Coalbed methane is an important alternative energy, and furthermore its development can help to avoid coalmine accidents and to reduce the emission of ...
ABSTRACT Coalbed methane is an important alternative energy, and furthermore its development can help to avoid coalmine accidents and to reduce the emission of methane during coal mining. This study focuses on the in-situ stress, pore pressure and permeability in the Southern Qinshui Basin, one of largest coalbed methane basins in China. Well tests show that permeability in this basin is higher than other coalbed methane reservoirs. This is because it is located in an extensional basin, where the normal faulting stress regime is dominated. This in-situ stress regime is advantageous to keep coal cleats open. Hydraulic fracturing tests indicate that the fracture gradient or minimum horizontal stress is much lower than the shales in the Gulf of Mexico and other oil basins. The minimum horizontal stress model is proposed with consideration of the stress coefficient based on the uniaxial strain method. This model provides a fairly good prediction on the minimum stress. Permeability data show that the effective stress dependent permeability is pronounced in the coalbed methane reservoir. This is significant for the dual-porosity and dual-permeability coal reservoir which is consisted of coal porous matrices and cleats. The reason is that a rapid increase in effective stress can induce the closure of cleats, which may cause a permanent lose of permeability in the cleats. This reduces the connectivity between the cleats and coal matrices, hence the coal matrices cannot deliver gas pressure to the cleats for supporting the cleat space. Therefore, slowing down the effective stress change during production (e.g. slowing reservoir drawdown) can decelerate the permeability reduction. This is particularly important for the reservoir in which
1
the pore pressure is not significantly overpressured, such that in the Southern Qinshui Basin.
Keywords: In-situ stress; Pore pressure; Southern Qinshui Basin; Stress and permeability; Coalbed methane
1. Introduction 1.1. Field description China has the world's third-largest coalbed methane resources, next only to Russia and Canada. Coalbed methane is an important alternative energy for China, and the development of coalbed methane, particularly the one at shallow depths, can also be helpful to avoid coalmine accidents and to reduce the emission of methane. Coalbed methane is deadly in underground coalmine operations if this gas is not pumped out prior to coal mining. China has the highest number of coalmine accident fatalities in the world, with about 80 percent of casualties attributable to gas (coalbed methane) explosions, causing annually direct losses of 93 million U.S. dollars. However, this No.1 “coalmine killer” is also a sort of clean energy [1]. The estimated coalbed methane reserve in China is about 36.8 trillion cubic meters, located no deeper than 2,000 m below the surface. Over 46 percent of China's coal mines are rich in the methane, and about 1.3 billion cubic meters of coalbed methane are being emitted each year with coal mining and without being effectively used. Coalbed methane is becoming a practical and reliable substitute of energy resource for natural gas, as the global shortage of energy resources worsens and conventional natural gas supply falls. Coalbed methane is developing vigorously in China. The Southern Qinshui Basin, located in Shanxi Province of the Central China, is one of largest coalbed methane reservoirs. It has 3.96 trillion cubic meters of total gas reserve. Coalbed methane wells are operating in the Qinshui Basin, the China's largest coal-bed methane exploitation base. The Southern Qinshui Basin has become China’s first commercial coalbed methane reservoir [2]. Coalbed methane reservoir is an unconventional gas reservoir and located at shallow depths compared to the conventional gas
2
reservoir. Therefore, in-situ stress, pore/reservoir pressure and permeability need to be investigated to better understand and develop coalbed methane reservoirs. The Southern Qinshui Basin refers to a region including Changzhi, Gaoping, Jincheng, Yangcheng, Qinshui, Anze in the southeast of Shanxi Province. It is the most important production base for high quality anthracite in China. The Southern Qinshui Basin measures approximately 120 kilometers from north to south and 80 kilometers from east to west, with an area of about 7000 square kilometers. Coal seams, generated in Carboniferous and Permian periods, contain abundant methane. Permeability in the coalbed reservoir is relatively high compared to other coalbed methane reservoirs in China. The exploration and production tests in this field have been conducted since 1990’s. The results show that the Qinshui Basin is a very promising coalbed methane reservoir with the most exploration wells, the best development prospect, and a higher commercialized production in China’s coalbed methane reservoirs. 1.2. Stress, pore pressure, and permeability measurements The hydraulic fracturing method, as described by [3, 4], has been applied to measure the in-situ stress in Southern Qinshui coalbed reservoir [5]. The minimum horizontal stress can be determined by direct measurements via the hydraulic fracturing method, or its oil field equivalent, the leak-off test (LOT) and extended leak-off test (XLOT). The maximum horizontal stress can be calculated from the extended leak-off test with two or more pressurization cycles. The in-situ stress data in 45 coalbed methane wells were mainly obtained from No. 3 coal seam located in Shanxi Group, Permian-aged formations using multi-cycle hydraulic fracturing tests (equivalent to XLOT). Laboratory tests of core samples were also conducted to understand the mechanical behaviors of the coal seam and its surrounding rocks. Table 1 lists the laboratory test data of rock mechanical properties in the coal seam and its surrounding rocks. The coal seam strength is very low compared to its roof and floor rocks. It is extremely important to have accurate measurements of reservoir permeability to design well completions and optimally manage reservoir performance in coalbed reservoirs. Well tests can be used to determine the reservoir permeability in coals. The use of 3
