A simple method for correcting for the presence

A simple method for correcting for the presence of minor gases when determining the adsorbed methane content inshaleChun-Yun Zhang a ,Xin-Sheng Chai a ,⇑,Xian-Ming Xiao ba State Key Laboratory of Pulp and Paper Engineering,South China University of Technology,Guangzhou,ChinabState Key Laboratory of Organic Geochemistry,Guangzhou Institute of Geochemistry,Chinese Academy of Sciences,Guangzhou,Chinah i g h l i g h t sDevelop an approach to use the HS-GC determined parameters in gas calculation. Convert the adsorption equilibration partition coefficient to Langmuir constants. The Langmuir constants of minor gases used in gas calculation are from HS-GC test.a r t i c l e i n f o Article history:Received 28October 2014Received in revised form 11February 2015Accepted 12February 2015Available online 23February 2015Keywords:Correcting Minor gasesAdsorbed methane content Langmuir isotherma b s t r a c tThis paper demonstrates a novel approach for correcting for the presence of minor gases when determin-ing the adsorbed methane content in shale.Based on the widely used Langmuir isotherm in calculating the adsorbed gas,an equation is derived that converts the adsorption equilibrium partition coefficient (K d )and maximal amount of adsorbed gas (N )at low pressure to Langmuir pressure (p L ).Headspace gas chromatography (HS-GC)is used to determine the K d and N of the minor gas species present in the shale.The results indicate that the method satisfactorily accounts for the presence of minor gases when estimating the amount of adsorbed methane.This HS-GC method is much more efficient than the isother-mal adsorption test currently used for the measurement of adsorption parameters of minor gas species in shale.Therefore,this new approach will improve the speed and accuracy of estimating the amount of adsorbed methane in shale deposits.Ó2015Elsevier Ltd.All rights reserved.1.IntroductionNatural gas production from hydrocarbon-rich shale forma-tions,known as ‘‘shale gas’’,is one of the most rapidly growing new sources of energy.For example,in recent years,there has been rapid progress in the development of unconventional shale gas recovery in North America [1].To produce similar results in China,which also has abundant estimated reserves of shale gas [2],addi-tional research is needed,including development of techniques for effectively and efficiently estimating the amount of shale gas in particular formations.This information is vital for identifying loca-tions of interest (i.e.,enriched zones)that would justify the invest-ment of resources to commercialize shale gas production.In addition to the free gas which dissociates with shale pores,the absorbed gas can account for $20–80%of the total gas entrapped in underground shale gas reservoirs [3,4]).When only methane (the major component of shale gas)is taken into consid-eration,the typical Langmuir equation [5]can be used,i.e.,G a ¼G aL p p þp Lð1Þwhere two parameters (i.e.,Langmuir volume (G aL )and Langmuir pressure (p L )of adsorbed methane)are required.Although these parameters can be obtained by the isothermal adsorption test [6,7],the experimental procedure required is complicated and time-consuming.In most cases,the problem is further complicated by the presence of several minor gas species (e.g.,ethane and car-bon dioxide)that coexist in shale.The neglecting of these coexisting minor gases results in an over-estimation of the absorbed methane in shale if the conventional Langmuir equation is used.In order to correct for the presence of minor gases,an extended Langmuir equation has been proposed to calculate the adsorbed methane gas (G Me a )in shale [8–10];i.e.,/10.1016/j.fuel.2015.02.0500016-2361/Ó2015Elsevier Ltd.All rights reserved.⇑Corresponding author.Tel./fax:+862087113713.E-mail address:xschai@ (X.-S.Chai).G Me a ¼G MeaLyMepp MeL1þP ni¼1y i pp iLð2ÞThis expression is similar to Eq.