Ind. Eng. Chem. Process Des. Dev. 7986, 2 5 , 1036-1041
7036
x
drop estimation for the low-AP case would require the Ergun equation and suitable correlations for holdup. Numerous holdup correlations have been cited in reviews by Gianetto et al. (1978), Hofmann (1978), Shah (1979), and Herskowitz and Smith (1983).
I--L'i
Nomenclature a, = specific surface (geometric surface area of packing particles divided by the particle volume) = effective particle size (defined by eq 3) = cylinder or tablet diameter D" = diameter of three-lobed extrudates ~ r r I ' diameter of quadralobe extrudates h, = interparticle static holdup hd = dynamic holdup k = interparticle dead space factor L' = cylinder (tablet or extrudate) length AP = pressure drop V, = superficial gas velocity
and D" = nominal diameter of the three-lobed extrudate. For quadralobe extrudates,
Greek Letters
and D"' = nominal diameter of the quadralobe extrudate. Literature Cited
0
3
t
t'
p p
= interparticle void fraction (dry bed)
= trickling flow interparticle void fraction (defined by eq 3 and 4) = density = viscosity
Appendix Calculation of Specific Surface (a,). For cylinders, 2 4 (5) av=L'+D' where L' = cylinder length and D' = cylinder diameter. The following two equations were used to describe the specific surface of three-lobed and quadralobe extrudates. These equations were derived from geometrical models. For th-ee-lobed extrudates, 2 10s G,. = (6) L' D"(sin (60O) + 1.25s)
+
where
CI1
Y
a,=-+
L'
u
D"'(0.75~+ 1)
(7)
where
Gianetto. A.; BaMI, 0.;Specchia, V.; Slcardi, S. AIChE J. 1978, 2 4 , 1087. Herskowitz, M.; Smith, J. M. AIChE J. 1983, 2 9 , 1. Hofmann, H. P. Catal. Rev. Sci. Eng. 1978, 17, 71. Hutton, B. E. T.; Leung, L. S. Chem. Eng. Sci. 1974, 2 9 , 1681. Hutton, B. E. T.; Leung, L. S.; Brooks, P. C.; Nicklin, D. J. Chem. Eng. Sci. 1974, 2 9 , 493. Kan, K.; Greenfield, P. F. I n d . Eng. Chem. Process. D e s . D e v . 1978, 17, 482. Larkins, R. P.; White, R. R.; Jeffrey, D. W. AIChE J. 1981, 7 , 231. Lockhart, R. W.; Martinelli, R. C. Chem. Eng. Prog. 1949, 45, 39. McCabe, W. L.; Smith, J. C. Unit Operations of Chemical Engineering; McGraw-Hili: New York, 1976 Chapter 7. Satterfield, C. N. A I U E J. 1975. 21, 209. Shah, Y. T. Gas-LiquM-SolM Reactor Design; McGraw-Hill: New York, 1979; Chapter 6. Specchia. V.; Ba!di, G. Chem. Eng. Sci. 1977, 3 2 , 515.
HarshawlFiltrol Partnership Research and Development Center Beachwood, Ohio 44122
Lawrence T . Novak* David D. Mateer
Received for review December 28, 1984 Revised manuscript received January 27, 1986 Accepted March 20,1986
Deplcting Temperature Enthalpy Diagrams for Gases In Solution Above and Below Their Critical Temperature I n process and flow sheet calculations it is often necessary to make heat balances where some components are above their critical temperatures at one point and below their critlcais at some other point in the process. For computer calculations it is necessary to have component enthalpies for a pure component that are consistent with the same component when it Is present in a solvent either above or below its critical temperature. A method of depictlng the temperature enthalpy data in a consistent manner is described here, and a procedure for estimating the partial molal enthalpy of absorption of a nonreacting nonpolar gas above its critical temperature using only the critical temperature is proposed for those cases where experimental data are not available.
