analysis of thermo-hydro-mechanical coupling of coal and

Research ArticleAnalysis of Thermo-Hydro-Mechanical Coupling of Coal andGas with AbsorptionDesorption Thermal Effect

Jianfeng Hao 1 Bing Liang 2 and Weiji Sun 2

1College of Mining Liaoning Technical University Fuxin Liaoning 123000 China2School of Mechanics and Engineering Liaoning Technical University Fuxin Liaoning 123000 China

Correspondence should be addressed to Jianfeng Hao 471610041stulntueducn

Received 2 November 2020 Revised 20 November 2020 Accepted 28 November 2020 Published 23 December 2020

Academic Editor Yuantian Sun

Copyright copy 2020 Jianfeng Hao et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Coal adsorptiondesorption gas can cause temperature changes Moreover the pressure difference between the high gas pressurearea and the low gas pressure area in the coal may affect the coal adsorptiondesorption gas thermal effect To study the effect ofadsorptiondesorption thermal effect on the evolution law of coal and gas outburst precursor information under different pressuredifferences the adsorptiondesorption thermal effect experiments were carried out And the thermo-hydro-mechanical couplingmodel was established which reflects the interaction between coal and gas Under the action of ground stress pore pressureadsorption expansion stress and thermal expansion stress the model includes the dynamic evolution of coal porosity andpermeability gas adsorption-desorption-diffusion-seepage and energy accumulation and dissipation Using the coupling modelthe mechanism of adsorptiondesorption thermal effect on the evolution of outburst precursor information and the mutualcoupling relation between coal and gas is analyzed e experimental results show that the relation between pressure differenceand coal sample temperature variation is linear and the pressure difference has a quadratic parabolic relation with the tem-perature accumulation of coal sample As the pressure difference increases the temperature variation of the coal sample graduallyincreases but the temperature accumulation gradually decreases Numerical simulation results show that as the pressure dif-ference increases the changes in coal temperature and gas pressure gradually decrease and the thermal expansion strain caused bythe adsorptiondesorption thermal effect decreases and the permeability increases Comparing the calculation results with orwithout the adsorptiondesorption thermal effect the volumetric strain temperature and permeability of the coal have significantchanges when the adsorptiondesorption thermal effect is considered and the gas drainage volume increases as the pressuredifference increases e effect of thermal expansion strain caused by adsorptiondesorption thermal effect on gas seepage isgreater than the effect of temperature change on gas seepage

1 Introduction

Coal and gas outburst is a complex dynamic disaster in theprocess of coal mining In recent years most of the majorsafety accidents in Chinarsquos coal mines are caused by theabnormal gas outflow and the coal and gas outburst Coaland gas outburst has always been a serious threat to coalmine safety production and has become a major issue thatneeds to be solved urgently in coal mining [1ndash5] As themining depth increases the in situ stress temperature andgas pressure of the coal seam increase and the permeabilitydecreases e interaction mechanism of coal and gas underthe coupling action of stress field seepage field and

temperature field is more complicated and the temperaturefield has become an important research target [6ndash9]Meanwhile the pressure difference between the high gaspressure area in front of the working face and the low gaspressure area near the coal wall is an important parameter tocontrol the outburst strength of coal and gas Moreover theadsorptiondesorption thermal effect may be different underdifferent pressure differences [10ndash13]

To study the characteristics of coal adsorptiondesorptiongas thermal effect the influence of adsorptiondesorptionthermal effect on the interaction of coal and gas and theevolution law and mutual coupling relation of coal and gasoutburst precursor information under multifield coupling

HindawiShock and VibrationVolume 2020 Article ID 6674107 16 pageshttpsdoiorg10115520206674107

scholars have carried out a lot of research work and estab-lished multifield coupling model suitable for a variety ofcomplex situations [14ndash17] Coal releases heat during theprocess of gas adsorption and absorbs heat during the processof gas desorption [18ndash20] Jacek [21] gave a calculationmethod of the maximum volume of work which can beperformed by a gas while being liberated from a coal bedRahman [22 23] reported the theoretical frameworks for thethermodynamic quantities for the adsorption of methaneonto various carbonaceous materials Temperature variationcauses deformation and deformation generates heat whichcauses temperature variation Liu [24] proposed the thermaldeformation effect of adsorptionndashdesorption on the basis ofthe molecular migration and energy conversion during theadsorptionndashdesorption At present multifield coupling is ahot research target [25ndash28] the fields of coalbed methaneextraction shale gas extraction coal and gas outburst pre-vention and nuclear waste treatment all involve thermo-hydro-mechanical coupling issues [29 30] araroop [31]believed that existing coal bed methane (CBM) simulatorsusually treat the coal seam as a dual pore and single per-meability system ignoring the influence of water in the coalmatrix e model includes the influence of moisture in thecoal matrix and the shrinkage and expansion of coal Con-sidering the competitive effects of thermal expansion non-isothermal gas adsorption and thermal fracturing Teng [32]established a fully coupled thermo-hydro-mechanical modelof coal deformation gas flow and heat transfer Zhu [33] usesthe finite element method to establish and solve a fullycoupled model of coal deformation gas transport and heattransport A general model was established to describe theevolution of coal porosity under the combined influence ofgas pressure thermally induced solid deformation thermallyinduced gas adsorption changes and solid deformationcaused by gas desorption Zhou [34] proposed a coupledthermal pore elastic model which considers the compress-ibility and thermal expansion of the convective heat flow ofthe components as well as the changes in the porosity andrelated characteristics of the saturated soil e model alsoconsiders the thermodynamically coupled water and heatflow Fall [35] gave a detailed formula for coupling moistureand gas transmission in deformable porous media is givenis model takes into account the fluid flow under damagecontrol and the coupling of hydraulic and mechanical pro-cesses e model also considers the coupling of diffusioncoefficient and mechanical deformation and considers thechanges in capillary pressure caused by changes in perme-ability and porosity To analyze the influence of gas desorptionon gas outburst An [36] established a mechanical processmodel in the process of gas migration and tunneling estudy understands the influence of absorption shrinkage andmechanical changes on the protrusion Tao [37] carried outphysical simulation experiments on coal and gas outburstsand established a thermo-hydro-mechanical coupling modelof gassy coal

In summary the existing research did not use experi-ments to analyze the influence of coal adsorptiondesorptiongas thermal effect on the evolution law of outburst precursorinformation In addition there are few quantitative studies

on the influence of adsorptiondesorption thermal effect onthe interaction between coal and gas Using the self-designedcoal and gas thermo-hydro-mechanical coupling experimentsystem and the cyclic-step adsorptiondesorption experi-ment method the temperature change of coal adsorptionand desorption gas under different pressure differences wasdiscussed Based on the experimental results a thermo-hydro-mechanical coupling model of gassy coal with theadsorptiondesorption thermal effect was established andthe model is solved by COMSOL Multiphysics Comparingthe calculation results with or without the adsorptionde-sorption thermal effect the effect of the adsorptionde-sorption thermal effect on the evolution law of precursorinformation and the effect of it on the mutual couplingrelation between coal and gas were studied

2 Materials and Methods

21 Experimental System To study the temperature evolu-tion law of coal adsorptiondesorption gas under differentpressure differences an experiment system of coal ad-sorption and desorption gas was designed e device usedin this experiment is to add a thermostat and a standard tankto the original device e experimental device is shown inFigure 1

22 Coal Samples and Experimental Methods e coalsample used in the experiment was taken from the XinjiangCoal Mine of Yangquan Coal Group which belongs to a highgas outburst minee 3 coal seam is the outburst coal seamObtain coal sample with the size of 40 cmtimes 40 cmtimes 60 cmfrom the tunneling head and send it to the laboratory afterbeing sealed and packed underground Use a cutting machineto cut the coal sample into a square specimen with a size of5 cmtimes 5 cmtimes 10 cm and then smooth it with a grinder ebasic parameters of the coal sample are shown in Table 1 andthe prepared coal sample is shown in Figure 2

e author designed a coal cycle-step adsorptionde-sorption gas experimente experimental method is shownin Table 2 e initial charging pressure is 04MPa and thepressure difference is 02MPa 04MPa and 06MPa einitial pressure of the desorption experiment is the maxi-mum adsorption equilibrium pressure of the adsorptionexperiment and the ambient temperature is maintained at30degC during the experiment

23 Experimental Procedures e experimental process isshown in Figure 3 e initial gas pressure is the same Aftereach adsorption equilibrium the pressure is increased by thesame pressure difference until the target pressure is reachedAnd then the pressure is reduced by the same pressuredifference to the minimum pressure

Step 1 Check the air tightness of the device install thesample connect the temperature measurement systemand the gas pressure measurement system turn on thethermostat adjust the temperature of the thermostat to30degC and start the data logger

2 Shock and Vibration

Step 2 Debug the triaxial stress loading system to adjustthe axial pressure and confining pressure to pre-determined valuesStep 3 Connect the high-pressure gas cylinder to theexperimental systemStep 4 Turn on the vacuum pump to vacuum degas thegas pressure loading systemStep 5 Carry out coal adsorption gas experimentAdjust the pressure reducing valve at the outlet of thehigh-pressure gas cylinder to the required pressurevalue so that the pressure of the standard tank reachesthe predetermined value After the gas pressure in thestandard tank is stable the gas in the standard tank issent to the adsorptiondesorption device for continu-ous adsorption for 12 hours Record temperature andpressure data

Step 6 Carry out coal desorption gas experiment Afterthe adsorption experiment is cycled to the targetpressure the gas pressure in the adsorptiondesorptiondevice is reduced with an equal pressure difference andthe desorption is continued for 12 hours Recordtemperature and pressure dataStep 7 Repeat steps 5 and 6 to adjust the gas pressuredifference to 02MPa 04MPa and 06MPa

24 Results

241 Temperature Variation during the Process of GasAdsorption Figure 4 shows the comparison of adsorptionexperiment results under different pressure differencesUnder the same pressure difference the temperature vari-ation of coal sample decreases during the step adsorptionprocess As the gas pressure difference increases the tem-perature variation of coal sample caused by each pressuri-zation gradually increases and the temperatureaccumulation decreases During the adsorption the tem-perature change of the coal sample increases with the in-crease of the pressure difference

242 Temperature Variation during the Process of GasDesorption Figure 5 shows the comparison of desorptionexperiment results under different pressure differencesUnder the same pressure difference the temperature vari-ation of coal sample decreases during the desorption As thegas pressure difference increases the temperature variationof coal sample caused by each pressure drop gradually in-creases and the temperature accumulation decreasesDuring the desorption the temperature change of the coalsample increases with the increase of the pressure difference

243 Change Law of Temperature Accumulation of CoalSample To further analyze the relation between the pressuredifference and the temperature accumulation of coal samplethe curve in Figure 6 was fittede fitting equation is shown inTable 3 It can be seen from the figure that the temperatureaccumulation first increases with the increase of gas pressureand then tends to be flat showing a trend of quadratic parabolicchange As the pressure difference increases the temperatureaccumulation gradually decreases When the pressure differ-ence is constant the temperature accumulation during theadsorption is slightly greater than that during the desorption

3 Multifield Coupling Model andGoverning Equations

Coal adsorptiondesorption gas is an important part of themutual coupling relation between coal and gas e coaladsorptiondesorption gas will be accompanied by the ab-sorption and release of heat erefore when scholars es-tablish the thermo-hydro-mechanical coupling model ofcoal and gas the adsorptiondesorption thermal effect hasbeen studied as an important coupling relation [38ndash42]Compared with previous research results scholars have not

Figure 2 Coal sample

a

b

d

c

e

f

g h

lki

mn

j

Figure 1 e schematic diagram of gas adsorption and desorptionexperiment system a pressure vessel b pressure-reducing valve cvacuum d gas collection e pressure gauge f incubator gstandard tank h coal sample i adsorptiondesorption j needlevalve k pressure regulator l hydraulic pump m data recorderand n computer

Table 1 Basic parameters of coal sample

Coal

Industrialparameters

Adsorptionparameters Gas pressure

(MPa)Mad()

Ad

()Vdaf()

VL

(m3t) PL (MPa)

Anthracite 119 631 825 3476 06521 13ndash26

Table 2 Experimental method

Gas pressuredifference(MPa)

Gas pressure loading path (MPa)

