1、GPA TP-3 73 3824677 0030739 578 1812 First Place Tech nical Publication TP-3 A Model for the Precise Calculation of Liquefied Natural Gas Densities Tulsa, Okla. 74103 M. A. Albright Phillips Petroleum Company Bartlesville, Oklahoma June, 1973 Phone: 9181582.5112 GPA TP-3 73 IPI 3824699 OOL0740 2T =
2、I FOREWORD The impending energy shortage has created a need for accurate liquefied natural gas density data. They are particularly nceded by those companies involved in the manufacture and/or transportation of the commodity. A correlation and computer program to calculate accurxe LNG deiisities was
3、recently developed by M. A. Albright, Phillips Petroleum Company. One of the convenient features of this program permits the easy insertion of new and more accurate experimental data as they become available. This program yhould be a bcneficial and worthwhile tool for the LNG industry. The Natural G
4、as Procesiors Association grate- fully acknowledges thi5 substantial contribution of time and effort bs. Mr. Albriglit ;id the release of this material by his company, lliillips Petroleum Com pan y. Bart les v il le, 0 k la homa. The publication of this material i5 part of ;I continuing effort by NG
5、IA to provide, for industry use, the latex experimcntnl dxa rind desigr, tech- nology. Such publicsition docs not constitute an endorseinent of either tlie data or the methods con- tiiiicd lierein; the publication may bc used by anyone desiring to do so, but neither NGPA nor Phillips Peti-olcum C.om
6、pany dl be held responsible or liable in my way for any los or drimagc that may result thcref roni. GPA TP-3 73 W 3824699 OOLO74L 126 A MODEL FOR THE PRECISE CALCULATION OF LIQUEFIED NATURAL GAS DENSITIES i M. A. Albright Phillips Petroleum Company GPA TP-3 73 W 3824b99 O030742 Ob2 . A MODEL FOR THE
7、 PRECISE CALCULATION OF LIQUEFIED NATURAL GAS DENSITIES A model which will reproduce the most accurate densities available for Liquefied Natural Gas mixtures is presented. to give the precision needed for custody transfer accounting. It is intended The model is based upon a cell model developed by E
8、ckert, Renon, and Praucnitz(1) with unsymmetrical binary interactions that are tempera- ture dependent as recommended by Yuan(2). by corresponding states based upon the liquid ethane densities measured by Pai(% The pressure dependence is As presented, the model will give high precision liquid densit
9、ies for pure components and mixtures of nitrogen, methane, ethane, propane, i-butane, n-butane, i-pentane, n-pentane, neopentane, n-hexane, ri-heptane, n-octane, n-nonane, n-decane, carbon dioxide, hydrogen sulfide, and water. The values are accurate up to 60 atm. for pure component reduced tempera-
10、 tures up to 0.99 and for mixtures with reduced temperatures below 0.90. The model, as presented, gives highly precise densities for those components where data are available. needed and will be available as a result of a joint industry-sponsored research project at the National Bureau of Standards
11、Cryogenic Laboratory at Boulder, Colorado, better binary interactions to be evaluated and introduced into this model. However, more binary data are As these data become available, they will allow GPA TP-3 73 3824699 0010743 TT9 Page ii 2 1 A (Continued) Part 2 of this report will deal with the densi
12、ties of Liquefied Petroleum Gas mixtures. near critical or supercritical components such as ethane are a special case as compared with Liquefied Natural Gases. These mixtures which contain large quantities of GPA TP-3 73 E 3824b77 0030744 735 Purpose of the Research The purpose of this research was
13、to develop a liquid density model which would calculate light hydrocarbon liquid densities within the repro- ducibility of the most highly precise experimental values available. Phis model can then be used to calculate densities for the sale or custody transfer of light hydrocarbon mixtures, LPG, an
14、d LNG. For those mixtures, at the temperatures and pressures normally encountered in industry, the assumption of additive volumes is not a valid assumption. higher than the actual mixture volume. the infinite number of possible compositions of the mixtures is impossible, the ability to predict densi
15、ties to high precision is required. The volume estimated by that assumption may be as much as 7% Since measurement of the densities of A point worth noting in sale and custody transfer is that if the densities used are biased for or against the buyer or seller, that bias will not even out but will r
