Table I. Comparison of Estimated and Experimental CPL
Liquid heat capacity, cal/g "C Compound T,,K P,, atm Ethanol Ethylene glycol
516.2 645
63 76
o
Temp, O
0.635
80
1.147
200 80 200
F
CPG", cal/g "C
Exptl
Meth. 1
Dev, %
Chueh and Swanson
0.341 0.395 0.375 0.432
0.585 0.767 0.577 0.649
0.774 0.864 0.818 0.895
32.4 12.7 41.8 37.9
0.579 0.736 0.574 0.681
Dev, % 1.0
4.0 0.5
4.9
of Lee and Edmister, Tyagi has treated these pressure terms as temperature independent and completely ignored the terms involved in dP,/dT. In addition, Tyagi's eq 8 has not included an o (acentric factor) term, and a number of parentheses are in the wrong place, presumably due to typographical errors. The correct equation should be:
and Swanson (1973) is the difficulty to interpolate the values of the constants, D, E, F, and G. As mentioned in Chueh and Swanson's paper, these constants and the enthalpy deviation equation itself were taken directly from the paper of Yen and Alexander (1965).The constants by themselves, indeed, vary quite abruptly with 2, as shown by Tyagi in his Figure 1.The enthalpy deviation, or its derivative, shown as eq 4 in Tyagi's paper, on the other hand, is a much smoother function of 2,. Therefore, to estimate the compound with 2, equal to, say 0.234, one will first calculate the derivative using the constants given a t 2, = 0.23 and then calculate the derivative again using constants a t 2, = 0.25. The final value of the derivative was obtained by linear interpolation between the two values
The dP,/dT term can be obtained by differentiating an Antoine equation or any other type of vapor pressure expression. This temperature derivative of pressure term has been included by Reid and Sobel (1965) and Chueh and Swanson (1973) in their calculation of d(H" - H,,)/dT. Granting that the terms are less important in the saturated liquid enthalpy ( H s ~departure ) than that in the saturated vapor enthalpy ( H s g departure, ) the omission of the pressure terms may still cause an error of 2 to 3% or even higher a t the reduced temperature above 0.9. Both the expressions of Lee and Edmister and Stevens and Thodos were developed from hydrocarbon information and their applications have been restricted to nonpolar substances by their original authors. Tyagi used their expressions on polar compounds such as ethanol and ethylene glycol and claimed to have obtained estimated liquid heat capacity within 2 to 3% of the experimental values. Our calculation, using Tyagi's method no. 1,resulted in more than a 30% deviation from the experimental value reported by Touloukian and Makita (1971). Some of the comparisons are shown in Table I. All the critical properties, the acentric factor, and ideal vapor heat capacity were taken from the latest compilation of Reid and Sherwood (1976). The main reservation Tyagi has on the method of Chueh
DHDT = [(DHDT)o,25- (DHDT)o.23] X [(Z, - 0.23)/(0.25 - 0.23)]
+ (DHDT)o,23
where DHDT is a shorthand for d(H" - H,,)/dT. This was the method of interpolation used by Yen (1972) to obtain enthalpy deviation in his paper coauthored with Alexander. All the estimated C p values ~ in Tables I11 and VI of the paper of Chueh and Swanson were also calculated by the above procedure. The maximum deviation from the experimental values is 11% with the average generally less than 5% even for the polar compounds such as alcohols. Literature Cited Chueh, C. F., Swanson, A. C., Can. J. Chem. Eng., 51,596 (1973). Lee, B., Edmister, W. C., Ind. Eng. Chem., fundam., 10, 229 (1971). Reid, R. C., Sobel, J. E., hd. Eng. Chem., Fundam., 4, 328 (1965). Reid, R. C.,Sherwood. T. K., "The Properties of Gases and Liquids," 3rd ed. to be published, 1976. Stevens, W. F.. Thodos, G., A./.Ch.€. J., 9, 293 (1963). Touloukian, Y. S.,Makita, T., "Thermophysical Properties of Matter, Vol. 6, Specific Heat, Non-Metallic Liquids and Gases," IFi/Plenum, New York. N.Y., 1971. Tyagi. K. P., Ind. Eng. Chem., Process Des. Dev., 14, 484 (1975) Watson, K. M., Ind. Eng. Chem., 35, 396 (1943). Yen. L. C.. private communication, 1972. Yen, L. C., Alexander, R. E., A./.Ch.E. J., 11, 334 (1965).
Halcon International, Inc. New York, New York 1001 7
C. F. Chueh
Heat Capacities of Liquids: Criticism of Tyagi's Paper Sir: Relative to a recent paper (Tyagi, 1975),we suggest that the conclusions are misleading and require discussion and clarification. First, however, two typographical errors should be noted in eq 7 and 8. The correct forms are HSL- H" = . . . . + o(AloTr2+ . . .) R TC d dT
- ( H S L- H " ) = R ( - A 3
(7)
- . , . + PI(-A7 - 6A8Tr2)
- 12AsTr3P12+ w(2AloT1 - . . .))