injection/falloff tests for estimating reservoir properties in coalbed methane or other low permeability reservoirs has become more common [6, 7]. Injection/falloff test is a testing of a well in which fluid is being injected into the reservoir. The pressure transient data is obtained during the injection. Then, a falloff test is conducted, in which injection is halted and the pressure decline is measured as a function of time. For an injection/falloff test, flow and shut-in time are critical parameters. However, because mechanical equipment at the surface provides the energy for the test, injection rate and fracturing pressure must also be considered. It is imperative that the test be performed without exceeding the fracture gradient of the formation in order to obtain meaningful analysis results. A good rule of thumb is that bottomhole flowing pressure should not exceed 80% of the formation fracture pressure. In lower permeability reservoirs, very low injection rates are needed to prevent fracturing. The design used for injection/ falloff testing in Southern Qinshui coalbed reservoir is described below. The well configuration used for testing is similar as the one described in [6]. After the borehole completions in the target coal seam, the test intervals are isolated and sealed with a bridge plug and packer assembly. Injection tests are conducted and water is injected down the tubing at a rate of on the order of 3-7 l/min for 12 to 18 hrs. Then, the well is shut in at the surface and pressure falloff is monitored for 24 to 36 hrs. The injection/falloff well tests data are analyzed and interpreted to determine the reservoir pressure and permeability. The results show that permeability is highly dependent on in-situ stress and the burial depth. These are critically important in designs of coalbed methane drilling, completion, and production. For instances, at the shallow depths vertical wells without hydraulic fracturing can obtain a reasonable depletion area because of high permeability of the coal seam. However, in the deep section, horizontal wells and stimulation method have to be applied to enhance gas production. This phenomenon is mainly caused by stress- and depth-dependent permeability. Theoretical analyses and experimental study in stress-dependent permeability in coal have been studied extensively [8-15]. However, field data of permeability in coal seams, particularly stress-dependent permeability is not widely reported, although a number of studies have been conducted [16-18]. This paper, based on field measured data, analyzes the relationship of permeability and in-situ stress in Southern Qinshui Basin. The analysis may be applicable in developing strategies in exploration, well 4
completion, and production of coalbed methane.
Table 1. Ranges and means of rock mechanical properties in No. 3 coal seam and its surrounding rocks*. Mechanical
Roof of No. 3 coal
No. 3 coal seam:
Floor of No. 3 coal
properties
seam: mudstone,
anthracite
seam: mudstone,
sandy mudstone
muddy siltstone
Uniaxial 31.45-39.28/36.1
2.51-20.91
20.39-36.05
36.10
11.10
27.92
Tensile strength
1.39-1.78
0.09-0.93
0.90-1.63
(MPa)
1.61
0.48
1.24
Young’s modulus
0.28-3.25
0.21-1.63
0.63-3.01
(GPa)
2.29
0.91
1.97
Poisson’s ratio
0.26-0.31
0.28-0.33
0.27-0.31
0.28
0.31
0.29
compressive strength (MPa)
*
The data representation is: Min. Max. . mean
2. In-situ stress and pore pressure The following sections analyze in-situ stress data obtained from hydraulic fracturing method with multi-cycle injection tests in 45 coalbed methane wells in the Southern Qinshui Basin. The fluid pressure tests in these wells are also analyzed to determine formation pore pressure. 2.1. Vertical stress Vertical stress, or overburden stress, is induced by the weight of the overlying formations. Vertical stress can be calculated when the bulk density of the overlying formations is known. Coal mining and density logging indicate that the vertical stress in this region can be accurately estimated by the following relationship [19]:
5
V 0.027 D
(1)
where V is the vertical stress in MPa; D is the burial depth from the surface in meters. 2.2. Pore pressure Pore pressure in the coalbed methane reservoir is an important parameter for drilling and production. Drilling and well tests show that pore pressure in the coalbed methane reservoir increases as the burial depth increases in Southern Qinshui Basin (Fig. 1). The measured pore pressure data and hydrostatic pore pressure (water gradient of 0.01 MPa/m) in Fig. 1 are plotted to analyze if the abnormal pressures exist in the basin. The pore pressure potentiometric level in the aquifer of Carboniferous and Permian coal measures is located at 140 m below the surface in this area. Figure 1 shows that the pore pressure in the coalbed methane reservoir is basically normal (hydrostatic) pressure and only has mild overpressure and underpressure at depths of 500-1100 m. Stress, presure (MPa) 0
5
10
15
20
25
30
35
0 Vertical stress Pore Pressure Hydrostatic Pp 140m
100 200
Burial Depth (m)
300 400 500 600 700 800 900 1000 1100 1200
Fig. 1. Pore pressure in coalbed reservoir and the hydrostatic water pressure with potentiometric level at 140 m below the surface in Southern Qinshui Basin.
