204
Ind. Eng. Chem. Process Des. Dev., Vol. 1 7 , No. 2, 1978
k2 = first-order rate constant for conversion of gasoline P = hydrogen peroxide concentration, M R1 = second-order rate constant for conversion of gas oil; transfer line kinetics R1' = stoichiometric coefficient times the second-order rate constant for conversion of gas oil; transfer line kinetics R:! = first-order rate constant for conversion of gasoline; transfer line kinetics t = clock time, h t , = catalyst residence time, h x = fractional hydrogen peroxide conversion y 1 = weight fraction of gas oil y n = weight fraction of gasoline Greek Letters = deactivation rate constant for second-order conversion, concentration-independent deactivation model /3 = deactivation rate constant for first-order conversion, concentration-dependent deactivation model 7 = flowing space time, ( l b of catalyst)/(s)(lbof oil) T = space time, (vol.)(h)/(vol.) N
Literature Cited Altomare, R. E., Greenfield, P. F., Kittrell, J. R., Biotechnol. Bioeng., 16, 1675 (1974). Handing, F. H., Ind. f n g . Chem., 45, 1186 (1953). Butt, J. B.. Adv. Chem. Ser., No. 109, 259 (1972). Froment, G. F., Bischoff, K. B., Chem. fng. Sci., 16, 189 (1961). Jacob, S. M., Gross, B., Voltz, S. E., Weekman, V. W. Jr., AICHf J., 22, 701 (1976). Levenspiel, O., J. Catai., 25, 265 (1972). Masamune, S., Smith, J. M., AIChEJ., 12, 384 (1966). Nace, D. M., Ind. fng. Chem. Prod. Res. Dev., 8, 24 (1969). Paraskos, J. A., Shah, Y. T., McKinney, J. D., Carr, N. L.. Ind. fng. Chem. Process Des. Dev., 15, 165 (1976). Sagara, M., Masamune, S., Smith, J. M., AIChf J., 13, 1226 (1967). Stangeland, B. E., Kittrell, J. R., Ind. Eng. Chem. Process Des. Dev., 11, 15 (1972). Szepe, S., Levenspiel, C . , "Chemical Reaction Engineering, Proceedings of Fourth European Symposium. Brussels 1968". p 265, Pergamon Press, Oxford, 1971. Voge, H. H., in "Catalysis", P. Emmett, Ed., Vol. 6, Chapter 5 , p 153, Reinhold, New York, N.Y., 1958. Weekman, V. W., Nace, D. M., AiChE J., 16, 397 (1970).
Received for review M a y 6 , 1977 Accepted December 5, 1977
Gas-Liquid Equilibrium in Mixtures of Hydrogen and Diphenylmethane James J. Simnick, Ki D. Liu, Ho-Mu Lin, and Kwang-Chu Chao' School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
Gas-liquid equilibrium in H2-diphenylmethane mixtures was experimentally determined at four temperatures from 190 to 430 O C and seven pressures from 20 to 250 atm. A flow apparatus was used to produce the saturated equilibrium phases. The data were found to be consistent with the Gibbs-Duhem equation by the method of orthogonal collocation. Vapor pressures of diphenylmethane required for the thermodynamic consistency calculations were determined with the same apparatus. Comparison of the new mixture equilibrium data is made with the correlations of Chao and Seader, and Grayson and Streed.
