movement. This concept is depicted in Fig. 16 in which the envelope that separates segregated flow pattern from plug flow pattern (cf. Fig. 2) becomes smaller as the inclination angle changes from 90° downward to horizontal and eventually to 90° upward. This means that (1) in those experiments varying gas rate at fixed liquid rate, the threshold gas rate at which the transition from segregated flow to plug flow takes place is lower (cf. vertical line (A) in Fig. 16) and (2) in those experiments varying total gas and liquid rate at fixed foam quality, the threshold total rate at which the transition from segregated flow to plug flow takes place
Qg (cc/min)
Slug flow pattern Highquality
2000
Qg (cc/min)
Slug flow pattern regime
Highquality
2000
regime 500
Lowquality
500
Low-
regime
quality regime
200
200
Plug or Segregated flow pattern Plug or Segregated flow pattern 40
20
Qw(cc/min) Fig. 13. Flow patterns observed in Base Case (Inclination 0°) (6× 107 cm3/min= 1 m3/s).
40
20
Qw (cc/min) Fig. 15. Flow patterns observed in Case 3 (Inclination 45° downward) (6 × 107 cm3/ min = 1 m3/s).
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Highquality regime
Superficial gas velocity, [ug]
Slug flow pattern
fg*
Δp or µapp contours
Plug flow pattern (A)
(B) 90o Downward 0o Horizontal
Lowquality regime
90o Upward
Segregated flow pattern Superficial liquid velocity [uw] Fig. 16. Boundaries separating three different patterns: the transition from segregated to plug flow is significantly affected by inclination angles.
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state pressure contours are sensitive to the inclination angles. The major distinction between these two cases is that the former is governed by viscous force, while the latter is governed by gravitational force. Fig. 17 shows a schematic figure with the nature of these inclinationangle-specific pressure drops. In horizontal flow with no gravity effect, the steady-state pressure drop increases with gas velocity showing a slightly shear-thinning behavior (e.g. Figs. 5 and 6). In case of upward flow, the pressure drop first decreases with gas velocity because the flow is segregated (i.e., the gravitational force is dominant); then increases with gas velocity and merges with the locus of horizontal flow because the viscous force becomes dominant. In the case of downward flow, the gravity is acting in the opposite way such that the pressure drops are even lower than those in horizontal flow before merging into the plug flow pattern where the viscous force is dominant. This inclination-angle-dependent transition from segregated-flow pattern to plug-flow pattern is believed to be very important in the evaluation of cutting transport in deviated wells, and developing theoretical models based on the physics presented in this study deserves further studies. 4. Conclusions
is also lower (cf. line (B) in Fig. 16), as the inclination angle moves from 90° downward to 90° upward. It should be noted that the shape of the envelope appears to be concave in general because an increase in liquid rate at the same gas rate tends to create fine-textured foam more easily. It should be emphasized that in many foam applications such as foam drilling and fracturing, the large interfacial area between gas and liquid is highly desirable for the purpose of maximizing cutting transport and proppant delivery. Therefore, the fact that the boundary between segregated flow and plug flow is sensitive to the changes in inclination angle (cf. Fig. 16) implies that the inclination angle should be an important parameter in field treatments. 3.3. Implication of results to pressure contours at different inclination angles The results in Figs. 13 through 15 indicate that the pressure contours obtained from horizontal flow experiments are still applicable to the case of other inclination angles as long as the flow patterns fall into either slug flow in the high-quality regime or plug flow in the low-quality regime. On the other hand, if the flow pattern falls within segregated flow in the low-quality regime, the steady-
Upward flow
Upward Horizontal
Pressure drop, Δp
Downward
Gravity Dominant (Segregated Flow)
Viscous Force Dominant (Plug Flow)
Horizontal flow
Transition from segregated to plug flow
Downward flow
Gas velocity, uv Fig. 17. A schematic showing the transition from segregated flow to plug flow at different inclination angles.
From foam flow experiments carried out at different inclination angles and in a wide range of gas and liquid injection velocities, the following conclusions can be made: 1. Experimental results show that there exist two foam flow regimes consistently at all different inclination angles tested, including 90° upward, 45° upward, horizontal (0°), 45° downward, and 90° downward. The value of fg*, which separates the high-quality regime from the low-quality regimes, does not seem to be affected noticeably by inclination angles. As previous studies in horizontal pipes observed, the high-quality regime is characterized by slug flow and the low-quality regime is characterized by either plug flow or segregated flow, irrespective of inclination angles. 2. Once foam flow exhibits either slug flow pattern in the highquality regime or plug flow pattern in the low-quality regime, the rheology is dominated by viscous force due to relatively fine foam texture. If this occurs, the steady-state pressure contours are almost unaffected by inclination angles. On the other hand, once foam flow exhibits segregated flow pattern in the low-quality regime, the rheology is dominated by the gravity and the steadystate pressure drops are sensitive to inclination angles. 3. The transition from segregated flow to plug flow, which is crucial in many foam applications, occurs at higher foam quality (if liquid rate is fixed) or at higher total injection velocity (if foam quality is fixed) as the inclination angle moves from 90° upward, 45° upward, horizontal (0°), 45° downward, and eventually to 90° downward. This is because, when it comes to the creation of finetextured foams, a sporadic back flow of liquid phase results in a favorable condition in upward flow, and a rapid flow down of liquid phase results in an unfavorable condition in downward flow. Nomenclature A cross-sectional area of a pipe, ft 2. d inner diameter of a pipe, in. L length of a pipe, ft. p pressure, psi. Qt Total flow rate, gal/min. Qw Liquid rate, gal/min. Qg Gas rate, gal/min. ug Superficial gas velocity, ft/s. adj ug, Superficial gas velocity adjusted at elevated pressure, ft/s. ut Total superficial liquid velocity, ft/s. uw Superficial liquid velocity, ft/s.