6
In most areas in the world, such as the western U.S.A., Canada, China, and Australia, coal seams contain significant quantities of groundwater. Often a coal seam is saturated with water, and the methane is held in the coal by water pressure, such as the Powder River Basin of the U.S.A. and the Bowen and Sydney Basins in Australia. In this kind of coalbed methane reservoir, the water is mainly saturated in the fractures or cleats of the coal seam, and gas is sealed within the pores of the coal matrices by the water pressure. Hence, coalbed methane is held in place by water pressure and does not require a sealed trap as do conventional gas accumulations. The coal matrices act as a source/reservoir for the methane gas while the water is the seal. Therefore, the gas pressure in coalbed methane reservoir is closely associated with the water pressure. Pore pressure is different in a formation when it is saturated with different fluids. We assume that the fractures are saturated with water and the pores in the coal matrices are filled with gas in a coal seam, as shown in Fig. 2. If the pores of the coal from Locations A to B are saturated with gas, and the pore pressure at Location B is equal to the water pressure in the aquifer (fractures), then the pore (gas) pressure at Location A caused by gas column (density) is [20]:
pgA pB g ghg
(2)
where pgA is the pore pressure at Location A; pB is the pore pressure at Location B (the gas-water contact); hg is the height of the gas column (the height from Locations A to B); g is the in-situ gas density; g is the acceleration due to gravity. If the pores from Locations A to B are saturated by water, then the water pressure can be written in the following:
pwA pB w ghg
(3)
Compared Eq. 2 to Eq. 3, the pore pressure increment (pgA – pwA) elevated by the gas column is (refer to Fig. 2):
pgu ( w g ) ghg
(4)
where pug is the pore pressure increment induced by gas column; w is the water density. Mouchet and Mitchell (1989) gave a similar equation for the conventional hydrocarbon reservoirs [21]. 7
The gas pressure in the deeper section (such as in Location C in Fig. 2) is reduced by gas gradient when the gas pressure has an updip pressure equalization with the hydrostatic water pressure (at Location B). The amount of the pore pressure reduction is shown in the following (e.g. the pressure at Location C in Fig. 3 with a gas column height of hg):
pgd ( w g ) ghg
(5)
where pdg is the pore pressure reduction induced by gas column. This pore pressure elevation/reduction is caused by buoyancy effect in hydrocarbon due to density contrasts of water and gas. The overpressure due to the difference in densities gradually decreases from the maximum value at the top of the reservoir to zero at the water-gas contact, as shown in Fig. 2. It is also possible that the gas column causes pore pressure decrease (refer to Eq. 5), in which the underpressured pore pressure also follows the gas gradient.
Fluid pressure (MPa) Gas Water
Gas in pores
gas
g , pg
A water
B
w , pw Water in fractures
Gas gradient 0.23g/cm3
pg
hg
pA pg pB
gas hg C
pw Water gradient 1.05 g/cc3
Water gradient 1.05 g/cm
Coal
Fig. 2. Schematic representation of pore pressure caused by gas column and density contrast between water and gas in a coal seam. This density contrast causes pore pressure increase in Location A compared to the one caused by water gradient. From locations B to A the gas
8
pressure has a downdip pressure equalization with the hydrostatic water pressure at Location B, i.e. pg = pw; pg is the gas pressure and pw is the water pressure. The gas pressure at Location C has an updip pressure equalization with the hydrostatic water pressure at Location B. The in-situ gas column/gradient in the Qinshui Basin is calculated to analyze the connectivity and compartmentalization of the coalbed methane reservoir at different depths. If the coalbed methane reservoir follows the same gas gradient at different depths, the reservoir is well connected and less compartmentalized. Assuming the in-situ gas gradient of 0.005MPa/m, two possible gas gradients are plotted in Fig. 3 with comparison to the measured gas pore pressures. Figure 3 shows that there is no obvious single gas column/gradient in this coalbed methane reservoir. However, it is very possible that two gas columns exist in this basin. One is at a shallow depth started at 428 m where the pressure in the gas compartment is equal to the hydrostatic water pressure, and deeper than 428 m the gas pressure (Line 2 in Fig. 3) is lower than normal hydrostatic pressure. In this case the gas pressure has an updip pressure equalization with the hydrostatic water pressure at depth of 428m. The other gas gradient may start at 800 m, and the gas pressure in this compartment (Line 1 in Fig. 3) is overpressured compared to the hydrostatic water pressure. In this case the gas pressure has a downdip pressure equalization with the hydrostatic water pressure. These gas gradients imply that the abnormal gas pressure may be caused by the buoyancy effect (density contrast between of water and gas) in different gas compartments. Figure 3 also demonstrates that there are only slight overpressure or underpressure. Therefore, hydrostatic water gradient with gas buoyancy effect is the main control on gas pressure in this area.
