789f175f9f0f75edd0a7b4c4c766fb14

Tq yi yi,j = activity coefficient of component i in general = absolute temperature = mole fraction of component i in solution u = solute species = yiF yiR Superscripts 00 activity coefficient of component i in the i binary = factor defined by Equation (34) or (56) = factor defined by Equation (23) -i LITERATURE CITED ’ s = = = unsymmetric normalization of activity coefficients value at infinite dilution value for solute-free mixture solvent species Abrams, D. S., F. Seneci, P. L. Chueh, and J. M. Prausnitz, “Thermodynamics of Multicomponent Liquid Mixtures Containing Subcritical and Supercritical Components,” Ind. Eng. Chem. Fundamentals, 14, 52 (1975). Prausnitz, J. M., and P. L. Chueh, Computer Calculations for High-pressure Vapor-Liquid Equilibria, Prentice-Hall, Englewood Cliffs, N.J. (1968). Van Ness, H. C., “On Use of Constant-Pressure Activity Coefficients,” Ind. Eng. Chem. Fundamentals in press (1979). Manuscript received lanuaty 2, 1979; revision received April 3, and accepted April 18, 1979, Subscripts = A New Correlation for Saturated Densities of Liquids and Their Mixtures RISDON W. HANKINSON A new correlation has been developed for the densities of saturated liquids and their mixtures. The correlation is relatively easy to use and is applicable to a wide variety of liquids. The saturated liquid density correlation is flexible and consistent and requires only reduced temperature, acentric factor, and a characteristic volume for each pure compound. Mixing rules are given. When tested against a data base of 2 657 points of pure compound liquid density data for 97 hydrocarbons and 1 851 points for 103 other compounds, the new correlation gave an average absolute error of 0.37% compared to 2.14% for the Yen-Woods correlation and 0.50% for the SDR equation as modified by Spencer and Danner. For 2 994 points of liquid mixture density data for 167 mixtures, the new correlation gave an average absolute error of 1.40% compared to 5.64v0 for the YenWoods correlation and 2.95% for the SDR equation. Characteristic volumes are listed for 200 compounds; they are generalized as functions of acentric factor for various types of compounds and are compared to critical volumes. and GEORGE H. THOMSON 308 TRW Building Technical Systems Development Phillips Petroleum Company Bartlesville, Oklahoma 74004 SCOPE The objective of this work was to develop and extensively test an equation for the computation of saturated liquid densities of pure compounds and their bubble point mixtures that has the following attributes: sufficiently general to apply to a wide range of compound classes, flexible enough to allow accurate calibration to known pure compound data, predictive in those cases where such data are unavailable or of uncertain accuracy, mathematically consistent in that there are no discontinuities in the value or slope in the range 0.25 < T R < 0.98, capable of being calibrated to mixtures for precise work, and simple enough for inclusion in process simulators and on microprocessors. In order to provide extensive testing and evaluation, it was necessary to develop an experimental data base representative of the wide variety of compounds and mixtures of interest. CONCLUSIONS AND SIGNIFICANCE A corresponding states equation which explicitly relates the saturated liquid volume of a pure compound to its reduced temperature and a readily available parameter, termed the characteristic volume, has been developed. The characteristic volumes are reported for 200 pure compounds. An evaluated set of mixing rules is presented. 0001-1541-79-2349-0653-$01.25. 0 The American Institute of ‘Chemical Engineers, 1979. The saturated liquid volumes obtained from the corresponding states liquid density (COSTALD) equation reproduce 4 508 points of experimental data on 190 different compounds to within 0.375 average absolute percent over the reduced temperaturc range of 0.25 < T R < 0.98. For 141 binary systems, 13 ternary systems, and 13 higher multicomponent systems, the 2 994 calculated densities agree with the experimental data to within 1.39 percent. For the 2 069 points of data on hydrocarbons and hydro- AlChE Journal (Vol. 25, No. 4) July, 1979 Page 6S3 A correlation for the saturated liquid densities of pure compounds and their mixtures that satisfies the majority of these requirements has been developed. McCarty. 1 3 0 3 data points for other organics. CORRELATION STUDY An extensive literature search was performed to locate saturated liquid density data on both pure compounds and their bubble point mixtures. we attempted to use the desirable features of the three general purpose correlations recommended by Spencer and Danner (1972) and to eliminate the least desirable ones. Yen-Woods The Yen-Woods (1966) equation is vc/vs = 1 -I. These models are not predictive. No mixing rules other than those proposed by Yen and Woods (1966) have been tested. and Rackett (1970) were the best. The supplement contains the complete reference list for the data base. In these cases.000Zc2 + 641. 1979 AlChE Journal (Voi. DATA SOURCES tions of Yen and Woods (1966). 1974. Mollerup and Rowlinson.214. Available data sets on the mercaptans. Diller.26%* A generalization of the experimentally based characteristic volumes is presented as a function of acentric factor for each class of compound studied. and are not general purpose in formulation.63772c + 107. all data included in the final data base were obtained from the original sources. The thirteen correlations studied included those demonstrated by previous review papers to be superior and those techniques published since the earlier reviews.1% when the generalized functions are used for pure hydrocarbons.211Zc3 if Zc 6 0.93 .5 to 6. 4) . 