02 04⟶ 06⟶ 08⟶10⟶12⟶14⟶1614⟵12⟵10⟵ 08⟵ 06⟵ 04

04 04⟶ 08⟶12⟶16⟶12⟶ 08⟶ 0406 04⟶10⟶16⟶10⟶ 04

Shock and Vibration 3

introduced the adsorptiondesorption thermal effect into thecoupled model from the experimental perspective and thereis no new research progress on the influence of adsorptiondesorption thermal effect on the interaction between coaland gas Based on the experiments of coal adsorption

desorption gas thermal effects with different pressure dif-ferences this paper explores the influence of adsorptiondesorption thermal effects on the temporal and spatialevolution of outburst precursor information and the mutualcoupling relation between coal and gas Using the theory ofcontinuum mechanics the laws of static force balance themass conservation and the energy conservation consideringthe mutual influence of each physical fields the thermo-hydro-mechanical coupling model of coal and gas is derived

31 Model Hypothesis e thermo-hydro-mechanical cou-pling of coal and gas is an extremely complex physicalprocess e establishment of mathematical equations andthe convenience of numerical calculations require certainsimplified assumptions is article uses the reasonableassumptions and laws established by the predecessors topropose the following assumptions

e deformation of the coal is small and the coal is in thelinear elastic deformation stage which obeys the generalizedHooke law

e effective stress change of the gassy coal skeletonfollows the modified Terzaghi effective stress law

e seepage law of gas in coal seams conforms toDarcyrsquos law

ndash06

ndash05

ndash04

ndash03

ndash02

ndash01

00

∆T = 0545 ndash 0075 p∆T = 056 ndash 01425 p

∆T = 063893 ndash 034464 p

Adsorption balance pressure (MPa)

Tem

pera

ture

var

iatio

n (deg

C)

02 MPa04 MPa06 MPa

02 04 06 08 10 12 14 16 18

Figure 5 Temperature variation during the gas desorption

04

08

12

16

20

24

cd

a

b

f

Gas pressure (MPa)

02 MPa desorption

04 MPa desorption

06 MPa desorption

e

02 MPa adsorption

04 MPa adsorption

06 MPa adsorption

04 06 08 10 12 14 16

Tem

pera

ture

accu

mul

atio

n (deg

C)

Figure 6 Change law of temperature cumulative amount of coalsample

Adsorption test Adsorptionbalance

Reducepressure

Step adsorption to target pressure and then desorption to minimum pressure

Change pressure difference

Targetpressure

Desorptionbalance

Cycling

Increasepressure

Desorption testMinimumpressure

Figure 3 Experimental procedure

00

01

02

02

03

04

04

05

06

06 08 10 12 14 16 18

02 MPa04 MPa06 MPa


Tem

pera

ture

var

iatio

n (deg

C)

ΔT = 055833 ndash 00751 p

∆T = 0575 ndash 01475 p

∆T = 0655 ndash 035357 p

Figure 4 Temperature variation during the gas adsorption

Table 3 Fitting equation of change law of temperature accumu-lation of coal sample

Curve Fitting equation R2

A T minus09256p2 + 322083p minus 065857 099884B T minus093155p2 + 320774p minus 067429 099868C T minus023437p2 + 148125p minus 00575 099955D T minus025p2 + 1495p minus 008 09997E T minus01805p2 + 11527p + 00677 09999F T minus02083p2 + 119167p + 003667 09999


e adsorbed gas in the coal obeys the Langmuir ad-sorption equilibrium equation and the free gas obeys thereal gas state equation

e coal is full of single-phase gasAt the same point the temperature of gas and coal are

equale inertial force and volume force in the process of gas

seepage and coal deformation are negligible

32DynamicPorosityandPermeabilityModels forGassyCoalCompression deformation and adsorption expansion de-formation caused by ground stress and gas pressure andthermal expansion deformation caused by temperaturechanges will cause the coal skeleton to deform As the burieddepth of the coal seam increases the temperature groundstress and gas pressure will change significantly and coalporosity is also in a process of dynamic change [43ndash47]According to the basic assumptions the porosity of coal canbe defined as

ϕ VP

V

VP0 + ΔVP

VB0 + ΔV 1 minus

1 minus ϕ0( 1113857

1 + e1 +ΔVS

VS01113888 1113889 (1)

where VS is the coal skeleton volume ΔVS is the change ofcoal skeleton volume VP is the pore volume ΔVP is thechange of pore volume ϕ0 is the initial porosity e is thevolume strain ΔV is the change of total coal volume and V

is the total coal volumee volumetric strain increment of coal particles is

mainly composed of three parts ΔVSVS0 is the strain in-crement caused by the pore gas pressure compressing coalparticles ΔVSFVS0 is the strain increment caused by theexpansion of coal particles during gas adsorption ΔVSTVS0is the strain increment caused by thermoelastic expansion

We obtain the porosity equation expressed in terms ofeffective stress and adsorption thermodynamic parameters

ϕ 1 minus1 minus ϕ01 + e

1 + αTΔT minus KYΔp +2ρRΔTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

(2)

In addition it is assumed that the coal permeability andporosity satisfy the following relation [48]

k k0ϕϕ0

1113888 1113889

3

(3)

erefore the permeability equation can be expressed as

k k0

ϕ301 minus

1 minus ϕ01 + e


3Vm 1 minus ϕ0( 11138571113888 11138891113890 1113891

3

(4)

where k0 is the initial permeability

33 Deformation of Gassy Coal e continuous solid me-dium will produce stress and strain under the action ofexternal force According to the basic assumption thestressndashstrain relation can be expressed as [49 50]

εij 12G

σij minus16G

minus19K

1113874 1113875σkkδij (5)

where εij is components of strain tensor σij is componentsof stress tensor G is shear modulus and K is bulk modulus

e temperature change will cause the expansion orcontraction of the coal and produce thermal strain Underthe assumption of isotropy the linear thermal expansionstrain can be expressed as

εT 13αTΔT (6)

where ΔT is temperature change and εT is the coefficient ofvolume thermal expansion of coal

For coal with free gas according to the porous linearelastic mechanics and the principle of effective stress thelinear compression strain caused by gas pressure is expressedas

εp minusKY

3Δp (7)

where KY is volume compressibility and Δp is gas pressurechange

After coal adsorbs gas the surface tension of coal par-ticles decreases and the coal will expand On the contraryafter coal desorbs gas the coal will shrink [51]erefore thelinear adsorption expansion strain caused by coal particlesadsorbing gas is expressed as

εX 2ρRaKYΔT

9Vm

ln(1 + bp) (8)

where ρ is the density of coal R is the universal gas constanta is the limit adsorption capacity per unit mass of coal atreference pressure b is the adsorption equilibrium constantof coal and Vm is the gas molar volume

Total strain includes strain caused by external force porecompression strain caused by free gas adsorption expansionstrain and thermal expansion strain under the couplingaction of stress gas pressure and temperature which can beexpressed as

εij 12G

σij minus16G

minus19K

1113874 1113875σkkδij +13αTΔTδij minus

KY

3Δpδij

+2ρRTaKY

9Vm

ln(1 + bp)δij

(9)

According to the elasticity theory and the revised ef-fective stress formula the effective stress can be expressed bythe balanced differential equation

σijj + αpδij1113872 1113873j

+ Fi 0 (10)

Strain component and displacement component accordwith Cauchyrsquos equation


εij 12

uij + uji1113872 1113873 (i j 1 2 3) (11)

According to the strainndashstress relation an equationexpressing stress with strain can be derived

σij 2Gεij +2G]1 minus 2]

εkkδij minus(3λ + 2G)

3αTΔTδij

minus(3λ minus 2G)

3KYΔpδij minus

(3λ + 2G)2ρRTaKY

9Vm

ln(1 + bp)δij

(12)

Substituting equations (11) and (12) into equation (10)we obtain the improved form of Navierrsquos equation expressedin displacement

Guiij +G]

1 minus 2]ujji minus

3λ + 2G

3αTΔTj minus

3λ minus 2G

3KYΔpi

minus(3λ + 2G)2ρRTaKY

9Vm

ln(1 + bp)i + αpi + Fi 0

(13)

34 Gas Flow in Coal e ideal gas equation only applies togases at low pressure and high temperature e com-pressibility of real gas and ideal gas is different ereforereal gas cannot simply be regarded as ideal gas Gas can beregarded as an incompressible fluid under the conditions oflow pressure difference low flow rate and small temperaturedifference e state equation of gas in coal seam is usuallyexpressed as

ρg Mp

RTZ (14)

where ρg is the gas density M is the gas molecular weight T

is the absolute temperature of the coal seam MR is the gasconstant of specific gas and Z is the compression factor

Assuming that the gas seepage in the coal seam conformsto Darcyrsquos law and the gravity effect is ignored the gasseepage velocity can be expressed as

qg minusk

μnablaP (15)

where qg is Darcyrsquos flow rate k is permeability nablaP is the gaspressure gradient and μ is the dynamic viscosity coefficientof gas

Coal is composed of solid framework and pores epores are filled with freely diffusing gas Changes in gaspressure temperature or pores will cause gas desorption oradsorption and then cause gas seepage in the cracks emass conservation equation of gas seepage in coal can beexpressed as

zm

zt+ nabla middot ρgqg1113872 1113873 Qs (16)

where Qs is the source and sink and m is the gas contentGas content includes free gas and adsorbed gas [52]

Assuming that free gas is an ideal gas the gas content of coalcan be expressed as

m ϕMg

RTp +

Mgpa

RTa

ρc

VLp

p + PL

(17)

where ρc is the density of coal Mg is the molar mass of gaspa is the gas pressure under standard conditions and Ta isthe temperature under standard conditions

e first derivative of the gas content equation can beexpressed as

zm

zt

Mgp

RT

zϕzt

+MgϕRT

zp

ztminus ρc

Mgpa

RTa

VLPL

p + PL( 11138572

zp

ztminus

Mgpϕ

RT2

zT

zt

(18)

Substituting equations (14) (15) and (18) into equation(16) we have

pzϕzt

+ ϕ minusρcpaVLPL

p + PL( 11138572

⎛⎝ ⎞⎠zp

ztminus

p

Tϕ

zT

ztminus nabla middot

k

μpnablaP1113888 1113889 0

(19)

e derivative of porosity with respect to time isexpressed as

zϕzt

1 minus ϕ0

(1 + e)2 αTΔT minus KYΔp +

2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

zt

minus1 minus ϕ01 + e

αT +2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

zT

zt

minus1 minus ϕ0( 1113857KY

1 + e

2ρRTab

3Vm 1 minus ϕ0( 1113857(1 + bp)1113888 1113889

zp

zt

(20)

Substituting equation (20) into equation (19) we have

p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

ztminus

p 1 minus ϕ0( 1113857

1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889zT

zt

+ ϕ minusρcpaVLPL

p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab

3Vm 1 minus ϕ0( 1113857(1 + bp)minus 11113888 1113889⎛⎝ ⎞⎠

zp


k

μpnablaP1113888 1113889 0

(21)


To simplify equation (21) we define some parameters as

C1 C3ze

zt+ C4

zT

zt

C2 ϕ minusρcpaVLPL

p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


C3 p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

C4 minusp 1 minus ϕ0( 1113857

1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889

(22)

erefore the equation (21) is simplified to

C1 + C2zp


k

μpnablaP1113888 1113889 0 (23)

Equation (23) is the governing equation of gas seepage incoal seams

35 Heat Transfer Equation If the heat filtering effect isignored but the heat convection effect is considered theconstitutive equation of heat conduction can be expressed byFourierrsquos law as

qT minusλMnablaT + ρgCgqgT (24)

λM (1 minus ϕ)λs + ϕλg (25)

where qT is heat flow through fluid and solid media λM isthermal conductivity of coal λs is thermal conductivity ofcoal particles λg is thermal conductivity of gas and Cs isconstant volume heat capacity of gas

Assuming that the heat balance between the solid and thefluid is maintained the heat balance equation on thecharacteristic unit body can be expressed as [53]

z (ρC)MT( 1113857

zt+ TKgαgnabla middot qg + TKαT

ze

zt minusnabla middot qT + Qht (26)

(ρC)M ϕ ρgCg1113872 1113873 +(1 minus ϕ) ρsCs( 1113857 (27)

where (ρC)M is the overall heat capacity of the porousmedium ρs is density of coal skeleton Cs is constant volumeheat capacity of coal matrix Kg is bulk modulus of gas αg isthe volumetric thermal expansion coefficient of gas underconstant pore pressure and stress and Qht is the heat causedby coal adsorptiondesorption gas

e first term on the left-hand side of equation (26) is thechange rate of internal energy per unit volume caused bytemperature change e second term represents the heatdissipation due to the thermal expansion of the fluid ethird term represents the heat dissipation due to the thermalexpansion of the coal matrix e right-hand side representsthe overall heat flow of fluid and solid medium [34]

Substituting equations (24) (25) and (27) into equation(26) according to the assumption of small deformation andthe law of conservation of mass it is further simplified as

