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Characterization of two-phase flow in a single rock joint
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International Journal of Rock Mechanics & Mining Sciences 43 (2006) 216–223 www.elsevier.com/locate/ijrmms
Characterization of two-phase flow in a single rock joint P.G. Ranjitha,, S.K. Choib, M. Fourarc a
Department of Civil Engineering, Monash University, VIC 3800, Australia b CSIRO, Division of Petroleum Resources, Victoria, Australia c Institut Franc- ais du Pe´trole, France Accepted 9 June 2005 Available online 15 August 2005
Abstract An experimental study using a triaxial apparatus was used to analyze the two-phase flow patterns in jointed rock specimens. Rock specimens having a single natural fracture were tested for two-phase flow of water and air. Triaxial tests were conducted to characterize the two-phase flow through fractured granite specimens at low confining pressures. It was found that for a relatively smooth joint (JRCo6), bubble flow pattern occurred within the rock joint when the gas velocity is below 15 m/s. The average velocity of water usually varied between 0.1 and 0.5 m/s for bubble flow patterns. In this velocity range, air bubbles were able to form along the joint walls or to be randomly displaced within the water phase. When the gas velocity inside the rock joint exceeded 22 m/s, the flow patterns took annular form for non-zero capillary pressures (i.e., injected gas pressure is not equal to injected water pressure). At elevated (40.25 MPa) gas injection pressures, the gas occupied the main part of the fracture and the liquid was able to flow as an unstable film forming an annular flow along the joint. When the annular flow developed, the mixture flow pattern was independent of the air flow velocity. This was due to the fact that once the injected air velocity reached a critical value (i.e., 20 m/s), water velocity inside the joint was negligible for a given confining pressure and injected water pressure. Further increase in inlet air pressures developed a single-phase air flow with no water flow. r 2005 Elsevier Ltd. All rights reserved. Keywords: Two-phase flow; Rock joints; Annular flow; Bubble flow; Triaxial
1. Introduction A rock mass carries both water and air through interconnected fractures and pores. On some occasions (e.g., in the petroleum recovery process), the rock mass may be partially saturated with three phases, such as oil–water–gas. Two-phase flow through jointed rock, which is the main focus in this study, has gained increased interest in both industry and academia due to the important applications in petroleum engineering, mining engineering and nuclear engineering. Two-phase flow in rock fractures can be in the form of gas–liquid, gas–solid, liquid–liquid or liquid–solid. The most complex form is the gas–liquid flow because of the complex Corresponding author. Tel.: +61 399054982.
E-mail address: [email protected] (P.G. Ranjith). 1365-1609/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2005.06.001
interaction between each phase [1]. For example, gas can dissolve in a liquid, and the solubility depends on temperature and pressure. The theory of flow through a saturated fracture has undergone much development during the past two decades [2–4]. In contrast, the flow mechanism of two-phase flow in fractures is still at its infancy because of the complex interaction between each phase and change of fluid flow patterns with time. Tokunaga and Wan [5] measured water flow as layers on a fracture surface of a Bishop Tuff. From their experiments, it was shown that the measured average surface film thickness along the rock fracture ranged from 2 to 70 mm with average film velocities in the range of 2–40 m/d. Persoff and Pruess [6] studied experimentally two-phase flow visualization and relative permeability through natural rough walled fractures. Transparent replicas of natural rock fractures were used
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for direct observation of the distribution of each phase along the fracture. Unlike in the other two-phase flow visualization experiments [7,8], Persoff and Pruess [6] did not report different types of two-phase flow patterns observed in natural rough fractures. Fourar et al. [8] observed different flow patterns via two parallel glass plates and two parallel brick layers, which were not subjected to external loads. The experimental results obtained in that work can be directly applied to simplified two-phase flow analysis, but are not suitable for the characterization of coupled mechanical-air-fluid flow that usually takes place within rock joints under stress. Transparent replicas of natural rock fractures were used for direct observation of the distribution of phases along the fracture. Different types of two-phase flow patterns were observed through natural rough fractures. None of the two-phase experiments reported in the literature has used natural rock fractures subjected to in situ stresses to characterize two-phase flow patterns for various inlet water and air pressures. Direct visual observation of two-phase flow in real rock fractures subjected to high-pressure triaxial loading conditions is difficult in conventional laboratory conditions. This problem is approached by considering an indirect approach (to be discussed below) used by other researchers in studying multiphase flow in pipes. The study described here is limited to the analysis of twophase flow structures consisting of water and gas only. This paper presents triaxial test results conducted to characterize two-phase flow patterns in smooth-walled
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fractures. The following sections describe the characteristics of two-phase flow patterns that have been observed based on the existing data for narrow channels and the flow mapping technique.
2. Types of flow patterns Knowledge of flow patterns is important in the study of transient flows and steady-state flows in order to incorporate the flow parameters (e.g., fluid properties and wall shear stresses) in numerical models. The inlet pressures of each phase, their physical properties, interactions between the phases and the geometry of flow paths determine the flow patterns in a pipe or rock joint. Depending on flow conditions, there are regions of a pipe or rock joint where (a) both phases are continuous, (b) one phase is continuous and the other is discontinuous or (c) both phases are discontinuous (Fig. 1). As shown in Fig. 1, common flow patterns which occur in a pipe can be categorized as stratified, bubble, droplet, annular, complex, plug and churn flows [7,9–12]. A wide variety of flow pattern definitions have been proposed for two-phase flow patterns [1]. Vertical flow through a rock joint was observed in the triaxial testing facility used in this study. Definitions of flow regimes for vertical flow are described according to the definitions given by Hetsroni [1]: (1) bubble flow—the liquid (water) phase is continuous and dispersion of bubbles flow within the liquid phase, (2) annular flow— gas occupies the center of the path while the liquid flows
Two-phase flow
Continuous flow
Discontinuous flow
(both phases)
Stratified flow
One phase
Annular flow
Bubble
Droplet flow
Both phases
Slug flow
Churn flow
Fig. 1. Common two-phase flow patterns observed in pipe flow.
Complex flow
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along the joint wall as a film. Detailed descriptions of other two-phase flow patterns are given elsewhere [1,9,10,13]. In continuous flow, both phases exist all along the flow path, whether stratified or annular. In discontinuous flow, one phase (or both) is discontinuous (e.g., bubble, droplet, slug and complex flows). Various types of flow patterns may develop due to the combined effects of the following: (1) magnitude of pressure of each phase, (2) properties of each phase (e.g., viscosity, density), (3) flow path geometry, and (4) flow path surface tension and surface contamination.
