In-situ stress, pore pressure and stress-dependent permeability in the S

In-situ stress, pore pressure and stress-dependent permeability in theSouthern Qinshui Basin Zhaoping Menga,b, Jincai Zhangc,n a College of Geosciences and Surveying Engineering, China U

In-situ stress, pore pressure and stress-dependent permeability in the

Southern Qinshui Basin

Zhaoping Menga,b, Jincai Zhangc,n

a

College of Geosciences and Surveying Engineering, China University of Mining and Technology, Beijing 100083, China

b Key Laboratory of Geological Hazards on Three Gorges Reservoir Area, Ministry of Education, China Three Gorges University, Yichang, Hubei 443002, China

c

Shell Exploration and Production Company, Houston, TX 77079, USA

a r t i c l e i n f o

Article history:

Received 5 February 2010

Received in revised form

5 October 2010

Accepted 6 October 2010

Available online 25 October 2010

Keywords:

In-situ stress

Pore pressure

Southern Qinshui Basin

Stress and permeability

Coalbed methane

a b s t r a c t

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 reservoirs, which consist 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 loss 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 the pore pressure is not significantly overpressured, such that in the Southern Qinshui Basin

&2010 Elsevier Ltd All rights reserved

1 Introduction

1.1 Field description

China has the world’s third-largest coalbed methane resources,

behind only to Russia and Canada Coalbed methane is an

impor-tant 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% of casualties attributable to gas (coalbed methane)

explosions, causing annually direct losses of US$93 million

How-ever, this No 1 ‘‘coalmine killer’’ is also a source of clean energy[1]

The estimated coalbed methane reserve in China is about

36.8 trillion m3, located no deeper than 2000 m below the surface

Over 46% of China’s coal mines are rich in methane, and about

1.3 billion m3of 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 devel-oping 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 m3 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 the 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 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 and Anze in the southeast of Shanxi Province It is the most important produc-tion base for high quality anthracite in China The Southern Qinshui Basin measures approximately 120 km from north to south and

80 km from east to west, with an area of about 7000 km2 Coal seams, generated in Carboniferous and Permian periods, contain

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International Journal of Rock Mechanics & Mining Sciences

1365-1609/$ - see front matter & 2010 Elsevier Ltd All rights reserved.

n

Corresponding author.

E-mail address: zhangjincai@yahoo.com (J Zhang).

abundant methane Permeability in the coalbed reservoir is

rela-tively high compared to other coalbed methane reservoirs in China

The exploration and production tests in this field have been

conducted since 1990s 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 the 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 an 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 from forty-five coalbed methane wells

were mainly obtained from No 3 coal seam located in the 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

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 the

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 12–18 h Then, the well is shut in at the surface and pressure falloff is monitored for 24–36 h

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 the stimulation method have to be applied

to enhance gas production This phenomenon is mainly caused by stress- and depth-dependent permeabilities 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 has been conducted [16–18] This paper, based on field measured data, analyzes the relationship of permeability and in-situ stress in the Southern Qinshui Basin The analysis may be applicable in developing strategies in exploration, well completion and production of coalbed methane

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 the 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]:

wheresVis 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 the Southern Qinshui Basin (Fig 1) The

Table 1

Ranges and means of rock mechanical properties in No 3 coal seam and its surrounding rocks a

Mechanical properties Roof of No 3 coal seam: mudstone

and sandy mudstone

No 3 coal seam: anthracite Floor of No 3 coal seam: mudstone

and muddy siltstone

a

The data representation is: Min:Max:

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

Fig 1shows that the pore pressure in the coalbed methane reservoir

is basically a normal (hydrostatic) pressure and only has mild

overpressure and underpressure at depths of 500–1100 m

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 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 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 inFig 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]

pgA¼pBrgghg ð2Þ

where pgAis the pore pressure at Location A; pBis the pore pressure

at Location B (the gas–water contact); hgis the height of the gas

column (the height from Locations A to B);rgis the in-situ gas

density; and 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 as follows:

Comparing Eq (2) with Eq (3), the pore pressure increment (pgA–pwA) elevated by the gas column is (seeFig 2)

