@ 9 Q ‘? $+ Density of Liquefied Natural Gas Robert H. Jensen, U. of Krmsas Fred Kurata, SPE-AIME, U. of Kansas Introduction Liquefied natural gas, LNG, is being handled in in- creasing quantities, and a reliable and convenient method of determining LNG density is desired. If a composition analysis is available, the correlations of Harmens’*2 and of Lyckman, Eckert, and Prausrdtzg may be used to calculate LNG density. Harmens’ correlation was developed for the den- sity of pure light hydrocarbon liquids at saturation and for the density of mixtures of such hydrocarbons, particularly of LNG, In the correlation, Eq. 1 is used to calculate liquid densi~: p=c Or’(Tr). . . . . . . ● (1) C and F(T,) were tabulated by Harmens. C is an empirical density constant, and F( T~) is Harmens’ generalized density function. T, is reduced tempera- ture, T/ T,, To apply the correlation to mixtures, mixing rules were givenl’2 to compute C and Tc from mixture composition and pure component values. In the correlation of Lyckrnan, Eckert, and Praus- nitz, reduced saturated volume v, is given as a quad- ratic function of acentric factor: v~= v/vc = v,(o) + @vf(l ) + Uzvr(z) . (2) p= M/v, . . . . . . . . (3) where v is molar volume, VCis critical molar volume, and M is mol cular weight. The generalized functions / of reduce temperature V~(0) j V~(*)~ad vr(z)) were tabulated by Lyckman, et al., in the range T, = 0.560 to T, = 0.990. Chueh and Prausnitz4 fitted the tabu- lated values to Eq. 4 and provided the coefficients @ to f(~). + e(~)/T, + j(~)ln(l -T,) . . . (4) Eq. 4 is valid for reduced temperatures from 0,560 to 0.995. Mixing rules were suggested by Chueh and Prausnitz to calculate pseudocritical volume and tem- perature, and mixture acentric factor, for application of the correlation to mixtures of known composition. In using the foregoing correlations, a composition analysis is required, and mixture pseudo constants must be calculated. To provide an easier and quicker procedure for the man in the field, a study was under- taken to correlate LNG density as a function of three measurable properties: tempera~re, pressure, and the gas gravity of gasified LNG. A technician can make these measurements routinely with commer- cially available equipment. Theory To derive the LNG density correlation, equations are required for computing ternary mixture composi- tions, gas gravities, and liquid densities at fixed tem- peratures and pressures. If the vapor phase over an ideal solution behaves An experimentally derived tabular correlation for LNG density as a function of temperature, pressure, and gas gravity has been designed for use in the field. The advantages of this correlation are that a gas gravity analysis is more easily obtained than a composition analysis and that density is determined by direct interpolation of the gas gravity tables. JUNE, 1969 683
Transcript
@
9 Q
‘?$+
Density of Liquefied Natural GasRobert H. Jensen, U. of KrmsasFred Kurata, SPE-AIME, U. of Kansas
IntroductionLiquefied natural gas, LNG, is being handled in in-creasing quantities, and a reliable and convenientmethod of determining LNG density is desired. If acomposition analysis is available, the correlations ofHarmens’*2 and of Lyckman, Eckert, and Prausrdtzgmay be used to calculate LNG density.
Harmens’ correlation was developed for the den-sity of pure light hydrocarbon liquids at saturationand for the density of mixtures of such hydrocarbons,particularly of LNG, In the correlation, Eq. 1 is usedto calculate liquid densi~:
p=c Or’(Tr). . . . . . . ● (1)
C and F(T,) were tabulated by Harmens. C is anempirical density constant, and F( T~) is Harmens’generalized density function. T, is reduced tempera-ture, T/ T,, To apply the correlation to mixtures,mixing rules were givenl’2 to compute C and Tc frommixture composition and pure component values.
In the correlation of Lyckrnan, Eckert, and Praus-nitz, reduced saturated volume v, is given as a quad-ratic function of acentric factor:
v~ = v/vc = v,(o) + @vf(l) + Uzvr(z) . (2)
p= M/v, . . . . . . . . (3)
where v is molar volume, VCis critical molar volume,and M is mol cular weight. The generalized functions
/of reduce temperature V~(0)j V~(*)~ad vr(z)) were
tabulated by Lyckman, et al., in the range T, = 0.560to T, = 0.990. Chueh and Prausnitz4 fitted the tabu-lated values to Eq. 4 and provided the coefficients@ to f(~).