1.00
Liquid superficial velocity,m/sec
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Bubble flow
Fingering bubble flow
0.10
P
Annular flow Complex flow
Q Droplet flow
0.01 Not investigated
R
S
3. Determination of flow patterns Two approaches are usually employed to identify flow structures: (1) visual observations supported by a photographic method, and (2) an indirect method based on selected fluid flow parameters such as superficial velocities. The visual observation method is only possible when the flow takes place through transparent materials like glass or plastic. A wide variety of highspeed photographic techniques are used in studying twophase flow patterns [11,14,15]. Experimental work on identification of gas–water flow patterns in a narrow horizontal channel using a combined visual observation and photographic method was carried out by Fourar and Bories [7]. They observed different flow patterns varying from bubble flow to droplet flow. Mishima and Hibiki [13] studied two-phase flow through smalldiameter (1.05–4.08 mm) vertical tubes, and they observed the transition of flow patterns from bubble flow to annular flow with the increase in gas pressure. Indirect methods of analyzing the flow pattern of a gas–liquid, two-phase flow system depend on measurements of some flow parameters (e.g., superficial velocity) and characterization of the results in terms of flow patterns [1]. This technique is particularly suitable when the flow takes place through rock fractures as flow is not visible under certain loading (e.g., triaxial) conditions. In multiphase flow analysis through pipes, the common procedure to identify flow patterns is to plot the liquid superficial velocity against the gas superficial velocity. Superficial velocity is defined by researchers as the flow rate of the phase per unit cross-sectional area [16,17]. Such a plot of water–gas flow through horizontal glass plates, artificially roughened horizontal plates and vertical small diameter tubes is shown in Fig. 2 [7]. Irrespective of the flow path geometry (i.e., smooth or rough), these researchers observed the same range of flow patterns in both smooth and rough fractures. Moreover, at small gas superficial velocity and large water superficial velocity, Fourar and Bories [7] found formation of bubble flow. Golan and Stenning [16], and Mishima and Hibiki [13] observed annular, oscillatory and slug flow patterns for elevated gas and liquid
0.00 0.01
0.10 1.00 Gas superficial velocity, m/sec
10.00
Fig. 2. Possible water–gas flow patterns in a channel (data from Fourar and Bories, 1995).
superficial velocities. This shows that bubble flow, in which liquid flow is dominant, occurs at low gas velocities. In contrast, annular flow may develop at elevated gas velocities. Unlike flow through transparent pipes, no direct observations or photographic techniques can be employed in determining the flow pattern through rock. Nevertheless, the photographic method may be used to map the flow pattern in artificial fractures made out of transparent plastics. For example, a natural rock joint surface may first be transformed into a transparent plastic surface, and subsequently water and air flow are driven through the plastic joint to observe the flow type when the joint is subjected to no loading or uniaxial loading. However, this approach cannot be used to visualize the two-phase flow pattern in rock fractures under triaxial test conditions, because a high-pressure triaxial cell designed for testing rock is constructed of high strength steel and the sample is covered with a thick membrane. Therefore, in this study, the indirect method discussed above is used to characterize two-phase flow patterns from the triaxial test data. The indirect approach may have limitations, but it is useful to identify whether the flow in natural rock joints is bubble or annular.
4. Experimental design and procedures Laboratory work on water–gas flow through fractured rocks is conducted using a two-phase, highpressure triaxial apparatus. The detailed design concepts of the apparatus, test procedures and test results on twophase flow rates for different boundary conditions are
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given elsewhere [9,10]. The following section briefly describes the salient features of the two-phase triaxial apparatus, which can measure relative permeability characteristics, as well as the stress–strain behavior of rocks subjected to axial and confining pressure conditions. The apparatus can be used for the study of both single- and two-phase flow through soft and hard rocks. In two-phase flow, both water and air simultaneously flow through the fractured specimen. In this equipment, water and air phases are carried by two separate tubes to the bottom end of the specimen (Fig. 3). In order to prevent water and air interaction before entering the specimen, the two tubes which carry water and air are integrated fitted with several on/off valves and check valves. These valves have been attached to the bottom plate to ensure that there is no back flow of one phase through the tube of the other phase. In order to measure the pressure of each phase, a pressure transducer is attached to each phase line. Fractured granite specimens having a diameter of 55 mm and length twice the diameter with low matrix permeability (about of 1019 m2) were selected for the laboratory investigation. All 55 mm diameter cores used for testing contained a single fracture. Measurements of fractured rock surfaces were made using a mechanical profilometer, which can digitise the joint surface in three dimensions by taking a series of parallel lines along the joint. In the course of the measurements, the digital pointer was lowered to the surface to obtain coordinates, and by moving the pointer systematically, many points of the surface were mapped. The individual joint profiles along each line segment were plotted (not included in the paper) in order to estimate the joint roughness coefficient (JRC) values for each profile. The individual joint profiles were matched with standard profiles [18] to estimate the average JRC value of the tested samples. The JRC values of the specimens were estimated as 4 and 5 which correspond to a fairly smooth joint surface. It should be noted that JRC estimation of rough joints should be carried out using
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either direct shear, tilting tests or more sensible statistical prameters such as mean and standard deviation [4,19]. However, the use of standard profiles approach is adequate enough for fairly smooth joints tested in this study. Specimen 1 (JRC ¼ 4) was subjected to higher confining pressure (1.0–3.0 MPa) than that of specimen 2 (0.5–1.0 MPa). The orientation of the fracture in the triaxial specimen was near vertical (Fig. 3). Oil was used as confining fluid in the cell and the axial stress was supplied by a servo-controlled Instron Machine. The magnitudes of fluid pressure of each phase and confining pressure were recorded by individual pressure transducers. For a given confining pressure and axial stress, the specimen was first saturated with water, and then the air phase was forced through the specimen. Two types of tests based on the magnitude of inlet fluid pressures were conducted: (a) inlet air pressure ¼ inlet water pressure (Pa ¼ Pw), and (b) Pa6¼Pw. Once the water and air mixture had passed through the Dreschel bottle, steadystate air flow rates and water flow volumes were recorded by the film flow meter [19] and electronic weighing scale, respectively [9,20].
5. Results and discussions Two-phase flow takes longer time than single-phase flow in a rock fracture to reach steady state. A transient state of two-phase fluid flow was observed and results of individual phase flow rates with time (in log scale) are shown in Fig. 4. In order to improve the clarity of the plot, the measured time was plotted in log scale while the water and air flow rates were plotted in two different scales (in normal scale) in the left and right vertical axes, respectively. The testing procedure for the results given in Fig. 4 is given below. The jointed granite rock 80
4.0 Steady state air flow
Two-phase flow Confining pressure0.5MPa
2.0
40
Pa = Pw = 0.2MPa Water flow Air flow
0.0
Air flow rate, ml/sec
Water flow rate, ml/sec
Trasient state of two-phase flow
Steady state water flow 1
10
100
0 1000
Time, min Fig. 3. Fluid pressure across the triaxail apparatus system.
Fig. 4. Observations of transient and steady-state two-phase flow through a fractured rock specimen.
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specimen was first saturated with water by applying an inlet water pressure of 0.2 MPa. After 45 min, a steadystate water flow rate (3.8 ml/s) was observed from the sample (the time, 45 min is not shown in Fig. 4). This indicated that the sample was fully saturated with water after 45 min under the given boundary conditions (i.e., confining pressure of 0.5 MPa and an inlet water pressure of 0.2 MPa). Once the steady-state water flow rate (3.8 ml/s) was observed from the specimen, the inlet air pressure was gradually increased from 0 to 0.2 MPa. Both inlet air and water pressures were then maintained at 0.2 MPa. At time (t) ¼ 0, the water flow rate was measured as 3.8 ml/s and no air flow rate was observed. At 8 min, the water flow rate had decreased to 1.6 ml/s and the measured air flow rate was 6.8 ml/s (note the two different scales for air and water flow rates). An increase in water flow rate was observed at 9 min. This occurred because the built up air phase inside the joint suddenly displaced water in the fracture causing a larger flow rate from the specimen. However beyond 9 min, the air flow rate continuously increased to 60 ml/s while the water flow rate decreased to 0.6 ml/s. It was noted that the steady-state two-phase flow was reached after 150 min and the steady-state value was further observed for another 200 min to make sure the two-phase flow rates were independent of time. For classification of flow patterns, the measured steady-state flow rates have been used in plots discussed in later sections. The measured steady-state flow rates were used to calculate the superficial velocity (va) of each phase, using Eqs. (1) and (2) given below [7,10,16,17]: ka K ra qP qz qa þ rg va ¼ ¼ , (1) qx qx a ma Aa ( ea ¼
12mq w qP=qx þ rg qz=qx
)1=3 ,
(2)
a
where a is the phase (a and w represent air and water phases, respectively); m the dynamic viscosity; k the intrinsic permeability; Kr the relative permeability; dP the pressure difference along the joint length, dx; q the flow rate; r the density; g the acceleration due to gravity; z the vertical distance; A the area perpendicular to the flow (e w), where e and w are mean joint aperture and joint width, respectively. As discussed by Olsson [23], the Reynolds number of fluid flow was used to ensure flow was laminar flow without turbulence. The measured individual flow rates were also used to calculate Reynolds numbers which were found to be well below 1000. The magnitude of critical Reynolds number representing the laminar flow regimes between parallel walls is 1000 [24]. This showed that the fluid flows (both air and water) within the rock joint were laminar.
