1、Designation: D 4784 93 (Reapproved 2003)Standard Specification forLNG Density Calculation Models1This standard is issued under the fixed designation D 4784; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision.
2、 A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThis standard is a description of four mathematical models of the equation of state for LNG-likemixtures that were adopted in 1988.
3、 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, is
4、o 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 o
5、f 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 e
6、xperimental measurements using specially developed equip-ment, and in using these data to develop predictive models for use in density calculations.1. Scope1.1 This standard covers LNG density calculation models2for use in the calculation or prediction of the densities ofsaturated LNG mixtures from
7、90 to 120K to within 0.1 % oftrue values given the pressure, temperature, and composition ofthe mixture.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and
8、health practices and determine the applica-bility of regulatory limitations prior to use.2. Significance and Use2.1 The models in this standard can be used to calculate thedensity of saturated liquid natural gas in the temperature range90 to 120K. The estimated uncertainty for the density calcula-ti
9、ons 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 4 %pentanes less than 2 %It is assumed that hydrocarbons with carbon numbers of sixor greater are not present in the LNG solution.3. Mo
10、dels3.1 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,oGoPhii,o/fii,o, T/fii,o# 2 RT ln hii,o! (2)where:Z = compressibility factor,G = Gibbs free energy,P = pressure,T = temperature,o = r
11、eference fluid, 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 transformatio
12、n functions. 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 of1This standard is under the jurisdiction of ASTM Committee D03 on GaseousFuels and is the direct responsibility of Subcommittee D03.0
13、8 on ThermophysicalProperties.Current edition approved May 10, 2003. Published May 2003. Originallyapproved in 1988. Last previous edition approved in 1998 as D 4784 93 (1998).2The formulation of the models and the supporting work was done by theNational Bureau of Standards under the sponsorship of
14、British Gas Corp., ChicagoBridge and Iron Co., 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.
15、, Tennessee Gas Pipeline, Texas EasternTransmission 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.
16、state to give a realistic vapor liquid phase boundary down to atemperature of 43K. This modification was necessary toaccommodate the very low reduced temperatures of the heavierhydrocarbons and was accomplished without changing theperformance of the equation of state above the triple point ofmethane
17、. 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, nTri1 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/Tiica
18、nd Vri5 V/Viic); each fluid requires a uniquewiwhich was estimated using pure fluid experimental data. Asingle set of the ns is used for all fluids. 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 (
19、Zc=PcVc/RTc) at the critical point. The param-eters ns and wiwere estimated using the experimental PVTdata set from NBS measurements and least squares estimationtechniques.3.1.1 The extension of the above to mixtures is nowaccomplished by the application of the following combiningrules:hx,o5(i(jxixj
20、hij,o(7)fx,ohx,o5(i(jxixjfij,ohij,o(8)fij,o5eijfii,ofjj,o!1/2(9)hij,o5hij S12hii,o1/3112hjj,o1/3D3(10)The eijand the hijare binary interaction parameters deter-mined by least squares from the PVTx data for binary mixtures.Values for the coefficients and other adjustable parameters aregiven in the Re
21、search 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 adjustable parameters,P = pressure,V = specific volume,T = temperature, andR = the gas constant.The equation is applied to mixtures by assuming the one-fluid theo
22、ry and applying the following combining rules.am5(i(jaijxixj(12)bm5(i(jbijxixj(13)cm5(i(jcijxixj(14)The mixing rules are:bij5Fbii1/31 bjj1/321 2 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 exc
23、ess volume is now calculated using theequation of state andVE5 Vm2 Vixi(18)where Vmand Viare calculated via Eq 11-17. The calculatedvalue of VEcan 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 experiment
24、aldata. Values for the coefficients and other adjustable parametersare given in the Research Report.33.3 Revised Klosek and McKinleyThe revised 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 t
25、he ithcompo-nent,XCH4= mole fraction of methane, andk1and k2= correction factors.Tables of values for the correction factors are given in theResearch Report.33.4 The Cell Model4Comparisons of NBS measured datawith the cell model were made during the course of the NBSstudy, but the details of the mod
26、el have not been reported.Additional information is available in NBS Monograph 172.54. Additional Information4.1 These models were originally published in NBS Mono-graph 172, which also contains the following:4.1.1 Descriptions of the experimental apparatus developed,constructed, and proven for use
27、in taking the necessary LNGdata points,3Supporting data have been filed at ASTM International Headquarters and maybe obtained by requesting Research Report RR: D031006.4The Cell Model was developed by M. A. Albright of Phillips Petroleum Co.from a correlation published by Renon, Eckert, and Prausnit
28、z, but a paperdocumenting its formulation and performance was never published.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.D
29、 4784 93 (2003)24.1.2 Descriptions of the operational procedures used 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 resulti
30、ng from the extensive LNGDensity Research project.ASTM International 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 right
31、s, and the riskof infringement of such rights, are entirely their own 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 r
32、evision of this standard or for additional standardsand should be addressed 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 y
33、ou shouldmake your views known to the ASTM Committee on Standards, 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 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org).D 4784 93 (2003)3