1976. the average error was 1.996 discontinuity between Equations (3) and ( 4 ) at Zc = Page 654 July. This improvement was subsequently included in the American Petroleum Institute Technical Data Book-Petroleum Refining ( 1972). Albright. thus allowing reasonable discrimination among the data sets.950/0. 1968. convergence properties. the correla- Spencer and Danner (1972) have shown that Equation (1) represents pure compound data very well if specific values of A and B for each compound are used. sulfides. 1974). are limited in scope because of the temperature range or type of compounds for which they may be used. be accurate and reliable. These generalized forms must be used in conjunction with pseudocritical mixing rules in order to use Equation (1) for mixtures. Hence. 1977. of course. Additional experimental data were also obtained on several heavy hydrocarbons of general industrial importance. In addition. Yu and Lu.28257 + 13. Function continuity is important because the presence of a discontinuity in the volumetric property can.26 (3) B = -3. Their study and development was based on 3 595 points of pure compound data on sixty-four hydrocarbons. the agreement is within o. evaluate the results of using the generalized forms of A and B as given by Equations ( 2 ) . new and independent experimental data were obtained.578Zc + 9 8 9 .48442c' + B = 60. the average absolute error in the estimation of critical volume was 1.26 (4) Spencer and Danner (1972) presented a critical review of thirteen correlations for predicting the effect of temperahire on the saturated liquid densities of pure fluids.402. The results obtained with this new correlation are compared with those obtained using three well-known correlations. Gunn and Yamada (1971). Reported values which were obtained from charts or nomographs and those which were derived by extrapolation or predictive techniques were excluded from the data base.T R ) l 1 3 + B (1. cause difficulties in process calculations. It must also. the optimum parameters required for its use were obtained for 200 compounds. they significantly improved the Rackett equation.T R ) ' 1 3 + (0. it must be predictive. and 2 994 points of data for 167 mixtures. For the forty-three hydrocarbons included in this set. Simplicity. I n addition. Spencer and Danner demonstrated that of those general purpose correlations based on readily available parameters. and function continuity become very important if a correlation is to be used in a process simulation or a flow computer. in substantial disagreement. 25.06Zc3 (2) -384.B) ( 1 . Of particular note are the models developed for LNG applications (Klosek and McKinley. and eleven inorganics. This adds an ad&tional predictive feature to the correlation.2091 . No. and 548 data points for inorganics.64y0. The final data base used to develop and evaluate the new correlation consisted of 4508 points of saturated liquid data for 190 pure compounds.4425 . and ( 4 ) .0632~ 501. however. or present significant size and convergence problems. (3). short computation times. in turn. in some cases. We find errors of 1. The pure compound data set included 2 657 data points for hydrocarbons. With few exceptions.A ( 1 . most often for LNG and LPG calculations. 6 2 5 2 ~~ 1522.TR)4'3 (1) where A and B may be determined as specific constants for each compound or may be obtained from generalized functions of Zc: A = 17. and disulfides were. A useful.0302~~ if Zc > 0. general correlation of the volumetric properties of liquids must be applicable to a wide variety of liquids including those for which no experimental data exist. The more important correlations published during or since the study by Spencer and Danner (1972) were developed for specific applications. thirty-six other organics. In the LNG and LPG ranges. AVAILABLE CORRELATIONS In developing this new correlation. The equation is demonstrated to be suitable for the vo'umes* Of the estimation Of Pure seventy-seven fluids tested.carbon/nitrogen mixtures. there is a 3. They did not. emphasis was given to data obtained from cooperative industrial and industrialgovernment research efforts which have been published in recent years. 1973. the equation may be calibrated with the known value VREFand used over the entire valid range of the equation in this form: July.) . 2. .0 vsc U s ) VSC (8) (9) V s=~Tc/P3ZRA[1+(l-T~)*/'1 (5) = v 0 . No.98.80 6 < T R < 1.260 0.0 '0' -12. Slope of the Yen-Woods "B" function.e is a known saturated liquid molar volume at a reduced temperature of 0. Gunn ond Yamada The correlation of Gunn and Yamada (1971).91534 (1. Equation ( 6 ) will give the correct limiting result only in the rare instance where ZRA = 2.09045 T R .0 (11) R ~ (12) The quantity Vo.200 ZC 0.C 1 .240 0.T R ) .T R ) % loglo (1. The SDR equation is simple and is accurate if experimental values of ZRA are used. 6 This equation is referred to as the SDR equation in this paper..0. the Zc of the mixture will cross the 0. These are shown in Figures 1 and 2. 1. is given by The equation developed by Rackett (1970) and modified by Spencer and Danner (1972) is vs = VR(O)(1.240 0.0 -4. Modified Rocketf Thus.3 (1 . the advantage of the accuracy obtained by using ZRA instead of 2.0 + 1. will be lost.2 to 0. which is claimed to be valid over the reduced temperature range of 0. ZRA is a unique constant for each compound and must be determined from experimental data if the reported accuracy of the equation is to be obtained.3862 .02512 T R 3 + 1. Plot of the Yen-Woods "B" function. ZC Fig.50879 (1. and where Vc is based on T.51941 T R ~ ..0 -8. to Equation ( 5 ) results in ~ 0.0 4 .26 which is accompanied by a sharp change in the slope of the curve. (RTCZRA/PC)t V C t (7) 0.260 I 0.11422 T R ~ if 0.33953 TR .0866 w VR'O)= 0. The ratio of Equation ( 6.1. This problem would be encountered in a process simulation of a mixture containing both light hydrocarbons through the octane range and heavier hydrocarbons.20.0. When the composition of the mixture changes.0.04842 T AfChE Journal (Vof.0 0. as the limit of composition approaches a purl compound.C 16. and Z. 1979 = 0. Hence.60 0. P .T R ) .200 Fig. 1972). If no data are available.0 I 0.33593 .20 < T R < 0.6. 