Fuel 136 (2014) 57–61

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Numerical simulation of hydraulic fracturing coalbed methane reservoir

http://dx.doi.org/10.1016/j.fuel.2014.07.0130016-2361/� 2014 Elsevier Ltd. All rights reserved.

⇑ Address: Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom.E-mail address: jingchen120@126.com

Jingchen Zhang ⇑Heriot-Watt University, Edinburgh EH14 4AS, United KingdomMOE Key Laboratory of Petroleum Engineering, China University of Petroleum (Beijing), Beijing 102249, China

h i g h l i g h t s

� A two-phase, three-dimensional model of fracturing coalbed methane is developed and coded.� Impact of permeability, original volume density, porosity, Langmuir pressure constant on production is analyzed.� Influence of hydraulic fracturing on production capability, desorption and diffusion is studied.

a r t i c l e i n f o

Article history:Received 21 May 2014Received in revised form 3 July 2014Accepted 8 July 2014Available online 24 July 2014

Keywords:Hydraulic fracturingCoal bed methaneNumerical solutionsGas desorption

a b s t r a c t

Some coal seam is well known for its three low characteristics: low permeability, low reservoir pressureand low gas saturation. Thus stimulation measures must be taken during coalbed methane developmentstage to enhance its recovery. Hydraulic fracturing transformation technology is an effective method forincreasing coalbed methane production.

This paper presents a two-phase, 3D flow and hydraulic fracturing model of dual-porosity media basedon the theories of oil–gas geology and mechanics of flow through porous media.

Correspondingly, a finite difference numerical model has been developed and applied successfully to acoalbed methane reservoir. Well test data from one western China basin is utilized for simulation. Resultsshow that hydraulic fracturing promotes desorption and diffusion of coalbed methane which in turnsubstantially increases production of coalbed methane.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Hydraulic fracturing transformation technology is the primarymeans in enhancing production of coalbed methane wells. Morethan 90% of coal seam is improved through hydraulic fracturingamong 14,000 multi-port coalbed methane wells in United States.There may be a number of far extended cracks in the internal offractured coal seams. This can result in the pressure drop in a largearea around borehole, thus gas desorption surface area of coalseam enlarged which guarantees the discharge of coalbed methanerapidly and sustainably. Coalbed methane production of fracturedcoal seams is 5–20 times of pre-fracturing condition.

Hao et al. [1] analyzed characteristics of pressure of coal seamfracturing and the relationship between depth and break pressuregradient. Zhang and Wang [2] introduced dynamic (potential) test-ing technique used for determination of fracturing azimuth, lengthand other parameters of coal seam. Yuan and Meng [3] used acous-tic detection system to carry out seismic tomography tests before

and after fracturing respectively in order to determine fracturingeffect. Michael et al. [4] analyzed hydraulic fracturing design onthe impact of ECBM (Enhanced Coal Bed Methane Recovery). McDariec [5] firstly applied hydraulic fracturing techniques to thestimulation work of coalbed methane wells. Zhao et al. [6]described hydraulic fracturing technique for coalbed methane gasreservoirs with low permeability and also developed a set ofoptimal design software for low permeability hydraulic fracturingcoalbed gas reservoirs. Boyer [7] conducted Laboratory and fieldtests to establish criteria for containment of an induced hydraulicfracture. Clarkson [8] provided a new workflows and analyticalapproaches for analyzing single and multi-phase flow of CBM fromvertical, hydraulically-fractured wells and horizontal wells. Wrightet al. [9] summarized a few enhancements for coal seam fracturingtechnology, as well as the present limitations and the necessaryadvancements required for superior coal seam fracture perfor-mance in future. Holditch [10] utilized hydraulic fracturing treat-ments to optimize recovery from most of the wells that drilledinto deep coal seams.

