1、Designation: D4784 93 (Reapproved 2010)Standard Specification forLNG Density Calculation Models1This standard is issued under the fixed designation D4784; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A
2、 number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.INTRODUCTIONThis specification is a description of four mathematical models of the equation of state for LNG-likemixtures that were adopted in 198
3、8. The four models include an extended corresponding states model,a cell model, a hard sphere model, and a revised Klosek and McKinley model. Each of the models hasbeen optimized to the same experimental data set which included data for pure nitrogen, methane,ethane, propane, iso and normal butane,
4、iso and normal pentane, and mixtures thereof. For LNG-likemixtures (mixtures of the orthobaric liquid state at temperatures of 120K or less and containing at least60 % methane, less than 4 % nitrogen, less than 4 % each of iso and normal butane, and less than 2 %total of iso and normal pentane), all
5、 of the models are estimated to predict densities to within 0.1 %of the true value. These models were developed by the National Institute of Standards and Technology(formerly the Bureau of Standards) upon culmination of seven years of effort in acquiring physicalproperties data, performing extensive
6、 experimental measurements using specially developed equip-ment, and in using these data to develop predictive models for use in density calculations.1. Scope1.1 This specification covers LNG density calculation mod-els2for use in the calculation or prediction of the densities ofsaturated LNG mixtur
7、es from 90 to 120K to within 0.1 % oftrue values given the pressure, temperature, and composition ofthe mixture.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.3 This standard does not purport to address all of thesafety c
8、oncerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Significance and Use2.1 The models in this specification can be used to calc
9、ulatethe density of saturated liquid natural gas in the temperaturerange 90 to 120K. The estimated uncertainty for the densitycalculations is 60.1 %. The restrictions on composition of theliquefied natural gas are:methane 60 % or greaternitrogen less than 4 %n-butane less than 4 %i-butane less than
10、4 %pentanes less than 2 %It is assumed that hydrocarbons with carbon numbers of sixor greater are not present in the LNG solution.3. Models3.1 Extended Corresponding StatesThe extended corre-sponding states method is defined by the following equations:ZiP,T 5 ZoPhii,o/fii,o, T/fii,o# (1)GiP,T 5 fii,
11、oGoPhii,o/fii,o, T/fii,o# 2 RT ln hii,o! (2)where:Z = compressibility factor,G = Gibbs free energy,1This standard is under the jurisdiction of ASTM Committee D03 on GaseousFuels and is the direct responsibility of Subcommittee D03.08 on ThermophysicalProperties.Current edition approved May 1, 2010.
12、Published July 2010. Originally approvedin 1988. Last previous edition approved in 2003 as D4784 93 (2003). DOI:10.1520/D4784-93R10.2The formulation of the models and the supporting work was done by theNational Bureau of Standards under the sponsorship of British Gas Corp., ChicagoBridge and Iron Co
13、., Columbia Gas Service Corp., Distrigas Corp., Easco Gas LNG,Inc., El Paso Natural Gas, Gaz de France, Marathon Oil Co., Mobil Oil Corp.,Natural Gas Pipeline Co., Phillips Petroleum Co., Shell International Gas, Ltd.,Sonatrach, Southern California Gas Co., Tennessee Gas Pipeline, Texas EasternTrans
14、mission Co., Tokyo Gas Co., Ltd., and Transcontinental Gas Pipe Line Corp.,through a grant administered by the American Gas Association, Inc.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.P = pressure,T = temperature,o = reference f
15、luid, andi = fluid for which properties are to be obtained via theequation of state for the reference fluid and thetransformation functions fii,oand hii,oare introduced toallow extension of the method to mixtures.The two defining Eq 1 and Eq 2 are necessary since there aretwo transformation function
16、s. In this case, an equation of statefor methane was chosen for the reference fluid. During thecourse of the study it was necessary to modify the equation ofstate to give a realistic vapor liquid phase boundary down to atemperature of 43K. This modification was necessary toaccommodate the very low r