25.0.0.2.26 value. If an experimental value is known at some other temperature TREF.O 0. 4 ) Page 655 . Zc may be used as an estimate of ZRA.T R ) ~ if 0.oo I as 3% YEN-WOODS 12.29607 . A disadvantage is the error introduced by the mixing rules given by Spencer and Danner (1973) and included in the American Petroleum Institute Technical Data Book-Petroleum Refining (chapter 6.0. The molar volume of a liquid mixture at its bubble point is given as where Vcm is obtained by the blending of pure compound critical volumes.80 (10) VR(O) = 1. 75 - The model is linear in acentric factor and contains the product of the spherical molecule function VR'O) and the function V R ( ~ to) represent the deviation function V R ( ' ) . A 1% error in the value of V.70 I 0.T R ) f d ( 1.( 1 -C c)[l+(l-Tfi)Z"l } and 4. The Gunn-Yamada equation also has an apparent advantage over the classical linear corresponding states form of Curl and Pitzer (1958) : V R = VR'O' Based on the analysis of the three correlations.95 1 + U(1 (17) In the Gunn-Yamada correlation.This is demonstrated by an error analysis in which a fractional error E is imposed on the best value of ZRA.80 I R 0. the deviation function VR(~ is )the product of VR'O)and 6. This product allows the use of a simpler mathematical function for the representation of 6 as a function of reduced temperature than is possible with V R ' ~However. Plot of the Gunn-Yamoda V R ( ~function.W SRKVR'"] ( 16) + W VR") (15) VRc6) . representing the value of the deviation function 6.43 TREF This correlation has the advantage of being dependent . the two portions of the VR'O) function [Equations (10) and (11)l when taken to a reduced temperature of 0. The SDR equation is. . also shows a discontinuity in that it does not approach zero as the reduced temperature approaches one. .79 0.64 -1.8642 1. EXPEC~ED ERROR IN MODIFIED hCKETT EQUATION (SDR) % error in V resulting from a -1.4249 % error = 100 (1 . Equation (12).4 0.00001) 0. 25.. No. This discontinuity is directly reflected in the calculated V s . The error in the computed saturated on neither V.938 1.460 101 aTR 0..7.6314 1.17 0. is required for each pure compound. however. result in a 1% error in the calculated Vs. The Yen and Woods form of Equation (1) 0.87 . more sensitive to the value of its adjustable parameter ZRA.2 0. the following model was proposed: vs = v R ' ' ' [ V" VRto) = 1 . Page 656 July.m 0. The resulting error in calculated volume is close to 2% at the lower reduced temperatures. will.78 -1. 0.50 0 .0% error in ZRA .465 0. The terms VR(~ and ) V R ( ~depend ) only on reduced temperature and are expressed by functions that contain no mathematical discontinuities.Y a m a d a V R ( * ) functioa.25 ' ~ < T R < 0.8.80 TR I 0.6 0.1.95 TABLE 1. assuming the validity of the corresponding states correlation.The resulting error in calculated volume is Exponent 1.Vs = (VREF) VR"' CI-W~I (13) TR 0.95 -1. 7/ I 0. ). CORRELATION DEVELOPMENT AND TESTING (14) Table 1 shows the sensitivity of the SDR equation to a 1 % error in the value of Z R A at various values of T R . called the characteristic voIume.25 < T R < 1.60 0.8 0.T R ) ' l 3 + b ( 1 .*55 - 0. 3.22% discontinuity in value and a sharp change in slope as shown in Figures 3 = [f? f f(TR) + gll'R2 + h T R 3 1 / ( T R . 4. 1979 AlChE Journal (Vol. A single adjustable parameter V'. ) Fig.83 Fig.70 0 .83 0.T R ) 2 / 3+ C( 1 . 4) .81 I 0 82 I 0.7697 1.0 (18) 0.78 I 0. nor Z molar volume is directly proportional to the error in the experimental volume used for calibration.445 0 140 0.T R ) ~ 0.1. m - 0.82 0.1. 5 0 - 0. Slope of the G u m .8 have a 0.40 0. No. while the characteristic volumes for two hundred compounds are given in Table 6. Spencer and Adler (1978) found that with revised parameters.23 0. the SDR equation gave slightly better results than the Gunn-Yamada equation and that the Joffe-Zudkevitch (1974) correlation gave poorer results than both the SDR and the Gunn-Yamada equations for hydrocarbons and organics. -1. The values of ZRA are given for most of the 200 compounds in Table 6. new values of ZRA were obtained from the same data sets used to develop COSTALD. COMPARISON is used to represent the spherical molecule function VR(*) over the entire range of reduced temperatures.95 0.141 -4. the fugacity of the liquid and the fugacity of the vapor.392 Cycloparffis Yen-Woods SDR COSTALD Albright Yen-Woods SDR COSTALD 1. and (18) and for the determination of the characteristic volumes.52 0.119 Sulfides 2. The table in the supplement also shows which data sets were used to obtain the parameters for both the SDR equation and COSTALD. since it was necessary to have the water correlation in a TABLE 3. Tables 3 and 6 show. and general acceptability of the O F PURE COMPOUND CORRELATIONS To insure an unbiased comparison between the new correlation COSTALD and the SDR equation. g.259 0. However.46 0. A limited data set containing values for 190 compounds was selected from the total pure compound data set of 4 508 points for the development of the parameters in Equations (16).62 0. C . but better results for associated liquids.200 Disulfides 2.592 0. d.738 organics 1.175 0. this form gives the correct value and slope at the critical point. the best set of acentric factors reported to date was published by Passut and Danner (1973) with some revisions by Henry and Danner (1978).119 Fluorocarbons 1.81446 0.52816 1.640 0. COSTALD is significantly better than the generalized Yen-Woods equation and generally slightly superior to the SDR equation. For similar reasons. b . This was done by a nonlinear minimization of the fractional errors between the experimental data and those values calculated from