Dpu

where Dpu is the pore pressure increment induced by the gas column;rw is the water density Mouchet and Mitchell gave a similar equation for the conventional hydrocarbon reservoirs[21] 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 inFig 3with a gas column height of hg)

where Dpd is the pore pressure reduction induced by the 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 inFig 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

The in-situ gas column/gradient in the Qinshui Basin is calcu-lated 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 compartmenta-lized Assuming the in-situ gas gradient of 0.005 MPa/m, two possible gas gradients are plotted inFig 3with comparison to the measured gas pore pressures.Fig 3shows that there is no obvious single gas column/gradient in this coalbed methane reservoir However, it is very much 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 inFig 3) is lower than the normal hydrostatic pressure In this case, the gas pressure has an updip pressure equalization with the hydrostatic water pressure at depth of 428 m

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

0

Stress, presure (MPa)

Vertical stress Pore Pressure Hydrostatic Pp 140m

Fig 1 Pore pressure in the coalbed reservoir and the hydrostatic water pressure

with potentiometric level at 140 m below the surface in the Southern Qinshui Basin.

Gas Water

Gas gradient 0.23g/cm

Gas in pores

water

h

pw

ρ , p

Fluid pressure (MPa)

Δpg

Water gradient 1.05 g/cm

A B

pA

pB gas

Coal Water in

fractures

ρ , p

gas C h

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 the water gradient From Locations B to A, the gas pressure has a downdip pressure equalization with the hydrostatic water pressure at Location B, i.e p g ¼p w ; p g is the gas pressure and p w

is the water pressure The gas pressure at Location C has an updip pressure equalization with the hydrostatic water pressure at Location B.

The other gas gradient may start at 800 m, and the gas pressure in

this compartment (Line 1 inFig 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 water and gas) in different gas compartments.Fig 3also

demonstrates that there is only a slight overpressure or

underpressure Therefore, hydrostatic water gradient with gas

buoyancy effect is the main control on gas pressure in this area

Based on measured pore pressure data in the Qinshui coalbed

methane basin, the pore pressure can be expressed to the following

form:

where ppis the pore pressure in MPa; D is the burial depth from the

surface in meters, D 4300 m 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

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

stimula-tion The minimum horizontal stress is commonly assumed to be

approximately 70% of the vertical stress magnitude in sedimentary

basins.Fig 4presents 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 the pore pressure, as shown inFig 5

We take out the two abnormal data points in the minimum horizontal stresses measured at depths of 560 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 toFig 5):

sh¼0:5045ðsVppÞ þpp ð7Þ whereshis the minimum horizontal stress;sVis the vertical stress;

ppis 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 introduced a variable of effective stress ratio into the minimum horizontal stress

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Stress, presure (MPa)

Vertical stress Minimum horizontal stress Pore Pressure

Hydrostatic Pp 140m 70%OBP

0 5 10 15 20 25 30 35

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.

0 2 4 6 8 10 12 14

0

σh

-pp

σv-pp

measured data Linear (measured data)

2 4 6 8 10 12 14 16 18 20 22

Fig 5 Relationship of the effective vertical stress and the effective minimum horizontal stress in coalbed methane reservoir in the Qinshui Basin.

0

Stress, presure (MPa)

Vertical stress Pore Pressure Hydrostatic Pp 140m Gas gradient 0.005MPa/m

1

2

0

100

200

300

400

500

600

700

800

900

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.

(or fracture gradient) prediction[22]

where K0 is the effective stress ratio, K0¼sh0/sv0; sh0 is the

minimum effective stress;sv0is the maximum effective stress

In this method, the values of K0were 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

K0is 0.505–0.54 (refer toFig 5), which is much lower than the

commonly used value (e.g K0¼0.8) in shales in deep petroleum

basins[23]

Fig 5shows 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]:

1nðsVppÞ þppþstec ð9Þ

wherenis the Poisson’s ratio;shis the minimum horizontal stress;

sVis the overburden stress; ppis the pore pressure; stecis 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 available

1nðsVppÞ þppþbsV ð10Þ

where b can be defined to be minimum stress coefficient, b ¼0.035

and the average Poisson’s ratio of the coal seamn¼0.31 in the

Southern Qinshui Basin (refer toTable 1)

It should be noted that Eqs (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