5.1. Characterization of flow patterns in a rock fracture Using the above-mentioned indirect technique (i.e., based on superficial velocity), the flow patterns within natural rock fractures were studied for different boundary conditions, including confining pressures and inlet fluid pressures. Based on measured steadystate two-phase flow rates, the estimated water superficial velocity and the air superficial velocity were plotted in Fig. 5. In order to improve the clarity of the plots, a logarithmic axis was selected for the water superficial velocity because the air superficial velocity was significantly higher than that of water. For the results shown in Figs. 5a and b, the specimen was first saturated with water and the inlet water pressure was maintained at a constant value of 0.25 MPa and the air injection was then started and increased stepwise (i.e., Pa6¼Pw). For example, at each new air pressure (e.g., 0.1 MPa), the steady state of air and water flow rates were measured after a long period of time. When steady state was reached for each phase, flow readings were measured. For the next step, the air pressure was increased to another value (e.g., 0.125 MPa) and the steady-state two-phase flow was measured (the inlet water pressure was maintained at 0.25 MPa). In a similar manner, the inlet air pressure was gradually increased until the specimen was fully saturated (the existence of an immobile water film or cognate water content) with air. Kostakis and Harrison [25] observed virtual stops of gas bubble movement due to high water flow in a natural rock fracture. 5.2. Use of superficial velocity to characterize flow patterns Using Eqs. (1) and (2), the superficial velocity of each phase was calculated for the measured steady-state twophase flow rate. The corresponding applied inlet air pressures are given in Fig. 5 on the top horizontal axis. It can be seen that the estimated air flow superficial velocities are extremely high compared to the water superficial velocities. With an increase of inlet air pressures (shown on top horizontal axis—Figs. 5a and b), the air phase occupies a larger part of the void space in the rock joint than the water phase at a given confining pressure. Therefore, due to the effects of relative permeability, the lower viscosity and the much higher compressibility of air compared to water, the measured two-phase air flow rate is much higher than that of water flow rate and as a result the estimated air superficial velocities are significantly larger. This has been observed by several researchers for two-phase flow in pipes and narrow smooth and rough channels [8,13,22]. It could be argued that air superficial velocities in Fig. 2 are substantially smaller than those of Fig. 5. This is because data shown in Fig. 2 are for two-phase
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Inlet air pressure, kPa 275
200
350
1.00 1.0
Specimen 1 (JRC=4)
Curve C
pa p and Pw = 0.25 MP a w Confining pressure = 1.0 MPa
Curve B
Confining pressure = 2.0 MPa
Inlet air pressure, kPa 115
pa p and Pw = 0.125MPa w
0
0
Confining pressure = 2.0MPa
5 10 Air superficial velocity, m/sec
Inlet air pressure, kPa 325
Annular flow
10 20 Air superficial velocity, m/sec
d Expecte
Water superficial velocity, m/sec
Water superficial velocity, m/sec
Specimen 2 (JRC=5)
15
(d)
trend
G G
F
Annular flow F
Specimen 2 (JRC=5) pa = pw Confining pressure = 0.5MPa Confining pressure = 1.0MPa
E
0
30
650
Bubble flow
0.1
Confining pressure = 1.0MPa
(b)
Confining pressure = 1.0MPa
26 1.0
Bubble flow
0.00
p = p w a
B
180
0.10
Confining pressure = 0.5MPa
Annular flow
A
(c)
Transition flow (e.g., slug, complex)
0.01
A
trend
1.00
0.1
30
D
Specimen 1 (JRC = 4)
Annular flow
10 20 Air superficial velocity, m/sec
50
B
cted
0
D
C
Expe
0.00 (a)
600
Bubble flow
end
Curve A
e c te d tr
Bubble flow
Inlet air pressure, kPa 400
C
E xp
0.10
Confining pressure = 3.0 MPa
200
Water superficial velocity, m/sec
Water superficial velocity, m/sec
Transition flow (e.g., slug, complex)
0.01
221
E
5 10 Air superficial velocity, m/sec
15
Fig. 5. (a) Possible flow patterns in a fractured granite specimen for capillary pressures (specimen 1: JRC ¼ 4). (b) Possible flow patterns in a fractured granite specimen for capillary pressures (specimen 2: JRC ¼ 5). (c) Possible flow patterns in a fractured granite specimen at zero capillary pressure (specimen 1: JRC ¼ 4). (d) Possible flow patterns in a fractured granite specimen at zero capillary pressure (specimen 2: JRC ¼ 5).
flow through a glass channel subjected to low inlet fluid pressures. In contrast, two-phase flow through natural rock fractures at given confining pressure and elevated inlet fluid pressures are shown in Fig. 5. Fig. 5a shows two-phase flow velocities for specimen 1 at confining pressures of 1.0, 2.0 and 3.0 MPa. Data shown in Fig. 5b are for specimen 2 which was subjected to relatively lower confining pressures (i.e., 0.5 and 1.0 MPa) than that of specimen 1. In order to characterize the twophase flow pattern through the tested rock fractures, the data shown in Fig. 5 were compared with the data in Fig. 2 which presents various flow patterns in a glass channel. The flow patterns changes with increasing air flow velocity in the tested rock joints are generally gradual (Figs. 5a, b) rather than staged as shown for
flow in tubes (Fig. 2), indicating gradual transition from bubble flow to complex flow. This may be due to combined effects of roughness of joints, triaxial boundary conditions and some other effects which need a substantial study to clarify them. One should not use the magnitude of superficial velocities to compare Figs. 2 and 5 since different boundary conditions were employed. Instead, the change in velocity trends which indicate change in flow patterns was used in this paper to classify flow patterns in a given rock joint in a triaxial cell. It is important to note here that the tested rock fracture surfaces were fairly smooth because the estimated joint roughness coefficients were 4 and 5 for specimens 1 and 2, respectively. However, one needs to take into account
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that the rock joints tested in this study were subjected to different loading conditions (e.g., confining pressures, axial stresses). In this study, bubble flow was usually experienced at relatively low air superficial velocities (curve PQ in Fig. 2). An abrupt change of water velocity with air velocity was associated with the formation of a new flow pattern (curves QR, RS in Fig. 2). According to Fig. 5, for both specimens, bubble flow was experienced when the air superficial velocity was below 15 m/s. In this region, air bubbles can form along the joint walls or can be randomly displaced within the water phase. A sudden change of water superficial velocity with air superficial velocity occurred once the air superficial velocity exceeded 15 m/s. This was due to the fact that the two-phase flow pattern within the fracture was changing. It was relatively difficult to predict the exact flow pattern when the air superficial velocity ranged from 15 to 20 m/s. The flow pattern within this range may have been a complex flow. Fourar and Bories [7] visually observed a complex flow in which an abrupt change of water velocity with air velocity occurred (Fig. 2). During the complex flow (Fig. 2), the water velocity dropped sharply from 0.02 to 0.0025 m/s and the air velocity increased from 0.2 to 1.0 m/s. Also, in Fig. 5, during the complex flow, the water superficial velocity decreased from 0.1 to 0.01 m/s and the air superficial velocity increased from 15 to 20 m/s for the applied confining pressure of 3.0 MPa. In addition several researchers [7,13,16] have reported similar types of flow patterns through narrow channels and pipes. According to Figs. 5a and 5b, two-phase flow became an annular flow when the air superficial velocity exceeded 20 m/s. At higher air superficial velocities (exceeding 20 m/s), the air occupied the main part of the fracture and the water flow as an unstable film along the walls. After the annular flow developed, the flow pattern was independent of the air flow velocity until single phase air flow formed. This is due to the fact that once the inlet air velocity reached a critical value (20 m/s), the water velocity in the joint was negligible for a given confining pressure and inlet water pressure. When the inlet air pressure increased up to 0.25 MPa, no water flow was observed through the sample. This indicates that the rock joint was completely filled with air (or rather the thin water film became immobile—cognate water).