+ e(~)/T, + j(~)ln(l -T,) . . . (4)
Eq. 4 is valid for reduced temperatures from 0,560 to0.995. Mixing rules were suggested by Chueh andPrausnitz to calculate pseudocritical volume and tem-perature, and mixture acentric factor, for applicationof the correlation to mixtures of known composition.
In using the foregoing correlations, a compositionanalysis is required, and mixture pseudo constantsmust be calculated. To provide an easier and quickerprocedure for the man in the field, a study was under-taken to correlate LNG density as a function of threemeasurable properties: tempera~re, pressure, andthe gas gravity of gasified LNG. A technician canmake these measurements routinely with commer-cially available equipment.
TheoryTo derive the LNG density correlation, equations arerequired for computing ternary mixture composi-tions, gas gravities, and liquid densities at fixed tem-peratures and pressures.
If the vapor phase over an ideal solution behaves
An experimentally derived tabular correlation for LNG density as a function oftemperature, pressure, and gas gravity has been designed for use in the field. Theadvantages of this correlation are that a gas gravity analysis is more easily obtainedthan a composition analysis and that density is determined by direct interpolationof the gas gravity tables.
JUNE, 1969 683
as a perfect gas, Raoult’s law is obeyed by eachcomponent: 5
Pi =xiPoi . . . . . . . . . (5)
Total pressure over a solution is the sum of the par-tial pressures, and liquid phase non-idealities are ac-counted for by activity coefficients:
For a binary methane-nitrogen mixture, total pres-sure is written in terms of mole fraction nitrogen, x5:
P = y, PO, + (y,Po, – y,Po, )x5 . . (7)
A plot of P vs x, does not necessarily result in astraight line, as Eq. 7 indicates, because YIand Y6arefunctions of composition. However, a P-x, plot maybe used to find y, and y. by applying Eq. 7 locally toP–x, curves, P and x, values above and below thepressure at which activity coefficients are desired aresubstituted into Eq. 7, and two equations are solvedsimultaneously for Y*and YE.Total pressure over aternary mixture is given by Eq, 8, where the sub-scripts 1 and 5 refer to methane and nitrogen, respec-tively, and the subscript j is equal to either 2, 3, or 4,referring to ethane, propane, or n-butane, respectively:
P = y,x,Po, + y,xJPo, + yjxjPoj ., . j =2, 3,4
. . ..$ . . . . (8)
At the low temperatures involved in this study, thevapor pressures of ethane, propane, and n-butane arenegligible. The third term in Eq. 8 is therefore setequal to zero. Solving for X5and x,:
x, = (P – y,xlPo,)/y,Po, . . . . (9)
Xj =l– X,-X,. . . . . , . (lo)
To compute an equilibrium ternary composition fora mixture containing methane, nitrogen, and eitherethane, propane, or n-butane as the third component,at a fixed temperature and pressure, mole fractionmethane xl is assumed; y, and y~ are assumed equalto the binary mixture methane and nitrogen activitycoefficients at that temperature and pressure; and X6and Xjare calculated from Eqs, 9 and 10, respectively.
If mixture composition is known, gas gravity maybe calculated, Gas gravity is defined as the ratio ofgas density at 60F (520°R) and 1 atm to the densityof air at the same conditions, 0,001224 gm/ccc:
G = %/~air= =/0.001224 . . . (11)
The ideal gas law is assumed for the gas; and 1 atm,52001{, and the ideal gas law constant are substitutedinto the equation:
G = PM/O.001224RT = 0.03449M
= 0.03449xt xiMi . . . . . . (12)
To calculate liquid density from composition, ex-cess specific volumes are utilized. The excess specificvolume, ‘cc/gin, of a binary mixture is equal to actualspecific volume minus ideal solution specific volume:
Ternary mixture excess specific volume is assumedequal to the weighted average of the excess specificvolumes of the two methane-containing bkary mix-tures at the same temperature and weight fractionmethane:
Ternary density is calculated from pure componentand binary mixture densities:
pl:j:fi= 1/vl,j,5 = I/(;I/p, + 2j/pj + :,/p.