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μapp γw τw Δp ΔpBG
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apparent viscosity, cp. the wall shear rate, s − 1. Wall shear stress, lbf/ft 2. pressure drop, psi. Pressure drop between transducer B and G, psi.
Acknowledgement This study is partly supported by Rural Research Institute and Keller professorship. We also express our appreciation to Stephan Company for their generous donations of surfactants and chemicals. We wish to recognize the assistance of Gerry Masterman, Darryl Bourgoyne and Fenelon Nunes for their help in setting up the laboratory. References Bogdanovic, M., Gajbhiye, R.N., Kam, S.I., 2009. Experimental study of foam flow in pipes: two distinct flow regimes. Colloids Surf. A Physicochem. Eng. Asp. 56–71 April. Bonilla, L.F., Shah, S.N., 2000. Experimental investigation on the rheology of foams. Paper SPE 59752 presented at 2000 SPE/CERI Gas Technology Symposium, Calgary. April 2000. Capo, J., Yu, M., Miska, S.Z., Takach, N., Ahmed, R.M., 2006. Cutting transport with aqueous foam at intermediate-inclined wells. SPE Drilling & Completion. June 2006, pp. 99–107. Chen, Z., Duan, M., Miska, S.Z., Yu, M., Ahmed, R.M., Hallman, J., 2009. Hydraulic predictions for polymer thickened foam flow in horizontal and directional wells. SPE Drilling & Completion. March 2009, pp. 40–49. David, A., Marsden, S.S., 1969. The rheology of foam. Paper SPE 2544 presented at Fall Meeting of the Society of Petroleum Engineers of AIME. September 1969. Deshpande, N.S., Barigou, M., 2000. The flow of gas liquid foams in vertical pipes. Chem. Eng. Sci. 4297–4309. February.
Gajbhiye, R.N., Kam, S.I., 2011. Characterization of foam flow in horizontal pipe by using two flow regime concept. Chem. Eng. Sci. 1536–1549. Grove Jr., C.S., Wise Jr., G.E., Marsh, W.E., Gray, J.B., 1951. Viscosity of fire-fighting foam. Ind. Eng. Chem. 1120–1122. May. Guo, B., Kai, S., Ali, G., 2003a. A closed form hydraulic equation for aerated mud drilling in inclined wells. Paper SPE 81070 presented at SPE Latin American & Caribbean Petroleum Engineering Conference. Trinidad, April 2003. Guo, B., Kai, S., Ali, G., 2003b. A closed form hydraulic equation for predicting bottomhole pressure in UBD with foam. Paper IADC/SPE 81640 presented at IADC/ SPE Underbalanced Technology Conference and Exhibition, Houston. March. 2003. Heller, J.P., Kuntamukkula, S.M., 1987. Critical review of the foam rheology literature. Ind. Eng. Chem. Res. 1987, 3187–3325. Herzhaft, B., Kakadjian, S., Moan, M., 2005. Measurement and modeling of the flow behavior of aqueous foams using a recirculating pipe viscometer. Colloids Surf. A Physicochem. Eng. Asp. 153–164. February. Kam, S.I., Gauglitz, P.A., Rossen, W.R., 2002. The yield stress of foamy sands. Colloids Surf. A Physicochem. Eng. Asp. 53–62. March. Kam, S.I., Rossen, W.R., 1999. Anomalous capillary pressure, stress, and stability of solids-coated bubbles. J. Colloid Interface Sci. 329–339. Martins, A.L., Lourenco, A.M.F., Sa, C.H.M., Silva Jr., V., 2001. Foam rheology characterization as a tool for predicting pressure while drilling wells in UBD conditions. Paper SPE/IADC 67691 presented at SPE/IADC Drilling conference, Amsterdam, February 2001. Mitchell, B.J. 1969. Viscosity of Foam, PhD Thesis, University of Oklahoma, USA. Okpobiri, G.A., Ikoku, C.U., 1986. Volumetric requirements for foam and mist drilling operations. SPE Drilling Engineering, February 1986, pp. 71–88. Osunde, O., Kuru, E., 2006. Numerical modeling of cutting transport with foam in inclined wells. Canadian International Petroleum Conference. Paper 2006–07. Saintpere, S., Yannick, M., Fabrice, B., Abdoulaye, T., 2000. Hole cleaning capabilities of drilling foams compared to conventional fluids. Paper SPE 63049 presented at SPE ATCE, Dallas, October, 2003. Schramm, L.L. (Ed.), 1994. Foams: Fundamentals and Applications in the Oil Industry. ACS Advances in Chemistry Series No.242. American Chemistry Society, Washington, DC. Sibree, J.O., 1934. The viscosity of froth. Faraday Soc. Trans. 325.