(1),except that in addition tothe Langmuir constants(i.e.,G MeaL and p MeL)for methane,the Lang-muir pressures for the minor gas(i.e.,p iL)are also required. Although the amounts of these minor gas species adsorbed in shale are much lower than that of methane,the same procedures must be individually performed for each gas species in the isothermal adsorption test[11].Therefore,a significant amount of time is required to evaluate the amounts of all of the adsorbed gases in the shale samples.The isothermal adsorption test is designed to simulate the adsorption behavior of gases at various pressures.For methane, the isothermal adsorption test conducted at high pressure is neces-sary to obtain the Langmuir constants because of the high partial pressure of methane in most shale gas reservoirs[12].For the minor gases,their partial pressures could be much lower than that of methane[12].In that case,the adsorption behavior can be described by their partitioning coefficients between the vapor and solid phases when the linear sorption isotherm is valid,which can then be converted to parameters used in the Langmuir equa-tion.This approach greatly reduces the time required to determine the amount of methane adsorbed in the shale.There are several methods that can be used for the determination of partition coefficients in a solid–vapor adsorption system[13–16], however are usually based on custom-designed devices.Recently, we have developed two novel methods,based on the commercial headspace gas chromatographic system(HS-GC),for the determina-tion of the adsorption equilibrium partition coefficient and maximal amount of adsorbed gas for the minor gases adsorbed in shale [17,18].Thus,the method lends itself to relatively easy standardiza-tion pared with the isothermal adsorption test,all these methods are much more efficient for the determination of the adsorption-related parameters for the minor gases adsorbed on shale.However,in the practical applications,the key step is the con-version of the parameters measured by these efficient methods to the parameters that appear in the extended Langmuir equation.The objective of the present work was to develop a new approach to correct for the presence of the minor gases in calculating the adsorbed methane in shale,using the parameters that efficiently determined by HS-GC.The main focuses were on the error analysis of the Langmuir equation for calculating the adsorbed gas and the derivation of the conversion of adsorption equilibrium partition coefficients to adsorption constants in the Langmuir equation.The derived relationship was tested by application to a case study of cal-culating the content of adsorbed methane in a shale sample.2.Experimental2.1.SamplesThe shale samples were obtained from shale gas reservoir in both China(sample A and B)and North America(sample C).Each sample was ground and screened to60–80mesh;the average particle size was214l m.The key information,including specific surface area,Langmuir constant,adsorption equilibrium partition coefficient,and maximal adsorbed gas,were obtained from analy-sis of core samples using BET method,the Langmuir isothermal adsorption test and the HS-GC methods.2.2.Apparatus and operationsAn electromagnetic ore grinder(DF-3,Huanan Instrument, China)was used in the preparation of the powder samples.A GC system(Agilent7890A,USA)and an automatic headspace sampler (DANI HS86.50,Italy)were used for HS-GC measurement.3.Results and discussion3.1.Error analysisWhen the Langmuir volume(G aL)and pressure(p L)of analyte(s) in the Langmuir equation,i.e.,Eq.(1),are available,the volume of the adsorbed analyte(s)(G a)at any pressure can be calculated. According to Eq.(1)and the propagation of uncertainty(or propagation of error)[19],the uncertainty of G a(as relative stan-dard deviation,RSD)can be expressed asRSD¼s GaG a¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi@ln G a@G aL2s2G aLþ@ln G a@pL2s2p Lþ@ln G a@p2s2psð3ÞAll symbols and definitions are listed in Table1.Combine Eqs.(1)and(3)to haveRSD¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1G aL2s2G aLþ1pþpL2s2p LþpLpðpþpLÞ2s2psð4ÞThus,it can be seen from Eq.(4)that the error in the G a mea-surement is a function of G aL,p L,and the pressurized pressure (p).Adopting the permitted uncertainties(i.e.,10%)in both G aL and p L measurement from Langmuir isotherm experiment and a margin of error of0.01MPa for the pressure[20],the standard errors(i.e.,s GaL,s pL,and s p)for G aL,p L,and p can be determined. Thus,the RSD of the Langmuir isotherm experiment at various pressures can be estimated using Eq.