106S.Haoetal./ColloidsandSurfacesA:Physicochem.Eng.Aspects444 (2014) 104–113

Theprecisionofthehigh-precisionpressuretransducerusedintheexperimentsis0.05%ofthefullscalevalue(maximumpressure10MPa).ThetemperaturesensorsarePt100 RTDswithanesti-mateduncertaintyof0.1K.ThelinesexposedtoairwerewrappedwithheatingtapecontrolledbyaPIDcontroller.Thepuritiesofthemethaneandheliumusedintheexperimentsare99.99and99.999%,respectively.

2.2.3.Isothermmodels

Alltheconventionalisothermequationswereoriginallyderivedforabsoluteadsorptionamount(nabsolute,mmol/g),thereforeitshouldbenabsolutetobeappliedforevaluatingthethermody-namicpropertyofadsorbedphase[34].However,thenabsolutethatrevealingthetruemasscon nedintheadsorbedphasecannotbedirectlymeasured.Theso-calledexcessadsorptionamount(nexcess,mmol/g)thatisapproachedfromtheexperimentalequilibriumdataisusedforthecalculationofnabsolute[27,29,31]:

nadsolute

=

nexcess

1 (1)

gasadsorbed

where gasand adsorbedarethedensityofthefreegasphaseandtheadsorbedphase,respectively(ing/cm3).

Amajorproblemindeterminingabsolutesorptionisthat adsorbedcannotbedetermineddirectlyandcertainassumptionshavetobemade.Sahaetal.[35]proposedanewmethodtoaccountfortheadsorbedphasevolume.Inthiswork,weusetheSaha’smethodtocalculatethedensityoftheadsorbedphase( adsorbed).TheSaha’smethodisasfollows[35],

adsorbed= bexp[ (T Tb)]

(2)

where bisthedensityoftheliquidmethaneatthenormalboil-ingpoint(0.4224g/cm3);Tbisnormalboilingpointofmethane(111.67K);and isthethermalexpansioncoef cientoftheadsorbedphasethatcanbeexpressedasfollows

[31,35,36].

=

1

vadsorbed

adsorbed

≈

1(3)

where adsorbedistheadsorbedphasespeci cvolume.

ngmuirmodel.TheformoftheLangmuirequationusedhereinisexpressedas[22]:

nabsolutebp

(4)

0=1+bp

wheren0isthelimitingadsorptioncapacity(inmmol/g);pistheequilibriumpressure(absolutepressureinMPa);bistheLangmuirconstant(inMPa 1).n0andbaretheadsorptionparametersthatareoptimizedfromtheleast-squarescriteriausingtheexperimen-taldata.

2.2.3.2.Dubinin–Astakhov(D–A)model.TheD–Amodelforadsorp-tionofmethaneontononhomogeneouscarbonaceoussolidsisexpressedas[22,31]:

W t

=(5)

0exp A

W=

nabsolute×10 3×MCH4

(6)

adsorbed

A=RTln

ps

(7)

where3Wisthevolumeofadsorbedphaseatequilibrium(incm/g);W0isthelimitingvolumethatthegascanoccupyintheadsorbent

Table2

Texturalcharacteristicsofthecoals.

Sample

SBET(m2/g)

Vmic(mm3/g)

Vt(mm3/g)Xingq-1–5#2.5810.44644.403Qingh-2–3#2.4550.37233.177Xujd-1#2.6350.51433.850Leiy-1#

7.486

3.1190

13.770

(incm3/g);Aistheadsorptionpotential(inJ/mol);Eisthechar-acteristicenergyoftheadsorptionsystem(inJ/mol);MCH4isthemolarmassofmethane(ing/mol);Risthegasconstant;andtisthestructuralheterogeneityparameter.

InordertocalculatetheadsorptionpotentialA,thevalueofthevaporpressurepsatagiventemperatureshouldbeknown.Satu-rationvaporpressuresareusedforadsorbateswhentemperaturesarebelowTc[22].However,aboveTc,thereisnoconceptofthevaporpressure;hencetheuseofpseudo-saturationvaporpressureswasproposed.Inthisstudy,weusethreeapproachesthatexistedintheliteraturestoevaluatethepseudo-saturationvaporpressureaboveTc[11,22,26]:

(1)UseAntoineequationforthesaturationvaporpressureandextrapolateittotemperaturesabovethecriticaltemperature[22,26]:

lnps=CB

(8)

whereB,C,andDareAntoineparameters.

(2)UsetheDubinin’smethod[11,22]:

p s=pc

T 2

(9)

c

wherethesubscriptcreferstothecriticalpoint(formethane,pcis4.5992MPa,andTcis190.56K).

(3)UsetheAmankwahandSchwarzmethod[22,26]:

p s=pc

T k

(10)

c

wherekisaparameterspeci ctotheadsorbate–adsorbentsystem.3.Resultsanddiscussion

3.1.Texturalcharacterization

Table2summarizesthetexturalparameterscalculatedfromthe

nitrogenisotherms.TheporesizedistributionsarepresentedinFig.S2.FromFig.S2,itcanbeobservedthattheXingq-1–5#,Qingh-2–3#,andXujd-1#havesimilarporesizedistribution.However,theporesizedistributionoftheLeiy-1#issigni cantlydifferentfromtheothers.

Fig.S1showstheSEMimagesofthetypicalcoalsamples.ItwasobservedthatthesurfacemorphologyofLeiy-1#showsalittledifferentfromtheXujd-1#.TheparticlesofLeiy-1#aresmallerandarrangemoretightlythanthoseoftheXujd-1#.ThedifferenceinthesurfacemorphologyisinagreementwiththeSBETandVmicdataofcoals.Iftheparticlesaresmallerandarrangemoretightly,theSBETorVmicofcoalwillbehigher.

ngmuircorrelations

Fig.1showsthemethaneuptakedatameasuredat303,313,

and323Kforthesamples.ThesolidlinesinFig.1areLangmuir tcurves.Theregressedadsorptionparameters(n0andb)arelistedinTable3.

AccordingtotheassumptionsoftheLangmuirmodel,thesat-urationcapacitynoissupposedtorepresenta xednumberof