5.3. Effects of confining pressure on water– gas flows The effects of confining pressure on two-phase flow are also discussed here. The average hydraulic apertures of specimen 1 at confining pressures of 1.0, 2.0 and 3.0 MPa were 4.1, 3.5 and 3.0 mm, respectively. Specimen 2 had average hydraulic apertures of 4.2 and 3.8 mm at confining pressures of 0.5 and 1.0 MPa. It was observed that an increase in confining pressure usually resulted in
a decrease of the two-phase flow rates due to the closure of the fracture. For the results shown in Figs. 5c and d, the experiment was conducted so that the magnitudes of inlet air pressure (Pa) equalled the inlet water pressure (Pw). When Pa equals Pw, capillary pressure, which is defined as the difference between inlet air pressure (Pa) and water pressure (Pw), at the inlet, was zero. For the data shown in Figs. 5c and d, the specimen was first saturated with water at a given inlet water pressure. The air injection was then started and the inlet air pressure was made to be equal to the applied inlet water pressure. For example, at given air and water pressures (e.g., Pa ¼ Pw ¼ 0.1 MPa), the steady-state air and water flow rates were measured. Before starting the next phase, the air injection was stopped and the sample was flushed and saturated with higher inlet water pressure (e.g., Pw ¼ 0.15 MPa) to remove all trapped air inside the fracture. The air phase was then introduced and increased to a pressure of 0.15 MPa, and the steadystate two-phase flow was measured. As explained before, two-phase flow rates were measured when capillary pressure equals zero at the inlet and the superficial velocity of each phase was estimated using Eqs. (1) and (2). The corresponding applied inlet air pressures are given on the top horizontal axis (Figs. 5c and d). At a given confining pressure (i.e., 1.0, 2.0 MPa) and low inlet air and water pressures, as expected, the two-phase superficial velocities were small because the measured flow rate of each phase was small. During the testing program, it was not possible to measure two-phase flow when inlet pressures were below 0.1 MPa for confining pressures of 1.0 and 2.0 MPa (Fig. 5c). The expected trends for small values of inlet water and air pressures are also shown in Figs. 5c and d (curves AB, A0 B0 and E0 F0 ). However, at a confining pressure of 0.5 MPa, it is possible to estimate superficial velocities of two-phase flow at small inlet fluid pressures (curve EF—Fig. 5d). With an increase in inlet fluid pressures (i.e., water and air pressures were injected so that Pa ¼ Pw), the relationship between the air and water superficial velocities is represented by Figs. 5c and d: Curves ABCD, A0 B0 C0 D0 , EFGH and E0 F0 G0 V w ¼ a ln V a þ b,
(3)
where V is the superficial velocity, a and b are coefficients and subscripts ‘a’ and ‘w’ represent air and water, respectively. It may be expected that at low air superficial velocities, the increase in water superficial velocity would be higher than at elevated air superficial velocities. However, as discussed above, in this study air superficial velocity was always higher than that of water superficial velocity irrespective of the magnitude of inlet air or water pressures. Once the air superficial velocity exceeded 12 m/s, the change in water superficial
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0
velocity was marginal (curves CD, C D0 and FG). At small inlet water and air pressures, air bubbles dispersed in the flowing liquid when the joint was initially saturated with water. As shown in Fig. 5, bubble flow was observed in an initially water saturated joint when the gas and water velocities are relatively small as well as for zero inlet capillary pressure. At elevated gas pressures, the flow pattern may be annular flow when the inlet capillary pressure is zero. Although these plots do not clearly distinguish the different flow regimes, they suggest the changes from bubble flow patterns to annular flow regimes, and can be used to study the change in gas-liquid flow patterns in a fractured rock mass.
6. Conclusions Different flow patterns have been observed by other researchers during laboratory experiments on two-phase air–water flow through replicas of natural rock fractures. These flow patterns could be stratified, bubble, droplet, annular, complex, plug and churn flows. The developed triaxial apparatus has been successfully used to study two-phase water and air flow through naturally fractured rock specimens. Different confining pressure and inlet water and gas pressures can be applied to the specimen. From the measured variation in superficial velocities of the gas and water phases under different stress and inflow boundary conditions, change of flow patterns in rock joints can be inferred from the results. From the experimental results, it has been observed that the flow pattern depends on the confining pressure and inlet water and air pressures. Annular flow usually occurs at elevated inlet gas pressures, whereas bubble flow may develop at high-liquid pressures compared to gas pressures. At higher gas inlet pressures, the gas occupies the main part of the fracture and the liquid may flow as an unstable film. The phase superficial velocity corresponding to the different flow patterns depends on the confining pressure.
References [1] Hetsroni G. Handbook of multiphase system, 1st ed. Hemisphere Publishing Corporation, 1982, ISBN:0-07-028460-1. [2] Lee CH, Farmer I. Fluid flow in discontinuities rocks. London: Chapman & Hall; 1993 169p.