(ρC)M

z(T)

ztminus TKgαgnabla middot

k

μnablaP1113888 1113889 + TKαT

ze

zt λMnabla

2T +

ρgapTaCg

paTnablaT middot

k

μnablaP1113888 1113889 + Qht (28)

Equations (13) (23) and (28) constitute an equationsrsquo setdescribing the interaction between coal and gas whichconsiders the coupling among the stress field seepage fieldand temperature field e solid mechanics module PDEmodule and solid heat transfer module of COMSOLMultiphysics can be used to solve the coupled model

36 Cross-Coupling Relations Figure 7 shows the cross-coupling relation between coal deformation gas seepageand temperature changes e stress changes the porosityand permeability of the coal and then affects the seepageprocess of free gase change of free gas pressure causes gasadsorption or desorption and causes the coal to expand orcontract e increase of temperature promotes the de-sorption of adsorbed gas and accelerates the seepage rate offree gas e adsorption and desorption of gas is accom-panied by the absorption and release of heat Heat con-vection and internal energy dissipation in the process of gasseepage speed up the heat transfer e temperature changeproduces thermal strain which causes the coal to expand orcontracte deformation of coal is also accompanied by thestorage or release of deformation energy [54 55]

e temperature change during coal and gas outburstincludes two aspects coal temperature rise in process of coalrupture and coal adsorption Gas desorption and gas ex-pansion lead to lower coal temperature According to theassumption of linear elasticity the temperature changeduring coal and gas outburst can be expressed as

ΔT ΔT1 + ΔT2 + ΔT3 (29)

where ΔT1 is temperature drop caused by gas expansionΔT2 is temperature drop caused by gas desorption and ΔT3is temperature rise caused by gas adsorption

According to the experimental results of coal adsorp-tiondesorption gas thermal effect under different pressuredifferences the energy change caused by coal adsorptiondesorption gas can be expressed as

Qh Cmρc ΔT2 + ΔT3( 1113857 (30)

As the increase of temperature the amount of adsorbedgas in the coal seam gradually decreases According to theexperiment results the relation between adsorption constantand temperature is fitted


a minus00112 T minus Ta( 11138572

+ 061114 T minus Ta( 1113857 + 270211

b minus0037 T minus Ta( 1113857 + 22735(31)

4 Model Validation

To verify the rationality of the thermo-hydro-mechanicalcoupling model established in this paper based on thephysical simulation experiment of coal and gas outburstcarried out by scholars the numerical simulation study onthe change law of gas pressure and temperature of coal in theaeration stage was carried out [37] e geometric model is

shown in Figure 8 e model has a width of 570mm and aheight of 365mm Boundary conditions of stress field theupper boundary applies a vertical force of 4MPa the rightboundary applies a horizontal force of 24MPa e left andlower boundaries are roller supports Boundary conditionsof the seepage field the upper left and right boundaries arezero flux the lower boundary has a constant gas pressure of1MPa and the initial gas pressure is 01MPa Boundaryconditions of the temperature field the temperature aroundthe model is constant at 293K and the initial temperature isalso 293K Point A is the gas pressure monitoring point andpoint B is the temperature monitoring point

Field equationgas flow

Field equationtherm al

Field equationcoal deform ation

Mechanical field

Hydraulic field

ermal field

Porosity evolutionequation

Adsorption constant

Adsorptionndashdesorption thermal

Permeability evolution equation

(1) (2)

(3)

(6)

0

k0 1ndash

(7) (8) (9) (10)

(11) (12)

(4)

(5)

(10) Adsorptiondesorption heat source(8) (9) Heat transfer and convection

(6) ermal expansion of fluid(2) Compres

sive s

train

(3) Adsorptio

n strain

(5) Perm

eabilit

y(1)

ermal strain

(7) ermal expansion of matrix

(4) Porosit

y

(11) (12) Adsorption constant(5) Gas seepage velocity gas density

9Vm

ndash

∆ ndash ∆

∆(p + PL)2

3Vm(1 ndash ϕ0)

3Vm(1 ndash ϕ0)1 + αT∆T ndash KγΔp +

1 + αT∆T ndash KγΔp +

1 + e

1 ndash ϕ0

1 + e

1 ndash ϕ0

paTQht

Qh = Cmρc (∆T2 + ∆T3)

TKαT

ρcpaVLPL

ρgapTaCg

2ρR∆TaKγln (1 + bp)


partΦ

partt

partp p

partt

partT

partt

parte

partt

part(T)

parttndash TKgαg

p P = 0

2T T= λM

kμ

∆ ∆ ∆

Pkμ

T

1n(1 + bp)i + αpi + Fi = 0

Gov

erni

ng eq

uatio

nsC

ross

-cou

plin

g eq

uatio

ns

Guiij uiij αTΔTj KΥΔPi3λ + 2G

(3λ + 2G)2ρRTaKΥ

3λ + 2GGv3 3

p

(ρC)M

+

+ ++

ϕ ndash

ϕ = 1 ndash

a = ndash00112(T ndash Ta)2 + 061114(T ndash Ta) + 270211 b = ndash0037(T ndash Ta) + 22735

ϕ3K =

ϕ

ndashndash

ndash

+1ndash2v

∆Pkμ

3

Figure 7 Cross-coupling relations and the basic THM governing equations


e numerical calculation results and experiment resultsare shown in Figure 9 e experiment results showed thatthe gas pressure at point A remains unchanged for the first8 seconds in the initial inflation stage and then the gaspressure increases rapidly After inflation to 110 s the gaspressure reaches 1MPa e temperature at point B in-creases rapidly after the start of inflation After inflating to100 s the temperature change rate decreases e maximumtemperature measured in the experiment is 2955 K Nu-merical calculation results under different pressure differ-ences show that the gas pressure at point A remainsunchanged for the first 10 seconds in the initial inflationstage and then the gas pressure increases rapidly Afterinflation to 110 s the gas pressure reaches 1MPa e gaspressure changes under different pressure differences are thesame and the change variation is small After the inflationstarts the temperature at point B increases rapidly With theincrease of the pressure difference the maximum temper-ature is 2973K 2960 K 2955 K e temperature changedecreases as the pressure difference increases e calculatedresult with a pressure difference of 06MPa is close to theexperimental result e temperature change rate measuredin the experiment after the start of inflation is greater thanthe numerical calculation result According to the analysisunder the assumption of small linear elastic deformation theenergy released by coal deformation is small and the fric-tional heat of coal particles is ignored in numerical calcu-latione difference in temperature changes under differentpressure differences will be analyzed below

Comparing the experimental results and the numericalcalculation results it is found that the numerical solutionand the experimental solution are in good agreement Insummary the thermo-hydro-mechanical coupling model ofcoal and gas can be used to simulate the evolution of pre-cursor information during the preparation stage of coal andgas outburst

5 Numerical Simulation and Discussion

Numerical calculations are carried out based on the thermo-hydro-mechanical coupling model of coal and gas whichconsiders the adsorptiondesorption thermal effect Com-paring the calculation results with or without the

adsorptiondesorption thermal effect the influence of theadsorptiondesorption thermal effect on the evolution ofcoal and gas outburst precursor information is analyzed andthe mechanism of the adsorptiondesorption thermal effecton the mutual coupling relation between coal and gas isstudied

51 Geometric Model e geometric model is shown inFigure 10 Model includes coal seam coal seam roof andcoal seam floor Designed working face and gas drainageborehole in the coal seam the size of the roof and floor of thecoal seam is 43mtimes 25mtimes 2m e size of the coal seam is43mtimes 25mtimes 3m e width of the working surface is 5me working face surface is 5m from the left boundary egas drainage borehole is 5m away from the coal wall of theworking face the borehole diameter is 0094m and theborehole depth is 20m e working face and the outside ofthe coal seam are free spaces which can be regarded asexposed coal walls Stress field boundary conditions theupper boundary of the coal seam roof is subjected to avertical uniform load of 98MPa the working face and thecoal wall are free boundaries the other boundaries aroundthe model are supported by rollers and the lower boundaryof the coal seam floor is a fixed displacement Boundaryconditions of the seepage field there is no gas flow betweenthe coal seam and the rock the initial gas pressure of the coalseam is 13MPa the gas pressure of the coal wall is 01MPathe suction pressure of the borehole is 14 kPa and otherboundaries have no flow Boundary conditions of temper-ature field there is no heat transfer between coal seam androck layer the initial temperature of coal seam is 2924 K thetemperature of coal wall is 29115K and other boundariesare zero flux Along the advancing direction of the workingface a monitoring line is arranged in the coal seam eparameters required for numerical calculation are shown inTable 4

52 Simulation Results and Discussion

521 Evolution Law of Precursor Information without Ad-sorptionDesorption ltermal Effect Figure 11 shows thedistribution characteristics of the stress gas pressure andtemperature of the coal in front of the working face and nearthe coal wall in the roadway without the adsorptionde-sorption thermal effect e stress on the bottom of theworking face is the smallest and the coal walls on both sidesand roof are stress concentration areas As shown in Fig-ure 12 the stress concentration area in the coal in front of theworking face is 0ndash2841m the gas discharge zone width is10m the maximum volumetric strain in the stress con-centration area is minus000628 and the maximum coal tem-perature is 29241 K e coal temperature rises by 001 Kand the minimum permeability is 883times10minus19m2 e in-crease in coal temperature without the adsorptiondesorp-tion thermal effect is caused by deformation energy Underthe assumption of small linear elastic deformation thevolumetric strain is small and the coal deformation gen-erates less heat e location where the volumetric strain is

570 mm

365 m

m

A

B

partpparty = 0 Fy = 40 MPa

p = 10 MPa F x =

24

MPa

partTparty = 0

partTparty = 0

partppartx = 0

partppartx = 0

partTpartx = 0

partTpartx = 0

Figure 8 Geometric model for inflation simulation


the largest has the smallest permeability Coal deformation isthe result of the combined action of ground stress ad-sorption expansion stress and pore compression stress

522 Evolution Law of Precursor Information with Ad-sorptionDesorption ltermal Effect Figure 13 shows thedistribution characteristics of the stress gas pressure andtemperature of the coal in front of the working face and nearthe coal wall in the roadway considering the adsorptiondesorption thermal effect under different pressure differ-ence As shown in Figure 12 when the pressure difference is02MPa the stress concentration area in the coal in front ofthe working face is 0ndash3205m the width of the gas dischargezone is 13m the maximum volume strain is minus000637 andthe maximum coal temperature is 29605K the coal tem-perature rises by 365K and the minimum coal permeabilityis 841times 10minus19m2 when the pressure difference is 04MPathe stress concentration area in the coal in front of theworking face is 0ndash2947m the width of the gas discharge

zone is 12m the maximum volume strain is minus000632 andthe maximum coal temperature is 29439K the coal tem-perature rises by 199 K and the minimum coal permeabilityis 860times10minus19m2 when the pressure difference is 06MPathe stress concentration area in the coal in front of theworking face is 0ndash2852m the width of the gas dischargezone is 11m the maximum volume strain is minus000630 andthe maximum coal temperature is 29324K the coal tem-perature rises by 085 K and the minimum coal permeabilityis 873times10minus19m2e gas pressure difference increased from02MPa to 04MPa the maximum difference in gas pressurewas 10023 Pa the increase in coal temperature decreased by166 K and the permeability increased by 194times10minus20m2e gas pressure difference increased from 04MPa to06MPa the maximum difference in gas pressure was5002 Pa the increase in coal temperature decreased by114K and the permeability increased by 126times10minus20m2 Asthe increase of the gas pressure difference the width of thegas discharge zone decreases and the temperature elevatedamount and change rate of the coal temperature gradually

coal

5 m 5 m

33 m

Survey line

Coal wallRock

Working face

Drilling

20 m

rock

(a)

z

y

x

partuparty = 0partTparty = 0partTpartx = 0

partppartx = 0

partppartx = 0partupartx = 0

partupartx = 0partTparty = 0

partTpartx = 0

partTparty = 0partpparty = 0

partuparty = 0

(b)

Figure 10 Geometry and boundary conditions for the coupled mechanical deformation gas flow and heat conduction process in coal seamwhere gas flow and heat conduction apply only in the coal seam

0 20 40 60 80 100 120 14000

02

04

06

08

10

12

Gas

pre

ssur

e (M

Pa)

Inflation adsorption time (s)

Experimental valueCalculated value (02 MPa)Calculated value (04 MPa)Calculated value (06 MPa)

(a)

0 400 800 1200 1600293

294

295

296

297

298

Tem

pera

ture

(K)


Experiment valueCalculated value (02 MPa)Calculated value (04 MPa)Calculated value (06 MPa)

(b)