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

inFig 6

sh¼0:0236D3:5177 ð11Þ

whereshis the minimum horizontal stress in MPa; D is the burial

depth in meters, D 4300 m 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

2 Strike-slip faulting stress regime In this case, the vertical stress

is the intermediate principal stress In this stress state, one has

3 Reverse (or thrust) faulting stress regime In this case, the

vertical stress is the least principal stress, i.e.sHZshZsV

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]:

h ¼sVppþqfpp

qf

ð12Þ

wheresLB

h 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:

qf¼1 þ sinjf

1sinjf ¼ ½ðm

2þ1Þ1=2

wherejfis the internal friction angle of the fault and mis the friction coefficient of the fault

In the normal and strike-slip faulting stress regimes, the minimum horizontal stress should be in between the lower bound

of the minimum horizontal stress and the overburden stress Assuming the friction coefficient of the fault ofm¼0.6, the lower bound of the minimum horizontal stress in the Qinshui Basin can be calculated from Eq (12).Fig 6 shows the lower bound of the minimum horizontal stress compared to the measured data It 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

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]

pb¼3shsHppþT0 ð14Þ where ppis the pore pressure in the formation; pbis the fracture breakdown pressure; T0is the tensile strength of the rock, and can

be obtained from the fracture reopening pressure

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Stress, presure (MPa)

Vertical stress Minimum horizontal stress Pore Pressure

Pp empirical Sh_LB

Sh empirical

5177 3 0236

0 −

= D

f

p f p v LB h

q

P q

P +

−

=

8886 2 0122

p

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.

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:

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:

sH¼0:0343D4:6618 ð16Þ

wheresHis the maximum horizontal stress in MPa; D is the burial

depth in meters, D 4300 m

The data also demonstrate that two horizontal stresses in the

studied area are not equal The ratios of the two horizontal principal

stresses (sH/sh) range 1.07–1.71 with an average of 1.46, i.e

1:07osH=sho1:71 ð17Þ

The measured data show that the maximum horizontal

stress direction is predominately in the North–East–East direction

(or North50–801East), which is parallel to the strike of the major

faults

2.5 Relationship of vertical stress and horizontal stresses

The lateral stress coefficient can be used to examine the relation-ship between horizontal stresses and the overburden stress[19] The lateral stress coefficient (l) is defined as the ratio of the average horizontal principal stress, ðsHþshÞ=2, to the vertical stress,sV, i.e

l¼ðsHþshÞ=2

ð18Þ The measured results in the 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 the 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 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 (o590 m) in the Qinshui Basin are located in the normal faulting stress regime or in an extensional basin, as shown in

Fig 8 The average horizontal stress in the extensional basin is less than the overburden stress, orlo1 In the extensional basin, more natural fractures and a higher permeability are expected than those in the compressional basin This is greatly 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 (l) is small when the burial depth is less than 590 m, andlranges 0.4–1.0 As the formations go deeper, the lateral stress coefficient increases andl¼0.8–1.1, if the two exceptionally high values are taken out inFig 8

3 Relationship between permeability of coal reservoir and the in-situ stress

Permeability in a coal seam is a key parameter in coalbed methane reservoir Reservoir permeability depends directly on

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

Stress, presure (MPa)

Vertical stress Minimum horizontal stress Pore Pressure

Pp empirical

SH empirical

Sh empirical SH

5177 3 0236

0 −

= D

8886 2 0122

p

6618 4 0343

H

σ

Fig 7 The measured data and empirical correlations of the maximum and

minimum horizontal stresses, overburden stress and pore pressure in coalbed

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

0

Lateral stress coefficient (λ)

Extensional basin

Transition zone

I

II

Fig 8 The ratio of the average of two horizontal principal stresses, (sH +sh )/2, to the

drilling and completion methods and reservoir development

strategy For instance, for a coalbed reservoir with a high

perme-ability 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 the

in-situ stress, burial depth and stress variation due to drilling and

production[31]

Laboratory measurements show that coal permeability decreases

exponentially with an 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]:

where K is the permeability (md) andseis the effective in-situ stress

(MPa) K0is the permeability under the initial in-situ stress condition

(md); and a is the fitting parameter

This permeability and an in-situ stress relationship fit 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 inFig 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 ¼ 58:135e0:435ðsV ppÞ