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Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
The effect of inclination angles on foam rheology in pipes R.N. Gajbhiye, S.I. Kam ⁎ Craft and Hawkins Department of Petroleum Engineering, Louisiana State University, Patrick F. Taylor Hall, Rm 3521, Baton Rouge, LA 70803, USA
a r t i c l e
i n f o
Article history: Received 14 December 2010 Accepted 14 March 2012 Available online 1 April 2012 Keywords: foams bubbles flow in pipes two flow regimes foam underbalanced drilling liquid unloading foam fracturing
a b s t r a c t Foams are regarded as a versatile means in many industrial applications due to its high viscosity and low density. Recent experimental studies in horizontal pipes show the existence of two flow regimes: the highquality regime exhibits a repetition of fine-textured foams and free gas sections (i.e. “slug flow” pattern) with fluctuating pressure responses; and the low-quality regime exhibits stable foams (either “plug flow” pattern with homogenous foams, or “segregated flow” pattern with upper foam layer and lower liquid layer) with stable pressure responses. In continuation with these previous studies, this study investigates the effects of inclination angles on foam rheology in pipes within the context of two-flow-regime concept. The results showed that foam rheology was not significantly altered as long as the slug flow or plug flow pattern was formed because of a viscous-force dominant environment. However, if flow conditions fell within the segregated flow pattern, foam rheology was governed by the gravitational force rather than the viscous force, and therefore the flow characteristics were sensitive to inclination angles. These findings were supported by visual observations as well as pressure responses. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Foam has been actively applied to numerous operations in oil and gas industry. Examples include underbalanced drilling, hydraulic fracturing, cementing, wellbore solid removal, and liquid unloading (Bonilla and Shah, 2000; David and Marsden, 1969; Herzhaft et al., 2005; Schramm, 1994) in which fine-textured foam exhibits desired properties by increasing apparent viscosity and interfacial area between gas and liquid. The size and shape of flow conduits may vary significantly depending on applications, from the case of flow through slits with an opening gap of less than a few inches in fracturing treatments, to the case of flow in pipes and annuli with an opening size of more than several inches in liquid unloading and drilling processes. The nature of foam flow also varies significantly — some with considerable amounts of solids and chemical additives (Kam and Rossen, 1999; Kam et al., 2002); and others with a wide range of well geometries (Capo et al., 2006). The direction of foam flow is an important parameter because a well trajectory often consists of vertical, inclined and horizontal segments (e.g. directional and horizontal drilling), the flow of interest can be either upward or downward (e.g. downward foam flow into the drilling pipe followed by upward foam flow along the annulus), and the efficiency of solid transport is inclination-dependent (e.g.
⁎ Corresponding author. Tel.: + 1 225 578 5216. E-mail address: [email protected] (S.I. Kam). 0920-4105/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2012.03.002
cutting transport in horizontal/inclined wells and upward movement of foamed cement slurry). Foam flow in pipe has been extensively investigated in many decades as shown by some early studies of Sibree (1934), Grove et al. (1951), and Mitchell (1969) which focus on foam rheology as a function of injection foam quality (i.e., the volume ratio of gas to total fluid injected). A comprehensive summary on foam flow in pipes is also available in Okpobiri and Ikoku (1986), Heller and Kuntamukkula (1987), and Deshpande and Barigou (2000). As pointed out by Deshpande and Barigou (2000), most foam flow studies consider certain inclination angles to meet their needs. As a result, there exist a limited number of experimental studies available showing how foam rheology changes as a function of inclination angle by keeping other test conditions identical. An example of such studies is given by Capo et al. (2006) which specifically examined the effect of inclination angle on the efficiency of cutting transport, by carrying out the experiments in a range of solid concentrations. They carried out experiments on a 90 ft long flow loop with an 8-inch inner-diameter transparent casing and a 4.4 inch outer-diameter drill pipe. Their study showed that the cutting transport efficiency at 45° inclination was better than those at 55° and 65° inclination for 70% foam quality, and lower foam quality (70%) performed better than higher foam quality (80%). Martins et al. (2001) experimentally examined the performance of foams in hole cleaning within horizontal (0°) and inclined (45° and 75°) well geometries. The hole cleaning performance was poor in the inclined wells (45° and 75°) as compared to the horizontal well. The results at 45° were very similar to 75° inclination though. The
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Fig. 1. Steady-state pressure contours showing two flow regimes for foam flow in pipe (Bogdanovic et al. 2009).