[3] Witherspoon PA, Wang JSY, Iwai K, Gale JE. Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour Res 1980;16(6):1016–24. [4] Zimmerman RW, Bodvarsson GS. Hydraulic conductivity of rock fractures. Transp Porous Media 1996;23:1–30. [5] Tokunaga TK, Wan J. Water film flow along fracture surfaces of porous rock. Water Resour Res 1997;33(6):1287–95. [6] Persoff P, Pruess K. Two-phase flow visualization and relative permeability measurement in natural rough-walled rock fractures. Water Resour Res 1995;31(5):1175–86. [7] Fourar M, Bories S. Experimental study of air-water two-phase flow through a fracture (narrow channel). Int J Multiphase Flow 1995;21(4):621–37. [8] Fourar M, Bories S, Lenormand R, Persoff P. Two-phase flow in smooth and rough fractures: measurement and correlation by porous medium and pipe flow models. Water Resour Res 1993;29(11):3699–708. [9] Indraratna B, Ranjith PG. Laboratory measurement of two-phase flow parameters in rock joints based on high-pressure triaxial testing. J Geotech GeoEnviron Eng-ASCE 2001;127(6):530–42. [10] Ranjith PG. Analytical and experimental modeling of coupled water and air flow through rock joints. PhD thesis, University of Wollongong, Australia; 2000. [11] Hewitt GF, Lovegrove PC. A mirror-scanner velocimeter and its application to wave velocity measurement in annular two-phase flow. Report AERE-R3598, UKAEA, Harwell; 1969. [12] Fiori, Bergles. A study of boiling water flow regimes at low pressure. MIT Rep 1966:3582–640. [13] Mishima K, Hibiki T. Some characteristics of air-water two-phase flow in small diameter vertical tubes. Int J Multiphase Flow 1996;22(4):703–12. [14] Delhaye JM. Optical methods in two-phase flow. Proceedings of the dynamic flow conference. Dynamic measurement unsteady flow; 1979. p. 321–43. [15] Arnold CR, Hewitt GF. Further developments in the photography of two-phase gas–liquid flow. Report AERE-R5318, UKAEA, Harwell; 1967. [16] Golan LP, Stenning AH. Two-phase vertical flow maps. Proc Inst Mech Eng 1969;184(3c):110–6. [17] Taitel Y, Dukler AE. A model for predicting flow regime transitions in horizontal and near horizontal gas–liquid flow. AIChE J 1976;22:47–55. [18] Barton N. Review of a new shear-strength criterion for rock joints. Eng Geol 1973;7(4):287–332. [19] Lanaro F. A random field model for surface roughness and aperture of rock fractures. Int J Rock Mech Min Sci 2000; 37:1195–210. [20] STEC, Film flow meter, instruction manual, Kyoto, Japan; 1999. [22] Gould TL. Vertical two-phase flow in oil and gas wells. PhD thesis, University of Michigan; 1972. [23] Olsson, R. Mechanical and hydromechanical behaviour of hard rock joints a laboratory study. PhD thesis, Chalmers University of Technology; 1998. [24] Street RL, Gary ZW, John KV. Elementary fluid mechanics, 7th ed. New York: Wiley; 1996 757p. [25] Kostakis K, Harrison JP. Numerical analysis of gas–bubble flow in water-filled natural fractures. Comput Geotech 1999; 24(1):3–28.
International Journal of Rock Mechanics & Mining Sciences 43 (2006) 216–223 www.elsevier.com/locate/ijrmms
Characterization of two-phase flow in a single rock joint P.G. Ranjitha,, S.K. Choib, M. Fourarc a
Department of Civil Engineering, Monash University, VIC 3800, Australia b CSIRO, Division of Petroleum Resources, Victoria, Australia c Institut Franc- ais du Pe´trole, France Accepted 9 June 2005 Available online 15 August 2005
Abstract An experimental study using a triaxial apparatus was used to analyze the two-phase flow patterns in jointed rock specimens. Rock specimens having a single natural fracture were tested for two-phase flow of water and air. Triaxial tests were conducted to characterize the two-phase flow through fractured granite specimens at low confining pressures. It was found that for a relatively smooth joint (JRCo6), bubble flow pattern occurred within the rock joint when the gas velocity is below 15 m/s. The average velocity of water usually varied between 0.1 and 0.5 m/s for bubble flow patterns. In this velocity range, air bubbles were able to form along the joint walls or to be randomly displaced within the water phase. When the gas velocity inside the rock joint exceeded 22 m/s, the flow patterns took annular form for non-zero capillary pressures (i.e., injected gas pressure is not equal to injected water pressure). At elevated (40.25 MPa) gas injection pressures, the gas occupied the main part of the fracture and the liquid was able to flow as an unstable film forming an annular flow along the joint. When the annular flow developed, the mixture flow pattern was independent of the air flow velocity. This was due to the fact that once the injected air velocity reached a critical value (i.e., 20 m/s), water velocity inside the joint was negligible for a given confining pressure and injected water pressure. Further increase in inlet air pressures developed a single-phase air flow with no water flow. r 2005 Elsevier Ltd. All rights reserved. Keywords: Two-phase flow; Rock joints; Annular flow; Bubble flow; Triaxial
1. Introduction A rock mass carries both water and air through interconnected fractures and pores. On some occasions (e.g., in the petroleum recovery process), the rock mass may be partially saturated with three phases, such as oil–water–gas. Two-phase flow through jointed rock, which is the main focus in this study, has gained increased interest in both industry and academia due to the important applications in petroleum engineering, mining engineering and nuclear engineering. Two-phase flow in rock fractures can be in the form of gas–liquid, gas–solid, liquid–liquid or liquid–solid. The most complex form is the gas–liquid flow because of the complex Corresponding author. Tel.: +61 399054982.
E-mail address: [email protected] (P.G. Ranjith). 1365-1609/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2005.06.001
interaction between each phase [1]. For example, gas can dissolve in a liquid, and the solubility depends on temperature and pressure. The theory of flow through a saturated fracture has undergone much development during the past two decades [2–4]. In contrast, the flow mechanism of two-phase flow in fractures is still at its infancy because of the complex interaction between each phase and change of fluid flow patterns with time. Tokunaga and Wan [5] measured water flow as layers on a fracture surface of a Bishop Tuff. From their experiments, it was shown that the measured average surface film thickness along the rock fracture ranged from 2 to 70 mm with average film velocities in the range of 2–40 m/d. Persoff and Pruess [6] studied experimentally two-phase flow visualization and relative permeability through natural rough walled fractures. Transparent replicas of natural rock fractures were used
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for direct observation of the distribution of each phase along the fracture. Unlike in the other two-phase flow visualization experiments [7,8], Persoff and Pruess [6] did not report different types of two-phase flow patterns observed in natural rough fractures. Fourar et al. [8] observed different flow patterns via two parallel glass plates and two parallel brick layers, which were not subjected to external loads. The experimental results obtained in that work can be directly applied to simplified two-phase flow analysis, but are not suitable for the characterization of coupled mechanical-air-fluid flow that usually takes place within rock joints under stress. Transparent replicas of natural rock fractures were used for direct observation of the distribution of phases along the fracture. Different types of two-phase flow patterns were observed through natural rough fractures. None of the two-phase experiments reported in the literature has used natural rock fractures subjected to in situ stresses to characterize two-phase flow patterns for various inlet water and air pressures. Direct visual observation of two-phase flow in real rock fractures subjected to high-pressure triaxial loading conditions is difficult in conventional laboratory conditions. This problem is approached by considering an indirect approach (to be discussed below) used by other researchers in studying multiphase flow in pipes. The study described here is limited to the analysis of twophase flow structures consisting of water and gas only. This paper presents triaxial test results conducted to characterize two-phase flow patterns in smooth-walled
217
fractures. The following sections describe the characteristics of two-phase flow patterns that have been observed based on the existing data for narrow channels and the flow mapping technique.
2. Types of flow patterns Knowledge of flow patterns is important in the study of transient flows and steady-state flows in order to incorporate the flow parameters (e.g., fluid properties and wall shear stresses) in numerical models. The inlet pressures of each phase, their physical properties, interactions between the phases and the geometry of flow paths determine the flow patterns in a pipe or rock joint. Depending on flow conditions, there are regions of a pipe or rock joint where (a) both phases are continuous, (b) one phase is continuous and the other is discontinuous or (c) both phases are discontinuous (Fig. 1). As shown in Fig. 1, common flow patterns which occur in a pipe can be categorized as stratified, bubble, droplet, annular, complex, plug and churn flows [7,9–12]. A wide variety of flow pattern definitions have been proposed for two-phase flow patterns [1]. Vertical flow through a rock joint was observed in the triaxial testing facility used in this study. Definitions of flow regimes for vertical flow are described according to the definitions given by Hetsroni [1]: (1) bubble flow—the liquid (water) phase is continuous and dispersion of bubbles flow within the liquid phase, (2) annular flow— gas occupies the center of the path while the liquid flows
Two-phase flow
Continuous flow
Discontinuous flow
(both phases)
Stratified flow
One phase
Annular flow
Bubble
Droplet flow
Both phases
Slug flow
Churn flow
Fig. 1. Common two-phase flow patterns observed in pipe flow.
