Prediction of methane and carbon dioxide solubility in water(4)

134S.Hashemietal./FluidPhaseEquilibria246(2006)131–136

starttodecomposeasthetemperatureisincreased.Asaresult,gastransferstotheliquidphaseandthesolubilityofthegashydrateformerincreases.Thistrendcontinuesuptothepointwherethevapor,liquidwaterandhydratephasesareatequi-librium.Afurtherincreaseintemperatureresultsincompletedecompositionofthehydratephase.In(Lw–V)equilibrium,thesolubility–temperaturetrendisreversedsincemoregaswillenterthevaporphaseasthetemperatureisfurtherincreased.Thesamesolubilitydependencyontemperatureisobservedwithothergashydrateformerssuchascarbondioxide,seeFig.4.ModelpredictioninFig.2alsoshowstheeffectofpressureonmethane–waterphaseequilibrium.Higherpressuresleadtoanincreaseinsolubilityatvapor–liquidwaterequilibriumand,bycontrast,adecreaseinsolubilityathydrate–liquidwaterequilib-rium.Thein uenceofpressureismorepronouncedin(Lw–V)thanin(H–Lw)equilibrium[22].Forexample,inthepresentcase,apressurechangefrom35to65barcausesmethanesol-ubilitytoincreaseby69.7%at284.15Kanddecreasebyonly1.6%at274.15K.

TheresultsofthemodelinFig.2arealsocomparedtotheexperimentaldataofServioandEnglezos[18].TheTrebble–Bishnoiequationofstatewasfoundtoalwaysunderes-timatethesolubilityofmethaneinwaterat(Lw–V)equilibriumbyanaverageabsoluterelativeerror(AARE)of14.8,15.3,and14.3%forsixexperimentaldatapointsofServioandEngle-zos[18]asshowninFig.2,forsixdatapointsofKimetal.at298.15K[23],andforeighteendatapointsofLekvamandBishnoi[12],respectivelyusingtheoriginalparameters.ThenegativebiasresultingfromtheTrebble–BishnoiequationofstatemightbeattributedtothemixingrulebinaryinteractionparameterstakenfromTrebble–Bishnoi[32]whichcoverdif-ferenttemperatureandpressurerangesof310.9–444.3Kand1–680bar,respectively.

Thepredictedsolubilityofmethaneinwaterat(H–Lw)equi-libriumisalsolowerthantheexperimentaldataofServioandEnglezos[18]aspresentedinFig.2andofKimetal.[23]byanaverageof24.3%forsixand30.5%forsixteendatapointsrespectively.Themodelofthisworkalsounderestimatesthesol-ubilityofmethaneat(H–Lw–V)equilibriumforthreedatapointsofServioandEnglezosbyanaverageof23.5%aspresentedinFig.2.However,fromFig.2,therelativeerrorisconsistentfor(H–Lw–V)and(H–Lw)suggestingthatthepredictedtrendcor-rectlyfollowstheexperimentaldata.TheLangmuirconstantsandthereferenceparametersthatrespectivelyappearinthevanderWaalsandPlatteeuw(Eq.(3))andHolder(Eq.(7))modelsareall ttedparameterstakenfromtheirwork.This,withthealreadymentionedde ciencyoftheTrebble–Bishnoiequationofstate,contributedtothebiasofthesolubilitymodel.

Carbondioxidesolubilityvalueswerealwaysunderestimatedexceptforonedatapointin(Lw–V)equilibrium.TheAAREonthesolubilitydataofServioandEnglezos[19]are3.6%(forsixdatapoints),9.2%(forthreedatapoints)and15.6%(fortendatapoints)for(Lw–V),(H–Lw–V)and(H–Lw)equilibrium,respec-tively.Thesmallerrelativeerrorscomparedtothoseobtainedinthemethane–watersystemsuggeststhatthebinaryinteractionparametersoftheTrebble–Bishnoiequationofstateareabetter tforthecarbondioxide–watersystem.

Table1

Vapor–liquidwaterexperimentaldataformethane–waterandcarbondioxide–water(*)systemsTrange(K)Prange(bars)No.ofpointsReference310.9–444.341.4–55218[10]274.2–285.710.1–70.511[12]278.7–284.435–656[18]298.2

23–1665[23]283.2–303.220–400.314[17]273.2–283.210.1–38.59*[13]278.1–283.220–376*[19]278.2–318.24.96–79.642*[14]323.2–353.1

50.6–131

26*

[15]

Table2

Mixingrulebinaryinteractionparameters

Ka

KbKcKdCH40.4199 0.1727 0.0001 1.2274CO2

0.9688

0.5181

0.3757

0.1647

Inordertoimprovethevapor–liquidwater(Lw–V)equilib-riumpredictionsformethane–waterandcarbondioxide–watersystems,themixingrulebinaryinteractionparametersintheTrebble–Bishnoiequationofstatewereoptimizedusingrecentvapor–liquidwaterequilibriumdatathatcoveragreatertemper-aturerange.Atotalof54experimentalsolubilitymeasurementswereusedforthemethane–watersystem,while83wereusedforthecarbondioxide–watersystem,seeTable1.ThenewlyoptimizedmixingrulebinaryinteractionsparametersusedintheTrebble–Bishnoiequationofstate,forbothmethane–waterandcarbondioxide–watersystems,aredisplayedinTable2.Toimprovethemodelpredictionsforthehydrate–liquidwater(H–Lw)equilibrium,boththereferencechemicalpotential

Table3

Hydrate–liquidwater–vaporexperimentaldataformethane–waterandcarbondioxide–water(*)systemsTrange(K)Prange(bars)No.ofpointsReference280.9–286.758.5–1083[1]273.2–294.326.5–285.78[1]283.2–288.771–131.14[1]273.7–285.927.7–97.813[1]295.7–302.0339.9–7754[1]285.7–301.696.2–680.410[1]275.2–291.230.2–185.57[1]275.4–282.228.7–616[1]273.4–286.426.8–105.711[1]276.3–282.135–653[18]273.7–282.913.2–43.219*[1]277.2–281.920.4–36.94*[1]271.8–283.210.5–45.036*[1]273.9–282.013.8–38.46*[1]279.6–282.827.4–43.63*[1]271.6–283.210.4–45.144*[1]274.3–282.914.2–43.79*[1]277.1–282.620–423*[19]273.9–282.2

13.7–38.5

7*

[16]