ð20Þ

K ¼ 2:6357e0:193ð s H ppÞ

ð21Þ

K ¼ 4:6752e0:446ð s h p p Þ ð22Þ

where K is the permeability in mD;sV,sHandshare the principal

vertical, maximum horizontal and minimum horizontal stresses,

respectively, in MPa; and ppis the pore pressure in MPa

Fig 9demonstrates 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

an 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

ofo590 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

Another characteristic of an in-situ stress in this basin is the

ratio of the maximum horizontal stress to the minimum horizontal

stress is small, ranging 1.07–1.71 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,

perme-ability 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 inFig 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 the in-situ stress as well as the transition in stress regimes, as shown inFigs 7 and 8 When the basin is in the 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 (o590 m) and deeper depths Hence, horizontal wells with hydraulic fracturing are needed for developing the deeper coalbed reservoir (depth4590 m)

Permeability data observed in the coal seam in the Southern Qinshui Basin demonstrate an exponential trend between

y = 58.135e 0.001

0.01 0.1 1 10 100

0

Effective vertical stress (MPa)

y = 2.6357e 0.001

0.01 0.1 1 10 100

0

Effective maximum horizontal stress (MPa)

y = 4.6752e 0.001

0.01 0.1

1

10 100

0

Effective minimum horizontal stress (MPa)

Fig 9 Effective in-situ stress versus permeability in the Southern Qinshui coalbed reservoir plotted with an 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.

permeability and the burial depth

K ¼ 11:642e0:0061D ð23Þ

where K is the permeability in the coal (mD) and 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 Mountains of

Western Canada, where the formations are mainly in the thrust

faulting stress regime

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 consisting of coal porous matrices and natural fissures

(cleats), as shown inFig 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 wells [42] Therefore, permeability measured from the well tests is primarily the permeability in the cleats The influence of the in-situ stress on coal permeability essentially reflects the results of the permeability change due to the deformation of the cleats in the coal reservoir

5.1 Compression and deformation of cleats in the coal reservoir

We found that the deformation in cleats under normal com-pressive 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 ¼ b0eð Ds n  D pÞ=b 0 k n ð24Þ where b0is the initial cleat aperture; b is the aperture change after the changes in normal stresssnand pore pressure pp;D snis the change in normal stress; D sn¼sn–sn; sn is the initial normal stress; The compressive stress is positive and tensile stress is negative;Dp is the change in fluid pressure (pore pressure) in the cleats,Dp ¼pp–p0; p0is the initial pore pressure; knis the normal stiffness of the cleats

5.2 Stress-dependent permeability in the coal reservoir

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]:

Kf¼cb gb3

where Kfis the permeability in cleats; b is the average aperture of cleats;gis the unit weight of the fluid;mis 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;bis a constant describing to the connectivity of cleats

Eq (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 an effective stress (Eq (24)) into Eq (25), the stress-sensitive permeability in one set of parallel cleats can be obtained

Kf¼K0e3ð Ds n  D pÞ=b 0 k n ð26Þ where K0is 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 inFig 11 This coal seam can be approximately represented by two groups of parallel fissures/cleats, as shown inFig 12 For two mutually orthogonal sets of cleats, as shown inFigs 11 and 12, the permeability change due to the aperture changes can be obtained by superposition as follows[31]:

Kz¼K0x 1Dbx

b0x

 3

þK0y 1Dby

b0y

 3

ð27Þ

where Kzis the permeability change due to aperture increments of

Dbxand Dby; the compressive displacement is positive and the tensile displacement is negative; K0xis the original permeability induced by cleats in the x-direction under the initial stress condition; K0y is the original permeability induced by cleats in the y-direction under the initial stress condition; K is an initial

y = 11.642e

0.001

0.01

0.1

1

10

100

0

Burial depth (m)

Fig 10 Permeability versus the burial depth in the Southern Qinshui coalbed

reservoir.