+ VE,:j:J. ..j =2,3,4 . (15)
Ternary mixture compositions, gas gravities, andliquid densities, at fixed temperatures and pressures,may therefore be calculated from Eqs. 9, 10, 12, and15, respectively,
Description of EquipmentTheexperimental apparatus consisted of three majorparts: a glass equilibrium cell, a low-temperature airbath, and a constant-temperature injection box. Thelast two parts were built by Sinor and were discussedin detail elsewhere.7*sThe Pyrex glass equilibriumcell had a volume of approximately 100 cc. Liquidvolume in the cell was determined with a cathetome-ter, and cell pressure was read with a mercury man-ometer in inches of Hg to the nearest 0.1 in. Tem-peratures in the low-temperature bath were measuredand controlled to within Zk0.02°C with a platinumresistance thermometer.
An experimental fluid was injected into the equi-librium cell by a positive displacement piston pumpat a known temperature and pressure. The injectedmass was calculated from the volume displaced bythe pump and from volumetric properties of the fluidat the pump temperature and pressure. For binarymixtures, two mixture mmponents were injected intothe cell separately. For the five-component systems,gaseous mixtures were injected into the cell, The massand volume of the vapor phase inside the ce!~werenegligible in comparison with the liquid phase. How-ever, a correction was made for vapor mass whencalculating experimental liquid densities,
An error analysis showed that the maximum ex-pected experimental error in pure component andbinary mixture liquid density measurements was+0,5 percent; the maximum expected experimental
TABLEI—LIQUID DENSITY OF PURE GRADE METHANEComposition: 99.39 mole percent CH,, 0.08 moie percentC,H,, 0.53 mole percent N,. Gas Gravity = 0.5559
In! Hg
.120!0-175,0-170.0-161.7-160.0
1;:;17.835.539.0
ExperimentalLfqu~,yl ty
. .
0.44920.4430:.:;;:
0:4213
Calculated Liquid Oensl ties, 9 Icc
Thi? Hmens’ Lyckman’sCorrelation Correlation CorrelationP %dev p %dev D %dev
error in the five-component experimental densitieswas *2.0 percent,
The hydrocarbons used in this work were obtainedfrom the Phillips Petroleum Co. They were analyz~dfor composition by gas chromatography. The chro-matographic analyses are given in Tables 1 through 3for pure grade methane, pure grade ethane, and instru-ment grade propane. No impuriti= were found in theinstrument grade n-butane that \ .s used in the five-component mixtures. The analyses are accurate to1.0 percent of the minor component concentrations.Water vapor and carbon dioxide were removed from
the hydrocarbons by passing them through phos-phorus pentoxide and ascarite drying tubes.
High-purity dry nitrogen was obtained from theLinde Co. The nitrogen had a guaranteed purity of99.995 percent and a moisture content of less than15 ppm,
Presentation of DataExperimental liquid densities and pressures are givenin Tables 1 through 7 for pure grade methane, puregrade ethane, and instrument grade propane; formethane-ethane, methane-propane, and methane-
TABLE 4-LIQUID DENSITY OF METHANE.ETHANE MiXTURESother Components: 0,01 mole percent C,H,,0.51 11’IOle13@rC@IItN,
nitrogen binary mixtures; and for three five-compo-nent mixtures, After these data were combined withdata from other sources~’0 equations were derivedfor saturated liquid density (gin/cc), as a functionof temperature (degrees C), for methane, ethane,propane, and n-butane:
Pf =A,j+A,j~+~,j~’,.cj=l,z,3, 4
. . . . . . . . . . (16)
The constants A,J, A,J, and A,j were determined bythe method of least squares. The constants and theirapplicable temperature ranges are given in Table 8.In developing the gas gravity correlation, the densityof pure liquid n-butane was extrapolated below itsfreezing point to – 175C, Equations were also de-rived for the density of binary m“xtures (gin/cc), asa function of temperature (‘C), and mole fractionheavy component, xj, for the composition range Oto 0.10 mole fraction heavy component.
pl:j= 0,0329 -33.548 “ 10-4T – 5,8381
● 10-6T2-t- /4.!jXj + ~@2j
+/lGjxsj. ..j =2,3,5 . . . (17)
Applicable temperature ranges and the least-squaresconstants A+j, A,~, and A Ojare given in Table 9, AtXj = O, Eq. 17 reduces to the equation for puremethane density as a function of composition.