Figure 9 (a) Gas pressure change and (b) temperature change curve during inflation


decrease e deformation energy and the adsorptionde-sorption thermal effect cause the coal temperature to changee higher the temperature the greater the volumetric strainand the lower the permeability e extreme point of vol-umetric strain and permeability overlaps with the positionwhere the extreme point of temperature appears Within therange of 0ndash10m in front of the working face near the ex-treme point temperature has a more obvious effect onvolumetric strain and permeability Within 10m from theworking front the variation range of volumetric strain ismainly controlled by ground stress and the influence oftemperature is relatively small

523 Effect of AdsorptionDesorption ltermal Effect on theMutual Coupling Relation between Coal and GasFigure 12 shows the influence of the adsorptiondesorptionthermal effect on the evolution of precursor information inthe preparation stage of coal and gas outburst Comparing theresearch results with or without the adsorptiondesorptionthermal effect it is found that the adsorptiondesorptionthermal effect have obvious effects on coal gas pressure

temperature volumetric strain permeability and other pa-rameters Comparing the evolution law of gas pressuretemperature volumetric strain and permeability of coal infront of the working face without the adsorptiondesorptionthermal effect the temperature change caused by the ad-sorptiondesorption thermal effect is larger and the coaltemperature increase is 364K 198K and 084K the ad-sorptiondesorption thermal effect has little effect on coal gaspressure and the maximum difference of gas pressure is20285 Pa 10596 Pa and 5600 Pa the adsorptiondesorptionthermal effect has a great influence on the volumetric strain ofcoal and the increase in volumetric strain of coal is 9times10minus54times10minus5 and 2times10minus5 the adsorptiondesorption thermaleffect has an obvious influence on permeability and thedecrease in permeability is 421times 10minus20m2 227times10minus20m2and 101times 10minus20m2 e location where the gas pressuredifference is the largest is about 15m in front of the workingface where the slope of the gas pressure curve is the largestand the temperature change is the largesterefore the effectof thermal expansion strain caused by adsorptiondesorptionthermal effect on coal permeability cannot be ignored ethermal expansion strain caused by the temperature change in

6420

2020

30123456

40

10 1000

times107676 times 107

311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

Figure 11 Stress gas pressure and temperature distribution without adsorptiondesorption thermal heat (a) Stress (b) Gas pressure (c)Temperature

Table 4 e parameters used for gas migration in coal seam

Variable Parameter Value UnitE Youngrsquos modulus of coal 256times103 MPa] Poissonrsquos ratio of coal 012ρc Density of coal 1400 kgmiddotmminus3

R Universal gas constant 83143 Jmiddotmolminus1 Kminus1

Vm Gas molar volume 224times10minus3 m3middotmolminus1

ϕ0 Initial porosity of coal 00436k0 Initial permeability of coal 177times10minus18 M2

T0 Initial temperature 2924 Kp0 Initial gas pressure of coal 13 MPaμ Methane dynamic viscosity 1087times10minus5 Pamiddotsρga Density of gas at standard condition 0717 kgmiddotmminus3

pa Pressure at standard condition 0101325 MPaVL Langmuirrsquos volume constant 003476 m3middotkgminus1

PL Langmuirrsquos pressure constant 06521 MPaTa Temperature at standard condition 273 KαT Volumetric thermal expansion of the solid matrix coefficient 0000116 Kminus1

λs ermal conductivity of coal particles 0443 Jmiddotmminus1middotsminus1 Kminus1

Cg Specific heat capacity of gas 216 kJmiddotkgminus1 Kminus1

Cs Specific heat capacity of coal 126 kJmiddotkgminus1 Kminus1


the preparation stage of coal and gas outburst leads to thedecrease of coal permeability and increases the outburst risk

Figure 14 shows the change law of gas pressure per-meability and temperature in the coal and gas drainagevolume around the borehole with or without the adsorptiondesorption thermal effect Figure 14(b) shows that thetemperature change is obvious within the influence range ofthe boreholee temperature change near the borehole wallis large and the farther away from the borehole the smallerthe temperature change As shown in Figure 14(d) themaximum gas drainage volume is 964m3 without the ad-sorptiondesorption thermal effect As the pressure differ-ence increases the gas drainage volume increases graduallyand the maximum gas drainage volume of a single hole is888m3 915m3 and 940m3 Comparing the calculationresults without the adsorptiondesorption thermal effect the

maximum gas drainage volume of a single hole is reduced by76m3 49m3 and 24m3 Assuming that 1000 boreholes arearranged in the working face the maximum gas drainagevolume of a single hole is reduced by 76times104m349times104m3 and 24times104m3 With the increase of gaspressure difference the volumetric strain of coal decreasesand the permeability increases which is beneficial to thedesorption of gas On the contrary the coal temperaturedecreases with the increase of gas pressure difference andthe decrease of temperature is not conducive to the de-sorption and flow of gas Analyzing the change law of gasdrainage volume in boreholes it can be seen that the effect ofthermal expansion strain caused by adsorptiondesorptionthermal effect on gas seepage is greater than the effect oftemperature change on gas seepage In summary the ad-sorptiondesorption thermal effect not only causes the coal

00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)

Distance to working face (m)

02 MPa (fully coupled)04 MPa (fully coupled)06 MPa (fully coupled)Without adsorptiondesorption heat

0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)

Distance to working face (m)0 5 10 15 20 25 30 35


(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)

Figure 12 Gas pressure permeability temperature and volume strain distribution along the monitoring line with or without adsorptiondesorption heat (a) Gas pressure (b) Temperature (c) Volume strain (d) Permeability


6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)

Figure 13 Stress gas pressure and temperature distribution at different pressure differences with adsorptiondesorption heat (a) 02MPastress (b) 02MPa gas pressure (c) 02MPa temperature (d) 04MPa stress (e) 04MPa gas pressure (f ) 04MPa temperature (g) 06MPastress (h) 06MPa gas pressure (i) 06MPa temperature

00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued


temperature change but also has a greater effect on coalseam gas seepage

6 Conclusions

Based on the coal adsorptiondesorption gas thermal effectexperiment this paper established a thermo-hydro-me-chanical coupling model of coal and gas considering theadsorptiondesorption thermal effect by analyzing themutual coupling relation among the stress gas and tem-perature e evolution of precursor information in thepreparation stage of coal and gas outburst is simulated withor without the adsorptiondesorption thermal effect and theeffect of the adsorptiondesorption thermal effect on themutual coupling relation between coal and gas is discussede main conclusions are as follows

(1) e relation between gas pressure difference and coaltemperature variation is linear Under the samepressure difference the increasing range of the tem-perature variation of the coal sample gradually de-creases with the increase of the gas pressure differencee gas pressure difference has a quadratic parabolicrelation with the temperature accumulation of coalsample When the pressure difference is constant thedecreasing range of temperature accumulation de-creases gradually with the increase of gas pressuredifference As the pressure difference increases thetemperature variation gradually increases but thetemperature accumulation gradually decreases

(2) Based on the interaction between coal and gas themechanical model reflecting the dynamic evolutionof porosity and permeability gas adsorption-de-sorption-diffusion and energy accumulation anddissipation was established with the adsorptionde-sorption thermal effect

(3) As the gas pressure difference increases the changesin coal temperature and gas pressure gradually de-crease the thermal expansion strain caused by theadsorptiondesorption thermal effect decreases andthe permeability gradually increases e evolutionlaw of coal temperature depends on the rate andvariation of gas pressure

(4) Considering the adsorptiondesorption thermal ef-fect the volume strain temperature and perme-ability have significant changes e gas drainagevolume increases significantly with the pressuredifference increases e thermal expansion straincaused by adsorptiondesorption thermal effect has agreater effect on gas seepage than temperaturechange

Data Availability

All the data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China (Grant nos 51874166 and 51774165)National Key Research and Development Program of China(Grant no 2016YFC0801404) Discipline Innovation Teamof Liaoning Technical University (LNTU20TD-11) NationalNatural Science Foundation of China Youth Fund (Grantno 52004118) and Youth Project of Education Departmentof Liaoning Province (LJ2019QL005 and LJ2020QNL009)

720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)

00 20 times 105 40 times 105 60 times 105 80 times 105 10 times 106

0

200

400

600

800

1000

06 MPa (fully coupled)Without adsorptiondesorption heat

Gas

dra

inag

e vol

ume (

m3 )

Gas drainage time (s)

02 MPa (fully coupled)04 MPa (fully coupled)

(d)

Figure 14 Gas pressure temperature permeability distribution in the coal near the borehole and gas extraction volume with or withoutadsorptiondesorption heat (a) Gas pressure (b) Temperature (c) Permeability (d) Gas drainage volume


References

[1] A J Hargraves ldquoInstantaneous outbursts of coal and gas-areview hargravesrdquo International Journal of Rock Mechanics ampMining sciences amp Geomechanics Abstract vol 20 no 5p 151 1983

[2] N Skoczylas ldquoCoal seam methane pressure as a parameterdetermining the level of the outburst risk-laboratory and insitu researchcisnienie złozowe jako parametr okreslajacy stanzagrozenia wyrzutami metanu I skał-badania laboratoryjne Ikopalnianerdquo Archives of Mining Sciences vol 57 no 4pp 861ndash869 2012

[3] D Li J Zhang Y Sun and G Li ldquoEvaluation of rockbursthazard in deep coalmines with large protective island coalpillarsrdquo Natural Resources Research vol 5 2020

[4] J Zhang F Jiang S Zhu and L Zhang ldquoWidth design forgobs and isolated coal pillars based on overall burst-instabilityprevention in coal minesrdquo Journal of Rock Mechanics andGeotechnical Engineering vol 8 no 4 pp 551ndash558 2016

[5] J Zhang F Jiang J Yang W Bai and L Zhang ldquoRockburstmechanism in soft coal seam within deep coal minesrdquo In-ternational Journal of Mining Science and Technology vol 27no 3 pp 551ndash556 2017

[6] S Chattaraj D Mohanty T Kumar and G Halder ldquoer-modynamics kinetics and modeling of sorption behaviour ofcoalbed methane - a reviewrdquo Journal of Unconventional Oiland Gas Resources vol 16 pp 14ndash33 2016

[7] W S Han G A Stillman M Lu C Lu B J McPherson andE Park ldquoEvaluation of potential nonisothermal processes andheat transport during CO2 sequestrationrdquo Journal of Geo-physical Research vol 115 no B7 2010

[8] J Sobczyk ldquoe influence of sorption processes on gas stressesleading to the coal and gas outburst in the laboratory con-ditionsrdquo Fuel vol 90 no 3 pp 1018ndash1023 2011

[9] J Sobczyk ldquoA comparison of the influence of adsorbed gaseson gas stresses leading to coal and gas outburstrdquo Fuel vol 115pp 288ndash294 2014

[10] Y Sun G Li J Zhang and D Qian ldquoStability control for therheological roadway by a novel high-efficiency jet groutingtechnique in deep underground coal minesrdquo Sustainabilityvol 11 no 22 p 6494 2019

[11] J Zhang D Li and Y Wang ldquoPredicting tunnel squeezingusing a hybrid classifier ensemble with incomplete datardquoBulletin of Engineering Geology and the Environment vol 112020

[12] R J Williams and J J Weissman ldquoGas emission and outburstassessment in mixed CO2 and CH4 environmentsrdquo Universityof New South Wales vol 1 pp 1ndash13 1995

[13] J Zhang and Y Wang ldquoAn ensemble method to improveprediction of earthquake-induced soil liquefaction a multi-dataset studyrdquo Neural Computing and Applications vol 22020

[14] J Rutqvist Y-S Wu C-F Tsang and G Bodvarsson ldquoAmodeling approach for analysis of coupled multiphase fluidflow heat transfer and deformation in fractured porousrockrdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 429ndash442 2002

[15] S Xue Y Wang J Xie and GWang ldquoA coupled approach tosimulate initiation of outbursts of coal and gas-model de-velopmentrdquo International Journal of Coal Geology vol 86no 2-3 pp 222ndash230 2011

[16] G Hu HWang X Fan Z Yuan and S Hong ldquoMathematicalmodel of coalbed gas flow with klinkenberg effects in multi-

physical fields and its analytic solutionrdquo Transport in PorousMedia vol 76 no 3 p 407 2009

[17] K Wu Z Shao S Qin and Z Chu ldquoA critical review on theperformance of yielding supports in squeezing tunnelsrdquoTunnelling and Underground Space Technology vol 109 no 12021

[18] D Johns and B G Neal ltermal Stress Analyses ElsevierBerlin Germany 1965

[19] H Basarir Y Sun and G Li ldquoGateway stability analysis byglobal-local modeling approachrdquo International Journal ofRock Mechanics and Mining Science vol 113 pp 31ndash40 2018