Equation ( 5 ) .296123 0. h.307 Acetylenes 3. but some of their values do not appear to be consistent and their tabulation does not include a number of compounds encountered in hydrocarbon processing.374 -0. which are given in Table 6 for 200 compounds. and.357 Summary all points Avg. 4) July.147 0.95 6. the original Yen-Woods correlation. both obtained from the Soave equation. An iterative procedure was used to find the value of acentric factor for each compound that minimized the fractional error between the liquid and vapor fugacities over the range of known vapor pressure data.43 0.181 0. must be equal.52 0.503 -0.21 0. where it applied. As observed by Lee and Kesler ( 1975). These values. The final correlation was obtained by a nonlinear regression of all of the selected data to minimize the fractional errors between the calculated and experimental molar volumes. absolute Bias percent 2.290 1.74 0.0480645 data in addition to a trial and error effort to determine the degree of internal consistency between available data sets for the same compound.188 0. the Albright correlation (1973) were tested against the entire 4508 point data set. The V R ( 6 ) function becomes asymptotic to one as the critical is approached. The parameters for Equations (17) and (18) are given in Table 2.49 1. SATURATED L X Q DENSJTY ~ RESULTS Tabular entries average absolute percent error between calculated and experimental Paraffins Olefins and diolefins 1. Lee and Kesler ( 1975) subsequently published a generalized correlation for acentric factor. 1979 Page 657 .386914 -0. in addition to the need to match pure compound vapor pressure data with the equation reported by Soave (1972).230 Solvents and miscellaneous 2.185 0.128 0. that for all pure compounds tested.TABLE 2.PAFIAMETERS FOR EQUATIONS ( 17) AND (18) a. The new correlation. although no polar compounds were used in their development. It was not possible to obtain an adequate fit of the pure water data with Equations (16).322 0. compare very well with those obtained from the Lee and Kesler (1975) correlation. e.125 AlChE Journal (Vol. gases Cryogenic liquids 2.179 Aromatics 3. we had previously developed a consistent set of acentric factors from current vapor pressure data using the Soave equation of state as the base correlation.54 0.06 0. At equilibrium. This selection was made based on the source.122 0. both the SDR and COSTALD correlations will fit such data reasonably well.190454 -0.502 0.08 0. A complete set of comparisons by each data set is given in the supplement and by each compound in Table 6. They also show that. In a review published after this work was completed.219 Other Yen-Woods SDR COSTALD 1.311 0. the SDR equation.911 0. f.70 Mercaptans 2. and (18). A summary of the results by class of compound is given in Table 3. age. (17).81 1.130 Albright Condens. 25.43907 -0. The acentric factor in Equation (16) was given the subscript SRK to denote the source of the values used. (17).368 0.609 Hydroxy compounds 3.25 0.0427258 -0.87 2. the SDR equation with mixing rules suggested by Spencer and Danner (1973). interaction parameters may.39 3.71 2. and (18) along with the parameters presented in Table 2 may be used with a single experimental datum point to obtain the characteristic volume and consequently the entire saturated TABLE 5. Of the rules examined. Tables 3.01 0. For pure water WSRK were used as adjustable V" = 43. No.65445 The temperature dependent criticals suggested by Prausnitz and Chueh (1968) were used for hydrogen and helium.95 At least one hydrocarbon and one nonhydrocarbon 572 pts. 25.45 1. Average absolute percent error 1. The use of Kay's simple additive rules (1936) to calculate critical properties of such mixtures lead to significant errors.09 0.45 -20. the best set of mixing ruies is suggested without the use of interaction parameters. The combinations of capital and small letters in the table headings indicate the combination of the three sets of Tcm. The results of this coniparison are presented in Table 5. and 6 reflect these adjustments for water.1 14. 4) . resulted in a higher error for the same set of rules for T. COMPARISON OF CORRELATIONS FOR MIXTURES = %f WSRKi Case Ba gave significantly better results for mixtures of nitrogen with hydrocarbons and hydrogen with hydrocarbons than the other combina- similar form.92 -2.42 bias bias 14.5669 cm3/g mole WRK = -0. and (24) was significantly better than the other rules. hydrogen. The COSTALD correlation exhibits both the lowest percentage error and the minimum bias in all four categories examined. Nonhydrocarbons 328 pts.13 5. be added for highly accurate work where sufficient precise binary data are available to justify their use.55 2. were evaluated. Alani.9 Page 658 July. MIXING RULES The values of any mixture property obtained from a corresponding states correlation are sensitive to the calculated pseudocritical constants of the mixture.15. The results are shown in Table 7. bias 70error 3. To improve the overall accuracy of CObTALD. It is significantly better than the SDR equation for the hydrocarbons and hydrocarbon/ nitrogen mixtures. (20). given in Equation (25). b.TABLE 4. the following combinations gave the most satisfactory results: The COSTALD correlation with mixing rules given by Equations (19). This is especially true for the wide boiling mixtures encountered in the petroleum industry.61 2.10 2. RESULTSOF THE EVALUATION OF MIXINGRULES B. For the general case. however. Hydrocarbon mixtures (Includes Nz) 2 069 pts. or C ) with the two sets of rules for the acentric factor ( a or b ) .6 -12. The set of mixing rules giving the minimum average absolute percent errors without the use of empirical interaction parameters was selected for use. SUMMARY OF M u r r u ~ ~ All data 2 969 pts. including Kay's rule. (21).05 .13.40 1.15. The set of rules designated as Aa and given by Equations (19). USE OF COSTALD A. In the development of the mixing rules. These are compared with the characteristic volumes listed in Table 6. T m = fixi V'i T d Z i x i V'i (22) Mixing rules case Aa Ab Bb Ba Cb Ca tions studied.8 .59 3. the characteristic volumes were treated as though they were the pure compound critical volumes.49 Correlation Yen-Woods SDR COSTALD % error 3. and helium. Equation (24). C. The volume average acentric factor.81 3.62 . CALCULATION OF CRITICAL VOLUMES Experimental critical volumes for 77 of the 200 compounds studied were obtained from the compilations of Kudchadker. 