9
Stress, presure (MPa) 0
5
10
15
20
25
30
35
0 Vertical stress Pore Pressure Hydrostatic Pp 140m Gas gradient 0.005MPa/m
100 200
Burial Depth (m)
300 400 500
1
600 700 800 900
2
1000 1100 1200
Fig. 3. Measured pore pressure in the coalbed methane reservoir and the gas gradients compared to the hydrostatic water pressure in the Qinshui Basin. Gas gradient 1 is overpressured with a downdip pressure equalization with the hydrostatic water pressure. Gas gradient 2 has the underpressure with an updip pressure equalization with the hydrostatic water pressure.
Based on measured pore pressure data in the Qinshui coalbed methane basin, the pore pressure can be expressed to the following form:
p p 0.0122D 2.8886
（6）
where pp is the pore pressure in MPa; D is the burial depth from the surface in meters, D >300m. This relationship can be used to predict the pore pressure in the new wells in this area.
2.3. Minimum horizontal stress and fracture gradient
2.3.1. Minimum horizontal stress, vertical stress, and pore pressure relationship 10
The minimum horizontal stress is a primary control on the fracture gradient and a major constraint on propagation of hydraulic fractures. Therefore, the minimum horizontal stress is a key parameter in designs of well drilling and reservoir stimulation. The minimum horizontal stress is commonly assumed to be approximately 70% of the vertical stress magnitude in sedimentary basins. Figure 4 presents the minimum horizontal stress measured from the hydraulic fracture tests in the coal seams of the Qinshui Basin. It shows that the 70% of the vertical stress magnitude cannot fairly describe the minimum stress in the coal seam. For example, at depths of 428 to 800 m the measured minimum stresses are lower than the 70% of the vertical stress magnitude. However, the minimum horizontal stress is also dependent on pore pressure, as shown in Fig. 5. We take out the two abnormal data points in the minimum horizontal stresses measured at depths of 560m and 660 m, as shown in Fig. 4, because the minimum horizontal stress should not be greater than the vertical stress in this area. Then, the effective vertical and minimum horizontal stresses in coal seams have the following correlation (refer to Fig. 5):
h 0.5045( V p p ) p p
(7)
where h is the minimum horizontal stress; V is the vertical stress; pp is the pore pressure. This relationship shows that the coal seam has a similar effective stress relationship as other sedimentary rocks in oil and gas basins. For instance, Matthews and Kelly (1967) introduced a variable of effective stress ratio into the minimum horizontal stress (or fracture gradient) prediction [22]:
h K 0 ( V p p ) p p
(8)
where K0 is the effective stress ratio, K0 = h/v ; h is the minimum effective stress; v is the maximum effective stress. In this method the values of K0 were established on the basis of fracture threshold values derived empirically in the field. The K0 can be obtained from leak-off tests (LOT) and regional experiences. The data in the Qinshui Basin show that an effective stress ratio of K0 is 0.505-0.54 (refer to Fig. 5), which is much lower than the commonly used value (e.g. K0 = 0.8) in shales in deep petroleum basins [23]. 11
Stress, presure (MPa) 0
5
10
15
20
25
30
35
0 Vertical stress Minimum horizontal stress Pore Pressure Hydrostatic Pp 140m 70%OBP
100 200
Burial Depth (m)
300 400 500 600 700 800 900 1000 1100 1200
Fig. 4. Vertical stress, measured pore pressure, and the minimum horizontal stress in coalbed methane reservoir in the Qinshui Basin. In the figure commonly assumed minimum horizontal stress (70% of the vertical stress magnitude, OBP) is also plotted.
Figure 5 shows that the effective vertical and minimum horizontal stress data do not have a very good fit. Hence, other expression may be used to predict the horizontal stress. Daines (1982) proposed the following expression to estimate the minimum horizontal stress based on uniaxial strain in-situ stress model [24]:
h
1
( V p p ) p p tec
(9)
where is the Poisson’s ratio; h is the minimum horizontal stress; V is the overburden stress; pp is the pore pressure; tec is the tectonic stress. Based on the measured data in the Qinshui Basin, the following equation can be used to estimate the minimum horizontal stress equation, when the measured data are not avaialable:
12
h
1
( V p p ) p p b V
(10)
where b can be defined to be minimum stress coefficient, b = 0.035 and the average Poisson’s ratio of the coal seam = 0.31 in the Southern Qinshui Basin (refer to Table 1). It should be noted that Equations 7-10 are designed for the cases in the normal stress and strike-slip faulting stress regimes. However, in the thrust stress regime these equations need to be modified.
14 measured data Linear (measured data)
12
h -pp
10 8
6 y = 0.5045x
4 2
0 0
2
4
6
8 10 12 14 16 18 20 22
v - pp
Fig. 5. Relationship of the effective vertical stress and the effective minimum horizontal stress in coalbed methane reservoir in the Qinshui Basin.