16、emain for the life of the contract. This is in contrast to the long-term averaging of measurements by properly calibrated volumetric flow meters. Characteristics of the Model The model proceeds as follows in its calculations: First, the hypothetical zero pressure liquid density partial volumes are c
17、alculated. Then those volumes are integrated in pressure to the requested pressure. The mixture volume is then calculated using the partial volume at pressure. The absence of any phase calculations in the model relieves the user of the need for calculation of highly precise bubble points. Since liqu
18、id GPA TP-3 73 3824699 0010745 871 Page 2 compressibilities are low, a small error in the estimated bubble point pressure will have no significant effect upon the densities calculated by this model. The parameters in the model are as complete and as accurate as presently available high precision den
19、sity data permit. precision binary data exist, the interaction parameters have been estimated by the use of less precise mixture data such as those of Klosek and McKinley(7). at the National Bureau of Standards Cryogenic Research Laboratory at oulder, Colorado. Where no high A joint industry-sponsor
20、ed research project is in progress As that project develops new ddta, the interaction prameters in this model can be modified to reflect the better information. Derivation of Equations In 1967, Eckert, et al.() published a molecular thermodynamic This model was applied for the calcu- nodel based upo
21、n the cell theory. latior, of excess properties of mixtures. If one takes their basic set of equations for a mixture at zero pressure, the density of a mixture can be calculated by the following sets of equations: where and Y T. rn -1 m Vi - -u3 Vi, and and Sim Eim (4) (51 GPA TP-3 73 ea 3824699 00L
22、074b 708 The energy interaction, the coordination number, and the cell probability for the components in the mixture are found by solving simultaneously: .? E. = 2 Pj cij lm j=i i 2 i, j=i 2 PjC2 Jm xi s, P: = U? i ci = - U?krypt on R Tkrypton c. 1 = hi Eckert, et al. proposed the mixing rules a, =
23、) and GPA TP-3 73 3824699 0030747 644 In investigating the use of this model for calculating liquid density, it was found that there was temperature dependence which was not being described, of Yuan(2). Therefore, the mixing rules were modified after the manner This gives the following and wnere the
24、 four As are constants determined from data and Finally, when the pressue dependence of the model of Eckert, et al. nas tested, it was fouid to be generally good, but not of the high precision which was the goal of this work. approach was applied. University by Pal and reported by Pope(3) were chang
25、ed to reduced form and Therefore, a correspondicg states The data on liquid ethane densities measured at Rice then curve-fitted to high precision. differentiated to give The resulting equation was then This equation is used to calculate the change in density from zero pressure to the actual pressure
26、 at the same temperature. given here do occasionally fail at TRl for light supercritical components. The equations are given in Appendix 1 (lines 499 to 529). The initial equations as GPA TP-3 73 H 3824699 0010748 580 Page 5 Pure Component Near Critical Densities The model as originally developed wa
27、s not intended to and does not follow the behavior of liquids as the critical temperature i3 approached. However, it was discovered that the model will indeed follow near critical behavior of liquids with only a modest change. If the R: in equations (7) and (8) are replaced by a function of temperat
28、ure which, in effect, reduces the number of neighbors in the cell as the temperature approaches critical, then the cell model will follow real liquid behavior. This function of temperature was empirically determined by calculating R; using the most accurate pure component data available. The data fr
29、om which the corresponding states equation was developed are shown in Figure 1. As can be seen fromthe graph, departure from the cell model occurs at a reduced temperature of about 0.8375 and RT decreases from 1.0 to about 0.675 at the critical temperature. This has the effect of reducing the number
30、 of neighbors in the cell from 10 to 6.6. 470) Results of the Research The equation fit to the data is given in Appendix 1 (lines 451 to The results of the model are shown in the following tables. The capabilities of the model as presently constructed are : Reduced Temperature .* IYd9 33 n a L VIX O
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