dead inside

AUTHORS

XiaojunCui$DepartmentofEarthand

OceanSciences,UniversityofBritish

Columbia,6339StoresRoad,Vancouver,

BC,CanadaV6T1Z4;xcui@

ingeology

fromtheChinaUniversityofGeosciences,

Wuhan,ingeodynamicsfrom

BeijingUniversity,ogical

sciencesfromtheUniversityofMissouri,

tlyapostdoctoralfellowat

theUniversityofBritishColumbia,hisre-

archappliescomputermodelingtofluid

flowinvariousgeologicalsystems.

stin$DepartmentofEarthand

OceanSciences,UniversityofBritishColum-

bia,6339StoresRoad,Vancouver,BC,Canada

V6T1Z4;mbustin@

stinisaprofessorofpetroleum

andcoalgeologyintheDepartmentof

EarthandOceanSciencesattheUniversity

ofBritishColumbiaandpresidentofRMB

EarthScienceConsultantsandaprincipalof

receivedhisPh.D.

fromtheUniversityofBritishColumbiaand

isaregisteredprofessionalgeoscientistinthe

provinceofBritishColumbia.

ACKNOWLEDGEMENTS

ThisrearchwasfundedbytheNational

ScienceandEngineeringRearchCouncil.

,k,andan

anonymousreviewerfortheirhelpfulre-

viewsandcommentstoimprovethiswork.

Volumetricstrain

associatedwithmethane

desorptionanditsimpact

oncoalbedgasproduction

fromdeepcoalams

stin

ABSTRACT

Thepermeabilityofdeep(>1000m;>3300ft)coalamsiscom-

pcoalams,significantrervoirpressure

drawdownisrequiredtopromotegasdesorptionbecauofthe

,alargeper-

meabilitydeclinemayoccurbecauofpressuredrawdownand

theresultingincreaineffectivestress,dependingoncoalprop-

r,theperme-

abilitydeclinecanpotentiallybeofftbythepermeabilityen-

hancementcaudbythematrixshrinkageassociatedwithmethane

dictabilityofvaryingpermeabilityiscritical

haveinvestigatedquantitativelytheeffectsofrervoirpressureand

sorption-inducedvolumetricstrainoncoal-ampermeabilitywith

constraintsfromtheadsorptionisothermandassociatedvolumet-

ricstrainmeasuredonaCretaceousMesaverdeGroupcoal(Pice-

ancebasin)andderivedastress-dependentpermeabilitymodel.

Ourresultssuggestthatthefavorablecoalpropertiesthat

canresultinlesspermeabilityreductionduringearlierproduction

andanearlierstrongpermeabilityrebound(increainperme-

abilitycaudbycoalshrinkage)withmethanedesorptioninclude

(1)largebulkorYoung’smodulus;(2)largeadsorptionorLang-

muirvolume;(3)highLangmuirpressure;(4)highinitialperme-

abilityanddencleatspacing;and(5)lowinitialrervoirpres-

bilityvariationwithgas

productionisfurtherdependentontheorientationofthecoal

am,therervoirstressfield,m-

pletionwithinjectionofN

2

anddisplacementofCH

4

onlyresults

AAPGBulletin,v.89,no.9(September2005),pp.1181–12021181

Copyright#htsrerved.

ManuscriptreceivedOctober19,2004;provisionalacceptanceDecember6,2004;revidmanuscript

receivedApril8,2005;finalacceptanceMay11,2005.

DOI:10.1306/

inshort-termenhancementofpermeabilityanddoes

notpromotetheoverallgasproductionforthecoal

studied.

INTRODUCTION

AsthecoalbedmethaneindustrymaturesinNorth

America,deepercoalamsarebeingtargetedforcoal-

bedmethanedevelopment(Murray,2003).Deeper

coalsareattractivebecautheyaregenerallyhigher

rankandthushavehighergascapacitiesthanshallower

coalsandgenerallyhaveabetterdevelopedfracture

(cleat)creasingdepthofburial,how-

ever,thereisamarked(generallyexponential)de-

creainpermeabilityaffectivestressincreas(Mckee

etal.,1988;Bustin,1997),leadingtothecommonlow

permeabilityofdeepcoalams.