Introduction Gas-liquid equilibrium in Hp-oil systems is of interest to coal hydrogenation and hydrotreating processes. The equilibrium data are needed for reliable and accurate design of plants for the processing of heterogeneous fluid systems that contain gaseous hydrogen in contact with oil liquids. Unfortunately, the needed information is largely unavailable, particularly a t conditions of elevated temperature and pressure that are employed in coal liquefaction and hydrotreating processes. Previous studies of the phase equilibrium of hydrogensolvent systems have been confined in the main to relatively low temperatures. The work which reached the highest temperature was by Grayson and Streed (1963), who presented a correlation of K values of hydrogen in heavy oils at 320-480 "C and pressures to 200 atm, but no data were reported. Simnick et al. (1977) briefly reviewed the experimental data and reported new data on Hn-tetralin from 190 to 430 "C a t pressures up to 250 atm. The present work is a continuation of the work reported by Simnick et al. (1977) to study the phase equilibrium of hydrogen-hydrocarbon systems a t elevated temperatures and pressures. Experimental Apparatus The equilibrium apparatus used in this study is of the flow type to reduce residence time of the hydrogen-diphenyl0019-7882/78/1117-0204$01.00/0
methane mixture fluids in the high-temperature zone, thus minimizing possible thermal decomposition. Detailed description of the apparatus was presented by Simnick et al. (1977). Only the main features will be described here for brevity. The entire high-pressure section of the apparatus is made of stainless steel 316 to prevent hydrogen embrittlement. The hydrogen gas is supplied from a tank through a Hoffer Model 500 MKU diaphragm compressor, which is bypassed during the lower pressure operations. The gas flows into a 500-mL vessel equipped with a regulator which sets the system pressure. The liquid diphenylmethane supply is pressurized by a Hills-McCanna reciprocating piston pump and the flow is damped after leaving the pump. Flow rates of the Ha and diphenylmethane are about 5.5 L/min STP and 500-2000 mL/h, respectively. The gas and liquid streams are joined at a tee and fed to the heating/mixing section. The heated two-phase mixture flows into the equilibrium cell in which the phases are separated. In the upper section of the cell a demister removes entrained drops from the gas stream. The liquid level at the lower section of the cell is sensed by a capacitor and displayed on an oscilloscope. The rate of liquid withdrawal is adjusted to maintain the level a t a suitable position. The cell is kept isothermal by a copper jacket 32 mm thick. Four heaters are wound on the jacket and are separately controlled by Variacs. A thick shell of insulation encloses the entire assembly to maintain high temperature.
0 1978 American Chemical Society
Ind. Eng. Chem. Process
The equilibrium cell temperature is sensed by a type-K thermocouple calibrated to an accuracy of 0.05 "C. The pressure is measured from a tap on the gas stream leaving the cell by a 340-atm Heise gauge accurate to f0.1% or 0.2 atm, whichever is greater. The cell effluents are diverted for sampling after they are reduced in pressure and in temperature and before they enter the separator. The diverted stream enters a trap where the heavy component is retained as a liquid at ambient conditions and later weighed with an analytical balance. The quantity of hydrogen gas coming out of the trap is determined volumetrically. The gas liberated from the liquid phase sample is collected in a graduated cylinder over water. A wet test meter is used to measure the large quantity of hydrogen in the gas phase samples. The volume determinations are accurate to 0.5%. Due to the enormous differences in volatilities of hydrogen and diphenylmethane, quantitative separation is obtained a t the liquid trap. Only minor corrections need to be made to the directly observed liquid weights and gas volumes to obtain the mole numbers of the components in the samples. The plug-flow residence time of the fluids in the heaters amounts to about 3-30 s depending on the pressure, temperature, and the feed rates employed. Only a small part of this residence time is spent a t the final temperature attained in the heater. The plug-flow residence time of the liquid in the equilibrium cell amounts to about 12-33 s a t the range of conditions of operation of this work. Determination of Vapor Pressure. The same apparatus is used to determine vapor pressures of diphenylmethane a t super-ambient pressures. In this mode of operation the solvent liquid alone is fed to the heater