Complex flow
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along the joint wall as a film. Detailed descriptions of other two-phase flow patterns are given elsewhere [1,9,10,13]. In continuous flow, both phases exist all along the flow path, whether stratified or annular. In discontinuous flow, one phase (or both) is discontinuous (e.g., bubble, droplet, slug and complex flows). Various types of flow patterns may develop due to the combined effects of the following: (1) magnitude of pressure of each phase, (2) properties of each phase (e.g., viscosity, density), (3) flow path geometry, and (4) flow path surface tension and surface contamination.
1.00
Liquid superficial velocity,m/sec
218
Bubble flow
Fingering bubble flow
0.10
P
Annular flow Complex flow
Q Droplet flow
0.01 Not investigated
R
S
3. Determination of flow patterns Two approaches are usually employed to identify flow structures: (1) visual observations supported by a photographic method, and (2) an indirect method based on selected fluid flow parameters such as superficial velocities. The visual observation method is only possible when the flow takes place through transparent materials like glass or plastic. A wide variety of highspeed photographic techniques are used in studying twophase flow patterns [11,14,15]. Experimental work on identification of gas–water flow patterns in a narrow horizontal channel using a combined visual observation and photographic method was carried out by Fourar and Bories [7]. They observed different flow patterns varying from bubble flow to droplet flow. Mishima and Hibiki [13] studied two-phase flow through smalldiameter (1.05–4.08 mm) vertical tubes, and they observed the transition of flow patterns from bubble flow to annular flow with the increase in gas pressure. Indirect methods of analyzing the flow pattern of a gas–liquid, two-phase flow system depend on measurements of some flow parameters (e.g., superficial velocity) and characterization of the results in terms of flow patterns [1]. This technique is particularly suitable when the flow takes place through rock fractures as flow is not visible under certain loading (e.g., triaxial) conditions. In multiphase flow analysis through pipes, the common procedure to identify flow patterns is to plot the liquid superficial velocity against the gas superficial velocity. Superficial velocity is defined by researchers as the flow rate of the phase per unit cross-sectional area [16,17]. Such a plot of water–gas flow through horizontal glass plates, artificially roughened horizontal plates and vertical small diameter tubes is shown in Fig. 2 [7]. Irrespective of the flow path geometry (i.e., smooth or rough), these researchers observed the same range of flow patterns in both smooth and rough fractures. Moreover, at small gas superficial velocity and large water superficial velocity, Fourar and Bories [7] found formation of bubble flow. Golan and Stenning [16], and Mishima and Hibiki [13] observed annular, oscillatory and slug flow patterns for elevated gas and liquid
0.00 0.01
0.10 1.00 Gas superficial velocity, m/sec
10.00
Fig. 2. Possible water–gas flow patterns in a channel (data from Fourar and Bories, 1995).
superficial velocities. This shows that bubble flow, in which liquid flow is dominant, occurs at low gas velocities. In contrast, annular flow may develop at elevated gas velocities. Unlike flow through transparent pipes, no direct observations or photographic techniques can be employed in determining the flow pattern through rock. Nevertheless, the photographic method may be used to map the flow pattern in artificial fractures made out of transparent plastics. For example, a natural rock joint surface may first be transformed into a transparent plastic surface, and subsequently water and air flow are driven through the plastic joint to observe the flow type when the joint is subjected to no loading or uniaxial loading. However, this approach cannot be used to visualize the two-phase flow pattern in rock fractures under triaxial test conditions, because a high-pressure triaxial cell designed for testing rock is constructed of high strength steel and the sample is covered with a thick membrane. Therefore, in this study, the indirect method discussed above is used to characterize two-phase flow patterns from the triaxial test data. The indirect approach may have limitations, but it is useful to identify whether the flow in natural rock joints is bubble or annular.
4. Experimental design and procedures Laboratory work on water–gas flow through fractured rocks is conducted using a two-phase, highpressure triaxial apparatus. The detailed design concepts of the apparatus, test procedures and test results on twophase flow rates for different boundary conditions are
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given elsewhere [9,10]. The following section briefly describes the salient features of the two-phase triaxial apparatus, which can measure relative permeability characteristics, as well as the stress–strain behavior of rocks subjected to axial and confining pressure conditions. The apparatus can be used for the study of both single- and two-phase flow through soft and hard rocks. In two-phase flow, both water and air simultaneously flow through the fractured specimen. In this equipment, water and air phases are carried by two separate tubes to the bottom end of the specimen (Fig. 3). In order to prevent water and air interaction before entering the specimen, the two tubes which carry water and air are integrated fitted with several on/off valves and check valves. These valves have been attached to the bottom plate to ensure that there is no back flow of one phase through the tube of the other phase. In order to measure the pressure of each phase, a pressure transducer is attached to each phase line. Fractured granite specimens having a diameter of 55 mm and length twice the diameter with low matrix permeability (about of 1019 m2) were selected for the laboratory investigation. All 55 mm diameter cores used for testing contained a single fracture. Measurements of fractured rock surfaces were made using a mechanical profilometer, which can digitise the joint surface in three dimensions by taking a series of parallel lines along the joint. In the course of the measurements, the digital pointer was lowered to the surface to obtain coordinates, and by moving the pointer systematically, many points of the surface were mapped. The individual joint profiles along each line segment were plotted (not included in the paper) in order to estimate the joint roughness coefficient (JRC) values for each profile. The individual joint profiles were matched with standard profiles [18] to estimate the average JRC value of the tested samples. The JRC values of the specimens were estimated as 4 and 5 which correspond to a fairly smooth joint surface. It should be noted that JRC estimation of rough joints should be carried out using
219
either direct shear, tilting tests or more sensible statistical prameters such as mean and standard deviation [4,19]. However, the use of standard profiles approach is adequate enough for fairly smooth joints tested in this study. Specimen 1 (JRC ¼ 4) was subjected to higher confining pressure (1.0–3.0 MPa) than that of specimen 2 (0.5–1.0 MPa). The orientation of the fracture in the triaxial specimen was near vertical (Fig. 3). Oil was used as confining fluid in the cell and the axial stress was supplied by a servo-controlled Instron Machine. The magnitudes of fluid pressure of each phase and confining pressure were recorded by individual pressure transducers. For a given confining pressure and axial stress, the specimen was first saturated with water, and then the air phase was forced through the specimen. Two types of tests based on the magnitude of inlet fluid pressures were conducted: (a) inlet air pressure ¼ inlet water pressure (Pa ¼ Pw), and (b) Pa6¼Pw. Once the water and air mixture had passed through the Dreschel bottle, steadystate air flow rates and water flow volumes were recorded by the film flow meter [19] and electronic weighing scale, respectively [9,20].
5. Results and discussions Two-phase flow takes longer time than single-phase flow in a rock fracture to reach steady state. A transient state of two-phase fluid flow was observed and results of individual phase flow rates with time (in log scale) are shown in Fig. 4. In order to improve the clarity of the plot, the measured time was plotted in log scale while the water and air flow rates were plotted in two different scales (in normal scale) in the left and right vertical axes, respectively. The testing procedure for the results given in Fig. 4 is given below. The jointed granite rock 80
4.0 Steady state air flow
Two-phase flow Confining pressure0.5MPa
2.0
40
Pa = Pw = 0.2MPa Water flow Air flow
0.0
Air flow rate, ml/sec
Water flow rate, ml/sec
Trasient state of two-phase flow
Steady state water flow 1
10
100
0 1000
Time, min Fig. 3. Fluid pressure across the triaxail apparatus system.