Although the computation of partial molal enthalpies of absorption hae been established for low-pressure systems (O'Brien 1960,1964),the engineer may find little aid when consulting standard sources such as Perry's Handbook (1973). An examination of the subject index to The Properties of Gases and Liquids, (Reid et al., 1977) fails to reveal methods of computation of partial molal enthalpies of absorption of a component out of mixtures. This communication is primarily concerned with gases dissolved in solvents of very low volatility.
Discussion a. Nonreacting Solvent-Gas Systems. A typical system of this type would be COz gas dissolved in a heavy
C12hydrocarbon solvent oil. Figure 1 shows the normal heat of vaporization of a pure component, COz in this example, depicted by the distance between the saturated liquid and vapor enthalpy curves. The saturation enthalpy envelope of COPwas plotted from Perry (1973) and the superheated vapor enthalpy curves were obtained from Din (1956). The latent heat of vaporization of pure C 0 2 at 32 "C (just above the critical temperature of COP)is zero by definition. However, the partial molal heat of absorption (or heat of vaporization) of C02in nonreacting solvents at 32 OC is still significant. It is shown on Figure 1as the distance between the lines marked HiGand HiL. In the figures used in this communication, the gas phase is as-
01SS-4305/86/ 1 125-lO36$0l.SO/O 0 1986 American Chemlcal Society
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1980
1037
2000
OATUMH. = 0 9 - 4 0 ° C
'L
0
-1000
-2000 -10
0
10
20
30
40
50
60
70
TEMPERATURE C
Figure 1. Partial molal enthalpy of C02 in nonreacting solvents.
4
T,
Figure 2. Hypothetical liquid fugacity of a component vs. reduced temperature of dissolved gas.
sumed to consist of only the pure gaseous component i, and the term HiG is designated as HiG. The enthalpy of
absorption of COz for nonreacting solvents was determined from the solubility of COz in dodecane based on data of
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986
1038
2.5
li
20
-
OATUMH. = O @ @ C
P a \
T
x-
t -I
10
9 IYI L
I
0
.8
.9
1.0
1.1
12
1
1.5
Figure 4. Reduced enthalpy of acetylene (schematic) vs. TR.
1.6
1.7
1.8
1.9
2.0
2.5
:
4000
3000
r" 2000 "!b 4 w
0
Gs \
3
1000
E
3
3
zs o -1
5 w
-1000
-2000
-3000
4000
0
10
20
30
40 TEMPERATURE C
Ba
60
70
Figure 5. Partial molal enthalpy of acetylene in DMF solutions.
Hayduk et al. (1972) and in decane based on the data of Nocon et al. (1983), using an integrated form of eq 1.
Nocon et al. (1983) have applied the UNIFAC method to predict the effect of temperature on the solubility of COP in hydrocarbons. Equation 1is given by Lewis et al. (1961) and Prausnitz (1969), where the term fppure as given in eq 2 can be taken as the fugacity of the pure component i at the system temperature and pressure. The slope of the f i L = fiLpureYiXi (2) Ha vs. T curve was estimated by means of a proposed correlation which will be described later. The term HiG in eq 1 is the enthalpy of the gas in its ideal state. For systems at higher pressures, the value of hi^ may be computed at the system pressure by using existing correlations and is represented by the difference between the two H i G curves in Figure 1.
The procedure described here and depicted in Figure 1 can be applied to any gas dissolving in a nonvolatile, nonreacting system. In the usual case, very little solubility data will be available above the critical temperature of the gas, and some method of extrapolating the gas and liquid enthalpy curves to higher temperatures is required.
Proposed Method of Estimating the Partial Molal Enthalpy of Absorption of Gases in Nonreacting Solvents. Equation 1suggests that if the term d In fiL/dT was available at higher temperatures, the enthalpy of absorption of the gas could be computed. For nonpolar gases, generalized temperature-liquid fugacity curves have been presented by Prausnitz and Shair (1961) and by Yen and McKetta (1962). These liquid fugacity curves off'" vs. T,were deduced by them from experimental measurements of gas solubilities in various solvents well below and above the critical temperatures of the various gases by making use of an equation having the form of eq 3. The
f?