results showed that an increase in total rate as well as a reduction in gas fraction (or foam quality) generally resulted in improved holecleaning performance, and this effect was more pronounced when the inclination angle was 0° (or horizontal). They also proposed a model to predict hole cleaning while under-balanced or near-balanced drilling conditions in horizontal wells as a function of foam quality and mixture Reynolds number. Osunde and Kuru (2006) investigated the mechanisms of cutting transport during drilling processes in inclined wells by performing 1D numerical modeling and transient simulation studies. Their model was constructed based on the assumption that foam behaved as a power-law fluid. The model could predict the optimum foam flow rate (liquid and gas) which maximized the cutting transport efficiency at a given inclination angle. Their model was validated by using data from Capo et al. (2006) with an error range from 4.65% to 21.65%. The study by Guo et al. (2003a,b) provides initial efforts to calculate bottomhole pressure when drilling with foam in a deviated
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hole using analytical models. Their model was similar to the model by Okpobiri and Ikoku (1986) but neglected solid friction factor of cuttings, which resulted in lower bottomhole pressure prediction. This model accounted for the frictional and hydrostatic pressure components in vertical and inclined wellbores, and was validated using bottomhole data from two wells drilled with stable foams in Parana basin, Brazil, where 12-1/4″ hole section was drilled with nitrogen foam for the depth from 152 to 1300 m. A study by Saintpere et al. (2000) evaluated the hole cleaning capability of foams in terms of dimensionless parameters such as Herschel–Bulkley number (Hb, the ratio of yield stress to viscous stress), specific volume expansion ratio (Ns, the ratio of foam volume to the specific volume of the base fluid) and shear thinning index (n) at different inclination angles (0–90°). The results showed that Hb and Ns had a strong correlation with hole-cleaning efficiency. The study of Chen et al. (2009) with polymer-thickened foams examined the effect of inclination on foam properties such as foam quality, density, and velocity showing the profiles of pressure, foam quality, velocity and density at different inclination angles. Addition of polymers increased the viscosity and density of foam, and caused a change in pressure profile and foam quality. The change in foam quality due to the compression of gas phase ranged from 77% to 67% for the vertical well, from 84% to 75% for the directional well (45° inclination angle), and from 86% to 77% for the horizontal well. They noticed that the foam properties in vertical wells changed more dramatically than inclined and horizontal wells. Recently Bogdanovic et al. (2009) came up with a two-flowregime concept to describe the steady-state pressure response during foam flow in pipes as shown in Fig. 1. Gajbhiye and Kam (2011) confirmed the findings by using visual observations as shown in Fig. 2: the high-quality regime (i.e., the regime above the threshold value of foam quality (fg⁎)) is characterized by the fluctuating pressure response with a repetition of fine-textured foam and free gas (i.e., slug flow); on the other hand, the low-quality regime (i.e., the regime below the threshold value of foam quality (fg⁎)) is characterized
Fig. 2. Characterization of foam flow in horizontal pipes by using two-flow regime concept (Gajbhiye and Kam, 2011).
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PRV L A
B
C
Pressure Gauge
Angle Finder
D
E
F
G
H
Pressure Transducers
Visual Cell
Pumps Gas Flow Controller
Surfactant Solution
N i t r o g e n
Foam Disposal Data Acquisition
Fig. 3. A schematic of the experimental set-up which can accommodate inclination angle from 0° to 90° in both upward and downward directions.
by the stable pressure response with either plug flow with finetextured homogeneous foams, or segregated flow between upper foam layer and lower liquid layer. In continuation with Bogdanovic et al. (2009) and Gajbhiye and Kam (2011), this study investigates the effect of inclination angles on foam rheology in pipe. Our aim is to present how foam rheology is affected by different inclination angles comprehensively when other experimental conditions are kept identical. The use of (i) two flow regimes with pressure and apparent-viscosity contours and (ii) visualization efforts with bubble size distributions lies in the heart of this study.
2. Methodology 2.1. Experimental set-up The experimental set-up is schematically shown in Fig. 3 followed by the actual photo in Fig. 4. The flowrate of nitrogen gas from the cylinder was controlled by a 5850E Brooks mass flow controller (Brooks Instruments, PA; maximum rate of 5000 cm 3/min), whereas the flowrate of liquid phase was controlled by a liquid injection pump (Optos 3HM Eldex, CA; maximum rate of 80 cm 3/min). The gas and liquid were co-injected at pre-determined rates until a steady-state
Pressure Transducers Magnetic compass
Data Acquisition
Flow Visual Movie System
Nitrogen Cylinder
Fig. 4. Laboratory set-up for the experiments.