Fig. 4. Observations of transient and steady-state two-phase flow through a fractured rock specimen.
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specimen was first saturated with water by applying an inlet water pressure of 0.2 MPa. After 45 min, a steadystate water flow rate (3.8 ml/s) was observed from the sample (the time, 45 min is not shown in Fig. 4). This indicated that the sample was fully saturated with water after 45 min under the given boundary conditions (i.e., confining pressure of 0.5 MPa and an inlet water pressure of 0.2 MPa). Once the steady-state water flow rate (3.8 ml/s) was observed from the specimen, the inlet air pressure was gradually increased from 0 to 0.2 MPa. Both inlet air and water pressures were then maintained at 0.2 MPa. At time (t) ¼ 0, the water flow rate was measured as 3.8 ml/s and no air flow rate was observed. At 8 min, the water flow rate had decreased to 1.6 ml/s and the measured air flow rate was 6.8 ml/s (note the two different scales for air and water flow rates). An increase in water flow rate was observed at 9 min. This occurred because the built up air phase inside the joint suddenly displaced water in the fracture causing a larger flow rate from the specimen. However beyond 9 min, the air flow rate continuously increased to 60 ml/s while the water flow rate decreased to 0.6 ml/s. It was noted that the steady-state two-phase flow was reached after 150 min and the steady-state value was further observed for another 200 min to make sure the two-phase flow rates were independent of time. For classification of flow patterns, the measured steady-state flow rates have been used in plots discussed in later sections. The measured steady-state flow rates were used to calculate the superficial velocity (va) of each phase, using Eqs. (1) and (2) given below [7,10,16,17]: ka K ra qP qz qa þ rg va ¼ ¼ , (1) qx qx a ma Aa ( ea ¼
12mq w qP=qx þ rg qz=qx
)1=3 ,
(2)
a
where a is the phase (a and w represent air and water phases, respectively); m the dynamic viscosity; k the intrinsic permeability; Kr the relative permeability; dP the pressure difference along the joint length, dx; q the flow rate; r the density; g the acceleration due to gravity; z the vertical distance; A the area perpendicular to the flow (e w), where e and w are mean joint aperture and joint width, respectively. As discussed by Olsson [23], the Reynolds number of fluid flow was used to ensure flow was laminar flow without turbulence. The measured individual flow rates were also used to calculate Reynolds numbers which were found to be well below 1000. The magnitude of critical Reynolds number representing the laminar flow regimes between parallel walls is 1000 [24]. This showed that the fluid flows (both air and water) within the rock joint were laminar.
5.1. Characterization of flow patterns in a rock fracture Using the above-mentioned indirect technique (i.e., based on superficial velocity), the flow patterns within natural rock fractures were studied for different boundary conditions, including confining pressures and inlet fluid pressures. Based on measured steadystate two-phase flow rates, the estimated water superficial velocity and the air superficial velocity were plotted in Fig. 5. In order to improve the clarity of the plots, a logarithmic axis was selected for the water superficial velocity because the air superficial velocity was significantly higher than that of water. For the results shown in Figs. 5a and b, the specimen was first saturated with water and the inlet water pressure was maintained at a constant value of 0.25 MPa and the air injection was then started and increased stepwise (i.e., Pa6¼Pw). For example, at each new air pressure (e.g., 0.1 MPa), the steady state of air and water flow rates were measured after a long period of time. When steady state was reached for each phase, flow readings were measured. For the next step, the air pressure was increased to another value (e.g., 0.125 MPa) and the steady-state two-phase flow was measured (the inlet water pressure was maintained at 0.25 MPa). In a similar manner, the inlet air pressure was gradually increased until the specimen was fully saturated (the existence of an immobile water film or cognate water content) with air. Kostakis and Harrison [25] observed virtual stops of gas bubble movement due to high water flow in a natural rock fracture. 5.2. Use of superficial velocity to characterize flow patterns Using Eqs. (1) and (2), the superficial velocity of each phase was calculated for the measured steady-state twophase flow rate. The corresponding applied inlet air pressures are given in Fig. 5 on the top horizontal axis. It can be seen that the estimated air flow superficial velocities are extremely high compared to the water superficial velocities. With an increase of inlet air pressures (shown on top horizontal axis—Figs. 5a and b), the air phase occupies a larger part of the void space in the rock joint than the water phase at a given confining pressure. Therefore, due to the effects of relative permeability, the lower viscosity and the much higher compressibility of air compared to water, the measured two-phase air flow rate is much higher than that of water flow rate and as a result the estimated air superficial velocities are significantly larger. This has been observed by several researchers for two-phase flow in pipes and narrow smooth and rough channels [8,13,22]. It could be argued that air superficial velocities in Fig. 2 are substantially smaller than those of Fig. 5. This is because data shown in Fig. 2 are for two-phase
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Inlet air pressure, kPa 275
200
350
1.00 1.0
Specimen 1 (JRC=4)
Curve C
pa p and Pw = 0.25 MP a w Confining pressure = 1.0 MPa
Curve B
Confining pressure = 2.0 MPa
Inlet air pressure, kPa 115
pa p and Pw = 0.125MPa w
0
0
Confining pressure = 2.0MPa
5 10 Air superficial velocity, m/sec
Inlet air pressure, kPa 325
Annular flow
10 20 Air superficial velocity, m/sec
d Expecte
Water superficial velocity, m/sec
Water superficial velocity, m/sec
Specimen 2 (JRC=5)
15
(d)
trend
G G
F
Annular flow F
Specimen 2 (JRC=5) pa = pw Confining pressure = 0.5MPa Confining pressure = 1.0MPa
E
0
30
650
Bubble flow
0.1
Confining pressure = 1.0MPa
(b)
Confining pressure = 1.0MPa
26 1.0
Bubble flow
0.00
p = p w a
B
180
0.10
Confining pressure = 0.5MPa
Annular flow
A
(c)
Transition flow (e.g., slug, complex)
0.01
A
trend
1.00
0.1
30
D
Specimen 1 (JRC = 4)
Annular flow
10 20 Air superficial velocity, m/sec
50
B
cted
0
D
C
Expe
0.00 (a)
600
Bubble flow
end
Curve A
e c te d tr
Bubble flow
Inlet air pressure, kPa 400
C
E xp
0.10
Confining pressure = 3.0 MPa
200
Water superficial velocity, m/sec
Water superficial velocity, m/sec
Transition flow (e.g., slug, complex)
0.01
221
E
5 10 Air superficial velocity, m/sec
15
Fig. 5. (a) Possible flow patterns in a fractured granite specimen for capillary pressures (specimen 1: JRC ¼ 4). (b) Possible flow patterns in a fractured granite specimen for capillary pressures (specimen 2: JRC ¼ 5). (c) Possible flow patterns in a fractured granite specimen at zero capillary pressure (specimen 1: JRC ¼ 4). (d) Possible flow patterns in a fractured granite specimen at zero capillary pressure (specimen 2: JRC ¼ 5).