where its extent of vaporization is maintained a t about 50%. The pressure measurement is modified for improved accuracy a t the lowered pressures of interest. A Texas Instruments fused quartz gauge is used for pressures up to 6.8 atm. This gauge is calibrated to an accuracy of atm. A Wallace and Tiernan gauge of the Bourdon type is used for higher pressures with an accuracy of 0.06% full scale of 34 atm. The gauges are isolated from the vapor by means of a differential pressure indicator sensitive to atm. Argon gas is used to balance the differential pressure indicator and the pressure of argon is measured. Materials. The hydrogen used in this study was supplied by Air Products Co. with a reported minimum purity of 99.95%. The diphenylmethane was originally obtained from Aldrich Chemical Co. with a purity of 99%. Samples of diphenylmethane were collected from the effluents of the equilibrium cell during all of the runs and were analyzed by a Chicago-Nuclear gas chromatograph on a 3%Dexsil G.C. on Anakrom Q 6-ft column and a Perkin-Elmer Model 601 liquid chromatograph to determine the degree of thermal decomposition. Within the accuracy of the chromatographic calibrations, the samples all showed less than 1% impurities. Nevertheless, liquid side cell effluent samples from the highest temperature studied (428.5 "C) showed a slight yellow coloration. Therefore, all diphenylmethane collected from the cell effluent was purified by vacuum distillation under a nitrogen atmosphere in a packed column. The distillate which was colorless was recycled back to the feed pump. The observed inertness of diphenylmethane in this work seems to be in agreement with the observation by Johns et al. (1962) that diphenylmethane decomposed 1 mol %/h a t 454 "C. Validation of Equilibrium. In view of the short residence time of the fluids in the flow apparatus of this work, it is of considerable interest to establish that equilibrium is indeed attained and that the cell effluents of this work are indeed saturated equilibrium phases. Three tests were made for this purpose. First, the liquid feed rates were varied between 500
Des. Dev., Vol. 17, No. 2, 1978 205
Table I. Vapor-Liquid Equilibrium Data for HaDinhenvlmethane 189.6 "C 0.143" 20 30 50 100 150 200 250
0.0 0.0123 0.0183 0.0300 0.0591 0.0830 0.1055 0.1240
1.088" 20 30 50 100 150 200 250
0.0 0.0159 0.0244 0.0408 0.0785 0.1105 0.1416 0.1724
0.0
0.9903 0.9935 0.9963 0.9980 0.9985 0.9988 0.9989 268.7 "C
80.5 54.3 33.2 16.88 12.03 9.47 8.06
0.00980 0.00657 0.00381 0.00213 0.00159 0.00140 0.00131
59.1 39.3 23.9 12.56 8.95 7.00 5.75
0.0620 0.0427 0.0270 0.01613 0.01182 0.01025 0.00956
40.0 27.5 17.10 9.50 6.57 5.11 4.26
0.269 0.1913 0.1239 0.0708 0.0546 0.0474 0.0421
14.70 10.10 5.71 4.17 3.41 2.93
0.568 0.388 0.246 0.1922 0.1618 0.1492
0.0
0.9390 0.9580 0.9741 0.9861 0.9895 0.9912 0.9921 348.6 "C 4.726O 0.0 0.0 0.7362 0.0184 20 0.8144 30 0.0296 0.8825 0.0516 50 0.9362 0.0985 100 0.9533 150 0.1450 0.9615 200 0.1880 0.9675 0.2272 250 428.5 "C 13.33" 0.0 0.0 0.4497 30 0.0306 0.6360 0.0630 50 0.7881 100 0.1380 0.2030 0.8469 150 0.8799 200 0.2577 0.3056 0.8964 250 " Vapor pressure of diphenylmethane.
and 2000 mL/h, and gas and liquid samples were taken a t a fixed temperature and pressure. No systematic variation in compositions was found. Second, equilibrium data on the system Hz-benzene were determined and compared with those reported by Connolly (1962) obtained from a static apparatus. The agreement was found in general to be within 2% with a maximum difference of 4%. Detailed comparisons have been reported by Simnick et al. (1977). Third, the Gibbs-
X
I 0 16
0 12 0 08 0 04 0
0
40
80
120
160
200
240
P, atm Figure 1. Solubility of hydrogen in diphenylmethane.
280
206
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978 189.6"C 268.7
348.6 428 5
0.8
0'71'i 0.6
*=
6-
0.5 0
Y
0.4
348.6
4-
32-
0.31
o.2
-
t
268.7
643-
'0
40
80
120
160 200
240
280
P, atm
2I
F i g u r e 2. Mole fraction of hydrogen in saturated gas.
Experimental Results The equilibrium saturated liquid and vapor compositions are presented in Table I. The mole fractions in the table represent average values obtained from multiple samples. The compositions of the samples generally do not deviate by more than 1%.Included in the table are also the K values of hydrogen and diphenylmethane and the vapor pressures of diphenylmethane. Figure 1shows the solubility of hydrogen in the liquid as a function of pressure a t different temperatures. The dotted line shown in the figure on the low-pressure side of each isotherm represents a smooth extrapolation of experimental data joining the vapor pressure of diphenylmethane a t X H = 0.