(8)
Tyagi might better refer to Watson's method (Watson, 1943) rather than Reid and Sobel (1965) whose only contri478
Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 3, 1976
bution was to use 2, as a third parameter. Chueh and Swanson (1973) also modified the Watson method and their principal contribution was to allow the exponent for Watson's (1943) heat of vaporization equation to vary with reduced temperature. Also, the treatment of Chueh and Swanson is incomplete. The latter authors employ a value of CSL a t 20 "C as a part of their method and this improves their accuracy significantly; we have used the Chueh and Swanson method without difficulty and with good results (San Jos6, 1975). Tyagi suggested three new estimation methods for CSLand we shall discuss these briefly later. First, however, we object to his technique of evaluating the proposed methods. In far too many instances, he compares his estimated values of CSL
Table I. Comparison of Errors in Estimating Liquid Heat Capacity Percent error, average Substance Ethane Propylene n-Heptane n-Decane Benzene Toluene Ethanol 1-Propanol 1-Butanol 2-Propanol
Reduced temperature scale
Method 1
Tyagi Method 2
0.30-0.59 0.32-0.965 0.25-0.62 0.82-0.94 0.338-0.963 0.40-0.52 0.50-0.628 0.475-0.65 0.32-0.57 0.60-0.74 0.28-0.67 0.34-0.52 0.54-0.62 0.54-0.93
24.5 13.8 9.9 9.6 2.7 4.7 2.4 0.7 44.7 18.1 21.6 11.9 4.0 8.3
15.0 11.4 21.0 19.5 9.6 19.0 17.9 13.4 12.8 18.2 19.8 21.8 25.8 23.6
11.6 11.7
1.4 6.6 9.0
2.1
2.6 4.6
7.1 9.2
2.1 2.0
Method 3
7.4
3.9 4.0 9.2 3.8 1.4 24.3 10.2 9.0
Swanson Yuan and and Chueh Stiel -
-
2.5 4.8 1.2
4.6 -
6.3 11.9
5.9 3.9 1.6 6.9 0.3 1.2 5.1 0.9 2.2 1.5
Acetone Methyl ethyl ketone Ethyl ether
0.35-0.58 0.35-0.60
2.5 2.9
26.1 23.7
8.8 9.8
3.5 4.6
5.9 10.2
0.35-0.62
6.2
25.0
11.7
4.4
5.7
Sulfur dioxide
0.63-0.75 0.46-0.60
3.6 4.1
12.9 26.0
4.6 2.8
2.9 8.8
3.2 5.3
0.74-0.92 0.51-0.93
6.5 11.3
3.5 7.7
6.9 15.3
10.2
2.0 2.8
Ammonia Nitrogen
not with experimental data but with estimated values as quoted in other sources. Let us select a few examples to underscore our objection. In propyl ether, Tyagi notes a range of T , of 0.44 to 0.88 and references Gallant. But Gallant (1968) indicates that for this liquid he could locate no experimental data and thus he estimated a vaiue a t 20 "C (using the method of Johnson and Huang (1955) which in itself is not particularly accurate and has been superseded by other methods, e.g., Shaw (1969)). Gallant then assumes that the product of density times heat capacity is a constant, independent of temperature, to obtain CSL a t other temperatures. For approximate engineering calculations, perhaps the Gallant method can be justified, but surely one cannot test a proposed estimation method by comparison with another estimation scheme! For methyl ether, Tyagi indicates a T , range of 0.44 to 0.95 with a reference to Gallant (1968) and Kennedyet al. (1941). The latter is the source reference, but Kennedy only studied this liquid from -133 to -33 "C ( T , = 0.35 to 0.6). Again Gallant approximated CSL at temperatures higher than T , = 0.6. We could continue but, t o summarize succinctly, the validation of the new methods noted by Tyagi is, in our opinion, inappropriate and misleading as in too many instances the comparison was not made with experimental data. To buttress our conclusions, we have compared Tyagi's methods against experimental data for 16 liquids in Table I. We have also indicated the results obtained if the methods of Chueh and Swanson (1973) or Yuan and Stiel(l970) had been employed instead. These results clearly indicate that both the latter methods are superior to any of the three methods proposed by Tyagi. Also, the errors for Tyagi's methods are appreciably larger than he indicated in his paper. A few final comments relative to the proposed methods. In no. 2 and 3, use is made of enthalpy departure functions for the saturated liquid and vapor with a reference to Stevens and Thodos (1963). These latter authors, however, empirically fit values from the Lydersen-Greenkorn-Hougen tables. Yen and
-