Foam Outlet
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was achieved which typically took 5 to 10 min. A visual cell was placed before the pipe inlet to ensure the formation of fine-textured foams, if needed. The pipe made of Nylon 6 (McMaster-Carr, GA) was installed on a wooden arm which could be adjusted to any inclination angles (i.e., from 0° to 90°, with the flow either upward or downward) with the help of a magnetic compass angle finder attached at the center of the arm. Eight pressure transducers (Omegadyne, Inc. OH) were installed to measure the sectional pressure drops along the pipe. The transducers were equally spaced, about 21 in. (or, 0.53 m) apart from each other. The eight pressure transducers, named A through H, were installed with transducer A at the immediate entry of the pipe and with pressure transducer H just before the exit. The fluid at the outlet was collected in a large bucket. Movies were taken at the section between pressure
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transducers C and D, for the analysis of bubble size and bubble size distribution. Cedepal FA-406, an anionic surfactant popularly used in drilling operations, was supplied by Stepan Company (Northfield, IL), and a concentration of 0.5 wt.% – typically applied in the field – was selected in this study. Five inclination angles were selected in this study: upward (45° and 90°), downward (45° and 90°), and horizontal directions. 2.2. Procedure Once the inclination angle of interest is determined, a series of flow experiments were carried out at four different liquid injection
Fig. 5. (A). Pressure response of the Base Case (Inclination 0°) at pressure ports A through H with liquid injection rate 20 cm3/min (6 × 10 7 cm3/min = 1 m3/s; 1 psi = 6.9 × 103 Pa). (B). Pressure response of the Base Case (Inclination 0°) at pressure ports A through H with liquid injection rate 40 cm3/min (6 × 10 7 cm3/min = 1 m3/s; 1 psi = 6.9 × 103 Pa). (C). Pressure response of the Base Case (Inclination 0°) at pressure ports A through H with liquid injection rate 60 cm3/min (6 × 107 cm3/min = 1 m3/s; 1 psi = 6.9 × 103 Pa). (D). Pressure response of the Base Case (Inclination 0°) at pressure ports A through H with liquid injection rate 80 cm 3/min (6 × 107 cm3/min = 1 m3/s; 1 psi = 6.9 × 103 Pa).
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Fig. 5 (continued).
rates (such as Qw = 20, 40, 60, and 80 cm 3/min), with each series progressively changing gas rates (Qg) from 200 to 5000 cm 3/min then back to 200 cm 3/min step by step. The procedure given below further explains the steps in detail. 1. Adjust the pipe to a required inclination angle by using the angle finder and inject surfactant solution at a pre-specified value. 2. If the injected surfactant solution comes out at the outlet, start to inject the nitrogen gas at low injection rate. 3. Ensure that the gas and liquid phases flow together from the visual cell installed upstream of pipe. If foam flow is observed, bypass the visual cell. 4. Activate the data acquisition system and continue to co-inject the gas and liquid phases at pre-determined rates until a steady state is obtained. When a sufficient amount of data is collected, vary the gas injection rates until a series of gas rates are tested. Typically
gas injection rates (Qg) of 200, 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, and 5000 cm 3/min were tried in an increasing order first, followed by a decreasing order. 5. Continue the experiments at different liquid rates, repeating all previous steps, with typical liquid injection rates (Qw) of 20, 40, 60, and 80 cm 3/min. Note that steps 1 through 5 allow the construction of one contour plot (more in the result section). 6. Repeat steps 1 through 5 at different angles to examine the impact of inclination angles. It should be noted that, for the given pipe inner diameter (d) of 0.38 in. (or, the cross-sectional area (A) of 0.113 in. 2), the nominal liquid velocities tested (uw) were 0.014, 0.029, 0.044, and 0.059 ft/s (or, 3.33 × 10− 7, 6.66 × 10− 7, 10 × 10 − 7, 1.33 × 10− 6 m/s) corresponding to the liquid rates (Qw) of 20, 40, 60, 80 cm3/min respectively, and the nominal gas velocities tested (ug) were from 0.149 to 3.73 ft/s (or
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Fig. 6. The steady-state pressure drops over 8.52 ft. pipe length at various gas rates, or the steady-state shear stress at various shear rates at fixed liquid velocity (Base Case with Inclination angle 0°) (6 × 107 cm3/min = 1 m3/s; 1 psi = 6.9 × 103 Pa; 1 lbf/ft2 = 4.882 kgf/m2; 1 ft = 0.3048 m).
0.0455 to 1.139 m/s) at standard condition corresponding to the gas rates (Qg) 200 to 5000 cm3/min (or 3.33 × 10− 6 to 8.33 × 10 − 5 m 3/s). 2.3. Data analysis
τ μ app ¼ 47; 880 w ; γw
For a flow in pipe, the shear stress at the wall is given by dΔP ; τw ¼ 3 L
ð1Þ
where τw is the wall shear stress [lbf/ft 2], ΔP is the pressure drop [psi], and d and L are the inner diameter [in] and the length of corresponding pipe segments [ft]. The shear rate for the flow in pipe is given by Q γ w ¼ 39:216 3t ; d
where, γw 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 below:
ð2Þ
ð3Þ
where μapp is the apparent foam viscosity [cp], τw is the shear stress [lbf/ft 2], and γw is the wall shear rate [s − 1]. 3. Results and discussions We investigate five different inclination angles: horizontal (i.e., inclination angle = 0°), 45° upward, 90° upward, 45° downward, and 90° downward, which are named Base Case, Case 1, Case 2, Case 3, and Case 4, respectively. Other than the inclination angles varied, all other experimental conditions are kept the same, including 0.5 wt.% Cedepal FA-406 and 0.36/0.5-inches ID/OD Nylon-6 pipes.
Fig. 7. The steady-state pressure drops over 8.52 ft. pipe length at various foam qualities or apparent foam viscosity at various shear rates (Base Case with Inclination angle 0°). (1 psi = 6.9 × 103 Pa; 1 cp = 10− 3 kg/(m s); 1 ft = 0.3048 m).
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Fig. 8. Pressure and apparent-viscosity contours for Base Case: (A) pressure values in psi over 8.52 ft length and (B) apparent-viscosity in cp calculated from pressure data. (1 psi = 6.9 × 103 Pa; 1 cp = 10− 3 kg/(m s); 1 ft = 0.3048 m).