1979 AlChE Journal (Vol. both V" and parameters. 5. This approach insures that the limits of the correlation are the pure compound values and eliminates the necessity of using uncertain values of critical volume. 70error 2. (21). The results of applying these various rules to the mixture data are shown in Table 4. (17).96 2. B. and ( 2 4 ) .75 4. This set is recommended for use with COSTALD. and Zwolinski (1968) and Mathews (1972). numerous sets of mixing rules.15 V'm same as above T m = [SixiV'i (Tci)'h12/(2:~iV'i)' Om (23) (24) The acentric factors were blended in two ways: a. V"m rules (A. (20).39 bias % error 3. The majority of the characteristic volumes obtained are well within the expected error band of the critical volumes and suggest that the use of COSTALD with experimental saturated liquid density data is a very satisfactory method of estimating pure compound critical volumes. and the Yen-Woods ( 1966) correlation with pseudocritical constants computed as suggested by the original authors were tested against 2 994 points of liquid mixture data.40 2.50 2. and Vem than did the molar average acentric factor.95 -13. Tcm = ZiZj XiXjVij" T c i j Vm' (19) Vm" = 1/4 {Zi xiVi" + 3 (Z~iVi"2'~) (Zi ~ i V i " l 'I ~) (20) (21) Vij"Tcij = (V*i Tci V"j Tcj)" COSTALD as given by Equations (16). 1989 1.0478 .6192 .0690 .3876 .0004 .4-Dlisetl~ylpenta11e 3 . 2 ~ 2 .2611 .0982 .lo26 1.7546 2.0001 .0291 .0766 ( 2) .3644 1. 2 706 .9124 .1128 .ZYB~ .3866 1.5125 .2690 .2.0001 000 3 .9772 1.6155 .2527 .2656 .OY n6 .1962 .2388 .2477 .mi .2076 1.1946 . 2 m .2-0 h e t h y l p e n t a n e 2.2059 .3195 .3754 1.2677 .6865 .0410 . 2 m .1655 -2199 .1539 .4225 .1154 2.2701 . L-Oinrthylbutane 2.0369 (2) . 3-Disr t l i y l p rn t a n e 2 .I458 .5937 .2917 .2426 .3902 .mn .4 790 .2.006 . Acetylene Methylacetylror Dlnie t h y l a c e t y l ene 1-Mutyne .6455 1.a753 1.2175 .0009 .4323 .2311 .2940 .2692 .a655 .5116 ( 2) .2766 .2720 .2711 39 16 1 1 .3634 .5839 1.3905 .0 . J-Ulrurtliylprncanr 2-Hr t thy 1lieXdnr 3-Hrthy Iht-xaur 3-Etliylpeotrtnr 2.7282 1.2153 .2236 . 8 972 0.29ni .2658 .4975 ***DIOLEFINS*** .2733 . Volume litertmole ZRA No.mi5 .1421 .a791 .5no7 .JL43 .399M .1700 3.inn Propadirne 1.2164 (2) .5266 .2363 n 66 46 1 54 44 41 39 .3-Tecramechylbutane N-Nonane N-Decane N-Uadrcane N-Dudrcdne N-Trldccatir N-Te trdrlecanr N-Prntadecane N-Hexadrcanr N-llepcadrcsne N-OcLadrcane N-Nunadacme N-ElCOadLW Hrneicovme Uocorane Tricosane Te t raL'osdne Pentdcus&lr Hrxacoamr 0.4336 0.2738 .4127 .nm .0074 .2591 .1201 .7960 .5926 0.4752 .1609 .1430 .2546 1.2883 .4462 inn2 .in99 0.1204 .2707 102 162 0.1532 .5Y6tl .4163 .2791 .2690 .6340 .0473 .1921 .3136 .264 1 .1757 .2437 .1594 .0511 .1508 .7891 1.2302 -- --2 -3 2 .2214 .4327 .2725 .0926 .1310 in29 .3639 .000 1 (Cotlti?lued 011 w x t )luge) AlChE Journal (Vol.zn~g .2850 .1289 . m i .0579 n 5 22 .2709 .n317 .2608 . 4 l25 .66no ( 2) .2499 .0829 41 30 18 14 40 30 10 . 25.1964 . 1 208 1.J040 .3014 4.0002 .5272 .0539 1 .0 .0481 0000 .7 17 4 6 4 4 23 1 1 14 14 14 1.6642 3.2596 .2511 .2704 .311M .1232 . .goon 1.0514 .2584 .26Ml 2973 A310 .3507 .1615 .2684 .5422 .H r pt c n e l-Oc t r n e l-Nunene l-Decene .7636 .3927 1.2343 . 7 ~ 1.4505 .0505 1.8667 .3096 .4750 .7154 2.0004 .0953 (2) .ti455 ***OLEPlNS*** 0.0699 .2892 .a166 2.3126 .1380 .1975 .0606 6.2492 .2Y51 .2281 .3677 .0w4 .2741 .6013 .3633 .2765 .2418) .3682 .2am .2110 .om .on82 .0546 .mn .TABLE 6 SUMMARY 0P PAWETERS AND ERRORS FOR INDIVIDUAL COHPOUNDS AVERACE ABSOLUZ'B PERCENT WROR Ac e n tric P a c t u r (SRK) C h a r .2473 ( .4135 .2315 .2430) ( .2355 .1700 ***ACETYLENES*** .7550 1.0207 .2672 .3799 .2671 .0601 .?I333 .4231 .2671 .7558 .4119 1.0657 .4710 .1275 3.2571 .1962 .6958 1.U I _ ***PARAFFINS*** Mrthdne Ethaw Propane N-k'rdae I so b u t d n r N-Pentme Isopentaw? Neupentanr N-Hexaar 2-He thy l p m t a n e 3-He t I t y l p e n t m e 2 .0477 1.3996 .3835 .5529 .2202 .1155 .2275 . No.n715 -4 .2011 .2310 .2082 .2208 .9022 . .3.2-Bucadlrne 1.2049 .x12 .0014 .2736 .2377 .3007 .0569 .2U4 .7835 .7667 .0174 1.2652 1 16.2627 .2266 .2501 .2717 .2693 . 2 705 .20 39 .om .21y1 .4113 .3-Mutedieur 1.I825 .1959 .nm .3-l)iuietliylbutane N-Hep t d i i r 2.9518 8.573H .mn 0.3916 .1167 .4137 .1524 .2369 .0002 .060 I .447n .2513 .2J30 .0561 1.3610 .09939 .0695 . j-'~rimr t h y l b u Lane N-Qc tdne Isooccane 2.7254 .0966 .0986 .1760 .7775 .3559 .2077 1 18 1 1 .2684 .2727 .3045 . .7746 . of Data Points Yen-Woods SDR C0STAl.2714 4.7668 1.2870 .0851 .27M .2171 1.49 1 6 .2562 .0594 Et hy I r n e Propylenr l-Mucene Cl!I-2-Mutunr Trdns-2-Uutrnr lsubutrnc l-Pmtcnu Cis-2-Pentene Trdna-2-Prl~tellr 2-Me tltyl-l-Mu t e n e 3-Me t h y 1-1-Mu t r n e 2-~ethyl-2-Butene l-Hexenr l .3609 1.3113 .2399 .?n01 .1455 .200n .5619 3. 2 in 4 . 1979 Page 659 .2592 .6187 .om .4274 .2568 .2604 .3461 .8862 .2712 .92 39 1.2944 2.2620 .2654 (2) 12) 1.6501 1.3000 1.2522 .2765 .2350 .2684 .2875 .2(Lon .2-Prntadiene Isoprene .7104 1 .2543 .5885 .2779 .2739 .6821 .2635 .2429 .4099 1.2341 4 -- -.7225 5.4304 .2277 1.3592 .4 904 .2703 130 133 112 123 51 57 112 9 9 5 13 62 22 7 7 7 1.272n .4176 .3509 .3784 1.2y14 .0630 .3122 .2539 .2400 .6289 2.2411 .1444 (2) .949n HCptacOYdnr ~CLdCUSalle .2892 .4251 .2654 . 000 1 .5081 1.h471 1.1934 .2234 .2419 (2) .1131 (2) ( 2) .0602 1.goo 1 .2675 .2501 .2367 .0340 .9988 .2001 .0707 .2953 .2466 .9420 1 .2301 3.4925 .0316 1. O Y ~ .3412 .2149 . 