(4).The relationship between the RSD and the pressurized pressure is shown in Fig.1.As shown in Fig.1,the Langmuir isotherm experiment can pro-vide a good measurement precision at higher pressure range,indi-cating that it is suitable to be used for the determination of the major gas(i.e.,methane)at the subterranean pressure.However, a significant error can be expected when the Langmuir isotherm experiment is used for measuring the amount of a minor gas,suchTable1Symbols and definitions.Symbols Definitions Unitsa Specific surface area m2/gb Adsorption constant MPaÀ1C a Gas concentration in the adsorbed phase g(gas)/m2C g Gas concentration in the vapor phase g(gas)/mLG a,G aL The adsorbed gas content and theLangmuir volume of gas,respectivelym3/tG Mea,G MeaLThe adsorbed methane and the Langmuirvolume of methane,respectivelyl mol/gK d Adsorption equilibrium partitioncoefficient(g/m2)/(g/mL) M Molecular weight of the gas species g(gas)/l mol N Maximal amount of adsorbed gas l mol/g(sample)p L,p MeL,p iLLangmuir pressure of universal gas,methane and the minor gasesMPap Formation pressure MPaR Molar gas constant J/l mol K s Ga,s GaLStandard error of adsorbed gas andLangmuir volume,respectively.l mol/g(sample) s pL,s p Standard error of Langmuir pressure andpressure,respectivelyMPaT Temperature Ky Me,y i Molar fraction of methane and minor gasesin shale gas,respectivelyh Fraction of coverage of shale pore surfaceby adsorbed gas%C.-Y.Zhang et al./Fuel150(2015)334–338335ethane and carbon dioxide,because of their lower partial Therefore,we can apply the efficient techniques thatthe adsorption parameters at lower pressure to thesein shale.Conversion of the parametersConverting the partition coefficient to the adsorption constant Langmuir pressuredefinition of vapor–solid adsorption equilibrium partition coefficient(K d)obtained by HS-GC method and the Langmuir equation are expressed,respectively,as the follows.agh¼bpþbpð6ÞWhen adsorption takes place at low partial pressure,e.g.,when it meets bp(1in Eq.(6),it agrees with the linear adsorption iso-therm.Thus,we haveh¼bpð7ÞAccording to the definition of h(i.e.,the fraction of coverage of the shale pore surface by adsorbed gas)and the equation of the state of gas,we haveh¼aC aNMð8Þandp¼C g RTMð9ÞMerging Eqs.(5),(7),(8)and(9),and make an arrangement,the correlation of K d and b in the linear adsorption isotherm range can be expressed asb¼aK dNRTð10ÞSince the Langmuir pressure(p L)is defined as the pressure at which one half of the maximal amount adsorbed gas is obtained, i.e.,h=1/2,the following equation can be obtained from Eq.(6),i.e.,p L ¼1bð11ÞSubstitute Eq.(11)to Eq.(10)to obtain the correlation of K d andp L,i.e.,pL¼NRTaK dð12Þ3.2.2.Scope of the conversion equationFig.2shows the difference between the curves drawn by Eqs.(6)and(7).It can be seen that the difference between these two models is not significant in the lower pressure range(e.g., <0.7MPa)for the shale sample with b=0.0926MPaÀ1(from Sichuan province,China).Therefore,we can make the above con-version in this linear adsorption isotherm range.Since the partial pressures of the minor gas species are basically located in the lin-ear range,we can use Eq.(12)to convert the K d(obtained from HS-GC measurement)to the Langmuir pressure(p L)for the minor gas species of involved.Fig.3shows the relationships between the relative errors and the pressures for shale samples with different K d s.It can be seen that the error is highly related to the K d of species.At an error tol-erance level of10%(required in the standard isothermal adsorption test),the maximum range of pressures for the conversion equation are about0.1,0.5,and1MPa,for the sample with the K d values of 0.05,0.01,and0.001,respectively.Therefore,the species with a larger K d has a wide linear pressure range that is suitable for the application of the conversion.3.3.New equation for calibrating the adsorbed methaneEq.(2)is an extended Langmuir equation for calculating the adsorbed methane gas in shale,in which the effect of multipleEffect of pressure on the measurement error in the Langmuir isothermal Fig.2.Linear range of the adsorption isotherm.The relative error for the replacement of Eq.(6)by the linear equationat different K d values.gas species(minor)coexisting in the sample is taken into consid-eration.Different from the traditional Langmuir isotherm test, the HS-GC method we developed can be used to efficiently deter-mine the equilibrium partition coefficients(K id)and maximal amount of adsorbed gas(N i)of these minor gases[17,18].Thus, we can use Eq.(12)to convert the parameters measured by HS-GC to those required in Eq.(2).The item of the sum of the partial pressures of the species in the denominator in Eq.(2)can be written asX n i¼1yipp iL¼yMepp MeLþX nÀ1i¼1yipp iLð13Þwhere the parameter(p MeL)of methane cannot be converted by Eq.(12)due to its high pressure,which is obtained from Langmuir adsorption isotherm test.Since the Langmuir pressure(p iL)of the minor gas species can bederived from K idand N i by Eq.(12),Eq.(13)can be further written asX n i¼1yipp iL¼yMeppLþX nÀ1i¼1yipaK idN i RTð14ÞSubstituting Eq.(14)into Eq.(2),we obtainG Me a ¼G MeaLyMepp MeL1þy Me pp MeLþnÀ1i¼1y i paK idN i RT!ð15ÞEq.