= fi0LYiXi
(3)
1040
Ind.
-10
0
10
20
30
40
50
60
TEMPERATURE C
Figure 6. Partial molal enthalpy of COz in reactive and nonreactive solvents.
term pLis the hypothetical liquid fugacity of a gaseous component if that gas existed as a pure liquid at 1-atm total pressure. Equation 1 may be rewritten in terms of the reduced temperature so that the derivative may be evaluated from the generalized reduced temperatureliquid fugacity curve of Yen and McKetta (1962) (Figure 2). With derivatives estimated from the Yen and McKetta correlation, Figure 2, the upper curve in Figure 3 was developed by use of eq 4. The derivative d In fioL/dTI,
as evaluated from Figure 2, becomes zero in the region where TI = 2.6 where the gas is near its Boyle point. The heat of absorption as obtained from the generalized fugacity curve does not apply to low molecular weight gases like H2 and He and is discussed by Prausnitz and Shair (1961). The upper curve in Figure 3 may be compared with the lower curve which represents the experimental measurements reported by Hildebrand and Lamoreaux (1974) and Prausnitz (1969) of the partial molal entropy of absorption of gases in various solvents at 25 OC. These entropies of absorption were computed from low-pressure gas solubility measurements at near room temperatures. Inasmuch as the variable fioL in eq 4 does not contain an activity coefficient, eq 4 is not able to take into account the effect of various solvents on the quantity H i -~Ha and is only presented here as a useful approximation. For systems where chemical reaction or hydrogen bonding is known to be present, experimental data must be used to prepare an enthalpy diagram. The bars on the vertical lines shown on the lower curve of Figure 3 indicate the variation of enthalpy of absorption of some of the gases from one solvent to another as given by Hildebrand and Lamoreaux (1974). The upper bar represents measurements in the solvent C8HI8,while the lower bar represents values in CS2. The higher the reduced
temperature, the greater is the effect of solvent properties on the enthalpy of absorption. The lower curve of Figure 3 has for its ordinate the quantity TASIRT, and was evaluated at T = 298 K. The upper limit of the partial molal entropy of absorption of gases forming regular solutions, according to Hildebrand and Lamoreaux (1974), is -21 cal/(g mol deg). By way of comparison, n-pentane at 1-atm pressure and 298 K has an entropy of condensation of about -21.3 cal/(g mol deg) which would correspond to an ordinate of -6.75 in Figure 3. When the upper curve of Figure 3 is used as a basis for the enthalpy of absorption of a gas, a schematic representation of the approximate shape of a dimensionless enthalpy diagram for acetylene gas can be hypothesized as shown in Figure 4. Figure 4 is for the case of a nonpolar, nonreacting gas in a nonvolatile solvent such that TI = 2.6 for the dissolved gas is far below the critical temperature of the solvent. The slope of such a liquid partial molal enthalpy curve will vary considerably, depending on the solvent-gas interactions as shown by Chappelow and Prausnitz (1974). The gas enthalpy line of Figure 4 was made linear to simplify the representation. Figure 4 could also have been developed by using the lower curve of Figure 3. To further amplify the procedure depicted by Figure 1, another example will be given. Figure 5 was developed from the data of Weber (1959) and Miller (1965) and unpublished gas solubility of acetylene in dimethylformamide (DMF). Acetylene apparently reacts with DMF to form a quasi-chemical complex. The slope of the Ha vs. T was determined from Figure 3 for the two hydrocarbon solvent curves, while the vs. T curves for DMF are based on experimental gas solubilities over the range shown. b. Extension of the Diagrams to Systems Where the Gas React8 Chemically with the Solvent. In cases where the solubility of the reacting gas in the solvent has been determined, eq 1 can again be used to compute the partial molal enthalpy of absorption of the gas. Figure 1