2.3.2. Minimum horizontal stress and burial depth Analyzing the measured minimum horizontal stress data, we obtain that the minimum horizontal stress and the burial depth has the following relationship in the Qinshui Basin, as shown in Fig. 6:
h 0.0236D 3.5177
(11)
13
where h is the minimum horizontal stress in MPa; D is the burial depth in meters, D >300m. This relationship can give an estimate of the minimum horizontal stress in the Qinshui basin when measured data are not available. 2.3.3. Lower bound of minimum horizontal stress Three stress regimes from Anderson’s faulting theory [25] can be used to describe the in-situ stress states (e.g. [26, 27]): 1. Normal faulting stress regime. In this case, gravity or vertical stress drives normal faulting, and fault slip occurs when the minimum stress reaches a sufficiently low value. In this stress state the vertical stress is the greatest principal stress, i.e. V H h. 2. Strike-slip faulting stress regime. In this case, the vertical stress is the intermediate
principal stress. In this stress state, one has H V h. 3. Reverse (or thrust) faulting stress regime. In this case, the vertical stress is the least
principal stress, i.e.H h V. From the measured data in the Qinshui Basin, the most possible stress regimes are normal and strip-slip stress regimes. Therefore, we can constrain the minimum stress magnitudes using the following lower bound of the minimum horizontal stress [28]:
hLB
V p p q f p p
(12)
qf
where hLB is the lower bound of the minimum horizontal stress; qf can be expressed in terms of the friction coefficient of the fault in the following form:
qf
1 sin f 1 sin f
( 2 1)1/ 2
2
(13)
where f is the internal friction angle of the fault; is the friction coefficient of the fault. In the normal and strike-slip faulting stress regimes, the minimum horizontal stress should be in between of the lower bound of the minimum horizontal stress and the overburden stress. Assuming the friction coefficient of the fault of = 0.6, the lower bound of the minimum horizontal stress in the Qinshui Basin can be calculated from Eq. 12. Figure 6 plots the lower bound of the minimum horizontal stress compared to the measured data. It
14
shows that the minimum horizontal stress can be constrained by the lower bound of the minimum horizontal stress with a friction coefficient of 0.6. Stress, presure (MPa) 0
5
10
15
20
25
30
35
0 Vertical stress Minimum horizontal stress Pore Pressure Pp empirical Sh_LB Sh empirical
100 200
Burial Depth (m)
300 400 500
h 0.0236D 3.5177
600 700
hLB
800
v Pp q f Pp qf
900 1000
pp 0.0122 D 2.8886
1100 1200
Fig. 6. The empirical correlations of pore pressure and the minimum horizontal stress in coalbed methane reservoir of the Qinshui Basin based on the measured data. The lower bound of the minimum horizontal stress and overburden stress are plotted to constrain the minimum horizontal stress.
2.4. Maximum horizontal stress The maximum horizontal stress was calculated from the hydraulic fracturing method with multi-cycle injection tests (equivalent to XLOT). Assuming that the rock behaves elastic and isotropic and no fluid penetrates to the fracture until fracture reopening, the horizontal stress magnitudes can be estimated from the fracture breakdown pressure [29, 4]:
pb 3 h H p p T0
(14)
where pp is the pore pressure in the formation; pb is the fracture breakdown pressure; T0 is the 15
tensile strength of the rock, and can be obtained from fracture reopening pressure. The fracture reopening pressure can be obtained from the XLOT tests. Therefore, we can modify the above equation to calculate the maximum horizontal stress. For a vertical borehole and no fluid penetration in the formation, the maximum horizontal stress can be calculated by the following equation:
H 3 h pb p p T0
(15)
The maximum horizontal stress data indicate that the studied formations are located in two different stress regimes at different depths in Southern Qinshui Basin (Fig. 7). When the burial depth is shallower than 590 m, the maximum horizontal stress is less than the overburden stress, and the in-situ stress is in the normal faulting stress regime. However, when the burial depth is deeper than 590 m, some data points of the maximum horizontal stress are greater than the overburden stress, and the in-situ stress belongs possibly to the strike-slip faulting regime. That is, larger horizontal stresses exist in the deeper formations, as shown in Fig. 7. Compared to the minimum horizontal stress, the maximum horizontal stress increases with a lower gradient as the burial depth increases. The maximum horizontal stress data can be expressed by the following empirical equation:
H 0.0343D 4.6618
(16)
where H is the maximum horizontal stress in MPa; D is the burial depth in meters, D >300m. The data also demonstrate that two horizontal stresses in the studied area are not equal. The ratios of the two horizontal principal stresses (σH/σh) range from 1.07 to 1.71 with an average of 1.46, i.e.:
H / h 1.07 1.71
(17)
The measured data show that the maximum horizontal stress direction is predominately in North-East-East direction (or North50-80East), which is parallel to the strike of the major faults.
16
Stress, presure (MPa) 0
5
10
15
20
25
30
35
0 Vertical stress Minimum horizontal stress Pore Pressure Pp empirical SH empirical Sh empirical SH
100 200
Burial Depth (m)
300 400 500 600 700
H 0.0343D 4.6618
800 900 1000
h 0.0236D 3.5177 pp 0.0122 D 2.8886
1100 1200 Fig. 7. The measured data and empirical correlations of the maximum and minimum horizontal stresses, overburden stress, and pore pressure in coalbed methane reservoir of the Qinshui Basin.
