Prediction of methane and carbon dioxide solubility in water(5)

S.Hashemietal./FluidPhaseEquilibria246(2006)131–136

135

Table4

Hydrate–liquidwaterexperimentaldataformethane–waterandcarbondioxide–water(*)systemsTrange(K)Prange(bar)No.ofpointsReferenceAARE(%)274.4–280.235–656[18]2.9276.2–281.750–14416[23]9.0274.0–278.2

20–60

10*

[19]

5.2

andthereferenceenthalpydifferencehydrateandpurewater,i.e., µMT Lbetweentheunoccupied

0(T)and hMT L0(T),atthereferencetemperature,werew0optimizedusingw

0three-phase(H–Lw–V)equilibriumdata.

Table3showsthe(H–Lw–V)datausedtooptimizethemodel,forbothmethane–water(69points)(131points)systems. µMT Landcarbondioxide–water

0(T)usedinthepresentstudyhasavalueof1256J/mol,w

0comparedbyHolderetal.[6].Similarly, hMT toL1245J/mol,asreported

0(T)usedinthecurrentworkhasavalueof 4822J/mol,w

0comparedto 4327J/mol,asreportedbyHolderetal.[6].

Table4presentsthehydrate–liquidwaterreferencesusedtoevaluatethemodelaccuracyunder(H–Lw)equilibriumforbothmethane–water(22points)andcarbondioxide–water(10points)systems.TheexperimentaldataofYangetal.[25]formethane–waterwasnotusedasitwasfounderroneousbyKimetal.[23].

Modelpredictionsofmethaneandcarbondioxidesolubil-ityinwaterusingthere-optimizedparametersaredisplayedinFigs.3and4,respectively.Singlepointsinthe gurescor-respondtothedataobtainedbyServioandEnglezos[18,19].Usingthenewlyoptimizedparameters,thecurrentmodelpre-dictsmethanesolubilityinwaterunder(H–Lw)equilibriumwithanAAREof2.9%forthesixdatapointsofServioandEngle-zos[18]and9.0%forthesixteendatapointsofKimetal.[23].Theoptimizedmodelpredictscarbondioxidesolubilityinwaterunder(H–Lw)equilibriumwithanAAREof5.2%fortendatapointsofServioandEnglezos[19].ResultsaresummarizedinTable4

.

parisonofcalculatedmethanesolubilityinliquidwaterbythepresentmodelusingthere-optimizedparameterswithexperimentaldataofServioandEnglezos[18]

.

parisonofcalculatedcarbondioxidesolubilityinliquidwaterbythepresentmodelusingthere-optimizedparameterswithexperimentaldataofServioandEnglezos[19].

Thebiasofthemodel(Fm)wastestedusingastatisticaltech-niquesimilartothatproposedbyBollesandFair[33]:

Fnm=expln(xcal/xexp)

(14)

wherexcalisthesolubilitypredictedbythemodel,xexpisthesolubilitymeasuredexperimentallyandnisthenumberofdatapoints.Theresultingbiasfactorat(H–Lw)equilibriumis0.93and0.95formethane–waterandcarbondioxide–watersystemsrespectively.Thefactthatthebiasvaluesareslightlylowerthanonedemonstratesthatthemodelpredictionspresentonlyaslightnegativebiastowardstheexperimentaldata.

Asmentionedbefore,Henry’slawhasbeenusuallyemployedtodeterminethegassolubilityat(H–Lw)[18,19]aswellasat(H–Lw–V)[5].Incalculatingthe(H–Lw)solubility,ServioandEnglezos[18,19]assumedthatthe(H–Lw)experimentalpressurecouldbereplacedbythethree-phaseequilibriumpres-surecorrespondingtotheexperimentaltemperatureasexplainedbefore.Thisassumptionmayneedtheinterpolationofthethree-phaseequilibriumpressurefromtheexperimentaldataatcertaintemperatures.TheAAREofHenry’slawformethanesolubil-itywas2.4%forthesixexperimentaldatapointsofServioandEnglezos[18].Thein uenceofpressureonthegassolubilityinthehydrate–liquidwaterzoneisnotsigni cantovertherangeinvestigated.Therefore,aslightchangeinpressurefromtwo-phase(H–Lw)tothree-phase(H–Lw–V)equilibriumdoesnotsigni cantlyaffectthesolubility.However,thepredictedeffectofapressureincreaseonmethanesolubilityinthehydrate–liquidwaterzoneresultingfromHenry’slawisoppositetothepresentmodelandtoexperimentalobservations,seeFig.3.Henry’scon-stantisafunctionoftemperatureand,atagiventemperature,gassolubilityisproportionaltothefugacityofthegasinvaporphasewhichincreaseswithpressure.4.Conclusion

TheTrebble–BishnoiequationofstatewasappliedalongwiththevanderWaalsandPlatteeuw,andHoldermodelstopredictthegassolubilityinwaterat(H–Lw)equilibrium