[20] Z Pan and L D Connell ldquoA theoretical model for gas ad-sorption-induced coal swellingrdquo International Journal of CoalGeology vol 69 no 4 pp 243ndash252 2007

[21] J Jagiełło M Lason and N Adam ldquoermodynamic de-scription of the process of gas liberation from a coal bedrdquoFuel vol 71 no 4 pp 431ndash435 1992

[22] K A Rahman A Chakraborty B B Saha and K C Ng ldquoOnthermodynamics of methane+carbonaceous materials ad-sorptionrdquo International Journal of Heat and Mass Transfervol 55 no 4 pp 565ndash573 2012

[23] K A Rahman W S Loh and K C Ng ldquoHeat of adsorptionand adsorbed phase specific heat capacity of methaneacti-vated carbon systemrdquo Procedia Engineering vol 56pp 118ndash125 2013

[24] Z Liu Z Feng Q Zhang D Zhao and H Guo ldquoHeat anddeformation effects of coal during adsorption and desorptionof carbon dioxiderdquo Journal of Natural Gas Science and En-gineering vol 25 pp 242ndash252 2015

[25] C A Tang L G am P K K Lee T H Yang and L C LildquoCoupled analysis of flow stress and damage (FSD) in rockfailurerdquo International Journal of Rock Mechanics and MiningSciences vol 39 no 4 pp 477ndash489 2002

[26] Y Sun G Li and J Zhang ldquoInvestigation on jet groutingsupport strategy for controlling time-dependent deformationin the roadwayrdquo Energy Science and Engineering vol 10pp 1ndash8 2020

[27] J Liu Z Chen and D Elsworth ldquoInteractions of multipleprocesses during CBM extraction a critical reviewrdquo Inter-national Journal of Coal Geology vol 87 no 3-4 pp 175ndash1892011

[28] K Wu and Z Shao ldquoVisco-elastic analysis on the effect offlexible layer on mechanical behavior of tunnelsrdquo Interna-tional Journal of Applied Mechanics vol 11 no 3 2019

[29] H Wang Z Liu L Yuan S Wang S Wei and D ZhangldquoExperimental test and particle mechanical analysis of gasadsorption-induced coal rock degradationrdquo Powder Tech-nology vol 362 pp 75ndash83 2020

[30] Y Zheng Q Li G Zhang Y Zhao and X Li ldquoStudy on thecoupling evolution of air and temperature field in coal minegoafs based on the similarity simulation experimentsrdquo Fuelvol 283 2021

[31] Pararoop Z T Karpyn and T Ertekin ldquoDevelopment of amulti-mechanistic dual-porosity dual-permeability nu-merical flow model for coalbed methane reservoirsrdquo Journalof Natural Gas Science and Engineering vol 8 pp 121ndash1312012

[32] T Teng Y Zhao F Gao J G Wang and W Wang ldquoA fullycoupled thermo-hydro-mechanical model for heat and gastransfer in thermal stimulation enhanced coal seam gas re-coveryrdquo International Journal of Heat and Mass Transfervol 125 pp 866ndash875 2018

[33] W Zhu C Wei J Liu H Qu and D Elsworth ldquoA model ofcoal-gas interaction under variable temperaturesrdquo


International Journal of Coal Geology vol 86 no 2-3pp 213ndash221 2011

[34] Y Zhou R K N D Rajapakse and J Graham ldquoA coupledthermoporoelastic model with thermo-osmosis and thermal-filtrationrdquo International Journal of Solids and Structuresvol 35 no 34-35 pp 4659ndash4683 1998

[35] M Fall O Nasir and T S Nguyen ldquoA coupled hydro-me-chanical model for simulation of gas migration in host sed-imentary rocks for nuclear waste repositoriesrdquo EngineeringGeology vol 176 pp 24ndash44 2014

[36] F-h An Y-p Cheng L Wang and W Li ldquoA numericalmodel for outburst including the effect of adsorbed gas on coaldeformation and mechanical propertiesrdquo Computers andGeotechnics vol 54 pp 222ndash231 2013

[37] Y Tao Study on the Gassy Coal THM Coupling Model andCoal and Gas Outburst Simulation Chongqing UniversityChongqing China 2015

[38] Y Sun G Li N Zhang Q Chang and J Zhang ldquoDevel-opment of ensemble learning models to evaluate the strengthof coal-grout materialsrdquo International Journal of MiningScience and Technology vol 5 2020

[39] J Zhang Y Wang Y Sun and G Li ldquoStrength of ensemblelearning in multiclass classification of rockburst intensityrdquoInternational Journal for Numerical and Analytical Methods inGeomechanics vol 5 pp 1ndash21 2020

[40] Y Chen T Chu X Chen and P Chen ldquoCoupling of stressand gas pressure in dual porosity medium during coal seamminingrdquo Powder Technology vol 367 pp 390ndash398 2020

[41] J Zhang Y Sun G Li YWang and J Li ldquoMachine-learning-assisted shear strength prediction of reinforced concretebeams with and without stirrupsrdquo Engineering With Com-puters vol 5 2020

[42] X Liu C Wu G Wei et al ldquoAdsorption deformationcharacteristics of coal and coupling with permeability duringgas injectionrdquo Journal of Petroleum Science and Engineeringvol 195 2020

[43] Y Sun J Zhang G Li Y Wang J Sun and C JiangldquoOptimized neural network using beetle antennae search forpredicting the unconfined compressive strength of jetgrouting coalcretesrdquo International Journal for Numerical andAnalytical Methods in Geomechanics vol 23 pp 1ndash13 2019

[44] Y Sun J Zhang G Li et al ldquoDetermination of Youngrsquosmodulus of jet grouted coalcretes using an intelligent modelrdquoEngineering Geology vol 252 pp 43ndash53 2019

[45] X Cui and R M Bustin ldquoVolumetric strain associated withmethane desorption and its impact on coalbed gas productionfrom deep coal seamsrdquo AAPG Bulletin vol 89 no 9pp 1181ndash1202 2005

[46] Y Sun G Li H Basarir A Karrech and M R AzadildquoLaboratory evaluation of shear strength properties for ce-ment-based grouted coal massrdquo Arabian Journal of Geoencesvol 12 no 22 p 690 2019

[47] Y Sun G Li J Zhang and D Qian ldquoExperimental andnumerical investigation on a novel support system for con-trolling roadway deformation in underground coal minesrdquoEnergy Science and Engineering vol 10 pp 1ndash11 2019

[48] I Palmer and J Mansoori ldquoHow permeability depends onstress and pore pressure in coalbeds a new modelrdquo SPEReservoir Evaluation amp Engineering vol 1 no 6 pp 539ndash5441998

[49] M Wierzbicki ldquoChanges in stress and strain of the briquetteduring provoking and initiation of the rock and gas outburstin the laboratory conditionsrdquo Transactions of the StrataMechanics Research Institute vol 4 2003

[50] KWu Z Shao S Qin N Zhao andH Hu ldquoAnalytical-basedassessment of effect of highly deformable elements on tunnellining within viscoelastic rocksrdquo International Journal ofApplied Mechanics vol 12 no 3 2020

[51] H Zhang J Liu and D Elsworth ldquoHow sorption-inducedmatrix deformation affects gas flow in coal seams a new FEmodelrdquo International Journal of Rock Mechanics and MiningSciences vol 45 no 8 pp 1226ndash1236 2008

[52] A Saghafi M Faiz and D Roberts ldquoCO2 storage and gasdiffusivity properties of coals from Sydney Basin AustraliardquoInternational Journal of Coal Geology vol 70 no 1ndash3pp 240ndash254 2007

[53] F Tong L Jing and R W Zimmerman ldquoA fully coupledthermo-hydro-mechanical model for simulating multiphaseflow deformation and heat transfer in buffer material androck massesrdquo International Journal of Rock Mechanics andMining Sciences vol 47 no 2 pp 205ndash217 2010

[54] T Liu Multifield Coupling Processes during Gas Drainage inDeep Fractured Coal Seam and its Engineering ResponseChina University of Mining and Technology Xuzhou China2019

[55] K Wu Z Shao and S Qin ldquoAn analytical design method forductile support structures in squeezing tunnelsrdquo Archives ofCivil and Mechanical Engineering vol 20 2020


scholars have carried out a lot of research work and estab-lished multifield coupling model suitable for a variety ofcomplex situations [14ndash17] Coal releases heat during theprocess of gas adsorption and absorbs heat during the processof gas desorption [18ndash20] Jacek [21] gave a calculationmethod of the maximum volume of work which can beperformed by a gas while being liberated from a coal bedRahman [22 23] reported the theoretical frameworks for thethermodynamic quantities for the adsorption of methaneonto various carbonaceous materials Temperature variationcauses deformation and deformation generates heat whichcauses temperature variation Liu [24] proposed the thermaldeformation effect of adsorptionndashdesorption on the basis ofthe molecular migration and energy conversion during theadsorptionndashdesorption At present multifield coupling is ahot research target [25ndash28] the fields of coalbed methaneextraction shale gas extraction coal and gas outburst pre-vention and nuclear waste treatment all involve thermo-hydro-mechanical coupling issues [29 30] araroop [31]believed that existing coal bed methane (CBM) simulatorsusually treat the coal seam as a dual pore and single per-meability system ignoring the influence of water in the coalmatrix e model includes the influence of moisture in thecoal matrix and the shrinkage and expansion of coal Con-sidering the competitive effects of thermal expansion non-isothermal gas adsorption and thermal fracturing Teng [32]established a fully coupled thermo-hydro-mechanical modelof coal deformation gas flow and heat transfer Zhu [33] usesthe finite element method to establish and solve a fullycoupled model of coal deformation gas transport and heattransport A general model was established to describe theevolution of coal porosity under the combined influence ofgas pressure thermally induced solid deformation thermallyinduced gas adsorption changes and solid deformationcaused by gas desorption Zhou [34] proposed a coupledthermal pore elastic model which considers the compress-ibility and thermal expansion of the convective heat flow ofthe components as well as the changes in the porosity andrelated characteristics of the saturated soil e model alsoconsiders the thermodynamically coupled water and heatflow Fall [35] gave a detailed formula for coupling moistureand gas transmission in deformable porous media is givenis model takes into account the fluid flow under damagecontrol and the coupling of hydraulic and mechanical pro-cesses e model also considers the coupling of diffusioncoefficient and mechanical deformation and considers thechanges in capillary pressure caused by changes in perme-ability and porosity To analyze the influence of gas desorptionon gas outburst An [36] established a mechanical processmodel in the process of gas migration and tunneling estudy understands the influence of absorption shrinkage andmechanical changes on the protrusion Tao [37] carried outphysical simulation experiments on coal and gas outburstsand established a thermo-hydro-mechanical coupling modelof gassy coal

In summary the existing research did not use experi-ments to analyze the influence of coal adsorptiondesorptiongas thermal effect on the evolution law of outburst precursorinformation In addition there are few quantitative studies

on the influence of adsorptiondesorption thermal effect onthe interaction between coal and gas Using the self-designedcoal and gas thermo-hydro-mechanical coupling experimentsystem and the cyclic-step adsorptiondesorption experi-ment method the temperature change of coal adsorptionand desorption gas under different pressure differences wasdiscussed Based on the experimental results a thermo-hydro-mechanical coupling model of gassy coal with theadsorptiondesorption thermal effect was established andthe model is solved by COMSOL Multiphysics Comparingthe calculation results with or without the adsorptionde-sorption thermal effect the effect of the adsorptionde-sorption thermal effect on the evolution law of precursorinformation and the effect of it on the mutual couplingrelation between coal and gas were studied

2 Materials and Methods

21 Experimental System To study the temperature evolu-tion law of coal adsorptiondesorption gas under differentpressure differences an experiment system of coal ad-sorption and desorption gas was designed e device usedin this experiment is to add a thermostat and a standard tankto the original device e experimental device is shown inFigure 1

22 Coal Samples and Experimental Methods e coalsample used in the experiment was taken from the XinjiangCoal Mine of Yangquan Coal Group which belongs to a highgas outburst minee 3 coal seam is the outburst coal seamObtain coal sample with the size of 40 cmtimes 40 cmtimes 60 cmfrom the tunneling head and send it to the laboratory afterbeing sealed and packed underground Use a cutting machineto cut the coal sample into a square specimen with a size of5 cmtimes 5 cmtimes 10 cm and then smooth it with a grinder ebasic parameters of the coal sample are shown in Table 1 andthe prepared coal sample is shown in Figure 2

e author designed a coal cycle-step adsorptionde-sorption gas experimente experimental method is shownin Table 2 e initial charging pressure is 04MPa and thepressure difference is 02MPa 04MPa and 06MPa einitial pressure of the desorption experiment is the maxi-mum adsorption equilibrium pressure of the adsorptionexperiment and the ambient temperature is maintained at30degC during the experiment