4) July.1934 .2600 .4461 .0b03 .2546 45 72 53 9 31 35 .2 756 .8133 1.2754 .2715 1. 09802 .2312 .2080 .3702 .a162 .5441 .2128 .2322 .1605 .1982 .04 14 .2420 .1048 3.9865 1.nr 1-Trans-3-Dilluthylcyclopentane 1-Trans-2-Dlmeth ylcyclopentane 1-Cis-3-Dimrthylcyclopentane 1-Cin-2-Uiolrthylcyclopentene .5536 .0664 .2812 . .1650 .7659 .3030 .2305 .2757 .2644 . 2 704 .3397 1.2254 .0379 .2856 .2493 29 38 57 26 1.9290 7.0295 .1331 .2640 26 30 1.1735 .3370 .3126 .2355 (2) (2) (2) Air Helium Hydrogen Nitrogen Oxygen - .2676 .2502 .1834 .1390 .66 1.4799 .2102 .9952 2.2571 1.1958 .2373 .1825 2.9134 2.1852 .3784 .1436 . No.2768 .2137 .5817 3.1590 .2444 .1345 .04 38 .2569 104 46 43 1 21 5 1 10 2.2896 .1038 1.~~114 .1375 .2460 .3665 .8704 1.2771 .2698 .0472 .06423 .2722 .2592 .1871 .6401 2.lea0 .2978 .1637 .5921 1.9218 9.3090 .1922 .1602 .3916 9.6906 .1018 1.2768 . 3060 2900 * 1 1 20 .2815 ***NITBOGEN COMPOUNDS*** Apmnia Hydrazine .0382 .1305 .0913 . I ***CYCLOPWFINS*** Cycloproyane Cyclopeiitane Methylcyclopentane Cyclohexane Ilrtliylcyclohexane 1.0532 .1727 .1752 .4766 .2699 33 13 1 1 24 36 6 4 4 4 4 8.2324 .2663 .5496 .7928 .4594 .1699 .4702 .0782 .2041 .5662 .4977 .6026 2.0266 4.3216 .3149 ***CHLORINE AND HALIDES*** Chlorlne Hydrogen Chloride .2683 1A116 1.1610 .1456 1.2120 .3796 .2540 1.6119 1.2954 . 4) .2691 .2617 .ooo2 2.8873 (Continued on opposite page) Page 660 July.2434 -- -- 58 37 38 .3071 1.0822 .1668 .1917 .1-Dimetrhylcyclopent.1371 .2745 .4289 1.4406 .2255 1.1399 .2040 .2981 .3330 1.3216 .2625 .2768 .9675 1.1516 .09233 .2763 .3048 .3137 .2114 .2413 .0534 22.0443 .3118 .1747 .04357 .0002 2.2973 (2) (2) (2) .4281 1.1225 7.07013 .0415 .08383 .2225 1.1715 .0508 .3522 .5986 .1684 .0fm2 2.3754 .3204 1. 25.1171 .6497 .3049 .4491 .0426 .4271 .2477 5 19 2.2592 .3482 .2272 .2371 .2651 .1902 -0722 .9919 1.2671 .a369 .9512 .1969 .2050 .9565 1.05457 .2705 .7619 ***CASES*** .6724 1.3852 .1755 5.08747 .2323 .2721 -2737 53 37 54 100 34 31 54 2.2689 .3740 .2147 .2018 4.6278 .0298 .4439 .3a25 .6249 .5512 .2120 .1357 .2198 ***GLYCOLS AND MINES*** Ethylene Glycol Dlethylene Clycol Triethylene Clycol Dierhnnoliunine .5198 1.TABLE 6 (Cont .3727 2.2242 1.8513 .1647 .2508 .04 32 .1691 .2634 .2711 .1198 .0031 .i67n .2632 .2269 .2338 .5053 .2767 .06 38 .1612 .1200 .6184 2.2745 .5705 2.2158 .8 23 .1693 1.7299 1.2578 .2825 .09012 .6378 .2488 .07382 .0872 .a799 Ethyl Ether .la07 .2215 .5347 .1566 3.a252 11.2823 .0621 1.2547 .0863 .1227 ***PWOROCARI)ONS*** Trichlorofluororrthane Dicblorodif luoromerhane C h l o r o t r i f luoromethane Dlcliioromono f luorome thane Honochlorod If hroromethane T r i c h l o r o t r i f looroethane Diclilorotetrafluoroetiiane .9404 1.6591 .1519 .3399 .1254 .2334 .2010 Water Cnrbon Honoxlde Carbon Dloxide Nitric Oxide Nitrogen Peroxide Nitrous Oxide N I trogen T e t roxide Ethylene Oxide .09844 .5837 .2620 .1351 .3709 .0002 .09384 .2462 .4709 21.0713 1.0697 .1688 .7476 .2560 .3277 .4279 1.2256 .2861 .3263 .0835 .9420 3.2668 .2313 .2582 .0255 2.8328 2.a229 6.1500 .2489 .1660 .7324 1.4 23 1 1 26 26 26 21 19 -- --9 -_ 3.1658 .0358 .1673 .2564 .3143 .z007 .2716 .a634 .5486 1.5561 .3906 .0409 Benzene Toluene Ethylbenzene 0-Xylenr M-Xylene P-Xylem Styrene Cuwne Pentylbenzene Heytylbenrene Nonylbrnrene Undecylbenzene Tridecylbenzrne Heytadrcylbrnrrne Tricosylbenzrne Heavy Aromatic .22no 1.3706 .2620 .1599 I880 .4104 5.6637 ***ALDWDES AND KETONES*** Acetaldehyde Acetone .0728 .5299 ***ALCMIOLS*** Methyl Alcohol Ethyl Alcohol N-Propyl Alcohol Inoyropyl Alcohol .09214 .2729 .2962 .a20 .4642 1.2905 102 69 6.2653 25 18 .3673 .1223 .2806 .05795 .5443 1.2600 .2657 .2647 .3410 ***OXIDES*** . 1979 AlChE Journal (Vol.09117 . m 3 .2527 1.3181 .2198 .3906 3.2541 .goo1 .1356 .3740 .2800 .26M5 ***ABarUTICS*** .2465 .1422 .5555 3.3068 (2) (2) (2) .5896 .0424 . 2532 .2653 .0296 .1851 3.3031 .3748 8.lo31 ***DISULFIOBS*** . 8866 1.1600 .4806 2.2683 .1915 .Oslo .2741 .2575 2.2494 .0265 (2) .2613 .3220 .3663 .0379 .2725 .2770 .4999 .3780 1.I931 .0212 .0102 .2494 .2023 .5763 .0428 .5041 .4332 .3987 .1915 .2935 .2692 .6707 .a180 3.1175 8.0201 .llE5 .5640 ***SULFIDES*** .2665 2704 .0740 (2) .4391 .2709 46 2 41 25 5 2.0736 .0337 .2552 .2638 .3421 .3803 .2664 .3235 .2583 .0356 .0762 .3556 .4335 .4906 . ***SOLVENTS AND MISCELLANEWS*** Lkwtherm A Sulfolane .2462 3.3666 .0441 .4408 .6301 .1052 (1) (2) Average Absoluta Percent Error - NP Volumetric Data Not Available or Not Used.2515 .7114 3.6424 .0670 .o008 .2390 .3139 .1708 .2525 25 2 2 6 1 6 16 16 1.5507 .2025 4.6181 .3129 .6602 3.2525 4 4 4 16 4 4 3 3 3 3 3 3 1.0334 .2810 .3730 .2641 .1844 2.2611 -2615 .4328 .1112 .4971 .2542 .3135 .2137 .2933 .0376 .2661 .4187 3.0783 .3133 .2855 .2781 .5844 4.1641 .2068 .0002 .Z7ll .1204 .1508 .7252 .0435 .4614 3.0415 a34 .0301 .2727 .0330 .8555 1.lo63 .2010 .1022 .1376 .2696 .0838 .3162 .26W .9399 .2559 .0378 . 1979 Page 661 .02W 3.1204 .2713 .0845 1.0156 .lo35 .0307 .3734 .2685 .4316 .3728 .3661 .2728 .a6 .0281 .1865 2.1869 .0102 .046a 4 2 2 2 2 2 16 4 .3398 .0004 .28M .3413 .2214 .4643 .2764 .2589 .M76 .3741 .6827 .0863 .0009 1 .lo39 .1999 .4335 .0766 .5025 .284n .2689 .5849 1.2606 .2751 .4049 .W38 Oirethyl Disulfide Oiethyl Disulfide Ethyl N-Propyl Disulfide Ethyl lsopropyl Oisulfide Di-N-Propyl Disulfide Propyl Isopropyl Disulfide Ethyl Tert-Butyl Oisulfide Diisopropyl Disulfide Oi-N-Butyl Disulfide Oi-N-Auyl Oisulfide Oi-N-ltexyl Disulfide . No.2694 .1170 4.4276 .2514 .w3 .2934 .3709 .8718 .7394 1.359 1 ***SULFUR COHPOUNOS*** .On62 .so12 .2572 .7251 .0573 .0266 .2643 .3728 .3932 .5616 .4255 .0965 .2109 .4160 .0091 .1378 .o 9 1 10 10 3 16 30 4 .3428 .5469 1.1936 .8564 .0597 .3726 .0771 3.TASLB 6 (Cont ) .2589 .0161 .2583 .8423 3.0083 OO65 .4808 .4950 .2831 .1223 .2435 .4392 .0517 .4403 .6258 .0594 .2666 .0237 10 12 11 3 2 3.2208 .9526 .2722 .6957 .1593 .2677 .3136 . 