Data source Witt and Kemp (1939) Wiebe et al. (1930) Powell and Giauque (1939) Auerbach et al. (1950) Douglas et al. (1954) Messerly et al. (1967) Burlew (1940) Burlew (1940) Kelley (1929a) Fiock et al. (1931) Counsell et al. (1968) Parks (1925) Williams and Daniels (1924) Ginnings and Corruccini (1948) Kelley (1929b) Andon et al. (1968) Parks and Huffman (19261, Counsell et al. (1971) Bass and Lamb (1957) Giauque and Stephenson (1938) Babcock (1920) Wiebe and Brevoort (1930)
Alexander (1965) comment that the fit is not always optimum and suggest more accurate relations. Chueh and Swanson (1973) use Yen and Alexander's fit and appear to be criticized as shown in the discussion of Figure 1 of Tyagi's paper. We suggest that the Stevens and Thodos' relations are not of sufficient accuracy to warrant differentiation to obtain the effect of temperature on these departure functions. In addition, in method 3, it does not appear that the Watson method is correctly interpreted. 4 3 is set equal to zero; therefore must be redefined as
41 = - ( l / T c ) [d/dTr(HO- H s g ) ] Many other items could be criticized; e.g., -1z, is incorrectly defined in eq 18, the Lee-Edmister enthalpy departure function was not designed to be differentiated with respect to temperature, etc. In conclusion, the estimation methods proposed by Tyagi are less accurate than others now available, the comparison of estimated and experimental values is often misleading, and the derivations do not indicate that the previous literature was fully appreciated. L i t e r a t u r e Cited Andon. R . J. L., et ai., J. Chem. Soc. A, 1894 (1968). Auerbach, C. E., et al., Ind. Eng. Chem., 42, 110 (1950). Babcock, H. A., Proc. Am. Acad. Arts Sci., 55 (E),325 (1920). Bass, R., Lamb, J., Proc. Roy. SOC.London, Ser. A, 243, 94 (1957). Burlew, J. S.,J. Am. Chem. Soc., 62, 696 (1940). Chueh, C. F., Swanson, C. A., Can. J. Chem. Eng., 51, 596 (1973). Counsell, J. F., et al., J. Chem. SOC.A, 1819 (1968). Counsell, J. F., et al., J. Chem. SOC.A, 313 (1971). Douglas, T. B., et ai., J. Res. Nat. Bur. Std., 53, 139 (1954). Fiock, E. F., et al., J. Res. Nat. Bur. Std., 6 , 881 (1931). Gallant, R. E., Hydrocarbon Process., 47 (9),269 (1968). Giauque, W. F., Stephenson, C. C., J. Am. Chem. Soc., 60, 1389 (1938). Ginnings. D.C., Corruccini. R. J., Ind. Eng. Chem., 40, 1990 (1948). Haggenmacher, J. E., J. Ghem. Soc., 68, 1633 (1946). Johnson, A. i., Huang, C. J.. Can. J. Techno/.,33, 421 (1955). Kelley, K.K.,J. Am. Chem. Soc., 51, 180 (1929a). Kelley, K. K., J. Am. Chem. Soc., 51, 1145 (1929b). Kennedy. R. M. et al., J. Am. Chem. SOC., 63, 2267 (1941). Messerly, J. F., et al.. J. Chem. Eng. Data, 12 (3),338 (lCF,7), Parks, G. S.,J. Am. Chem. Soc., 47, 338 (1925).
Ind. Eng. Chem., Process Des. Dev., Vol 15, No. 3, 1976
479
Parks, G. S.. Huffman, H. M.. J. Am. Cbem. Soc., 48, 2788 (1926). Powell, T. M., Giauque, W. F., J. Am. Cbem. Soc., 61, 2366 (1939). Reid. R. C., Sobel. J. E., Ind. Eng. Cbem. Fundam., 4, 328 (1965). San Jose, J. L., Sc.D. Thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1975. Shaw, R., J. Cbem. Eng. Data, 14 (4), 461 (1969). Stevens, W. F.. Thodos, G., AICbE J., 9, 293 (1963). Tyagi, K. P., lnd. Eng. Chem. Process Des. Dev., 14, 484 (1975) Watson. K. M.. Ind. €no. Cbem.. 3 5 . 398 (1943). Wiebe, R., et al., J. A h . Cbem. SOC.,52,‘611 (1930).
Wiebe, R., Brevoort, M. J., J. Am. Cbem. Soc., 52, 622 (1930). Williams, J. W., Daniels, F., J. Am. Cbem. SOC.,46, 903 (1924). Witt, R. K.. Kemp. J. D., J. Am. Cbem. Soc., 59, 273 (1937). Yen, L. C.. Alexander, R. E., AlCbEJ., 11, 337 (1965). Yuan, T. F., Stiei, L. I., lnd. Eng. Cbem., Fundam., 9, 393 (1970).
Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts 02139
CORRECTION In the article, “Simultaneous Chemical and Phase Equilibrium Calculation,” by R. V. Sanderson and H. H. Y. Chien [Znd.Eng. Chem., Process Des. Deu., 12,81 (1973)],Table I11 mistakenly showed the results of a case with the equilibrium constant of K = exp[70O/T(OR)] = 2.96189, T = 644.67(’R). George et al., in their paper in this issue on “Computation of Multicomponent, Multiphase Equilibrium,” discuss this error. The authors apologize to the readers for this unfortunate error.
480
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 3, 1976
Robert C. Reid* Juan L. San Jose