3.1. Base Case (Inclination 0°) Fig. 5(A) through (D) show the base-case experiments at the liquid injection rate (Qw) of 20, 40, 60 and 80 cm3/min. In each experiment, the gas injection rate (Qg) varies from 200 to 5000 cm3/min step by step, first in an increasing order followed by a decreasing order. The results of sectional pressure drops from transducers A through H show a few interesting behaviors: (1) the plots are in general symmetric, meaning that there is no hysteresis involved with the change in gas flow rates; (2) there is a threshold value of gas flow rate, below which the steady-state sectional pressure drop increases with gas rate, but above which the steady-state sectional pressure drop decreases with gas rate, as well demonstrated in Fig. 5(A) and (B); and (3) the pressure data collected during the experiments look relatively stable below the threshold gas flow rate and relatively scattered above the threshold gas flow rate. These effects described in (2) and (3) are consistent with previous observations made by Gajbhiye and Kam (2011) in their horizontal-flow experiments (e.g. Fig. 2) in which the high-quality regime is characterized by alternating free gas and fine-textured foams (called “slug flow pattern”) and the low-quality regime is characterized by either finetextured homogeneous foam flow (called “plug flow pattern”) or segregated layered flow between foams and liquid (called “segregated flow pattern”).
Fig. 9. Pressure and apparent-viscosity contours for Case 1 (Inclination 45° upward): (A) pressure values in psi over 8.52 ft length and (B) apparent-viscosity in cp calculated from pressure data. (1 psi = 6.9 × 103 Pa; 1 cp= 10− 3 kg/(m s); 1 ft= 0.3048 m).
The steady-state pressure values read from Fig. 5(A) through (D) can be used to construct a plot of pressure drop (ΔP) vs. gas rate (Qg) (or, shear stress (τw) vs. shear rate (γw)) as shown in Fig. 6, and a plot of pressure drop (ΔP) vs. foam quality (fg) (or, apparent foam viscosity (μapp) vs. shear rate (γw)) as shown in Fig. 7. These plots can be drawn in a form of pressure or apparent viscosity contours as shown in Fig. 8. These figures clearly indicate that there exist two very distinct foam flow regimes which are separated by the threshold foam quality values, fg*. It should be noted that the pressure-drop values reported here are from pressure transducers B though G because of possible entry and exit effect, and the gas rates in Figs. 6 and 8 are values adjusted at the average pressure within the pipe (i.e., (pB + pG)/2). 3.1.1. Effect of inclination on two flow regimes (Case 1 through Case 4) Similar flow experiments are conducted at different inclination angles. They are named Case 1 through Case 4 for 45° upward, 90° upward, 45° downward, and 90° downward, respectively, of which the steady-state pressure drops and apparent foam viscosities are presented as shown in Figs. 9 through 12. The results from these figures show that the overall shape of pressure and viscosity contours are not noticeably affected by inclination angles. A closer look at the contour plots in Figs. 9 through 12 shows that the maximum apparent viscosity values are
A Superficial gas velocity (adjusted), ug[ft/sec]
A Contour values
Measured values
fg*
Superficial gas velocity (adjusted), ug[ft/sec]
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Calculated values
fg*
Superficial liquid velocity, uw[ft/sec] Fig. 10. Pressure and apparent-viscosity contours for Case 2 (Inclination 90° upward): (A) pressure values in psi over 8.52 ft length and (B) apparent-viscosity in cp calculated from pressure data. (1 psi = 6.9 × 103 Pa; 1 cp= 10− 3 kg/(m s); 1 ft = 0.3048 m).
around 300 cp, which indicates that the whole process is dominated by viscous force rather than gravitational force once fine-textured foams are formed. This implies that for foam rheology to be strongly affected by inclination angle, the region of interest should be where the apparent foam viscosity is relatively low. This in turn implies that the objective of this study is more relevant to the lower foam quality region in the low-quality regime, especially near or below the transition from segregated flow to plug flow pattern, which is discussed more in the following section.
3.2. Transition from segregated to plug flow pattern (Case 5) A series of experiments are followed in order to observe the pattern of foam flow in pipes. The results are shown in Figs. 13, 14, and 15 for horizontal, 45° upward and 45° downward experiments, respectively. As visualized by Gajbhiye and Kam (2011) from their flow experiments in horizontal pipes, three different flow patterns are also observed in our horizontal flow experiments: slug flow pattern in the high-quality regime where the pressure contours have some finite slopes (cf. Figs. 8 through 12); and either plug flow pattern or segregated flow pattern in the low-quality regime where the pressure contours are relatively flat (cf. Figs. 8 through 12).
Superficial gas velocity (adjusted), ug[ft/sec]
Superficial gas velocity (adjusted), ug[ft/sec]
B Contour values
Contour values Measured values
fg*
Superficial liquid velocity, uw[ft/sec]
Superficial liquid velocity, uw[ft/sec]
B
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Contour values
Calculated values
fg*
Superficial liquid velocity, uw[ft/sec] Fig. 11. Pressure and apparent-viscosity contours for Case 3 (Inclination 45° downward): (A) pressure values in psi over 8.52 ft length and (B) apparent-viscosity in cp calculated from pressure data. (1 psi = 6.9 × 103 Pa; 1 cp= 10− 3 kg/(m s); 1 ft= 0.3048 m).