25.0331 .34W .2Y40 .2785 .a767 .3716 .2569 .2781 .3697 .3521 5.5185 .0348 .0345 .9644 3.5955 1.2644 .2938 .6171 2.2561 .1690 -1410 .2384 17 8 3.0579 .1520 .5616 .0535 .5388 .9167 Methyl Mercaptan Ethyl krcaptnn N-Propyl Mercaptan lsopropyl Mercaptan N-Bury1 Mercaptan Sec-llutyl Hercuptan Ivobutyl krcapcan Tert-l)ucyl Hercaptan N-Amy1 Mercaptan 2-Pentnnethiol 3-Pentanethi01 lroamyl Mercaptan 3-tiethyl-l-Uutanethiol Tert-Amy1 Hercaptan Sec-Isoamyl krceptsn N-Heryl Mercaptan Sec-Hexyl Mercaptan Tert-kryl Hercaptan Dliaopropyl Mercaptan N-Heptyl Hercaptan Sec-Heptyl Hercaptan N-Octyl Mercaptan Sec-Octyl Mercaptan N-Nonyl Hercapcan Sec-Nonyl tiercaptan N-Decyl Mercapten Sec-Decyl Hercapcan .W98 .3159 .2496 .04W .1549 .4824 .4059 .2634 .w54 .2932 .1196 .2946 .6142 .2861 .0734 1.1222 .0w9 .2658 .7803 .0792 .3902 .1831 .4310 .3676 .0340 .2557 2614 .3404 .0580 .3137 .0125 .2698 .7811 1.5265 2.2671 .5304 3.2720 .09941 .2493 .4477 .0166 .2562 .1222 .2645 .3706 2.3705 .0843 .0870 .2534 .1Y33 .2387 .0155 .5986 .1535 .3250 .2685 .0202 .0819 .2620 .0307 .1413 (2) .0861 .0174 .8223 . .4233 .2731 .3482 .2662 15 2.7013 .2216 .1333 .7951 4.2658 . M23 .0705 .4054 1.1567 .0m5 . V* Computed From Equation (26) AlChE Journol (Vol.2289 .lo07 .5048 .0663 .3674 .0m3 Sulfur Oioxide Sulfur Trioxide Hydrogen Sulfide Carbon Dlsulfide Carbonyl Sulfide .2610 .6359 .0661 .0442 .2105 .0426 .2688 .I464 .0971 .3715 .2808 .4253 .5579 .3424 .2641 .7928 . 4) July.0m4 .4288 .1923 .5216 .0015 Dimetliyl Sulfide Methyl Ethyl Sulfide Methyl N-Yropyl Sulfide Diethyl Sulfide Methyl Isopropyl Sulfide Methyl N-Bucyl Sulfide Ethyl -N-Propyl Sulfide Muthyl Sec-Butyl Sulfida Methyl Isobutyl Sulfide Ethyl Isopropyl Sulfide Methyl Tcrt-Butyl Sulfide Ethyl N-Butyl Sulfide Di-N-Propyl Sulfide N-Propyl Isopropyl Sulfide Ethyl Sec-Uutyl Sulfide Ethyl Ivobutyl Sulfide Ethyl Terr-llutyl Strlfide Diiropropyl Sulfide Di-N-Duty1 Sulfide Oiisosryl Sulfide Dlallyl Sulfide .2360 .7919 .1993 .0419 .1999 1.0131 .4084 .oooo 3493 .6678 20 2 2 J973 .2646 4 21 21 4 22 9 4 20 9 13 3 4 8 -- -.1021 **WEBCAPTANS*** .2931 .4939 .1966 .0137 .0503 .4327 .37w .3730 .2704 .0979 .4142 3.1826 . 17. Recent comparison of COSTALD with hlcCarty’s ( 1977) modification of the Klosek-McKinley method’ (for Ci . T / T c = critical volume = temperature.1753972 1.00% Aromatics 0.c = constants as given in Table 8 and Equation (26) Pc = critical pressure Danner R SDR = gas constant = Rackett equation as modified by Spencer and = critical temperature = critical temperature of mixture = reduced temperature.05488500 -0. 50.44676 error. “A Corresponding States Correlation of Saturated Liquid Volumes. be superior to those obtained from the generalized Yen-Woods correlation. Brobst. the results obtained by their use will.202%.346916 5.3070619 0. 1977).89 4. R. Thus. Henry.2905331 . Technical Duta Book-Petroleum Refin. P.407302 0. R.2834693 1. and c for nine classes of fluids.35 0.85% -0.. 70.3053426 -0.2828447 -0.” NBSIR 77-867.b.2717636 -0. 1341 (1971). and T.TABLE 7. 4) ..” AIChE Symposium Ser.64 We are greatly indebted to J.08057958 0. Process Design Develop. A. 95” to 150°K) gave for 222 pure liquid points. 25.06379110 0.33 0. “Volurnetric and Thermodynamic Properties of Fluids-Enthalpy. the single datum point required is not readily available.39 1.67 1. D. “LNG Density Determination.2851686 -0. Equation (9) V’ Z C Vm” = characteristic volume of mixture = characteristic volume.” Tech. American Petroleum Institute. 0.02276965 1. COSTALD biases were slightly smaller also. Consequently. McCarty: 0.58% All hydrocarbons 0. TP-3.89% Condensable gases 0. W.373 1978)..23% Sulfur compds.. 140. J.89 3. A. R. COSTALD: 0. 142 ( Apr. and revisions ( 1972). S. (1977). National Bureau of Standards. Danner.1901563 0.’> Ind. and for 370 mixture points. 17.. Free Energy. Okla. and D. on the average. K. S. E. COSTALD: 0.291%.ng..391715 7.03 0. PTOC.1703247 0.283% average absolute error.98% Avg abs. b. Diller. and R.56. Pitzer. Page 662 July. No.65% Avg abs.01379173 1.B = Yen-Woods constants. Eng. NOTATION Class Paraffins Olefins Diolefins Acetylenes Cycloparaffins Aromatics Gases Alcohols Ketones Chlorine and Halides Fluorocarbons Nitrogen compounds Sulfur containing gases Mercaptans Sulfides Overall average for 77 points A. Gas Processors Association.442388 1.” AlChE J..37 1. the Characteristic volumes have been correlated with the following expression: VS VSC = saturated liquid volume = Gunn-Yamada scaling volume. Tulsa. R.05759377 0.0. 1979 AlChE Journal (Vol. Boulder. Chem. “Correlation of Liquid Densities of Polar and Nonpolar Compounds. D. Coker. Zudkevitch.27 2. % error liquid density curve for fluids not covered in Table 6. Eng.1050570 3.89 2.. “A Model for the Precise Calculation of Liquified Natural Gas Densities. PARAMETERS FOR GENERALIZED COSTALD TABLE Paraffins a b C Olefins and diolefins Cycloparaffins 0. ( 1973). Ledgenvood for their help in this work.62 1. P.43% 0. absolute Tc Tm T TR v c Vcm = critical volume of mixture VR‘O)= corresponding states function for normal fluids V R ( ~= ) corresponding states deviation function VR(~ =) deviation function for new correlation 8.. = acentric factor = acentric factor from the Soave equation of state = Gunn-Yamada deviation functions wm = acentric factor of mixture LITERATURE CITED hlcC-rty.82% Fluorocarbons Cryogenic liquids 0.22 (1974).C5 paraffins and nitrogen. Blancett.265 (1958).03 0. 2 ed. l/mole = critical compressibility factor Z R A = SDR Z factor b = ZRA ~ SDR Z factor of mixture 6 w WSRK Table 8 presents the values of the constants a. % error a b C 0. to provide a predictive capability for such cases. the average percent errors given for each class in Table 8 also represent the anticipated errors in calculated volumetric properties. No. Equations ( 1 ) to (4) a. and K. F.5218098 -2. Cunn. COMPARISON OF EXPERIMENTAL CRITICAL VOLUMES WITH CHARACTERISTIC VOLUMES Percent difference = ACKNOWLEDGMENT loo( Ve . D. “A Comparison of Mathematical Models for the Prediction of LNG Densities.46 2. Chem.6564296 -3. M.. Yamada. 