2.5. Relationship of vertical stress and horizontal stresses The lateral stress coefficient can be used to examine the relationship between horizontal stresses and overburden stress [19]. The lateral stress coefficient (λ) is defined as the ratio of the average horizontal principal stress, ( H h ) / 2 , to the vertical stress, V, i.e.:
( H h ) / 2
(18)
V
The measured results in Southern Qinshui Basin show that the lateral stress coefficients range generally from 0.42 to 1.42 with an average value of 0.82. It should be noted that the data in Southern Qinshui Basin have a different trend compared to the collated in-situ stress data from [19]. The difference is mainly caused by the different stress regimes at the shallow 17
depth. The data compiled by [19], refer to [30], show that the shallow formations are mainly in compressional basin or strike-slip and thrust faulting regimes. However, the shallow coal formations (< 590 m) in the Qinshui Basin are located in the normal faulting stress regime or in extensional basin, as shown in Fig. 8. The average horizontal stress in the extensional basin is less than the overburden stress, or λ < 1. In the extensional basin more natural fractures and a higher permeability are expected than those in the compressional basin. This is great advantageous in coalbed methane potential and productivity. When the depth is greater than 590 m (Fig. 8), most data points show the studied area is still in the extensional basin, although it may be in a transition zone from the extensional basin to compressional basin. The lateral stress coefficient value (λ) is small when the burial depth is less than 590 m, and λ ranges from 0.4 to 1.0. As the formations go deeper, the lateral stress coefficient increases and λ = 0.8 - 1.1, if the two exceptionally high values are taken out in Fig. 8.
Lateral stress coefficient (λ) 0
0.2 0.4 0.6 0.8
1
1.2 1.4 1.6
0
Burial depth (m)
100 200 300 400
Extensional basin
I
500 600 700 800 900 1000
II Transition zone
1100 1200 Fig. 8. The ratio of the average of two horizontal principal stresses, ( H h ) / 2 , to the overburden stress versus the burial depth.
3. Relationship between permeability of coal reservoir and in-situ stress 18
Permeability in a coal seam is a key parameter in coalbed methane reservoir. Reservoir permeability depends directly on drilling and completion methods and reservoir development strategy. For instance, for a coalbed reservoir with a high permeability vertical wells can be used for depletion. However, horizontal wells with stimulation completion have to be adopted for a low permeability reservoir. Permeability is highly dependent on in-situ stress, burial depth, and stress variation due to drilling and production [31]. Laboratory measurements show that coal permeability decreases exponentially with increasing effective stress [8, 10]. Permeability and the in-situ stress in the coalbed methane reservoir can be represented by an exponential relationship as follows [15, 32, 33]:
K K 0 e a e
(19)
where K is the permeability (md); e is the effective in-situ stress (MPa). K0 is the permeability under the initial in-situ stress condition (md); and a is the fitting parameter. This permeability and in-situ stress relationship fits the data in some coalbed basins in the world, such as the Bowen Basins, Sydney Basin, and Glouscester Basin in Australia [34]; the Black Warrior Basin, Alabama in the U.S.A. [17]. Field measured permeability decreases markedly as the in-situ stress increases in the Southern Qinshui Basin, as shown in Fig. 9. The effective in-situ stresses and permeability in the Southern Qinshui coalbed methane reservoir can be approximately represented by the following exponential relationships, similar to Eq. 19, although the data are not in good fits: K 58.135e
0.435(V p p )
K 2.6357e
0.193( H p p )
K 4.6752e
0.446( h p p )
(20) (21) (22)
where K is the permeability in md; V, H, and h are the principal vertical, maximum horizontal, and minimum horizontal stresses respectively in MPa; pp is the pore pressure in MPa.
19
Permeability (md)
100 10 1 0.1 0.01
y = 58.135e-0.435x
0.001 0
5
10
15
20
25
Effective vertical stress (MPa) (a)
Permeability (md)
100 10 1 0.1 0.01
y = 2.6357e-0.193x
0.001 0
10
20
30
40
Effective maximum horizontal stress (MPa) (b)
20
Permeability (md)
100 10 1 0.1 0.01
y = 4.6752e-0.446x
0.001 0
5
10
15
20
Effective minimum horizontal stress (MPa) (c) Fig. 9. Effective in-situ stress versus permeability in the Southern Qinshui coalbed reservoir plotted with exponential fit in each figure: (a) permeability versus the effective vertical principal stress; (b) permeability versus the effective maximum principal horizontal stress; and (c) permeability versus the effective minimum principal horizontal stress.
Figure 9 demonstrates that a higher in-situ stress corresponds to a lower permeability. This is because the coal seam in the subsurface is in a three-dimensional compressive stress state, i.e., under compression of the vertical stress and two horizontal stresses. In elastic deformation stage, the larger compressive stress magnitudes are, the lower permeability is [31, 35]. Therefore, permeability in the coal seam is highly dependent on the in-situ stress state and its configurations. For example, the permeability is higher in the normal faulting stress regime than the thrust and strike-slip faulting stress regimes. This is the fact that the normal faulting stress regime has the lowest compressive stresses than the other two stress regimes. In the Southern Qinshui Basin the permeability is higher, particularly at the shallow depth of < 590 m, than other coalbed methane reservoirs in China. This is because the Southern Qinshui Basin is located in an extensional basin, where the normal faulting stress regime is dominated.