Additional data used in this study were pure liquidnitrogen densities from the International Critical
Tables’z and excess specific volumes of methane-rz-butanemixtures from Shana’a.1°Eq. 18 was derivedfrom data of Shana’a.:
V@l:,= –6.0419x4/M . . . . . . (18)
Derivation of CorrelationAfter equations were established for computing ter-nary compositions, gas gravities, and liquid densities,a computer routine was developed to find LNG den-sity as a function of gas gravity at desired tempera-tures and pressures, To illustrate the routine, an ex-ample will be given for —175C and 30 in. Hg.
The P–x5 plot used for finding binary mixtureactivity coefficients for methane and nitrogen is shownin Fig, 1. At - 175C and pressures of 28 in. Hg and32 in. Hg, corresponding x, values are 0,0651 and0,0536, respectively. These pressure and compositionvalues, together with POl = 7.6 in. Hgll and P“b=198 in. Hg,’2 are substituted into Eq. 7. The resultingtwo equations are solved simultaneously to obtainyl = 1.231 and y. = 1.804.
The binary methane-nitrogen mixture at – 175Cand 30 in. Hg contains 0.9407 mole fraction methaneand 0.0593 mole fraction nitrogen, as shown in thefirst row of Table 10. Gas gravity and liquid densityfor the binary mixture are calculated from Eqs. 12and 17, respectively, and are entered in the last twocolumns of the table. To form the first ternary mix-ture, the methane mole fraction is arbitrarily reduced
OL I 1 1 ! t
o 0.02 0.04 0.06 0.08 0.10
MOLE FRACTION NITROGEN
IN LIQUID PHASE
Fig. 1—P vs X, methanemltrogen system.
JUNE, 1969 687
to 0.9357; and x, and x, are calculated from Eqs. 9and 10, respectively. Gas gravity and liquid densityfor the ternary mixture are calculated from Eqs. 12and 15, respectively, and are entered in the last twocolumns. The third component is changed successive-ly to propane and n-butane, and gas gravity andliquid density are computed for these mixtures, Thisprocedure is continued down and across the table toa methane mole fraction of 0.8707, using yl = 1.231and yo = 1.804 in all cases. By varying ternary com-position in this reamer, pressure is maintained at 30in. Hg, and gas gravities and liquid densities are ob-tained over the widest possible LNG range. Themethod of least squares is then applied to the last twocolumns of Table 10 to find an equation for LNGdensity, lb/cu ft, as a function of gas gravity at– 175C and 30 in. Hg; standard deviation is 0.083lb/cu ft :
pLKO= 10.840 -t 30.939G . . . . (19)*
A linear equation similar to Eq. 19 was derived foreach pressure and temperature covered by the cor-relation, LNG densities were computed from theseequations at gas gravity intervals of 0.005, beginningwith the gas gravity of the methane-nitrogen binary
●The constants in the type of Eq. 19 can be obtained from theauthom upon request,
densities are Iistd- in th= c&relafion of Tables 11through 16, from which LNG density can be foundby linear interpolation.
ConclusionsIn Tables 1 through 7, experimental liquid densitiesare compared with densities predicted by the gasgravity correlation, Tables 11 through 16, and withdensities calculated from the correlations of Harmensand of Lyckman, et al. The six gas gravity tables werelinearly extrapolated for data outside their tempera-ture and pressure ranges. Much of the data were takenat reduced temperatures less than 0.560. To applythe correlation of Lyckman, et al., for T, <0.560,the generalized functions v,(o), v~fl), and v,(z) wereplotted vs T, and extrapolated below T, = 0,560 toT, = 0,250. Extrapolated values of v,(~) were usedfor T, <0,560, and Eq. 4 was used for T, >0.560.
