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

107

ngmuircurve tstomethaneisothermdataforsamples:(a)Xingq-1–5#;(b)Qingh-2–3#;(c)Xujd-1#;and(d)Leiy-1#.Solidlinesarecurve ts.

surfaceadsorptionsite.Itshouldthereforebeatemperature-independentconstant[37].However,asshowninTable3,thesaturationcapacitynoisafunctionoftemperature.Similarobser-vationsweremadebyZhouandZhou[38]andClarksonetal.[11].Ruthven[37]heldthattheconstantsderivedbymatch-ingtheexperimentaldatatotheLangmuirmodelmightlackphysicalsigni cance,thoughtheLangmuirmodelwasofthecorrectqualitativeformtorepresentatypeIisotherm.Sat-urationcapacitynobeingafunctionoftemperatureinZhouandZhou’s,Clarksonetal.’sandourstudiescon rmRuthven’sview.

3.3.Determinationofcharacteristiccurves

Table3

AdsorptionparametersoftheLangmuirmodelforadsorptionisothermsofmethaneonthecoalsat303,313,and323K.

Sample

T(K)

no(mmol/g)

b(MPa 1)

R20.99480.99470.99490.99500.99480.99470.99510.99490.99490.99490.99480.9947

Xingq-1–5#

Qingh-2–3#

Xujd-1#

Leiy-1#

303313323303313323303313323303313323

0.95481.04071.11490.72470.72780.75960.69800.73580.77481.84891.87111.9093

0.16630.12170.09590.18480.16280.13270.14080.11300.09250.42570.35040.2838

3.3.1.ExtrapolationAntoineequationmethod

TheAntoineparametersB,C,andDinEq.(8)wereobtainedfromregressionanalysisofmethanesaturationvaporpressuredatabelowTc.Themethanesaturationvaporpressurepsatagiventem-peratureT(rangefrom100to190K)wereobtainedfromtheNISTwebsite[39].TherelationshipbetweenTandpsformethaneisshowninFig.S3.ThedotlinesinFig.S3istheAntoineequation ttingcurve.Theregressedadsorptionparameters(B,C,andD)are7.7437,1306.5485,and19.4362,respectively.

InordertoutilizetheD–Aequation,itsthreeparameters(W0,E,andt)wereevaluatedbyanon-linearregressionprocedure.Theinputdatafortheregressionwerethevolumeofadsorbedphase,W,andtheadsorptionpotential,A.

Fig.2showsthecharacteristicplotsforthecoals.ThevolumeofadsorbedphaseWwascalculatedbyEq.(6).Theadsorptionpoten-tialAwascalculatedbyEq.(7),inwhichthepseudo-saturationvaporpressurepswascalculatedbyextrapolationofAntoineequa-tion.

Theformofthetemperature-invariantcharacteristiccurvetobeutilizedisoneoftheimportantproblemsassociatedwiththeapplicationofpotentialtheories[11].AmankwahandSchwarz[26],andClarksonetal.[11]didnotgivetheformofthecharacteristiccurveintheirworks.Lietal.[40],Suetal.[41]andFengetal.[42]usedpolynomialtoexpressthecharacteristiccurve.Althoughthismethodissimple,thequadraticorcubicpolynomialparametersarelackofphysicalmeaning.Inthepresentwork,wededucedan