23 Experimental Procedures e experimental process isshown in Figure 3 e initial gas pressure is the same Aftereach adsorption equilibrium the pressure is increased by thesame pressure difference until the target pressure is reachedAnd then the pressure is reduced by the same pressuredifference to the minimum pressure

Step 1 Check the air tightness of the device install thesample connect the temperature measurement systemand the gas pressure measurement system turn on thethermostat adjust the temperature of the thermostat to30degC and start the data logger




24 Results







a

b

d

c

e

f

g h

lki

mn

j



Coal



(MPa)Mad()

Ad

()Vdaf()

VL

(m3t) PL (MPa)





02 04⟶ 06⟶ 08⟶10⟶12⟶14⟶1614⟵12⟵10⟵ 08⟵ 06⟵ 04

04 04⟶ 08⟶12⟶16⟶12⟶ 08⟶ 0406 04⟶10⟶16⟶10⟶ 04








ndash06

ndash05

ndash04

ndash03

ndash02

ndash01

00

∆T = 0545 ndash 0075 p∆T = 056 ndash 01425 p

∆T = 063893 ndash 034464 p


Tem

pera

ture

var

iatio

n (deg

C)

02 MPa04 MPa06 MPa

02 04 06 08 10 12 14 16 18


04

08

12

16

20

24

cd

a

b

f

Gas pressure (MPa)

02 MPa desorption

04 MPa desorption

06 MPa desorption

e

02 MPa adsorption

04 MPa adsorption

06 MPa adsorption

04 06 08 10 12 14 16

Tem

pera

ture

accu

mul

atio

n (deg

C)



Reducepressure



Targetpressure

Desorptionbalance

Cycling

Increasepressure



00

01

02

02

03

04

04

05

06

06 08 10 12 14 16 18

02 MPa04 MPa06 MPa


Tem

pera

ture

var

iatio

n (deg

C)

ΔT = 055833 ndash 00751 p

∆T = 0575 ndash 01475 p

∆T = 0655 ndash 035357 p











ϕ VP

V

VP0 + ΔVP

VB0 + ΔV 1 minus

1 minus ϕ0( 1113857

1 + e1 +ΔVS

VS01113888 1113889 (1)







3Vm 1 minus ϕ0( 11138571113888 1113889

(2)


k k0ϕϕ0

1113888 1113889

3

(3)


k k0

ϕ301 minus

1 minus ϕ01 + e


3Vm 1 minus ϕ0( 11138571113888 11138891113890 1113891

3

(4)



εij 12G

σij minus16G

minus19K

1113874 1113875σkkδij (5)



εT 13αTΔT (6)



εp minusKY

3Δp (7)



εX 2ρRaKYΔT

9Vm

ln(1 + bp) (8)



εij 12G

σij minus16G

minus19K


KY

3Δpδij

+2ρRTaKY

9Vm

ln(1 + bp)δij

(9)


σijj + αpδij1113872 1113873j

+ Fi 0 (10)



εij 12

uij + uji1113872 1113873 (i j 1 2 3) (11)




3αTΔTδij

minus(3λ minus 2G)

3KYΔpδij minus

(3λ + 2G)2ρRTaKY

9Vm

ln(1 + bp)δij

(12)


Guiij +G]


3λ + 2G

3αTΔTj minus

3λ minus 2G

3KYΔpi


9Vm


(13)


ρg Mp

RTZ (14)




qg minusk

μnablaP (15)



zm




m ϕMg

RTp +

Mgpa

RTa

ρc

VLp

p + PL

(17)



zm

zt

Mgp

RT

zϕzt

+MgϕRT

zp

ztminus ρc

Mgpa

RTa

VLPL

p + PL( 11138572

zp

ztminus

Mgpϕ

RT2

zT

zt

(18)


pzϕzt

+ ϕ minusρcpaVLPL

p + PL( 11138572

⎛⎝ ⎞⎠zp

ztminus

p

Tϕ

zT


k

μpnablaP1113888 1113889 0

(19)


zϕzt

1 minus ϕ0


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

zt



3Vm 1 minus ϕ0( 11138571113888 1113889

zT

zt


1 + e

2ρRTab

3Vm 1 minus ϕ0( 1113857(1 + bp)1113888 1113889

zp

zt

(20)


p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

ztminus

p 1 minus ϕ0( 1113857

1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889zT

zt

+ ϕ minusρcpaVLPL

p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


zp


k

μpnablaP1113888 1113889 0

(21)



C1 C3ze

zt+ C4

zT

zt


p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


C3 p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889


1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889

(22)


C1 + C2zp


k

μpnablaP1113888 1113889 0 (23)







z (ρC)MT( 1113857


ze






(ρC)M

z(T)


k

μnablaP1113888 1113889 + TKαT

ze

zt λMnabla

2T +

ρgapTaCg

paTnablaT middot

k

μnablaP1113888 1113889 + Qht (28)




ΔT ΔT1 + ΔT2 + ΔT3 (29)



Qh Cmρc ΔT2 + ΔT3( 1113857 (30)




+ 061114 T minus Ta( 1113857 + 270211

b minus0037 T minus Ta( 1113857 + 22735(31)

4 Model Validation






Mechanical field

Hydraulic field

ermal field


Adsorption constant



(1) (2)

(3)

(6)

0

k0 1ndash

(7) (8) (9) (10)

(11) (12)

(4)

(5)



sive s

train

(3) Adsorptio

n strain

(5) Perm

eabilit

y(1)

ermal strain


(4) Porosit

y


9Vm

ndash

∆ ndash ∆

∆(p + PL)2

3Vm(1 ndash ϕ0)



1 + e

1 ndash ϕ0

1 + e

1 ndash ϕ0

paTQht

Qh = Cmρc (∆T2 + ∆T3)

TKαT

ρcpaVLPL

ρgapTaCg



partΦ

partt

partp p

partt

partT

partt

parte

partt

part(T)

parttndash TKgαg

p P = 0

2T T= λM

kμ

∆ ∆ ∆

Pkμ

T

1n(1 + bp)i + αpi + Fi = 0

Gov

erni

ng eq

uatio

nsC

ross

-cou

plin

g eq

uatio

ns


(3λ + 2G)2ρRTaKΥ

3λ + 2GGv3 3

p

(ρC)M

+

+ ++

ϕ ndash

ϕ = 1 ndash


ϕ3K =

ϕ

ndashndash

ndash

+1ndash2v

∆Pkμ

3











570 mm

365 m

m

A

B


p = 10 MPa F x =

24

MPa

partTparty = 0

partTparty = 0

partppartx = 0

partppartx = 0

partTpartx = 0

partTpartx = 0






coal

5 m 5 m

33 m

Survey line

Coal wallRock

Working face

Drilling

20 m

rock

(a)

z

y

x


partppartx = 0



partTpartx = 0


partuparty = 0

(b)


0 20 40 60 80 100 120 14000

02

04

06

08

10

12

Gas

pre

ssur

e (M

Pa)



(a)

0 400 800 1200 1600293

294

295

296

297

298

Tem

pera

ture

(K)



(b)






6420

2020

30123456

40

10 1000


311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

















00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References






























































24 Results







a

b

d

c

e

f

g h

lki

mn

j



Coal



(MPa)Mad()

Ad

()Vdaf()

VL

(m3t) PL (MPa)





02 04⟶ 06⟶ 08⟶10⟶12⟶14⟶1614⟵12⟵10⟵ 08⟵ 06⟵ 04

04 04⟶ 08⟶12⟶16⟶12⟶ 08⟶ 0406 04⟶10⟶16⟶10⟶ 04








ndash06

ndash05

ndash04

ndash03

ndash02

ndash01

00

∆T = 0545 ndash 0075 p∆T = 056 ndash 01425 p

∆T = 063893 ndash 034464 p


Tem

pera

ture

var

iatio

n (deg

C)

02 MPa04 MPa06 MPa

02 04 06 08 10 12 14 16 18


04

08

12

16

20

24

cd

a

b

f

Gas pressure (MPa)

02 MPa desorption

04 MPa desorption

06 MPa desorption

e

02 MPa adsorption

04 MPa adsorption

06 MPa adsorption

04 06 08 10 12 14 16

Tem

pera

ture

accu

mul

atio

n (deg

C)



Reducepressure



Targetpressure

Desorptionbalance

Cycling

Increasepressure



00

01

02

02

03

04

04

05

06

06 08 10 12 14 16 18

02 MPa04 MPa06 MPa


Tem

pera

ture

var

iatio

n (deg

C)

ΔT = 055833 ndash 00751 p

∆T = 0575 ndash 01475 p

∆T = 0655 ndash 035357 p











ϕ VP

V

VP0 + ΔVP

VB0 + ΔV 1 minus

1 minus ϕ0( 1113857

1 + e1 +ΔVS

VS01113888 1113889 (1)







3Vm 1 minus ϕ0( 11138571113888 1113889

(2)


k k0ϕϕ0

1113888 1113889

3

(3)


k k0

ϕ301 minus

1 minus ϕ01 + e


3Vm 1 minus ϕ0( 11138571113888 11138891113890 1113891

3

(4)



εij 12G

σij minus16G

minus19K

1113874 1113875σkkδij (5)



εT 13αTΔT (6)



εp minusKY

3Δp (7)



εX 2ρRaKYΔT

9Vm

ln(1 + bp) (8)



εij 12G

σij minus16G

minus19K


KY

3Δpδij

+2ρRTaKY

9Vm

ln(1 + bp)δij

(9)


σijj + αpδij1113872 1113873j

+ Fi 0 (10)



εij 12

uij + uji1113872 1113873 (i j 1 2 3) (11)




3αTΔTδij

minus(3λ minus 2G)

3KYΔpδij minus

(3λ + 2G)2ρRTaKY

9Vm

ln(1 + bp)δij

(12)


Guiij +G]


3λ + 2G

3αTΔTj minus

3λ minus 2G

3KYΔpi


9Vm


(13)


ρg Mp

RTZ (14)




qg minusk

μnablaP (15)



zm




m ϕMg

RTp +

Mgpa

RTa

ρc

VLp

p + PL

(17)



zm

zt

Mgp

RT

zϕzt

+MgϕRT

zp

ztminus ρc

Mgpa

RTa

VLPL

p + PL( 11138572

zp

ztminus

Mgpϕ

RT2

zT

zt

(18)


pzϕzt

+ ϕ minusρcpaVLPL

p + PL( 11138572

⎛⎝ ⎞⎠zp

ztminus

p

Tϕ

zT


k

μpnablaP1113888 1113889 0

(19)


zϕzt

1 minus ϕ0


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

zt



3Vm 1 minus ϕ0( 11138571113888 1113889

zT

zt


1 + e

2ρRTab

3Vm 1 minus ϕ0( 1113857(1 + bp)1113888 1113889

zp

zt

(20)


p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

ztminus

p 1 minus ϕ0( 1113857

1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889zT

zt

+ ϕ minusρcpaVLPL

p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


zp


k

μpnablaP1113888 1113889 0

(21)



C1 C3ze

zt+ C4

zT

zt


p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


C3 p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889


1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889

(22)


C1 + C2zp


k

μpnablaP1113888 1113889 0 (23)







z (ρC)MT( 1113857


ze






(ρC)M

z(T)


k

μnablaP1113888 1113889 + TKαT

ze

zt λMnabla

2T +

ρgapTaCg

paTnablaT middot

k

μnablaP1113888 1113889 + Qht (28)




ΔT ΔT1 + ΔT2 + ΔT3 (29)



Qh Cmρc ΔT2 + ΔT3( 1113857 (30)




+ 061114 T minus Ta( 1113857 + 270211

b minus0037 T minus Ta( 1113857 + 22735(31)

4 Model Validation






Mechanical field

Hydraulic field

ermal field


Adsorption constant



(1) (2)

(3)

(6)

0

k0 1ndash

(7) (8) (9) (10)

(11) (12)

(4)

(5)



sive s

train

(3) Adsorptio

n strain

(5) Perm

eabilit

y(1)

ermal strain


(4) Porosit

y


9Vm

ndash

∆ ndash ∆

∆(p + PL)2

3Vm(1 ndash ϕ0)



1 + e

1 ndash ϕ0

1 + e

1 ndash ϕ0

paTQht

Qh = Cmρc (∆T2 + ∆T3)