17、educed temperatures of the heavierhydrocarbons and was accomplished without changing theperformance of the equation of state above the triple point ofmethane. The fii,oand hii,oare defined asfii,o5 Tcii/Tco! uii,oTri,Vri! (3)andhii,o5 Vcii,o/Vco! fii,oTri,Vri! (4)where:uii,o5 1 1 wi2 wo! n12 n2, nTr
18、i1 n32 n4/Tri! Vri2 n5!#(5)andfii,o5ZocZic1 1 wi2 wo! n6Vri2 n7! 2n8Vri2 n9! ,nTri# (6)The Vriand Triare reduced temperature and volume (that is,Tri5 T/Tiicand Vri5 V/Viic); each fluid requires a uniquewiwhich was estimated using pure fluid experimental data. Asingle set of the ns is used for all fl
19、uids. The ns wereestimated using all of the pure fluid experimental data from theNBS Boulder Study. The Zco/Zciis the ratio of the compress-ibility factors (Zc=PcVc/RTc) at the critical point. The param-eters ns and wiwere estimated using the experimental PVTdata set from NBS measurements and least
20、squares estimationtechniques.3.1.1 The extension of the above to mixtures is nowaccomplished by the application of the following combiningrules:hx,o5(i(jxixjhij,o(7)fx,ohx,o5(i(jxixjfij,ohij,o(8)fij,o5ijfii,ofjj,o!1/2(9)hij,o5hij S12hii,o1/3112hjj,o1/3D3(10)The ijand the hijare binary interaction pa
21、rameters deter-mined by least squares from the PVTx data for binary mixtures.Values for the coefficients and other adjustable parameters aregiven in the Research Report.33.2 Hard SphereThe hard sphere model equation of state:PVRT5 c1 1 y 1 y21 2 y!32aRTV(11)where:y = b/4V and a, b, and c are adjusta
22、ble parameters,P = pressure,V = specific volume,T = temperature, andR = the gas constant.The equation is applied to mixtures by assuming the one-fluid theory and applying the following combining rules.am5(i(jaijxixj(12)bm5(i(jbijxixj(13)cm5(i(jcijxixj(14)The mixing rules are:bij5 Fbii1/31 bjj1/321 2
23、 jij!G3(15)aij5 aiiajj!1/2Fbij2biibjjG1/21 2 kij! (16)cij5cii1 cij2(17)The parameters jijand kijare in this case the binary interac-tion parameters. The excess volume is now calculated using theequation of state andVE5 Vm2 Vixi(18)where Vmand Viare calculated via Eq 11-17. The calculatedvalue of VEc
24、an now be used with measured values Vixito givean actual volume of the mixture. Then:Vm5(iVixi1 VE(19)where the VEis from Eq 18 and the Viis from experimentaldata. Values for the coefficients and other adjustable parametersare given in the Research Report.33.3 Revised Klosek and McKinleyThe revised
25、Klosek andMcKinley model equation is:Vmix5 ( xiVi2 k11 k22 k1! xN2/0.0425 xCH4(20)where:Vmix= volume of the mixture,Xiand Vi= mole fraction and volume of the ithcompo-nent,XCH4= mole fraction of methane, andk1and k2= correction factors.Tables of values for the correction factors are given in theRese
26、arch Report.33.4 The Cell Model4Comparisons of NBS measured datawith the cell model were made during the course of the NBS3Supporting data have been filed at ASTM International Headquarters and maybe obtained by requesting Research Report RR:D03-1006.4The Cell Model was developed by M. A. Albright o
27、f Phillips Petroleum Co.from a correlation published by Renon, Eckert, and Prausnitz, but a paperdocumenting its formulation and performance was never published.D4784 93 (2010)2study, but the details of the model have not been reported.Additional information is available in NBS Monograph 172.54. Add
28、itional Information4.1 These models were originally published in NBS Mono-graph 172,5which also contains the following:4.1.1 Descriptions of the experimental apparatus developed,constructed, and proven for use in taking the necessary LNGdata points,4.1.2 Descriptions of the operational procedures us
29、ed withthe special apparatus in obtaining the required data pointmeasurements,4.1.3 Descriptions of the data point measurement programs,4.1.4 Descriptions of the development of the various mod-els, and4.1.5 Basic publications resulting from the extensive LNGDensity Research project.ASTM Internationa
30、l takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their o
31、wn responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be a
32、ddressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards,
33、at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-958
34、5 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the ASTM website (www.astm.org/COPYRIGHT/).5NBS Monograph 172, Liquified Natural Gas Densities: Summary of ResearchProgram at the National Bureau of Standards, is available from the Superintendentof Documents, U.S. Government Printing Office, Washington, DC 20402.D4784 93 (2010)3