Although many scholars had studied the exploitation of CBM(Coal Bed Methane) as well as the impact of hydraulic fracturing

Nomenclature

vg gas area velocity of cleat, cm/sBg gas volume factor of cleatqvg gas production items, cm3/(cm3 s)D depth away from the datum, cmqmfg gas diffusion rate of gas cross flow from matrix to cleat,

cm3/(cm3 s)/f porosity of cleat, decimalsg gas saturation of cleat, decimalr Hamilton operatorkf permeability of cleat, lm2

krg gas relative permeability of cleat, decimalpfg gas pressure of cleat, 10�1 MPalg gas viscosity of cleat, mPa sqg gas density of cleat, g/cm3

krw water relative permeability of cleat, decimalBw water volume factor of cleatlw water viscosity of cleat, mPa sqw water density of cleat, g/cm3

pfw water pressure of cleat, 10�1 MPasw water saturation of cleat, decimalVm average concentration of gas in matrix element,

cm3/cm3

VE gas concentration in the surface of matrix element,cm3/cm3

s desorption time of coalbed methane, slmg gas viscosity of matrix element, mPa sFG geometry-related factorp0

fg initial reservoir pressure of coalbed methane, a givenfunction

s0g initial gas saturation of coalbed methane, a given func-

tionrw radius of wellborekfx, kfy permeability in different directions of cleat systemC outer boundary of coalbed methane, n represents exter-

nal normal direction of outer boundarype(x, y, z, t) known function related to pressure

58 J. Zhang / Fuel 136 (2014) 57–61

on CBM, few had taken hydraulic fracturing into consideration inthree dimensional and two phase coalbed methane reservoir. Thispaper is rightly to address this problem and presents a numericalsimulation with independent fracture system. A computer pro-gram has been coded. Well test data from one western China Basin,which include all parameters needed in simulation work, provethat the model established in this paper is reasonable and feasible.

2. Mathematical model of coalbed methane reservoir

2.1. Gas seepage equation in the cleat system

According to continuity equation, Darcy’s law, general form ofwater flow seepage equation is shown as follows:

r �qgkf krg

lgðrðpfg � qggDÞÞ þ Dfr

sg

Bg

� �" #þ qvg þ qmfg

¼ @

@t/f sg

Bg

� �ð1Þ

2.2. Water seepage equation in the cleat system

Similarly, water seepage equation in the cleat system can bedescribed as follows:

r � kf krw

Bwlwðrðpfw � qwgDÞ

� �þ qvw ¼

@

@t/f sw

Bw

� �ð2Þ

2.3. State equation in the cleat system

Eqs. (1) and (2) are the second-order nonlinear partial differen-tial equations which contain four unkowns: pfg, sg, pfw, sw. At thesame time, pfg, sg, pfw, sw satisfy state equation as follows:

sg þ sw ¼ 1 ð3Þ

pcgwðsgÞ ¼ pfg � pfw ð4Þ

The pcgw(sg) in Eq. (4) is called capillary pressure function, whichis a given function.

2.4. Gas desorption and transportation equation in the cleat system

Considering the steady-state case, average gas concentration inthe matrix is subject to desorption of adsorption gas, thus gasconcentration changes during the process of gas desorption andtransport in the matrix system can be expressed as the followingequation:

dVm

dt¼ 1

s½VEðpfgÞ � Vm� ð5Þ

Accordingly, from the matrix cell proliferation by channellingflow into cleat system, gases diffused and crossflowed from matrixunit to cleat system is:

qmfg ¼ �FGdVm

dtð6Þ

Here, while taking both free gas and adsorbed gas into account,gas concentration both in the surface and internal of the matrixelement can be described as follows according to Langmuir equa-tion and real gas law:

VEðpfgÞ ¼VLpfg

PL þ pfgþ

/f Mpfg

qsczRTð7Þ

Vm ¼/mMpmg

qsczRTþ

VLpmg

PL þ pmgð8Þ

Eq. (7) linkes up average pressure and average concentration inthe matrix system, then combined with Eq. (5) the pressure ofmatrix element can be got.