Becauofthedual-porositystructureofcoalams

(i.e.,microporouscoalmatrixandmacroporouscleat/

fracturenetwork),methaneisstoredpredominantly

-

ductionofmethanefromcoalamsisachievedwith

cleatpressuredrawdowninducedgenerallybypump-

ingwater,whichresultsindesorptionanddiffusionof

methanefromthecoalmicroporousmatrixandthen

flowofmethanethroughthecleattotheproducing

wdownofcleatfluidpressuretoinitiate

methaneproductionresultsinanincreaineffective

stressandreducesthealreadygenerallylowpermeabil-

uently,thereducedper-

meabilitylimitssignificantlytheproducibilityofmeth-

iallyoffttingthelossof

permeabilitycaudbyincreadeffectivestressisthe

markedshrinkageofcoalcaudbymethanedesorp-

tion,whichwidenscleataperturesandenhancesper-

meability.(Adsorptionreferstotheexcessamountof

acompetentprentatthegas-solidinterfaceover

thatwhichwouldbeprentatthesameequilibrium

etheden-

sityoftheadsorbedphaisgreaterthanthenon-

adsorbedpha,highconcentrationsofgasmayoccur

creadpressure,thead-

sorbedvolumeincreas,which,incoal,followsthe

tionisthereverofadsorp-

otheInternationalUnionofPureandAp-

pliedChemistry[/dhtml_home

.html]forafulldiscussionoftermsanddefinitions.)

Thenetreductionorenhancementofpermeabilityac-

companyinggasproductionisthuscontrolledcom-

petitivelybytheoppositeeffectsofdecreasingfluid

eenshowncon-

clusivelyinfieldtestsinsomeareasoftheSanJuan

basin,UnitedStates,thattherehasbeenasignificant

increainabsolutepermeabilityaccompanyinggas

rmeabilityenhancementduring

production,ifanticipatedinthedeeppartsofthebasin

suchasthePiceancebasinindeepercoalsintheWest-

ernCanadadimentarybasin,wouldhaveamajor

impactonexplorationandproduction.

Inthisstudy,usingcoalfromthePiceancebasinas

anexample,wedeterminetherelationshipbetween

volumetricstrainandgassorptiontounderstandbetter

thevariationofcoalpermeabilityduringgasproduc-

thePiceancebasiniscurrentlyproduc-

ingatdepthsinexcessof1500m(5000ft)andlocally

intheWhiteRiverDomeareainexcessof2135m

(7000ft)(Murray,2003).Experimentswerefirstun-

dertakentodeterminethevolumetricstraininduced

,analogoustothetheory

oflinearnonisothermalporoelasticity,astress-dependent

permeabilitymodelforin-situcoalwasderived,which

integratesthecontrolsofbothfluidpressureand

n-

straintsfromthePiceancebasincoal,thepossibledy-

namicchangeinpermeabilitywithgasproductionis

actsofthestress-

dependentcoalpermeabilityongasproductionfor

coalamswithawiderangeofproperties,especially

deepcoals,arestudiednumerically,andtheirimpli-

cationsarediscusd.

EXPERIMENTS

ExperimentalProcedure

Twocompetentcoalcoresoutof10fresh,high-rank,

candidatecoresfromtheMesaverdeGroupinthe

eci-

sionstraingauges(twonormalandtwoparalleltoband-

ing)werecementedinplaceandwiredtotheinstru-

othestartoftheexperiment,strain

gaugeswerecalibratedfortemperaturevariation,and

thecalibrationwasincorporatedintostrain-measuring

softwareforcalculatingthevolumetricchangesduring

lsamplevolume

andthedeadvolumeinsidetheveslweredetermined

withheliumexpansionrunsupto5MPainincreasing

steps,whichwereudforadsorptionisothermcalcu-

hevoidvolumeruns,thesampleswere

evacuatedfor30min,andthesystemwasallowedto

1182VolumetricStrainAssociatedwithMethaneDesorption

onisothermswerethenrun

withcontinuousstreamingtoacomputerdiskofthe

straindatafromallgauges,aswellastemperatureand

alexperimentaltimewas8weeks.