(15)is the new equation for calculating the adsorbed methane content in shale samples based on the Langmuir isotherm test,in which the effect of minor gases on methane adsorption is corrected by the parameters measured by HS-GC.3.4.ApplicationsThree samples(designated A,B and C)from shale gas wells in both China and North America were collected,and the parameters required in the calculation were obtained from analysis of core samples using rock characterization instruments,the Langmuir isothermal adsorption test and the HS-GC methods.The data are listed in Table2.Based on the data in Table2,the amounts of adsorbed methane in these samples can be calculated.Table3shows the comparison of results of the adsorbed methane content in the shale samples calculated by the different methods,i.e.,Langmuir model(L), Extended Langmuir model(EL),and the present(P)method.It can be seen that the data calculated by the EL and P methods have a good match(RSD<4%),indicating that the present method is justifiable to be used in the application.Clearly,if ignoring minor gases effect,more than15%of the adsorbed methanol in the shale sample could be over-estimated,this will have a significant impact on any management decision regarding possible development of a particular resource.4.ConclusionsThis study presents a new approach for correcting for the pres-ence of minor gases when calculating the adsorbed methane in shale.A theoretical correlation was developed to convert the vapor–solid partition coefficient determined by HS-GC to the Lang-muir constants that are related to the amount of adsorbed gases. We have also shown the circumstances under which this conver-sion yields results of acceptable precision.Based on the conversion, the HS-GC determined parameters can be easily used to correct for the presence of minor gases when estimating adsorbed methane based on the extended Langmuir model.A case study of three samples illustrates the value of the new approach when making a management decision regarding possible development of a particular resource.AcknowledgementsThis study was jointly supported by National key Basic Research Program of China(973Program:2012CB214705),the Natural Science Foundation of China(No.21037001),and Research Fund for the Doctoral Program of Higher Education of China(No. 20110172110026).References[1]U.S.,Energy Information Administration.Effect of increased natural gasexports on domestic energy markets;2012.</ programs/gasrerulation/reports/feeialng.pdf>.[2]U.S.,Energy Information Administration.World shale gas resources:An initialassessment of14regions outside the United States;2011.<http://www.eia.gov/analysis/studies/worldshalegas/pdf>.[3]Curtis JB.Fracture shale-gas systems.AAPG Bull2002;86:1921.Table2The core information of shale samples.Sample ID Component y,%G a,L,l mol/g p L,MPa K d,(g/m2)/(g/mL)N,l mol/g T,°C p,MPa a,m2/gA Methane9470.8a10.8a––82.220.8 5.6Ethane3– 5.14a0.0109b115bCarbon dioxide2–7.76a0.0169b183bB Methane8087.2a 3.33a––86.49.627.9Ethane7–12.8a0.0106b327bPropane5–38.4a0.00658b719bButane5–45.3a0.00533b253bPentane2–10.2a0.0226b509bC Methane8681.9a8.16a––79.410.210.1Ethane7– 3.89a0.00550b106bPropane3– 4.25a0.0113b226bCarbon dioxide3– 4.89a0.00922b183ba andb represent the isothermal adsorption test data and the HS-GC test data,respectively.Table3The comparison of the adsorbed methane content in the shale samples calculated bythe Langmuir(L),extended Langmuir(EL),and present(P)methods,respectively.Samples Adsorbed methane,l mol/g Relativedifference,%Present Extended Langmuir Langmuir EL vs.P L vs.ELA42.842.945.6À0.23 6.29B58.758.860.9À0.17 3.57C38.236.842.4 3.8015.2C.-Y.Zhang et al./Fuel150(2015)334–338337[4]Jenkins CD,Boyer CM.Coalbed and shale gas reservoirs.J Petrol Technol2008;60:92–9.[5]Langmuir I.The adsorption of gases on plane surfaces of glass,mica andplatinum.J Am Chem Soc1918;40:1403–61.[6]Kim AG.Estimating methane content of bituminous coalbeds from adsorption Bur Mines,Rep Invest1977;8245:22.[7]Ambrose RJ,Hartman RC,Akkutlu IY.Multi-component sorbed-phaseconsiderations for shale gas in place calculations.SPE J2011:27–9.[8]Myers AL.Adsorption of gas mixtures.Ind Eng Chem1968;60:45–9.[9]Myers AL,Prausnitz JM.Thermodynamics of mixed gas adsorption.AIChE J1965;11:121.[10]Ritter JA,Yang RT.Equilibrium adsorption of multicomponent gas mixtures atelevated pressures.Ind Eng Chem1987;26:1679–86.[11]GB/T19560-2008.Experimental method of high-pressure isothermaladsorption to coal;2008.[12]Price LC,Schoell M.Constraints on the origins of hydrocarbon gas fromcompositions of gases at their site of origin.Nature1995;378:368–71. 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