Methane adsorption characteristics on coal surface abo(8)

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

111

Fig.5.Characteristiccurvesfor(a)Xingq-1–5#,(b)Qingh-2–3#,(c)Xujd-1#,and(d)Leiy-1#.Thepswascalculatedbythemodi edSchwarz’smethod.

meaning.AsshowninFig.5,thedifferentcharacteristiccurveformcouldresultindifferentW0value.TheW0valuesobtainedfromcubicpolynomialregressionarelargerthanthoseobtainedfromEq.(11)regressionforallcoals.Todeterminethecharacteristiccurveformtobeutilized,weusetheregressionparametersinTable5andTable6,topredicttheisothermsat333and343K,respectively.

reportedinTable6intothefollowingequation,i.e.Eq.(16),apre-dictiveisothermequation.i.e.Eq.(17)isobtained.

nabsolute=

W adsorbed

×1000

CH4

=62.5 adsorbeda0+a1A+a2A2+a3A3

(16)

k

RTlnpcT/Tc RTln nabsolute=62.5 adsorbed a0+a1+a2

3

10106

pcT/Tck

2

+a3

RTln

pcT/Tck

3

(17)

109

WhenEq.(11)isusedascharacteristiccurveform,bysubstitut-ingtheregressionparametersvaluesreportedinTable5intoEq.(13),apredictiveisothermequationisobtainedforthesamplesatdifferenttemperaturewhichisasfollows:

k t

pcT/TcRT

lnnabsolute=n0exp

(14)

where

W0 adsorbed

n0=×1000

CH4

ThevalueofkinEqs.(14)and(17)is2.69forXingq-1–5#,2.24forQingh-2–3#,2.26forXujd-1#,and2.70forLeiy-1#,respectively(see3.3.4).Itshouldbenotedthatthedensityofadsorbedphase, adsorbed,isafunctionoftemperaturewhichiscalculatedbyEq.(2).Eqs.(14)and(17)allowforthegenerationofpredictiveisothermswhichcanbecomparedtotheexperimentaldata.Plotsofisothermsshowingacomparisonoftheexperimentalandpre-dictivevaluesareshowninFig.6.ThelinesinFig.6refertothepredictiveisotherms,whilepointsrefertothelaboratorydata.Thepredictionuncertaintyisdeterminedbythemeanrelativedeviation :

(15)

Correspondingly,whencubicpolynomialisusedascharacter-isticcurveform,bysubstitutingtheregressionparametersvalues

N 1 nexp,i ncal,i2 =

i=1

exp,i

(18)