TKαT

ρcpaVLPL

ρgapTaCg



partΦ

partt

partp p

partt

partT

partt

parte

partt

part(T)

parttndash TKgαg

p P = 0

2T T= λM

kμ

∆ ∆ ∆

Pkμ

T

1n(1 + bp)i + αpi + Fi = 0

Gov

erni

ng eq

uatio

nsC

ross

-cou

plin

g eq

uatio

ns


(3λ + 2G)2ρRTaKΥ

3λ + 2GGv3 3

p

(ρC)M

+

+ ++

ϕ ndash

ϕ = 1 ndash


ϕ3K =

ϕ

ndashndash

ndash

+1ndash2v

∆Pkμ

3











570 mm

365 m

m

A

B


p = 10 MPa F x =

24

MPa

partTparty = 0

partTparty = 0

partppartx = 0

partppartx = 0

partTpartx = 0

partTpartx = 0






coal

5 m 5 m

33 m

Survey line

Coal wallRock

Working face

Drilling

20 m

rock

(a)

z

y

x


partppartx = 0



partTpartx = 0


partuparty = 0

(b)


0 20 40 60 80 100 120 14000

02

04

06

08

10

12

Gas

pre

ssur

e (M

Pa)



(a)

0 400 800 1200 1600293

294

295

296

297

298

Tem

pera

ture

(K)



(b)






6420

2020

30123456

40

10 1000


311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

















00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References


































































ndash06

ndash05

ndash04

ndash03

ndash02

ndash01

00

∆T = 0545 ndash 0075 p∆T = 056 ndash 01425 p

∆T = 063893 ndash 034464 p


Tem

pera

ture

var

iatio

n (deg

C)

02 MPa04 MPa06 MPa

02 04 06 08 10 12 14 16 18


04

08

12

16

20

24

cd

a

b

f

Gas pressure (MPa)

02 MPa desorption

04 MPa desorption

06 MPa desorption

e

02 MPa adsorption

04 MPa adsorption

06 MPa adsorption

04 06 08 10 12 14 16

Tem

pera

ture

accu

mul

atio

n (deg

C)



Reducepressure



Targetpressure

Desorptionbalance

Cycling

Increasepressure



00

01

02

02

03

04

04

05

06

06 08 10 12 14 16 18

02 MPa04 MPa06 MPa


Tem

pera

ture

var

iatio

n (deg

C)

ΔT = 055833 ndash 00751 p

∆T = 0575 ndash 01475 p

∆T = 0655 ndash 035357 p











ϕ VP

V

VP0 + ΔVP

VB0 + ΔV 1 minus

1 minus ϕ0( 1113857

1 + e1 +ΔVS

VS01113888 1113889 (1)







3Vm 1 minus ϕ0( 11138571113888 1113889

(2)


k k0ϕϕ0

1113888 1113889

3

(3)


k k0

ϕ301 minus

1 minus ϕ01 + e


3Vm 1 minus ϕ0( 11138571113888 11138891113890 1113891

3

(4)



εij 12G

σij minus16G

minus19K

1113874 1113875σkkδij (5)



εT 13αTΔT (6)



εp minusKY

3Δp (7)



εX 2ρRaKYΔT

9Vm

ln(1 + bp) (8)



εij 12G

σij minus16G

minus19K


KY

3Δpδij

+2ρRTaKY

9Vm

ln(1 + bp)δij

(9)


σijj + αpδij1113872 1113873j

+ Fi 0 (10)



εij 12

uij + uji1113872 1113873 (i j 1 2 3) (11)




3αTΔTδij

minus(3λ minus 2G)

3KYΔpδij minus

(3λ + 2G)2ρRTaKY

9Vm

ln(1 + bp)δij

(12)


Guiij +G]


3λ + 2G

3αTΔTj minus

3λ minus 2G

3KYΔpi


9Vm


(13)


ρg Mp

RTZ (14)




qg minusk

μnablaP (15)



zm




m ϕMg

RTp +

Mgpa

RTa

ρc

VLp

p + PL

(17)



zm

zt

Mgp

RT

zϕzt

+MgϕRT

zp

ztminus ρc

Mgpa

RTa

VLPL

p + PL( 11138572

zp

ztminus

Mgpϕ

RT2

zT

zt

(18)


pzϕzt

+ ϕ minusρcpaVLPL

p + PL( 11138572

⎛⎝ ⎞⎠zp

ztminus

p

Tϕ

zT


k

μpnablaP1113888 1113889 0

(19)


zϕzt

1 minus ϕ0


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

zt



3Vm 1 minus ϕ0( 11138571113888 1113889

zT

zt


1 + e

2ρRTab

3Vm 1 minus ϕ0( 1113857(1 + bp)1113888 1113889

zp

zt

(20)


p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

ztminus

p 1 minus ϕ0( 1113857

1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889zT

zt

+ ϕ minusρcpaVLPL

p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


zp


k

μpnablaP1113888 1113889 0

(21)



C1 C3ze

zt+ C4

zT

zt


p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


C3 p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889


1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889

(22)


C1 + C2zp


k

μpnablaP1113888 1113889 0 (23)







z (ρC)MT( 1113857


ze






(ρC)M

z(T)


k

μnablaP1113888 1113889 + TKαT

ze

zt λMnabla

2T +

ρgapTaCg

paTnablaT middot

k

μnablaP1113888 1113889 + Qht (28)




ΔT ΔT1 + ΔT2 + ΔT3 (29)



Qh Cmρc ΔT2 + ΔT3( 1113857 (30)




+ 061114 T minus Ta( 1113857 + 270211

b minus0037 T minus Ta( 1113857 + 22735(31)

4 Model Validation






Mechanical field

Hydraulic field

ermal field


Adsorption constant



(1) (2)

(3)

(6)

0

k0 1ndash

(7) (8) (9) (10)

(11) (12)

(4)

(5)



sive s

train

(3) Adsorptio

n strain

(5) Perm

eabilit

y(1)

ermal strain


(4) Porosit

y


9Vm

ndash

∆ ndash ∆

∆(p + PL)2

3Vm(1 ndash ϕ0)



1 + e

1 ndash ϕ0

1 + e

1 ndash ϕ0

paTQht

Qh = Cmρc (∆T2 + ∆T3)

TKαT

ρcpaVLPL

ρgapTaCg



partΦ

partt

partp p

partt

partT

partt

parte

partt

part(T)

parttndash TKgαg

p P = 0

2T T= λM

kμ

∆ ∆ ∆

Pkμ

T

1n(1 + bp)i + αpi + Fi = 0

Gov

erni

ng eq

uatio

nsC

ross

-cou

plin

g eq

uatio

ns


(3λ + 2G)2ρRTaKΥ

3λ + 2GGv3 3

p

(ρC)M

+

+ ++

ϕ ndash

ϕ = 1 ndash


ϕ3K =

ϕ

ndashndash

ndash

+1ndash2v

∆Pkμ

3











570 mm

365 m

m

A

B


p = 10 MPa F x =

24

MPa

partTparty = 0

partTparty = 0

partppartx = 0

partppartx = 0

partTpartx = 0

partTpartx = 0






coal

5 m 5 m

33 m

Survey line

Coal wallRock

Working face

Drilling

20 m

rock

(a)

z

y

x


partppartx = 0



partTpartx = 0


partuparty = 0

(b)


0 20 40 60 80 100 120 14000

02

04

06

08

10

12

Gas

pre

ssur

e (M

Pa)



(a)

0 400 800 1200 1600293

294

295

296

297

298

Tem

pera

ture

(K)



(b)






6420

2020

30123456

40

10 1000


311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

















00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References

































































ϕ VP

V

VP0 + ΔVP

VB0 + ΔV 1 minus

1 minus ϕ0( 1113857

1 + e1 +ΔVS

VS01113888 1113889 (1)







3Vm 1 minus ϕ0( 11138571113888 1113889

(2)


k k0ϕϕ0

1113888 1113889

3

(3)


k k0

ϕ301 minus

1 minus ϕ01 + e


3Vm 1 minus ϕ0( 11138571113888 11138891113890 1113891

3

(4)



εij 12G

σij minus16G

minus19K

1113874 1113875σkkδij (5)



εT 13αTΔT (6)



εp minusKY

3Δp (7)



εX 2ρRaKYΔT

9Vm

ln(1 + bp) (8)



εij 12G

σij minus16G

minus19K


KY

3Δpδij

+2ρRTaKY

9Vm

ln(1 + bp)δij

(9)


σijj + αpδij1113872 1113873j

+ Fi 0 (10)



εij 12

uij + uji1113872 1113873 (i j 1 2 3) (11)




3αTΔTδij

minus(3λ minus 2G)

3KYΔpδij minus

(3λ + 2G)2ρRTaKY

9Vm

ln(1 + bp)δij

(12)


Guiij +G]


3λ + 2G

3αTΔTj minus

3λ minus 2G

3KYΔpi


9Vm


(13)


ρg Mp

RTZ (14)




qg minusk

μnablaP (15)



zm




m ϕMg

RTp +

Mgpa

RTa

ρc

VLp

p + PL

(17)



zm

zt

Mgp

RT

zϕzt

+MgϕRT

zp

ztminus ρc

Mgpa

RTa

VLPL

p + PL( 11138572

zp

ztminus

Mgpϕ

RT2

zT

zt

(18)


pzϕzt

+ ϕ minusρcpaVLPL

p + PL( 11138572

⎛⎝ ⎞⎠zp

ztminus

p

Tϕ

zT


k

μpnablaP1113888 1113889 0

(19)


zϕzt

1 minus ϕ0


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

zt



3Vm 1 minus ϕ0( 11138571113888 1113889

zT

zt


1 + e

2ρRTab

3Vm 1 minus ϕ0( 1113857(1 + bp)1113888 1113889

zp

zt

(20)


p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

ztminus

p 1 minus ϕ0( 1113857

1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889zT

zt

+ ϕ minusρcpaVLPL

p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


zp


k

μpnablaP1113888 1113889 0

(21)



C1 C3ze

zt+ C4

zT

zt


p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


C3 p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889


1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889

(22)


C1 + C2zp


k

μpnablaP1113888 1113889 0 (23)







z (ρC)MT( 1113857


ze






(ρC)M

z(T)


k

μnablaP1113888 1113889 + TKαT

ze

zt λMnabla

2T +

ρgapTaCg

paTnablaT middot

k

μnablaP1113888 1113889 + Qht (28)




ΔT ΔT1 + ΔT2 + ΔT3 (29)



Qh Cmρc ΔT2 + ΔT3( 1113857 (30)




+ 061114 T minus Ta( 1113857 + 270211

b minus0037 T minus Ta( 1113857 + 22735(31)

4 Model Validation






Mechanical field

Hydraulic field

ermal field


Adsorption constant



(1) (2)

(3)

(6)

0

k0 1ndash

(7) (8) (9) (10)

(11) (12)

(4)

(5)



sive s

train

(3) Adsorptio

n strain

(5) Perm

eabilit

y(1)

ermal strain


(4) Porosit

y


9Vm

ndash

∆ ndash ∆

∆(p + PL)2

3Vm(1 ndash ϕ0)



1 + e

1 ndash ϕ0

1 + e

1 ndash ϕ0

paTQht

Qh = Cmρc (∆T2 + ∆T3)

TKαT

ρcpaVLPL

ρgapTaCg



partΦ

partt

partp p

partt

partT

partt

parte

partt

part(T)

parttndash TKgαg

p P = 0

2T T= λM

kμ

∆ ∆ ∆

Pkμ

T

1n(1 + bp)i + αpi + Fi = 0

Gov

erni

ng eq

uatio

nsC

ross

-cou

plin

g eq

uatio

ns


(3λ + 2G)2ρRTaKΥ

3λ + 2GGv3 3

p

(ρC)M

+

+ ++

ϕ ndash

ϕ = 1 ndash


ϕ3K =

ϕ

ndashndash

ndash

+1ndash2v

∆Pkμ

3











570 mm

365 m

m

A

B


p = 10 MPa F x =

24

MPa

partTparty = 0

partTparty = 0

partppartx = 0

partppartx = 0

partTpartx = 0

partTpartx = 0






coal

5 m 5 m

33 m

Survey line

Coal wallRock

Working face

Drilling

20 m

rock

(a)

z

y

x


partppartx = 0



partTpartx = 0


partuparty = 0

(b)


0 20 40 60 80 100 120 14000

02

04

06

08

10

12

Gas

pre

ssur

e (M

Pa)



(a)

0 400 800 1200 1600293

294

295

296

297

298

Tem

pera

ture

(K)



(b)






6420

2020

30123456

40

10 1000


311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

















00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References




























































εij 12

uij + uji1113872 1113873 (i j 1 2 3) (11)