2.5. Initial conditions of the model

pfgðx; y; z;0Þ ¼ p0fgðx; y; zÞ ð9Þ

sgðx; y; z;0Þ ¼ s0gðx; y; zÞ ð10Þ

Vm

��t�0 ¼

VLp0fg

PL þ p0fg

þ/f Mp0

fg

qsczRTð11Þ

(1) Inner boundary conditions

J. Zhang / Fuel 136 (2014) 57–61 59

Qvg ¼2phkkrg

Bglgðln rerwþ sÞ ðpfg � pwf Þ ð12Þ

Qvw ¼2phkkrw

Bwlw ln rerwþ s

� � ðpfw � pwf Þ ð13Þ

k ¼ffiffiffiffiffiffiffiffiffiffiffikfxkfy

q; re ¼ 0:28

kfx

kfy

� �12Dy2 þ kfy

kfx

� �12Dx2

� �12

kfx

kfy

� �14 þ kfy

kfx

� �14

(2) Outer boundary conditionConstant pressure outer boundary:

pfgðx; y; z; tÞ��ðx;y;zÞ2C ¼ peðx; y; z; tÞ ð14Þ

@sg

@n

����C

¼ 0 ð15Þ

Closed outer boundary:

@pfg

@n

����C

¼ 0 ð16Þ

@sg

@n

����C

¼ 0 ð17Þ

3. Numerical solutions of coalbed methane model

The coalbed methane models established above can be classi-fied into complex non-linear partial differential equations thatare difficult to solve directly. IMPES (Implicit Pressure Explicit Sat-uration) and finite difference method are utilized to solve CBMnumerical model under non-uniform grid conditions.

Hydraulic fracture should be treated in a reasonable way inorder to forecast production of coalbed methane wells during theprocess of coalbed methane numerical simulation. A two phaseand three dimensional model is set as an example for meshing inseepage field. Firstly, take step length LX, LY, LZ along direction X,Y, Z and make two parallel lines to divide the studied domain intomany grid blocks. Secondly, take 1/4 seam as research unit owingto the symmetry of coal seam, grid becomes gradually sparse fromwellbore to boundary and performs as arithmetical progression toensure convergence and stability of difference schemes’ solution.Corresponding computing unit is shown in Fig. 1.

For the treatment of hydraulic fracturing, if fracture is consid-ered as a separate grid row, volume of mesh block is extremelysmall due to small actual width, also internal formation near frac-

Fig. 1. Formational situation before hydraulic fracture enlarged.

ture gradually sparse from wellbore to boundary to ensure conver-gence and stability of difference schemes’ solution, however thiswill undoubtedly increase the time and memory share ofcomputer.

To solve this problem, it needs regarding the fracture as ahypertonic band in the formation, and hence adopting the equiva-lent conductivity method to amplify the fracture. The regulation isto amplify the fracture width appropriately and adjust the perme-ability accordingly, under the limitation of equivalent conductivity(jf � wf).

4. Numerical simulation results analysis

Parameters used during the simulation process of three dimen-sional coalbed methane are listed in Table 1.

Cleat permeability is the main factor in determining water andgas flow in reservoir and therefore has significant influence on gasproduction. As can be seen from Fig. 2, gas production drops signif-icantly even fluctuation of cleat permeability is small. What’smore, the larger the permeability, the greater the gas productionin initial stage. However, gas production drop obviously in laterstage for the highest permeability.

Fig. 3 shows the effects of porosity variation on gas production.Coal seam porosity determines the amount of free-gas and water inthe system. However, it also plays a role in the amount of gas thatcan be adsorbed on the surface of the coal seam. Gas production issensitive to the porosity of the coal cleat system, the greater theporosity, the shorter the breakthrough time.

It can be seen from Fig. 4 that gas production increases in accor-dance with the increase of Langmuir pressure (PI in Fig. 4) whenLangmuir pressure constant is low. Gas production increase canbe attributed to the increased breakthrough times. However, thisincrease tend is reversed with time going on, there will be a reduc-tion on gas production and a stabilizing of the breakthrough times.

From Fig. 5 it can be deduced that the increase of Langmuirvolume (VL in Fig. 5) constant results in a corresponding decreasein gas production and a shorter breakthrough time. This can beattributed to the drop of diffusion rate affected by the Langmuirvolume.