flow through a glass channel subjected to low inlet fluid pressures. In contrast, two-phase flow through natural rock fractures at given confining pressure and elevated inlet fluid pressures are shown in Fig. 5. Fig. 5a shows two-phase flow velocities for specimen 1 at confining pressures of 1.0, 2.0 and 3.0 MPa. Data shown in Fig. 5b are for specimen 2 which was subjected to relatively lower confining pressures (i.e., 0.5 and 1.0 MPa) than that of specimen 1. In order to characterize the twophase flow pattern through the tested rock fractures, the data shown in Fig. 5 were compared with the data in Fig. 2 which presents various flow patterns in a glass channel. The flow patterns changes with increasing air flow velocity in the tested rock joints are generally gradual (Figs. 5a, b) rather than staged as shown for
flow in tubes (Fig. 2), indicating gradual transition from bubble flow to complex flow. This may be due to combined effects of roughness of joints, triaxial boundary conditions and some other effects which need a substantial study to clarify them. One should not use the magnitude of superficial velocities to compare Figs. 2 and 5 since different boundary conditions were employed. Instead, the change in velocity trends which indicate change in flow patterns was used in this paper to classify flow patterns in a given rock joint in a triaxial cell. It is important to note here that the tested rock fracture surfaces were fairly smooth because the estimated joint roughness coefficients were 4 and 5 for specimens 1 and 2, respectively. However, one needs to take into account
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that the rock joints tested in this study were subjected to different loading conditions (e.g., confining pressures, axial stresses). In this study, bubble flow was usually experienced at relatively low air superficial velocities (curve PQ in Fig. 2). An abrupt change of water velocity with air velocity was associated with the formation of a new flow pattern (curves QR, RS in Fig. 2). According to Fig. 5, for both specimens, bubble flow was experienced when the air superficial velocity was below 15 m/s. In this region, air bubbles can form along the joint walls or can be randomly displaced within the water phase. A sudden change of water superficial velocity with air superficial velocity occurred once the air superficial velocity exceeded 15 m/s. This was due to the fact that the two-phase flow pattern within the fracture was changing. It was relatively difficult to predict the exact flow pattern when the air superficial velocity ranged from 15 to 20 m/s. The flow pattern within this range may have been a complex flow. Fourar and Bories [7] visually observed a complex flow in which an abrupt change of water velocity with air velocity occurred (Fig. 2). During the complex flow (Fig. 2), the water velocity dropped sharply from 0.02 to 0.0025 m/s and the air velocity increased from 0.2 to 1.0 m/s. Also, in Fig. 5, during the complex flow, the water superficial velocity decreased from 0.1 to 0.01 m/s and the air superficial velocity increased from 15 to 20 m/s for the applied confining pressure of 3.0 MPa. In addition several researchers [7,13,16] have reported similar types of flow patterns through narrow channels and pipes. According to Figs. 5a and 5b, two-phase flow became an annular flow when the air superficial velocity exceeded 20 m/s. At higher air superficial velocities (exceeding 20 m/s), the air occupied the main part of the fracture and the water flow as an unstable film along the walls. After the annular flow developed, the flow pattern was independent of the air flow velocity until single phase air flow formed. This is due to the fact that once the inlet air velocity reached a critical value (20 m/s), the water velocity in the joint was negligible for a given confining pressure and inlet water pressure. When the inlet air pressure increased up to 0.25 MPa, no water flow was observed through the sample. This indicates that the rock joint was completely filled with air (or rather the thin water film became immobile—cognate water).
5.3. Effects of confining pressure on water– gas flows The effects of confining pressure on two-phase flow are also discussed here. The average hydraulic apertures of specimen 1 at confining pressures of 1.0, 2.0 and 3.0 MPa were 4.1, 3.5 and 3.0 mm, respectively. Specimen 2 had average hydraulic apertures of 4.2 and 3.8 mm at confining pressures of 0.5 and 1.0 MPa. It was observed that an increase in confining pressure usually resulted in
a decrease of the two-phase flow rates due to the closure of the fracture. For the results shown in Figs. 5c and d, the experiment was conducted so that the magnitudes of inlet air pressure (Pa) equalled the inlet water pressure (Pw). When Pa equals Pw, capillary pressure, which is defined as the difference between inlet air pressure (Pa) and water pressure (Pw), at the inlet, was zero. For the data shown in Figs. 5c and d, the specimen was first saturated with water at a given inlet water pressure. The air injection was then started and the inlet air pressure was made to be equal to the applied inlet water pressure. For example, at given air and water pressures (e.g., Pa ¼ Pw ¼ 0.1 MPa), the steady-state air and water flow rates were measured. Before starting the next phase, the air injection was stopped and the sample was flushed and saturated with higher inlet water pressure (e.g., Pw ¼ 0.15 MPa) to remove all trapped air inside the fracture. The air phase was then introduced and increased to a pressure of 0.15 MPa, and the steadystate two-phase flow was measured. As explained before, two-phase flow rates were measured when capillary pressure equals zero at the inlet and the superficial velocity of each phase was estimated using Eqs. (1) and (2). The corresponding applied inlet air pressures are given on the top horizontal axis (Figs. 5c and d). At a given confining pressure (i.e., 1.0, 2.0 MPa) and low inlet air and water pressures, as expected, the two-phase superficial velocities were small because the measured flow rate of each phase was small. During the testing program, it was not possible to measure two-phase flow when inlet pressures were below 0.1 MPa for confining pressures of 1.0 and 2.0 MPa (Fig. 5c). The expected trends for small values of inlet water and air pressures are also shown in Figs. 5c and d (curves AB, A0 B0 and E0 F0 ). However, at a confining pressure of 0.5 MPa, it is possible to estimate superficial velocities of two-phase flow at small inlet fluid pressures (curve EF—Fig. 5d). With an increase in inlet fluid pressures (i.e., water and air pressures were injected so that Pa ¼ Pw), the relationship between the air and water superficial velocities is represented by Figs. 5c and d: Curves ABCD, A0 B0 C0 D0 , EFGH and E0 F0 G0 V w ¼ a ln V a þ b,
(3)
where V is the superficial velocity, a and b are coefficients and subscripts ‘a’ and ‘w’ represent air and water, respectively. It may be expected that at low air superficial velocities, the increase in water superficial velocity would be higher than at elevated air superficial velocities. However, as discussed above, in this study air superficial velocity was always higher than that of water superficial velocity irrespective of the magnitude of inlet air or water pressures. Once the air superficial velocity exceeded 12 m/s, the change in water superficial
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0
velocity was marginal (curves CD, C D0 and FG). At small inlet water and air pressures, air bubbles dispersed in the flowing liquid when the joint was initially saturated with water. As shown in Fig. 5, bubble flow was observed in an initially water saturated joint when the gas and water velocities are relatively small as well as for zero inlet capillary pressure. At elevated gas pressures, the flow pattern may be annular flow when the inlet capillary pressure is zero. Although these plots do not clearly distinguish the different flow regimes, they suggest the changes from bubble flow patterns to annular flow regimes, and can be used to study the change in gas-liquid flow patterns in a fractured rock mass.
6. Conclusions Different flow patterns have been observed by other researchers during laboratory experiments on two-phase air–water flow through replicas of natural rock fractures. These flow patterns could be stratified, bubble, droplet, annular, complex, plug and churn flows. The developed triaxial apparatus has been successfully used to study two-phase water and air flow through naturally fractured rock specimens. Different confining pressure and inlet water and gas pressures can be applied to the specimen. From the measured variation in superficial velocities of the gas and water phases under different stress and inflow boundary conditions, change of flow patterns in rock joints can be inferred from the results. From the experimental results, it has been observed that the flow pattern depends on the confining pressure and inlet water and air pressures. Annular flow usually occurs at elevated inlet gas pressures, whereas bubble flow may develop at high-liquid pressures compared to gas pressures. At higher gas inlet pressures, the gas occupies the main part of the fracture and the liquid may flow as an unstable film. The phase superficial velocity corresponding to the different flow patterns depends on the confining pressure.
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