1 cm

1 cm

Face cleat

Butt cleat

Matrix

Fig 11 Photograph of a coal sample in the Qinshui anthracite, showing the

orientations and spacings of the face and butt cleats and matrices.

total the permeability induced by the two sets of cleats, and

K0z¼K0x+ K0y; b0x is the initial average normal aperture of the

original fracture in the x-direction; b0yis the initial average normal

aperture of the original fracture in the y-direction

Substituting the aperture changes,DbxandDbyin the face and

butt cleats induced by an effective stress (Dbx¼b0x–bxin Eq (24))

into Eq (27), the stress-sensitive permeability in two sets of cleats

can be obtained

Kz¼K0xe3ð Ds nx  D pÞ=b 0x k nxþK0ye3ð Ds ny  D pÞ=b 0y k ny ð28Þ

where b0xand b0yare 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; D snx is the

normal stress change in the x-direction; D snx¼snx–snx0; snx0 is

the initial normal stress in the x-direction;D snyis the normal stress

change in the y-direction;Dp is the change in fluid pressure (pore

pressure) in the cleats,Dp ¼pp–p0; p0is the initial pore pressure; knx

is the normal stiffness of the cleats in the x-direction, knyis the

normal stiffness of the cleats in the y-direction

This relationship shows that the effective stress change has a

pronounced impact in permeability This effective

stress-depen-dent permeability is significant for dual-porosity and

dual-perme-ability coal reservoirs, because the rapid change in an effective

stress can induce the closure of cleats, which may cause permanent

loss 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 the

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 Eqs (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 (si) can be used to describe the

sorption/desorption-induced volumetric strain in the matrices Liu and Rutgvist in 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, Eqs (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

KCBM¼K0e3ð Ds n  D p þ s i Þ=b 0 k n ð29Þ where KCBMis the coalbed permeability after stress changes; K0is the initial permeability;si 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 following form:

Kz¼K0xe3ð Ds nx  D p þ Ds i Þ=b0xk nxþK0ye3ð Ds ny  D p þ Ds i Þ=b0yk ny ð30Þ

The matrix internal stress can be obtained from laboratory tests

or estimated from[13,44] Eqs (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 an 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 (o590 m) This is because the extensional basin has lower horizontal stresses than the compressive basins, which is advantageous to keep fractures/cleats open That is, permeability is higher in the normal faulting stress regime than those in the thrust and strike-slip faulting stress regimes

The pore pressure in the Southern Qinshui Basin is not sig-nificantly overpressured or underpressured, compared to the hydrostatic water pressure The mild abnormal gas pressure is mainly caused by the density contrast between water and methane

or the buoyancy effect of the gas column in different gas compart-ments Measured data in the coalbed methane basin show that the minimum horizontal stress can be fairly constrained by the Anderson’s faulting theory with a friction coefficient of 0.6 The minimum horizontal stress can also be calculated from the modified uniaxial strain in-situ stress model The measured data also demonstrate that the coal seam has a similar relationship between effective vertical stress and effective minimum horizontal stress, but a smaller effective stress ratio than other sedimentary rocks in petroleum basins It should be noted that the effective stress ratio in the coal seams is much lower (hence lower fracture gradient) than the shales in the Gulf of Mexico and other oil basins Therefore, mud losses while drilling may be encountered in the coalbed basins

Permeability decreases markedly as the in-situ stress increases

in the Southern Qinshui coal reservoir This is mainly induced by the high effective stress in the deep reservoir, which causes the reduction in cleat apertures The effective stress-dependent per-meability is significant for dual-porosity and dual-perper-meability porous media The reason is that a rapid change in an effective stress can induce the closure in cleats, which may cause the cleats

to lose permeability permanently This blocks the coal matrices to supply enough gas to the cleats Therefore, slowing down the effective stress change during production can decelerate the permeability reduction For example, slowing reservoir drawdown can reduce fast increase in effective stress, thus reduce perme-ability decrease Also, reducing deformation in cleats can ensure the connectivity of the cleats and coal matrices, so that the coal matrices can deliver gas pressure to the cleats for supporting the cleat space

x z

y

bx

by

sx

sy

Fig 12 Simplified multiple fracture system for two mutually orthogonal sets of

parallel cleats in the z-direction [31].

This work is partially supported by the National Basic Research

Program of China (973 Program under the Project no

2007CB209405) and the National Natural Science Foundation of

China (Nos 40772100 and 41030422) Authors are grateful to

Qinshui Lianyan Coalbed Methane Co Ltd for its permission

to publish the field data We also thank reviewers and editors

for their constructive comments and suggestions on improving the

manuscript

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