Fig. 6 indicates that gas production of coalbed methane wellsincreases significantly after hydraulic fracturing process. This isbecause coal seam pressure drops obviously after hydraulicfracturing process and results in desorption of coalbed methaneas well as continuous seepage.

In order to further illustrate fracture parameter’s impact onproduction. This paper carries out sensitive analysis of fracturehalf-length and fracture conductivity.

As can be seen from Fig. 7, production curve of fracturedcoalbed methane follows low- high-low form. The reason for thisphenomenon is described in details as follows. When fracturedwell is opened to produce, fluid both in and around fracture isproduced quickly owing to high fracture conductivity. At this time,original coal seam which has low permeability already has no abil-ity to provide adequate supplies for the fracture, so pressure in andaround the fracture drops below critical desorption pressure, andthe entire flow in this stage is controlled mainly by fracture, coal-bed methane in it desorbs quickly which results in a gas produc-tion peak (first peak period of fracturing effect).

When most of adsorbed gas in and around fracture is desorbedout, gas production is gradually stable and has a rebound trend ascan be seen from the curves, then the second peak appears in tran-sitional stage of normal production period. Hydraulic fracturingmeasurement can more or less form the first gas production peak.Further analysis of diagram also reveals that the first gas produc-tion peak resulting from fracturing effect delays as fracture lengthincreases while the second gas production peak turns out in

Table 1Simulation parameter of three dimensional coalbed methane model.

Reservoir physical parameters Dynamic production parameters

Depth 457.2 m Langmuir volume 20.60 m3/t Well bottom pressure 0.345 MPaThickness 7.62 m Langmuir pressure 3.94 MPaPorosity 0.02 Adsorption time 35.0 day Half length of fractured crack 50 mPermeability 3.0 md Coal density 1.3 t/m3

Gas viscosity 0.58 cp Wellbore radius 0.088392 m Fractured crack width 0.006 mSkin factor �2.5 MPa Initial pressure 10.342 MPaInitial gas content 12.74 m3/t Absolute permeability of fractured crack 20 mdInitial water saturation 0.92

Fig. 2. Effects of different permeability on gas production.

Fig. 3. Effects of different porosity on the gas production.

Fig. 4. Effects of different langmuir pressure on the gas production.

Fig. 5. Effects of different langmuir volume on the gas production.

Fig. 6. Comparison of fracture and fracture free effect on the gas production.

Fig. 7. Effects of different fracture half length on the gas production.

60 J. Zhang / Fuel 136 (2014) 57–61

Fig. 8. Effects of different fracture capacity on the gas production.

J. Zhang / Fuel 136 (2014) 57–61 61

advance, in addition, gas production peak increases with a reduc-ing speed, and the curve is almost converge to one point with pro-duction time increases.

Fig. 8 is a semi-log diagram which demonstrates gas productionchanges with fracture conductivity. With fracture conductivityincreases, gas production peak appears earlier and gas productionalso increases, so is the yield-increasing effect. However, gasincreasing rate experiences a declining trend during the process,and gas increasing rate is nearly negligible when fracture conduc-tivity increases to a certain degree. Yield-increasing effect is moreobvious at initial stage, while this becomes blurred as the shift ofproduction time.

5. Conclusions

A two-phase, three-dimensional model of single fracturing coal-bed methane well is developed in this paper. Correspondingly, a

numerical simulation program based on IMPES method isdeveloped. The impact of permeability, porosity, langmuir pressureconstant and other parameters on gas production is analyzed.Influence of hydraulic fracturing on production capability, desorp-tion and diffusion of coalbed methane wells is also studied. Resultsvalidate the developed two-phase, three-dimensional fracturingmodel of coalbed methane. Hydraulic fracturing promotes desorp-tion and diffusion of coalbed methane and therefore can greatlyimprove productivity of coalbed methane wells, which conse-quently is an effective method in exploiting coalbed methanewells.

The developed model can be adopted for enhanced coalbedmethane recovery, corresponding conclusion may provide guid-ance for coal bed methane prediction and evaluation.

References

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