3. and M. McCarty: 0. “Revised Acentric Factor Values.. the Table 8 parameters and Equation (26) should never be used in preference to characteristic volumes obtained from reliable experimental data. and to Phillips Petroleum Company for permission to publish it. Since the expected error in calculated volume or density is directly proportional to the error in characteristic volume.13 0.05527757 0. T.63 3. However. Albright. Often. No. Publ. Curl. and Entropy. JoEe.V c ) / V c Number of compounds 24 6 1 2 4 6 9 4 1 2 7 1 5 2 2 Average absolute percent difference 1.2368581 0..” Ind. however.2960998 -0. Colo.” Hydrocarbon.1183987 0. M. G.Kay.. Lee. I n studying heat transfer in packed beds. Thus. S. B. C. P. 1979. L. “Improved Equation for Prediction of Saturated Liquid Density. G. “The Critical Constants of Inorganic Substances..” Chem. Zwolinski. 659 ( 1968) .. 230 ( 1973). the particle size. C. M. Madison. 03437 with the National Auxiliary Publications Service (NAPS)... C. Queens Village. A. The main objective of this paper and contribution to the profession. 365 (1973). Eng. Wisconsin 53706. rather than empirical. J. G. 12. Sci. “A Generalized Equation for Computer Calculation of Liquid Densities. Ill. Chem. and the essential physical properties of the fluid such as the viscosity. 0 The American Institute of Chemical Engineers. 2. No. “A Modified Benedict-Webb-Rubin Equation of State for Methane Using Recent Experimental Data. No. Reu. 21.Y. “The Critical Constants of Organic Substances. P. R. Yen. Eng.” AlChE J.. By theoretical approach.” Ind. 1978. and accepted March 29. Paper 22. 28. and R. the mean bed voidage. 17. Sci.” ibid. G. what values do the effective axial and radial conductivity of the bed and the wall heat transfer coefficient take? This question has Correspondence concerning this paper should be addressed to David L. no satisfactory answer has been found. Chem. Chicago. Prentice-Hall.. Prausnitz. by producing yet more empirical correlations.” Chem. N. 1014 ( 1936). “Prediction of Bubble-Point Density of Mixtures. Data. Computer Calculations for High-pressure Vapor-Liquid Equilibria. and S . Process Design Deuelop. we believe. L.” Ind. P. F.. Chem. Kesler. Alani. “The Prediction of Densities of Liquified Natural Gas and of Lower Molecular Weight Hydrocarbons. Eng. and.. and molecular conductivity. Manuscript received September 6. Eng. H. Woods. 15. Chueh. “Acentric Factor. 12. 95 (1966). Theoretical Prediction of Effective Heat Transfer Parameters in Packed Beds ANTHONY G. and B. Danner. 236 ( 1972). F. C. 68.... Cresswell. approach.” J . J. 15.. D. Reu. H. S. J.” J. Eng. shape and conductivity.T. I. “A Critical Review of Equations for Predicting Saturated Liquid Density. First lnt. “A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States. McKinley. 1. 11428. Chem. A. specific heat. Danner. Con:. 1979 Page 663 . B. and C. The predictions of the theory are compared with reliable literature data for qualitative trends in parameter relations as much as for absolute accuracy. “Densities of Liquified Natural Gas and of Low Molecular Weight Hydrocarbons. F. Passut. N. on LNG.221 (1976). Eng. we attempt to answer the following question: Given the mass velocity of the fluid. 14.” AlChE J. DIXON A theory for predicting the effective axial and radial thermal conductivities and the apparent wall heat transfer coefficient for fluid flow through packed beds is derived from a two-phase continuum model containing the essential underlying and independently measurable heat transfer processes.” Chem. Chem. Supplementary material has been deposited as Document No. 27. Yu. .. Adler. Soave.” ibid. The theory is shown to explain much of the confused literature and pinpoints the remaining major areas of uncertainty. (1968). 29. Process Design Deuelop.. 71 ( 1972 ). Nor will it be answered.” Chem. RaEkett. dogged researchers for the past 25 yr. 72.. Dixon is at the Mathematics Research Center. “Prediction of Saturated Liquid Densities of LNG Mixtures. 18. “Ehuation ‘of State for Saturated Liquids.514 ( 1970). We feel that a thorough testing of our theory must await further experimental work on several of the basic heat transfer steps. University of Wisconsin. “Density of Hydrocarbon Gases and Vapors at High Temperature and Pressure. Session 5. 82 (1978).. the tube diameter. Rowhson. Spencer. W.. J. 276 ( 1974 ). McCarty.T. 0001-1541-79-2713-0663-$01. Lu.510 (1975). despite the vast literature. J. and DAVID I . D. B. and B. Anthony G... 4) July. no empirical or adjustable constants are involved. AlChE Journal (Vol. 23. C. further investigation of which is needed before secure prediction is possible. A Valuable Correlating Parameter for the Properties of Hydrocarbons. 214-13 Jamaica Ave. No. Kudchadker. revision received March 19.. Eng.” Ind. Switzerland SCOPE Knowledge of the effective thermal conductivity and wall heat transfer coefficient for fluid flow through packed tubular beds forms an important aspect in the design of catalytic reactors. (1968). and P.” Proc. and M.-Zentrum CH-8092Zurich.. Mathews.” Cryogenics.-Y.. c/o Microfiche Publicctions. and S. Data. We have accounted for seven such basic heat transfer steps which we have felt necessary to review in the middle part of our paper. and J. 25. CRESSWELL Systems Engineering Group E. Englewood Cliffs. 1979. Klosek. 1373 ( 1974). is to direct attention towards a theoretical. Spencer.. 1197 (1972). H. and R.55. . “Equilibrium Constants from a Modified RedlichKwong Equation o€ State. we hope. Mollerup... we imply the development of a model relating effective heat transfer parameters to the essential underlying and independently measurable heat transfer processes... 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