112S.Haoetal./ColloidsandSurfacesA:Physicochem.Eng.Aspects444 (2014) 104–113

Fig.6.Experimentalvs.predictiveisothermsofmethaneon:(a)Xingq-1–5#,(b)Qingh-2–3#,(c)Xujd-1#,and(d)Leiy-1#.TheredlinesarepredictiveisothermswhichbasedonEq.(17)andtheblacklinesarethosewhichbasedonEq.(14).

whereNisthenumberofdatapoints.

Themeanrelativedeviation forthetwodifferentcharacteristiccurveformsisevaluatedandshowninTable7.

AsshowninFig.6andTable7,themeanrelativedeviation forusingEq.(11)ascharacteristiccurveformissmallerthanthatforusingcubicpolynomialascharacteristiccurveform.Inaddition,theuseofcubicpolynomialasthecharacteristiccurveformcouldresultinanabnormalpredictivevaluethattheadsorptionamountincreasewiththepressuredroppingwhenthepressureislessthanapproximately0.9MPaforXingq-1–5#andXujd-1#,0.8MPaforQingh-2–3#,and0.5MPaforLeiy-1#.

ThermodynamicssuggeststhatanadsorptionisothermmustexhibittheHenrylawbehaviorwhenpressureisverylow.Unfortu-nately,theD–AequationsdonothavethecorrectHenrylawwhenthepressureisapproachingzero.TheslopeoftheD–Aadsorption

isothermiszerowhenthepressureapproacheszerowhent>1[22].However,asshowninFig.6,theslopeoftheD–Aadsorptionisothermforusingcubicpolynomialascharacteristiccurveformisin nitywhenthepressureapproacheszero.AlltheseindicatethatusingEq.(11)ascharacteristiccurveformismorereasonablethanusingthepolynomial.

4.Conclusion

Table7

Relativedeviation( )forpredictiveisotherms.

Sample

T(K)

Relativedeviation, (%)

Eq.(11)

Cubicpolynomial

Xingq-1–5#

Qingh-2–3#

Xujd-1#

Leiy-1#

333343333343333343333343

2.091.831.311.272.431.651.792.30

3.215.731.822.126.592.172.324.29

Inthiswork,highpressure(upto8.3MPa)adsorptionisothermsformethanewereobtainedat vetemperaturesforfourdifferentrankcoals.TheLangmuirandD–Aequationshavebeenappliedtomodeltheadsorptionofmethaneoncoalsabovesupercriticaltemperature.

ThetemperaturedependenceoftheLangmuirparameter,n0,indicatesthattheassumptionofanenergeticallyhomogeneoussurfaceofadsorptionisnotstrictlytrueformethaneadsorptiononcoal.

Todeterminewhichmethodtoevaluatethepseudo-saturationvaporpressureismostsuitableforanalyzingtheadsorptiondataabovetheTcofmethane.TheextrapolationofAntoine’sequation,Dubinin’smethodandSchwarz’smethodforestimatingpseudo-saturationvaporpressurewereusedtotestthehypothesisthatthedataforeachadsorptionsystemcouldbecollapsedontosinglecharacteristiccurves.ItwasfoundthatthedeviationofcharacteristiccurvedataforusingDubinin’smethodtoestimatepseudo-saturationvaporwassmallerthanthoseforusingtheothertwomethods.However,Dubinin’smethoddonottakeinto