The same visualization experiments are shown in Figs. 14 and 15 at 45° upward and 45° downward inclination angles. There are a few important aspects observed which should be noted as follows: (1) the three flow patterns observed in horizontal flow (i.e., slug, plug, and segregated flows) are still present in a wide range of inclination angles (all the way from 90° upward to 90° downward, although results are shown only for 45° upward and 45° downward); (2) for upward flow (e.g. Fig. 14), if the flow condition falls within the segregated flow pattern in the horizontal flow, the system repeats two states of (a) the layered flow of foam and liquid, both flowing together upward and (b) the upper foam layer flowing upward but the lower liquid layer flowing downward (the downward motion of liquid is accompanied by the accumulation of liquid at a certain location first, then as the liquid moving downward due to gravity is taken up by the following rising foams, the liquid either moves together with the foams as a distinct layer or merges into next-following foams helping create fine-textured foams); and (3) for downward flow (e.g. Fig. 15), if the flow condition falls within the segregated flow pattern in the horizontal flow, the lower liquid layer runs faster and the upper foam layer runs more slowly as the inclination becomes steeper (because of the liquid running faster, the liquid layer is thinner during downward flow compared to that during horizontal flow). These observations in upward and downward flow directions show that the formation of fine-textured foams, which is required for
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A
Superficial gas velocity (adjusted),ug[ft/sec]
254
Qg (cc/min)
Contour values
Slug flow pattern High-
Measured values
quality
2000
regime
fg* 500
Lowquality regime
200
B
Superficial gas velocity (adjusted),ug[ft/sec]
Superficial liquid velocity, uw[ft/sec]
Plug or Segregated flow pattern
Contour values
40
20
Qw(cc/min)
Calculated values
fg*
Superficial liquid velocity, uw[ft/sec] Fig. 12. Pressure and apparent-viscosity contours for Case 4 (Inclination 90° downward): (A) pressure values in psi over 8.52 ft length and (B) apparent-viscosity in cp calculated from pressure data. (1 psi = 6.9 × 103 Pa; 1 cp = 10− 3 kg/(m s); 1 ft = 0.3048 m).
Fig. 14. Flow patterns observed in Case 1 (Inclination 45° upward) (6 × 107 cm3/ min = 1 m3/s).
the transition from segregated flow pattern to plug flow pattern, is more favored for upward flow due to the relatively higher liquid fraction caused by sporadic downward flow of accumulated liquid, but less favored for downward flow due to the relatively lower liquid fraction caused by rapid downward liquid movement. This concept is depicted in Fig. 16 in which the envelope that separates segregated flow pattern from plug flow pattern (cf. Fig. 2) becomes smaller as the inclination angle changes from 90° downward to horizontal and eventually to 90° upward. This means that (1) in those experiments varying gas rate at fixed liquid rate, the threshold gas rate at which the transition from segregated flow to plug flow takes place is lower (cf. vertical line (A) in Fig. 16) and (2) in those experiments varying total gas and liquid rate at fixed foam quality, the threshold total rate at which the transition from segregated flow to plug flow takes place
Qg (cc/min)
Slug flow pattern Highquality
2000
Qg (cc/min)
Slug flow pattern regime
Highquality
2000
regime 500
Lowquality
500
Low-
regime
quality regime
200
200
Plug or Segregated flow pattern Plug or Segregated flow pattern 40
20
Qw(cc/min) Fig. 13. Flow patterns observed in Base Case (Inclination 0°) (6× 107 cm3/min= 1 m3/s).
40
20
Qw (cc/min) Fig. 15. Flow patterns observed in Case 3 (Inclination 45° downward) (6 × 107 cm3/ min = 1 m3/s).
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Highquality regime
Superficial gas velocity, [ug]
Slug flow pattern
fg*
Δp or µapp contours
Plug flow pattern (A)
(B) 90o Downward 0o Horizontal
Lowquality regime
90o Upward
Segregated flow pattern Superficial liquid velocity [uw] Fig. 16. Boundaries separating three different patterns: the transition from segregated to plug flow is significantly affected by inclination angles.