Sorption-InducedVolumetricStrain

Volumetricstrainassociatedwithgasadsorptionor

desorptioncanbemodeledintermsofeitherthead-

sorbedgasvolumeatstandardpressure(1bar)and

temperature(0jC)study,

wechotoapproximatethevolumetricstrain(e

V

)

asalinearfunctionoftheadsorbedgasvolume(V

g

),

although,tosomeextent,itdeviatesfromalinearre-

antageof

usingalinearfunctionisthatobtainingprecivol-

umetricstraindataisdifficultbecauofthecom-

plexityoftheexperiments,andsofar,volumetricstrain

experimentshavebeenconductedonveryfewcoals.

Thus,thesorption-relatedvolumetricstrainduring

thegasproductionfordifferentcoalscanbereadily

modeledevenifonlytheisothermisknown,andthus,

thechonlinearrelationshipinourstudyhasmuch

widerandeasierapplicabilityevenforcoalswhereno

morepreci

nonlinearrelationshiptodescribetherelationshipbe-

tweenvolumetricstrainandadsorbedgasdoesnotsig-

nificantlyimproveourfundamentalunderstandingon

thehydromechanicalbehavior,particularlywhenmany

otherparametersarepoorlyconstrained.

Thevolumetricstrainassociatedwithmethanead-

sorptionordesorptionat82jC(179.6jF)isgivenin

sthatthesorption-inducedvolumetric

strainisapproximatelyproportionaltothevolumeof

adsorbedgas(Figure1a).Thecoefficientofsorption-

inducedvolumetricstrain(e

g

)ortheslopeofthe

fittedstraightlinepassingthroughtheoriginis7.4Â

10À4g/cm3,whichisquiteclotothatofothercoals

wehavestudied(Chikatamarlaetal.,2004).Theap-

proximatelylinearrelationshipbetweenthevolume

ofadsorbate(V

g

)andthesorption-inducedvolumet-

ricstrain(e

V

)isthusdescribedas

e

V

¼e

g

V

g

ð1Þ

TheadsorbatevolumeV

g

isdeterminedwiththe

experimentalLangmuirisotherm

V

g

¼

V

L

p

pþp

L

ð2Þ

TheLangmuirconstantsarefitparametersofmea-

suredpressureandadsorbedvolumedata.V

L

and

p

L

andothervariablesinthetextaredescribedin

Table1,andtheadsorptionpropertiesoftheMesa-

tion2,

pisthepressureatwhichV

g

(volumeofgasadsorbed)

gmuirvolumeisthevol-

umeatinfinitepressure,andtheLangmuirpressure

isthepressureatone-halftheLangmuirvolume.

Withthemodeldescribedaboveandthespeci-

fiedparameters,thevolumetricstrainforthecoal

atdifferentpressurescanbepredicted(Figure1b).Up

to1%expansioncaudbysorptionofCH

4

occurs

erimentalvolumetricstrain(a)andthe

predictedvolumetricstraininducedbyCH

4

adsorptionfor

aMesaverdeGroupcoalusinganisothermmeasuredat

82jC(b).RefertothetextandTable1foranexplanationof

thesymbolsud.

CuiandBustin1183

forthecoalatapressureof25MPa,whichstrong-

lyaffectsthecoal-ampermeabilityduringgas

production.

PERMEABILITYMODEL

Becauofitsimportanceinmethaneproduction,

coal-ampermeabilityhasbeeninvestigatedinmany

entstress-permeabilityrela-

tionshavebeenobtainedfromexperimentaldata(i.e.,

Somertonetal.,1975;DurucanandEdwards,1986;

McKeeetal.,1988;Bustin,1997)orfromtheoretical

analysis(i.e.,Seidleetal.,1992).Theinfluenceofgas-

sorption-inducedstrainoncoal-ampermeabilityhas

alsobeenwidelystudied(i.e.,Gary,1987;Harpalani

andChen,1995;PalmerandMansoori,1998;Gilman

andBeckie,2000;Cuietal.,2004;ShiandDurucan,

2004).However,differentformulaewerederivedby

thorearchers(refertoShiandDurucan,2004).

Here,analogoustothetheoryoflinearnonisothermal

poroelasticity,wederiveastress-dependentperme-

lyderivedmodeliscompared

withthemodelspropodbypreviousinvestigators.