3αTΔTδij

minus(3λ minus 2G)

3KYΔpδij minus

(3λ + 2G)2ρRTaKY

9Vm

ln(1 + bp)δij

(12)


Guiij +G]


3λ + 2G

3αTΔTj minus

3λ minus 2G

3KYΔpi


9Vm


(13)


ρg Mp

RTZ (14)




qg minusk

μnablaP (15)



zm




m ϕMg

RTp +

Mgpa

RTa

ρc

VLp

p + PL

(17)



zm

zt

Mgp

RT

zϕzt

+MgϕRT

zp

ztminus ρc

Mgpa

RTa

VLPL

p + PL( 11138572

zp

ztminus

Mgpϕ

RT2

zT

zt

(18)


pzϕzt

+ ϕ minusρcpaVLPL

p + PL( 11138572

⎛⎝ ⎞⎠zp

ztminus

p

Tϕ

zT


k

μpnablaP1113888 1113889 0

(19)


zϕzt

1 minus ϕ0


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

zt



3Vm 1 minus ϕ0( 11138571113888 1113889

zT

zt


1 + e

2ρRTab

3Vm 1 minus ϕ0( 1113857(1 + bp)1113888 1113889

zp

zt

(20)


p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889

ze

ztminus

p 1 minus ϕ0( 1113857

1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889zT

zt

+ ϕ minusρcpaVLPL

p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


zp


k

μpnablaP1113888 1113889 0

(21)



C1 C3ze

zt+ C4

zT

zt


p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


C3 p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889


1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889

(22)


C1 + C2zp


k

μpnablaP1113888 1113889 0 (23)







z (ρC)MT( 1113857


ze






(ρC)M

z(T)


k

μnablaP1113888 1113889 + TKαT

ze

zt λMnabla

2T +

ρgapTaCg

paTnablaT middot

k

μnablaP1113888 1113889 + Qht (28)




ΔT ΔT1 + ΔT2 + ΔT3 (29)



Qh Cmρc ΔT2 + ΔT3( 1113857 (30)




+ 061114 T minus Ta( 1113857 + 270211

b minus0037 T minus Ta( 1113857 + 22735(31)

4 Model Validation






Mechanical field

Hydraulic field

ermal field


Adsorption constant



(1) (2)

(3)

(6)

0

k0 1ndash

(7) (8) (9) (10)

(11) (12)

(4)

(5)



sive s

train

(3) Adsorptio

n strain

(5) Perm

eabilit

y(1)

ermal strain


(4) Porosit

y


9Vm

ndash

∆ ndash ∆

∆(p + PL)2

3Vm(1 ndash ϕ0)



1 + e

1 ndash ϕ0

1 + e

1 ndash ϕ0

paTQht

Qh = Cmρc (∆T2 + ∆T3)

TKαT

ρcpaVLPL

ρgapTaCg



partΦ

partt

partp p

partt

partT

partt

parte

partt

part(T)

parttndash TKgαg

p P = 0

2T T= λM

kμ

∆ ∆ ∆

Pkμ

T

1n(1 + bp)i + αpi + Fi = 0

Gov

erni

ng eq

uatio

nsC

ross

-cou

plin

g eq

uatio

ns


(3λ + 2G)2ρRTaKΥ

3λ + 2GGv3 3

p

(ρC)M

+

+ ++

ϕ ndash

ϕ = 1 ndash


ϕ3K =

ϕ

ndashndash

ndash

+1ndash2v

∆Pkμ

3











570 mm

365 m

m

A

B


p = 10 MPa F x =

24

MPa

partTparty = 0

partTparty = 0

partppartx = 0

partppartx = 0

partTpartx = 0

partTpartx = 0






coal

5 m 5 m

33 m

Survey line

Coal wallRock

Working face

Drilling

20 m

rock

(a)

z

y

x


partppartx = 0



partTpartx = 0


partuparty = 0

(b)


0 20 40 60 80 100 120 14000

02

04

06

08

10

12

Gas

pre

ssur

e (M

Pa)



(a)

0 400 800 1200 1600293

294

295

296

297

298

Tem

pera

ture

(K)



(b)






6420

2020

30123456

40

10 1000


311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

















00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References





























































C1 C3ze

zt+ C4

zT

zt


p + PL( 11138572 minus

p 1 minus ϕ0( 1113857KY

1 + e

2ρRTab


C3 p 1 minus ϕ0( 1113857


2ρRTaKYln(1 + bp)

3Vm 1 minus ϕ0( 11138571113888 1113889


1 + eαT +

2ρRaKYln(1 + bp)

3Vm 1 minus ϕ0( 1113857+ϕT

1113888 1113889

(22)


C1 + C2zp


k

μpnablaP1113888 1113889 0 (23)







z (ρC)MT( 1113857


ze






(ρC)M

z(T)


k

μnablaP1113888 1113889 + TKαT

ze

zt λMnabla

2T +

ρgapTaCg

paTnablaT middot

k

μnablaP1113888 1113889 + Qht (28)




ΔT ΔT1 + ΔT2 + ΔT3 (29)



Qh Cmρc ΔT2 + ΔT3( 1113857 (30)




+ 061114 T minus Ta( 1113857 + 270211

b minus0037 T minus Ta( 1113857 + 22735(31)

4 Model Validation






Mechanical field

Hydraulic field

ermal field


Adsorption constant



(1) (2)

(3)

(6)

0

k0 1ndash

(7) (8) (9) (10)

(11) (12)

(4)

(5)



sive s

train

(3) Adsorptio

n strain

(5) Perm

eabilit

y(1)

ermal strain


(4) Porosit

y


9Vm

ndash

∆ ndash ∆

∆(p + PL)2

3Vm(1 ndash ϕ0)



1 + e

1 ndash ϕ0

1 + e

1 ndash ϕ0

paTQht

Qh = Cmρc (∆T2 + ∆T3)

TKαT

ρcpaVLPL

ρgapTaCg



partΦ

partt

partp p

partt

partT

partt

parte

partt

part(T)

parttndash TKgαg

p P = 0

2T T= λM

kμ

∆ ∆ ∆

Pkμ

T

1n(1 + bp)i + αpi + Fi = 0

Gov

erni

ng eq

uatio

nsC

ross

-cou

plin

g eq

uatio

ns


(3λ + 2G)2ρRTaKΥ

3λ + 2GGv3 3

p

(ρC)M

+

+ ++

ϕ ndash

ϕ = 1 ndash


ϕ3K =

ϕ

ndashndash

ndash

+1ndash2v

∆Pkμ

3











570 mm

365 m

m

A

B


p = 10 MPa F x =

24

MPa

partTparty = 0

partTparty = 0

partppartx = 0

partppartx = 0

partTpartx = 0

partTpartx = 0






coal

5 m 5 m

33 m

Survey line

Coal wallRock

Working face

Drilling

20 m

rock

(a)

z

y

x


partppartx = 0



partTpartx = 0


partuparty = 0

(b)


0 20 40 60 80 100 120 14000

02

04

06

08

10

12

Gas

pre

ssur

e (M

Pa)



(a)

0 400 800 1200 1600293

294

295

296

297

298

Tem

pera

ture

(K)



(b)






6420

2020

30123456

40

10 1000


311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

















00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References





























































+ 061114 T minus Ta( 1113857 + 270211

b minus0037 T minus Ta( 1113857 + 22735(31)

4 Model Validation






Mechanical field

Hydraulic field

ermal field


Adsorption constant



(1) (2)

(3)

(6)

0

k0 1ndash

(7) (8) (9) (10)

(11) (12)

(4)

(5)



sive s

train

(3) Adsorptio

n strain

(5) Perm

eabilit

y(1)

ermal strain


(4) Porosit

y


9Vm

ndash

∆ ndash ∆

∆(p + PL)2

3Vm(1 ndash ϕ0)



1 + e

1 ndash ϕ0

1 + e

1 ndash ϕ0

paTQht

Qh = Cmρc (∆T2 + ∆T3)

TKαT

ρcpaVLPL

ρgapTaCg



partΦ

partt

partp p

partt

partT

partt

parte

partt

part(T)

parttndash TKgαg

p P = 0

2T T= λM

kμ

∆ ∆ ∆

Pkμ

T

1n(1 + bp)i + αpi + Fi = 0

Gov

erni

ng eq

uatio

nsC

ross

-cou

plin

g eq

uatio

ns


(3λ + 2G)2ρRTaKΥ

3λ + 2GGv3 3

p

(ρC)M

+

+ ++

ϕ ndash

ϕ = 1 ndash


ϕ3K =

ϕ

ndashndash

ndash

+1ndash2v

∆Pkμ

3











570 mm

365 m

m

A

B


p = 10 MPa F x =

24

MPa

partTparty = 0

partTparty = 0

partppartx = 0

partppartx = 0

partTpartx = 0

partTpartx = 0






coal

5 m 5 m

33 m

Survey line

Coal wallRock

Working face

Drilling

20 m

rock

(a)

z

y

x


partppartx = 0



partTpartx = 0


partuparty = 0

(b)


0 20 40 60 80 100 120 14000

02

04

06

08

10

12

Gas

pre

ssur

e (M

Pa)



(a)

0 400 800 1200 1600293

294

295

296

297

298

Tem

pera

ture

(K)



(b)






6420

2020

30123456

40

10 1000


311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

















00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References




































































570 mm

365 m

m

A

B


p = 10 MPa F x =

24

MPa

partTparty = 0

partTparty = 0

partppartx = 0

partppartx = 0

partTpartx = 0

partTpartx = 0






coal

5 m 5 m

33 m

Survey line

Coal wallRock

Working face

Drilling

20 m

rock

(a)

z

y

x


partppartx = 0



partTpartx = 0


partuparty = 0

(b)


0 20 40 60 80 100 120 14000

02

04

06

08

10

12

Gas

pre

ssur

e (M

Pa)



(a)

0 400 800 1200 1600293

294

295

296

297

298

Tem

pera

ture

(K)



(b)






6420

2020

30123456

40

10 1000


311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

















00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References































































coal

5 m 5 m

33 m

Survey line

Coal wallRock

Working face

Drilling

20 m

rock

(a)

z

y

x


partppartx = 0



partTpartx = 0


partuparty = 0

(b)


0 20 40 60 80 100 120 14000

02

04

06

08

10

12

Gas

pre

ssur

e (M

Pa)



(a)

0 400 800 1200 1600293

294

295

296

297

298

Tem

pera

ture

(K)



(b)






6420

2020

30123456

40

10 1000


311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

















00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References































































6420

2020

30123456

40

10 1000


311 times 105

(a)

6420

02040608112

2030

40

100

2010

0

times106

86 times 104

13 times 106

(b)

6420

2010

0

2030

40

292

291

292

100

(c)

















00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References































































00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



0 5 10 15 20 25 30 35

(a)

0 5 10 15 20 25 30 35

85 times 10ndash19

90 times 10ndash19

95 times 10ndash19

10 times 10ndash18

10 times 10ndash18

Perm

eabi

lity

(m2 )



(b)

292

293

294

295

296

297

Tem

pera

ture

(K)



(c)

ndash00065

ndash00060

ndash00055

ndash00050

ndash00045

ndash00040

ndash00035Vo

lum

e str

ain


0 5 10 15 20 25 30 35


(d)



6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References




























































6420

2010

0

2030

40

100

123456


314 times 105

(a)

6420 20

100

2030

40

100

02040608112times10613 times 106

86 times 104

(b)

6420

2010

0

2030

40

100

292

294295296297

293

291

298

(c)

6420

2010

0

2030

40

100

123456


312 times 105

(d)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(e)

6420

2010

0

2030

40

100

292

294

295

293

291

295

(f)

6420

2010

0

2030

40

100

123456


311 times 105

(g)

6420

2010

0

2030

40

100

02040608112times10613 times 106

86 times 104

(h)

6420

2010

0

2030

40

100

292

293

291

294

(i)


00

20 times 105

40 times 105

60 times 105

80 times 105

10 times 106

12 times 106

14 times 106

Gas

pre

ssur

e (Pa

)



(a)

292

293

294

295

296

297

Tem

pera

ture

(K)



(b)

Figure 14 Continued



6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References





























































6 Conclusions






Data Availability




Acknowledgments


720 times 10ndash19

765 times 10ndash19

810 times 10ndash19

855 times 10ndash19

900 times 10ndash19

945 times 10ndash19

990 times 10ndash19

103 times 10ndash18

Perm

eabi

lity

(m2 )



(c)


0

200

400

600

800

1000


Gas

dra

inag

e vol

ume (

m3 )



(d)



References




























































References




























































analysis of thermo-hydro-mechanical coupling of coal and

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