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986
Table I. Enthalpy of Solution of C 0 2 in MEA Solutions, -(Ha,.- Had.K cal/(a mol) (Leeet al.. 1974) a (mole ratio in liquid, COz gas/MEA) 0.2 0.4 0.6 0.8 1.0 1.2 AHico2 20.4 15.8 12.1 9.22 7.05 5.52 ~
can be augmented to depict the liquid partial molal enthalpy of COPgas in an aqueous solution containing2.5 N MEA, as shown in Figure 6. The vertical distance between the curve HiG and HiLwas determined from the data of Lee e t al. (1974) shown in Table I. The authors used a form of eq 1 to compute the value HiG- RiLfrom the partial pressures of COz over MEA solutions and noted that the enthalpy values did not vary significantly with temperature. This weak temperature dependency suggests that the curve8 HiG and RL are almost parallel over a small temperature range for the C02-MEA (aqueous) system. The slope of the Rz vs. T for the MEA solution curves was calculated from the upper curve Figure 3 in the absence of any recommendation by Lee et al. (1974). Acknowledgment I thank R. L. Pigford and M. E. Paulaitis for their many helpful suggestions. Nomenclature pL= fugacity of a hypothetical liquid component, atm f L = f!gacity of a component in the liquid phase, atm H~G -Ha = partial molal enthalpy of vaporization of a gaseous component, cal/(g mol), where H~G is the value in the ideal gas state P, = critical pressure of a pure component present as a dissolved gas, atm R = gas constant, cal/(deg mol), = 1.987 A S = partial molal enthalpy of absorption of a gas, cal/(deg g mol) T = temperature, K T,= critical temperature of the gas, K
1041
x = mole fraction of a component in the liquid phase
Subscripts and Superscripts
i = single component number L = liquid phase G = vapor or gas phase r = reduced variable T/T,of the dissolved gas X = denotes constant liquid composition Greek Letters
activity coefficient, dimensionless total pressure, atm X = heat of vaporization of a pure component below its critical temperature
y = a =
Literature Cited Chappelow. C. C.; Prausnltz, J. M. AIChE J . 1074, 20. 1097. Din, F. Thermodynamic Funcfhms of Gases: Butterworths: London, 1956; Vol. 1, p 131. Hayduk, W.; Walter, E. B.; Simpson, P. J . Chem. Eng. Data 1072, 17(1). 59. Hlldebrand, J. H.; Lamoreaux, R. H. Ind. Eng. Chem. Fundam. 1974. 13, 110-1 14. Lee, J. I.; Otto, F. D.; Mather, A. E. Can. J . Chem. Eng. 1074, 52, 803. Lewis, G. N.: Randall, M.; Pltzer, K. S.; Brewer, L. Thermodynamics. 2nd ed.; McGraw-Hill: New York, 1961; p 204. Miller, S. A. Acetylene; Academic: New York, 1965; p 91. Nocon, 0.; Weldllch. U.; Gmehllng, J.; Onken, U. Ber. Bunsenges. Phy. Chem. 1083, 8 7 , 17-23. O’Brlen, N. G.; Turner, R. L. Advances in Computation; CEP Symposium S a ries 31; Wiley: New York, 1960; Vol. 56, p 28. O’Brlen. N. 0. Ind. Eng. Chem. Fundam. 1964, 3 , 352. Perry. T. ChemhlEnglneers’ Handbook, 5th ed.: McGraw-Hill: New York. 1973; pp 3-162. Prausnltz, J. M.; Shalr. F. H. AIChEJ. 1061, 7 , 682. Prausnltz, J. M. Molecular Thermodynamics of FluM-Phase Equilibrla; PrenticaHall: New York. 1969; pp 183, 363. Reid, R. C.; Prausnltz, J. M.; Sherwcad. T. K. The Properties of Gases and LlauMs. 3rd ed.: McGraw-Hill: New York.’ 1977. Weber, J.’H. AIChEJ. 1050, 5 , 17-18. Yen, L.; Mc Keita, J. J. AIChE J . 1962, 8, 501.
P.O. Box 304 Newark, Delaware 19715
Noel G. O’Brien
Received for review March 28, 1985 Revised manuscript received December 23, 1985 Accepted April 10,1986