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state pressure contours are sensitive to the inclination angles. The major distinction between these two cases is that the former is governed by viscous force, while the latter is governed by gravitational force. Fig. 17 shows a schematic figure with the nature of these inclinationangle-specific pressure drops. In horizontal flow with no gravity effect, the steady-state pressure drop increases with gas velocity showing a slightly shear-thinning behavior (e.g. Figs. 5 and 6). In case of upward flow, the pressure drop first decreases with gas velocity because the flow is segregated (i.e., the gravitational force is dominant); then increases with gas velocity and merges with the locus of horizontal flow because the viscous force becomes dominant. In the case of downward flow, the gravity is acting in the opposite way such that the pressure drops are even lower than those in horizontal flow before merging into the plug flow pattern where the viscous force is dominant. This inclination-angle-dependent transition from segregated-flow pattern to plug-flow pattern is believed to be very important in the evaluation of cutting transport in deviated wells, and developing theoretical models based on the physics presented in this study deserves further studies. 4. Conclusions
is also lower (cf. line (B) in Fig. 16), as the inclination angle moves from 90° downward to 90° upward. It should be noted that the shape of the envelope appears to be concave in general because an increase in liquid rate at the same gas rate tends to create fine-textured foam more easily. It should be emphasized that in many foam applications such as foam drilling and fracturing, the large interfacial area between gas and liquid is highly desirable for the purpose of maximizing cutting transport and proppant delivery. Therefore, the fact that the boundary between segregated flow and plug flow is sensitive to the changes in inclination angle (cf. Fig. 16) implies that the inclination angle should be an important parameter in field treatments. 3.3. Implication of results to pressure contours at different inclination angles The results in Figs. 13 through 15 indicate that the pressure contours obtained from horizontal flow experiments are still applicable to the case of other inclination angles as long as the flow patterns fall into either slug flow in the high-quality regime or plug flow in the low-quality regime. On the other hand, if the flow pattern falls within segregated flow in the low-quality regime, the steady-
Upward flow
Upward Horizontal
Pressure drop, Δp
Downward
Gravity Dominant (Segregated Flow)
Viscous Force Dominant (Plug Flow)
Horizontal flow
Transition from segregated to plug flow
Downward flow
Gas velocity, uv Fig. 17. A schematic showing the transition from segregated flow to plug flow at different inclination angles.
From foam flow experiments carried out at different inclination angles and in a wide range of gas and liquid injection velocities, the following conclusions can be made: 1. Experimental results show that there exist two foam flow regimes consistently at all different inclination angles tested, including 90° upward, 45° upward, horizontal (0°), 45° downward, and 90° downward. The value of fg*, which separates the high-quality regime from the low-quality regimes, does not seem to be affected noticeably by inclination angles. As previous studies in horizontal pipes observed, the high-quality regime is characterized by slug flow and the low-quality regime is characterized by either plug flow or segregated flow, irrespective of inclination angles. 2. Once foam flow exhibits either slug flow pattern in the highquality regime or plug flow pattern in the low-quality regime, the rheology is dominated by viscous force due to relatively fine foam texture. If this occurs, the steady-state pressure contours are almost unaffected by inclination angles. On the other hand, once foam flow exhibits segregated flow pattern in the low-quality regime, the rheology is dominated by the gravity and the steadystate pressure drops are sensitive to inclination angles. 3. The transition from segregated flow to plug flow, which is crucial in many foam applications, occurs at higher foam quality (if liquid rate is fixed) or at higher total injection velocity (if foam quality is fixed) as the inclination angle moves from 90° upward, 45° upward, horizontal (0°), 45° downward, and eventually to 90° downward. This is because, when it comes to the creation of finetextured foams, a sporadic back flow of liquid phase results in a favorable condition in upward flow, and a rapid flow down of liquid phase results in an unfavorable condition in downward flow. Nomenclature A cross-sectional area of a pipe, ft 2. d inner diameter of a pipe, in. L length of a pipe, ft. p pressure, psi. Qt Total flow rate, gal/min. Qw Liquid rate, gal/min. Qg Gas rate, gal/min. ug Superficial gas velocity, ft/s. adj ug, Superficial gas velocity adjusted at elevated pressure, ft/s. ut Total superficial liquid velocity, ft/s. uw Superficial liquid velocity, ft/s.
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μapp γw τw Δp ΔpBG
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apparent viscosity, cp. the wall shear rate, s − 1. Wall shear stress, lbf/ft 2. pressure drop, psi. Pressure drop between transducer B and G, psi.
Acknowledgement This study is partly supported by Rural Research Institute and Keller professorship. We also express our appreciation to Stephan Company for their generous donations of surfactants and chemicals. We wish to recognize the assistance of Gerry Masterman, Darryl Bourgoyne and Fenelon Nunes for their help in setting up the laboratory. References Bogdanovic, M., Gajbhiye, R.N., Kam, S.I., 2009. Experimental study of foam flow in pipes: two distinct flow regimes. Colloids Surf. A Physicochem. Eng. Asp. 56–71 April. Bonilla, L.F., Shah, S.N., 2000. Experimental investigation on the rheology of foams. Paper SPE 59752 presented at 2000 SPE/CERI Gas Technology Symposium, Calgary. April 2000. Capo, J., Yu, M., Miska, S.Z., Takach, N., Ahmed, R.M., 2006. Cutting transport with aqueous foam at intermediate-inclined wells. SPE Drilling & Completion. June 2006, pp. 99–107. Chen, Z., Duan, M., Miska, S.Z., Yu, M., Ahmed, R.M., Hallman, J., 2009. Hydraulic predictions for polymer thickened foam flow in horizontal and directional wells. SPE Drilling & Completion. March 2009, pp. 40–49. David, A., Marsden, S.S., 1969. The rheology of foam. Paper SPE 2544 presented at Fall Meeting of the Society of Petroleum Engineers of AIME. September 1969. Deshpande, N.S., Barigou, M., 2000. The flow of gas liquid foams in vertical pipes. Chem. Eng. Sci. 4297–4309. February.
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