Liquid densities determined by the three correla-tions, p,,],, are compared with experimental densities,P.SXP,by computing percent deviations:
percent dev = [(PW – Peal .)/pcalcl(l00 percent)
. . . . . . . . (20)
Percent deviations for the correlations are given in
TABLE 11—LNG DENSITY,LB/CU IT, As A FUNCTION OF GAS GRAVITY ANDTEMPERATURE AT A PRESSURE OF 20 IN. Hg
Tables 1 through 7. The greatest deviations are shownin Table 7 and are for the five-component systems.In this table, the maximum deviation of the gas gravi-ty correlation from the data is +2.71 percent, Thecorrelations of Harmens and of Lyckman et a/. givemaximum deviations of +1.57 percent and +3.42
percent, respectively. On the basis of the expe$-mental results, Harmens’ correlation is the more ac-curate of the two procedures tested for calculatingLNG density from its composition.
The gas gravity-LNG density tables are accurateto approximately 3 perwmt for LNG mixtures con-
TABLE 12—LNG DENSITY, LB/CU F?, AS A FUNCTION OF GAS GRAVITY ANDTEMPERATURE AT A PRESSURE OF 25 IN. Hg
tainkqj 85 to 90 mole percent methane. The tablesare accurate to within 1 percent for higher methaneconcentrations. The correlation is based on a limitedamount of experimental data and could be improvedas more data become available. The effect of carbondioxide and pentanes on LNG density is one areathat needs study.
The gas gravity-LNG density correlation requires
three LNG measurements: temperature, pressure, andthe gas gravity of gasified LNG. The correlation cov-ers the temperature range – 175 to – 162C and theabsolute pressure range 20 in. Hg to 45 in. Hg. Sinceneither a composition analysis of the LNG nor time-consuming calculations are involved, the tabular cor-relation can be quickly and reliably used by the manin the field.
TABLE 14-LNG DENSITV, LB/CU FT, AS A FUNCTION OF GAS GRAVITV ANDTEMPERATURE AT A PRESSURE OF 35 IN. Hg
16and 17empirical density constantgenerali=d density functiongas gravitygas density at 60F and 1 atmmolecular weightpartial pressuretotal pressurevapor pressureideal gas law constanttemperaturecritical temperaturereduced temperaturemolar volumecritical molar volumereduced molar volumefunctions of reduced
temperatures~ecificvolume
VE = eicess specificvolume‘ps = ideal solution speeificvolume
AcknowkdgmentsThis investigation was supported by National ScienceFoundation grant No. NSF GK-705. Financial sup-port through a.-DowChemical Co. Fellowship is alsogratefully acknowledged. The facilities of the U. of
JUNE, 1969
Kansas Computation Center were used for computercalculations.
References1.Harmens, A.: “Orthobaric Densities of Liquefied Light
4, Chueh, P. L, and Prausnitz, 1. M.: “Vapor-Liquid Equi-libria at High Pressures: Calculation of Partial MolarVolumes in Nonpolar Liquid Mixtures”, AKhE J. (1%7)13, No. 6, 1099.
5. Lewis, G, N, and Randall, M.: Thermod namics, 2nd1’Ed.. McGraw-HilIBook Co., Inc.. New Yor (1961) 233,
7. Sinor, J. E.: The Sohib~lity, Part!al Molat Volume, andDiffusivity of Helium in Liquid Methane, PhD disserta-tion, U, of Kansas, Lawrence (1965).
8. Jeneen, R. H.: An Experimerftal and Theoretical Studyof the Density of Liquefied Natural Gas, MS thesis, U. ofKansas, Lawrence (1967).
9. Rossini, F. D., et al.: Selected Values of Properties oHydrocarbons and Related Compounds, API Resmrc1Project 44, Carnegie Institute of Technology (1958).
10.Shana’a, M. Y.: Liquid Density and Excess Volume ofLight Hydrocarbon Mixtures at - 16S.OC and at Satura-tion Pressure, PhD dissertation, U. of Oklahoma, Nor-man (1966).
11, Matthews, C. S. and Hurd, C. O.: “Thermod amicrProperties of Methane”, Trans., AIChE (1946) 4, 55.
12, International Critical Tables, VOI.3, McGraw-Hill BookCo., Inc., New York (1928) 204. JPT
Orlglnal manuscript received In Society of Petroleum Englneeraoffice July 19, 196S. Revised manuscript received March U, 1969,Paper (SPE 2351) was presented at SPE Regional Gas TechnologySymposium held irr Omaha, Nebr., Sept. 12.13, 196S. @ Copyright1969 American Institute of Mlnlng, Matallurgloal, and PetroleumEngineers, Inc.