6ot \\ -
40
y '
30
-
20
-
,b l 1 8 9 . 6
I
20 30 50
IO
Duhem equation was integrated to generate y-x data from the experimental isothermal p-x data. The calculated y values are then compared with the experimentally determined values. This test is described in the section following the next.
I
100 200 300
P, atm F i g u r e 4. Vaporization equilibrium ratio of diphenylmethane.
The mole fraction of hydrogen in the saturated gas phase is presented in Figure 2. Individual sample compositions are shown in the figures. These are essentially identical a t the same T and p except a t the highest T studied. Figures 3 and 4 show the K values of hydrogen and diphenylmethane, respectively. Only the average value is shown a t a given T and P. Test for Thermodynamic Consistency. The compositions of the saturated gas and liquid phases in equilibrium are interrelated by the Gibbs-Duhem equation. For a binary system a t constant temperature, the Gibbs-Duhem equation can be integrated to yield the equilibrium vapor composition (y) from the known total pressure ( p ) as a function of liquid composition ( x ) . The experimentally determined y should in principle agree with the calculated y to within experimental accuracy if equilibrium is attained. Thus a comparison of the calculated and the experimental y values furnishes a check as to the attainment of equilibrium conditions. The method of orthogonal collocation (Christiansen and Fredenslund, 1975; Fredenslund and Grausd, 1975) is used in this work to integrate the Gibbs-Duhem equation for the calculation of vapor phase compositions. The rapid variation of p with x makes the integration difficult. Orthogonal collocation has been found to be successful in dealing with this type of equilibrium behavior.
10-
86-
Y '10
20
30 4 0 5 0 6 0 80 100
09':
348.6 428.5
200 300
P , atm F i g u r e 3. Vaporization equilibrium ratio of hydrogen.
-=
+/
0.8
II '' '
0105
0'15
0'10
0'20
0125
xH
F i g u r e 5. Orthogonal collocation results for He-diphenylmethane.
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
Table 11. Henry’s Law Constants of Hydrogen in Diphenylmethane t,O
100 80
-G - S
H , atm
C
189.6 268.7 348.6 428.5
1560 1150 815 510
In addition to the experimental isothermal p-x data, the following quantities are required to be known in the application of the method: (I)vapor pressure of the solvent; (2) excess volume of the liquid solution; and (3) fugacity coefficients of the components in the vapor mixture. The vapor pressure serves to define the initial condition for the integration of the Gibbs-Duhem equation, and values from Table I are used in the calculations. The vapor pressure a t 189.6 “ C was obtained by interpolation of reported data by Weast (1973). The remaining values are from this work. The excess volume of the liquid solution and the fugacity coefficients of the vapor phase components were estimated with a modified Redlich-Kwong equation of state (Prausnitz and Chueh, 1968). The partial volume of hydrogen needed in the calculation was estimated according to Brelvi and O’Connell’s (1972) correlation. Critical properties and acentric factors of the components are required in the calculations. For diphenylmethane the critical constants were obtained from Lydersen’s methods, ,as will be discussed later. Table I11 reports the values used in this work. Figure 5 shows the comparison between the calculated and experimental y values. Good agreement is obtained with a maximum deviation of 0.9% at 348.6 “C and 200 atm. The deviations are within the uncertainty of experimental error. The thermodynamic consistency of the data seems to be established. Figure 5 shows three isotherms a t the lower temperatures of this work. The fourth and highest temperature is beyond the applicable range of Brelvi and O’Connell’s correlation as the reduced density of diphenylmethane is less than 2.0. Calculations are not made at this temperature. Henry’s Constant. Henry’s constant gives a useful indication of the solubility of a gas in dilute liquid solutions. It is defined by
--c-s 40 30
20 -
108-
64-
32-
I1 IO
I
20
I
I
I
I
30 4050 70
I
100
I
I
200 300
P, atm Figure 7. Comparison of K H data with correlations.