21
Another characteristic of in-situ stress in this basin is the ratio of the maximum horizontal stress to the minimum horizontal stress is small, ranging from 1.07 to 1.71. This implies that permeability anisotropy in horizontal direction may not be so pronounced.
4. Relationship between permeability of the coal reservoir and its burial depth Permeability data indicate that the burial depth depends highly on permeability of the coal seam. Permeability in this coalbed reservoir is fairly high at the shallow depth. For instance, permeability magnitudes range mostly from 0.1 to 5 md in the Southern Qinshui Basin, when the burial depth is less than 590 m (refer to Fig. 10). The higher permeability is most possibly caused by the extensional basin at this depth, as shown in Fig. 8, where the normal faulting stress regime is favorable to develop fractures and cleats in the coal seam. As the burial depth increases, permeability of the coal reservoir decreases markedly. This is mainly caused by the increase in in-situ stress as well as the transition in stress regimes, as shown in Figs. 7 and 8. When the basin is in compressional state, much larger maximum horizontal stresses make coal matrices and cleats more compacted. This causes permeability reduction in the deeper coal seam. Therefore, different drilling and development strategies may need for coalbed methane reservoir at shallower (< 590 m) and deeper depths. Hence, horizontal wells with hydraulic fracturing are needed for developing the deeper coalbed reservoir (depth > 590 m). Permeability data observed in the coal seam in the Southern Qinshui Basin demonstrate an exponential trend between permeability and the burial depth. K 11.642e0.0061D
(23)
where K is the permeability in the coal (md); D is the burial depth (m). This permeability-depth relationship is very similar to the permeability envelope in the Foothills and Mountains of Western Canada [36]. However, the permeability in the Southern Qinshui Basin is higher than that in coal seams of the Foothills and Mountains of Western Canada. The lower permeability may be caused by the tectonic stresses in the Foothills and
22
Mountains of Western Canada, where the formations are mainly in the thrust faulting stress regime.
Permeability (md)
100 10 1 y = 11.642e-0.006x
0.1 0.01
0.001 0
500
1000
1500
Burial depth (m) Fig. 10. Permeability versus burial depth in the Southern Qinshui coalbed reservoir.
5. Stress and deformation dependent permeability in the coal reservoir Stress-dependent permeability has been extensively studied in fractured rocks (e.g. [37-41]). However, the coalbed methane reservoir has low permeability and strong gas adsorption, which is quite different from the conventional oil and gas reservoirs. Coal reservoirs also belong to double porosity and double permeability media consisted of coal porous matrices and natural fissures (cleats), as shown in Fig. 11. In a double porosity coal seam the primary porosity in the coal matrices is mainly controlled by deposition, while the secondary porosity is controlled by cleats and other fractures. Thus, the fracture and matrix systems in a coal seam are distinctly different in both porosity and permeability. The global flow occurs primarily through the high-permeability, low-porosity cleat/fracture systems surrounding the matrix coal blocks. The matrix blocks contain the majority of the reservoir storage volume and act as local source or sink terms to the cleat/fracture system. The cleats/fractures are interconnected and provide the main fluid flow path to the production
23
wells [42]. Therefore, permeability measured from the well tests is primarily the permeability in the cleats. The influence of in-situ stress on coal permeability reflects essentially the results of the permeability change due to the deformation of the cleats in the coal reservoir.
Butt cleat
Matrix
Face cleat 1 cm
Fig. 11. Photograph of a coal sample in Qinshui anthracite showing the orientations and spacings of the face and butt cleats and matrices. 5.1. Compression and deformation of cleats in the coal reservoir We found that the deformation in cleats under normal compressive stress state has a similar result as other fractures in rocks. The normal compressive stress and displacement in coal cleats follow the following exponential relationship [33]:
b b0 e
( n p ) b0 k n
(24)
where b0 is the initial cleat aperture; b is the aperture change after the changes in normal stress n and pore pressure pp; n is the change in normal stress; n = n – n0; n0 is the initial normal stress; The compressive stress is positive and tensile stress is negative; p is the change in fluid pressure (pore pressure) in the cleats, p = pp – p0; p0 is the initial pore pressure; kn is the normal stiffness of the cleats. 5.2. Stress-dependent permeability in the coal reservoir
24
The coal seams in the Qinshui basin are cut by groups of cleats (Fig. 11) which can be simplified by groups of parallel fissures/cleats. Therefore, we can apply the “parallel plate” theory to model the cleat permeability in the coal seam. For a set of parallel cleats with a constant aperture (or average aperture), the cleat permeability can be expressed in the following form [43]: K f c
b 3 12s
(25)
where Kf is the permeability in cleats; b is the average aperture of cleats; is the unit weight of the fluid; is the dynamic viscosity of the fluid; s is the average spacing of the cleats; c is a constant related to surface roughness of the cleats; is a constant describing to the connectivity of cleats. Equation 25 indicates that the cleat permeability is highly sensitive to the cleat aperture. When the opening of the cleat changes due to applied stress and fluid pore pressure, the permeability changes accordingly. Substituting the aperture change induced by effective stress (Eq. 24) into Eq. 25, the stress-sensitive permeability in one set of parallel cleats can be obtained: K f K0e