Ithasbeenrecognizedfordecadesthatgassorp-

tioncauscoaltoswell(e.g.,MoffatandWeale,1955).

Experimentalsorption-inducedstraindatafroma

recentstudy(Chikatamarlaetal.,2004)andthisstudy

indicatethatthegas-sorption-inducedvolumetric

strainisapproximatelyproportionaltothevolume

,theeffectsofgassorptionon

thedeformationofcoalamscanbetreatedanalogous

Symbols

SymbolDefinitionandUnits

aCleatspacing

bCleataperturewidth(m)

dSymbolforexactdifferential

kPermeability(m2)

k

0

Initialpermeability(m2)

k

rg

Gas-relativepermeabilityfactor

k

rw

Water-relativepermeability

pFluidpressureincleatnetwork(Pa)

p

0

Initialfluidpressureincleatnetwork(Pa)

p

m

Fluidpressureincoalmatrix(Pa)

p

L

Langmuirpressure(Pa)

p

rb

Pressureatwhichpermeabilityrebounds(Pa)

p

rc

Recoverypressureatwhichpermeability

recoversitsinitialvalue(Pa)

p

w

Wellpressure(Pa)

x,y,zDirectionalcoordinates

EYoung’smodulus(Pa)

KBulkmodulusofporousmedium

(E/3(1À2u)(Pa)

K

s

Modulusofsolidskeletonofporousmedia(Pa)

K

p

Modulusofporevolume(Pa)

S

w

Watersaturation

S

w0

Initialwatersaturation

V

b

Bulkvolume(m3)

V

p

Porevolume(m3)

V

g

Adsorbedgasvolumeatstandardpressure(1bar)

andtemperature(0jC)(cm3gÀ1)

V

L

LangmuirvolumeatstandardpandT(cm3gÀ1)

e

b

Bulkvolumetricstrain,e

xx

+e

yy

+e

zz

e

ij

Straintensor(i=x,y,z;j=x,y,z)

e

g

Volumetricstraincoefficientassociatedwith

gassorption(gcmÀ3)

e

p

Porevolumestrain

e

V

Sorption-inducedvolumetricstrain

e

V0

Initialvolumetricstrainvalue

fPorosityofcleatnetwork

f

0

Initialporosityatpressurep

0

andstresss

0

sMeannormalstressorconfiningpressure(Pa)

s

0

Initialmeannormalstressorconfiningpressure(Pa)

s

h

Meanhorizontalstress(s

xx

+s

yy

)/2(Pa)

s

h0

Initialmeanhorizontalstress(s

xx

+s

yy

)/2(Pa)

s

ij

Stresstensor(i=x,y,z;j=x,y,z:x,y,

andzaredirectionalcoordinates)(Pa)

uPoisson’sratio

d

ij

Kronecker’sdelta,equalto1wheni=j

and0wheni¼j

zBoit’scoefficient,generalrangingbetween0and1

tiesoftheMesaverdeCoal*

ParameterCH

4

N

2

**

Langmuirpressure

(P

L

,MPa)

7.210

Langmuirvolume

(V

L

,cm3/g)

17.75

Volumetricstraincoefficient

(e

g

,g/cm3)

7.4Â10À44.0Â10À4

Diffusivityincoalmatrix

(D

m

,m2sÀ1)

1.0Â10À112.0Â10À12

*DensityoftheMesaverdecoalis1.45g/diffusivityinthemi-

croporouscoalmatrixisarbitrarilytaken,butitreflectsthegeneralrelation

forCH

4

andN

2

incoals(e.g.,Cuietal.,2004).

**TheLangmuirconstantsandvolumetricstraincoefficientareartificially

r,theyareoftypicalvaluesforhighrankcoals.

1184VolumetricStrainAssociatedwithMethaneDesorption

totheeffectsoftemperatureforelasticporousmedia

(e.g.,PalmerandMansoori,1998).Followingthecon-

ventioninrockmechanics,compressivestrainand

rtotheconstitutiverelation

ofporoelasticmedia(e.g.,PalciauskasandDomenico,

1982;Neuzil,2003),thestress(s

ij

)andstrain(e

ij

)

relationfordeformingcoalamscanbedescribedas

s

ij

¼

E

1þu

e

ij

þ

u

1À2u

e

b

d

ij