3( n p ) b0 kn
(26)
where K0 is the permeability under the initial stress condition. The coal seams in the Qinshui basin are normally cut by two groups of cleats (butt and face cleats), as shown in Fig. 11. This coal seam can be approximately represented by two groups of parallel fissures/cleats, as shown in Fig. 12. For two mutually orthogonal sets of cleats, as shown in Figs. 11 and 12, the permeability change due to the aperture changes can be obtained by superposition as following [31]:
b K z K 0 x 1 x b0 x
b K 0 y 1 y b0 y 3
3
(27)
where Kz is the permeability change due to aperture increments of bx and by; the compressive displacement is positive and tensile displacement is negative; K0x is the original 25
permeability induced by cleats in x direction under the initial stress condition; K0y is the original permeability induced by cleats in y direction under the initial stress condition; K0z is initial total the permeability induced by the two sets of cleats, and K0z = K0x + K0y; b0x is the initial average normal aperture of the original fracture in the x direction; b0y is the initial average normal aperture of the original fracture in the y direction. Substituting the aperture changes, bx and by in the face and butt cleats induced by effective stress (bx = b0x – bx in Eq. 24) into Eq. 27, the stress-sensitive permeability in two sets of cleats can be obtained:
K z K0x e
3( nx p ) b0 x knx
3( ny p )
K0 y e
b0 y kny
(28)
where b0x and b0y are the initial cleat apertures in the face and butt cleats (in x and y directions); K0x + K0y is the initial total the permeability induced by the two sets of cleats; nx is the normal stress change in x-direction; nx = nx – nx0; nx0 is the initial normal stress in x direction; ny is the normal stress change in y direction; p is the change in fluid pressure (pore pressure) in the cleats, p = pp – p0; p0 is the initial pore pressure; knx is the normal stiffness of the cleats in the x direction, kny is the normal stiffness of the cleats in the y-direction.
sy y by z bx
x
sx
Fig. 12. Simplified multiple fracture system for two mutually orthogonal sets of parallel cleats in z-direction [31]. This relationship shows that the effective stress change has a pronounced impact in 26
permeability. This effective stress-dependent permeability is significant for dual-porosity and dual-permeability coal reservoirs, because the rapid change in effective stress can induce the closure of cleats, which may cause permanent lose of permeability in the cleats. Therefore, slowing down the effective stress change during production of the coal reservoir can decelerate the permeability reduction. For example, slowing reservoir drawdown can reduce fast increase in effective stress, thus reduce permeability decrease. Also, reducing deformation in cleats can ensure coal matrices to supply enough gas (pressure) to the cleats to support the cleat space. Equations 26 and 28 can also be applied to explain the permeability decrease as the depth increases. A deep reservoir has a higher in-situ stress, thus it has a higher effective stress if the gas pressure is not highly overpressured. Therefore, the high effective stress in the deep reservoir causes cleat aperture reduction (even closed) and permeability decrease. During coalbed methane production (desorption) and acid gas injection (adsorption), fluid pressure changes and the volumetric strain induced by gas desorption or adsorption also induces changes in the stress field. Variations in the stresses in turn cause the porosity to change [44]. For instance, the gas desorption causes matrix shrinkage and the adsorption causes matrix swelling, which influence permeability of coal [13]. An internal stress in coal matrices (i) can be used to describe the sorption/desorption-induced volumetric strain in the matrices. Liu and Rutgvist (2010) called this stress to be “internal swelling stress” [15]. Actually this internal stress could also cause the matrix shrinkage due to methane desorption. Therefore, we call it “matrix internal stress”. Using the internal stress concept, Equations 26 and 28 can be rewritten as below. For one set of parallel cleats, the following form can be used to count for the sorption/desorption effects. KCBM K0e
3( n p i ) b0kn
(29)
where KCBM is the coalbed permeability after stress changes; K0 is the initial permeability; i is the matrix internal stress, and is positive for matrix swelling and negative for matrix shrinkage. For two mutually orthogonal sets of cleats with considerations of the methane sorption/desorption effects, the permeability and stress relationship can be rewritten to the
27
following form:
K z K0x e
3( nx p i ) b0 x knx
3( ny p i )
K0 y e
b0 y kny
(30)
The matrix internal stress can be obtained from laboratory tests or estimated from [13, 44]. Equations 29 and 30 show that the matrix internal stress has influences on permeability of coal. In other words, the gas desorption-induced matrix shrinkage causes increase in permeability of coal, and the adsorption-induced matrix swelling causes decrease in coalbed permeability.
6. Summary and Conclusions The Southern Qinshui Basin is located in an extensional basin, where the normal faulting stress regime is dominated. Therefore, permeability is higher than other coalbed methane reservoirs in China, particularly at the shallow depth (