the three lower temperatures. Included in this table is also Henry’s constant a t 428.5 OC. This value was determined from a plot of f H / x H vs. X H extrapolated to X H = 0 , where f H was determined by the Redlich-Kwong equation (Prausnitz and Chueh, 1968). Figure 6 shows the Henry’s constants as a function of temperature. Data from both this work and Cukor and Prausnitz (1972) are included. The latter set was obtained from a low-pressure, glass, static apparatus. In spite of the very different experiments the two sets of data appear to be consistent. Comparison with Chao-Seader a n d Grayson-Streed Correlations. The Chao-Seader K value correlation (1961) has been in common use in engineering calculations. Although
- G-S
Orthogonal collocation provides the necessary information to calculate Henry’s constants. Table I1 gives the results for
7
1
4
A
CUKOR and PRAUSNITZ
0
THIS WORK
4 -
3x10’
10-310 20 30 50
100 200 300
P, atm Figure 6. Henry’s constant for hydrogen in diphenylmethane.
207
Figure 8. Comparison of K D data with correlations.
208
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
Table 111. Some Properties of Diphenylmethane Tc pc VC 0
6
D (liq. at 25 "C)
770.2 K 28.2 atm 527.0 cm3/g-mol 0.434 9.6 (~al/cm3)"~ 167.2 cm3/g-mol
the maximum applicable temperature was stated as 260 "C for hydrogen, the use of the correlation at higher temperatures has persisted. Grayson and Streed (1963) extended the Chao-Seader correlation to higher temperatures through a modification of the equations for the pure liquid fugacities. It is of interest to test both correlations with the present data to obtain some indication as to the direction and magnitude of deviations. Figures 7 and 8 show the comparison of the correlations with the experimental K values for hydrogen and diphenylmethane, respectively. Only the highest and the lowest isotherms are shown in Figure 7 to avoid overcrowding as the intermediate isotherms are similar. K values for hydrogen from the Chao-Seader correlation appear consistently low with a maximum deviation of about 35%. Substantial deviations of the data from the Grayson-Streed correlation are also observed, with a maximum of approximately 20%. The K values of diphenylmethane are reasonably represented by both correlations up to the highest pressure studied. The comparison shows that a new and improved correlation is needed to describe the solubility of hydrogen in oils a t the elevated temperatures and pressures of interest. The use of the correlations requires the values of the component parameters be known for both hydrogen and diphenylmethane. The parameter values used in the calculations reported here are shown in Table 111. The values for hydrogen are taken from Chao and Seader (1961). For diphenylmethane all the properties are estimated. The critical properties are estimated by Riedel's method (Reid and Sherwood, 1966). The method was originally developed by Riedel who employed structural contributions to estimate P,, and later extended by Lydersen to treat more types of molecules and also to estimate T , and V, (Reid and Sherwood, 1966). The results agree well with those by the method of Forman and Thodos (Reid and Sherwood, 1966) and are comparable with the values reported in the literature (Gould, 1955; Reid and Sherwood, 1966). However, Reid, Prausnitz, and Sherwood, in their recently published book, recommended the values of T , = 494.0 "C and P, = 29.9 atm. Acentric factor, o,is determined from the vapor pressure a t T , = 0.7, which is in agreement with the estimated value from Edmister's method (Reid and Sherwood, 1966). Note that the value of o = 0.348 given by Reid and Sherwood from Edmister's method was misprinted, the correct value is 0.438.
The revised value in their latest book is 0.471. The Hildebrand equation (Hildebrand and Scott, 1964) is applied to calculate the heat of vaporization and thus the value of solubility parameter. The result is in agreement with the estimated value from the Pitzer acentric-factor correlation (Reid and Sherwood, 1966). Gould (1955) reported the value of heat of vaporization A H , = 94.97 cal/g a t 25 "C, corresponding to 6 = 9.59 ( ~ a l / c m ~ ) However, ~/*. Cukor and Prausnitz (1972) gave a value of 6 = 9.09. Nomenclature f = fugacity H = Henry's law constant K = vaporization equilibrium ratio = y / x p = pressure T = absolute temperature V = volume x = mole fraction, liquid phase y = mole fraction, vapor phase
Greek Letters 6 = solubility parameter o = acentric factor
Subscripts c = critical constant H = hydrogen i = componenti D = diphenylmethane Literature Cited Brelvi, S. W.. O'Connell, P. O., AlChEJ., 18, 1239 (1972). Chao, K. C., Seader, J. D., AlChEJ., 7, 598 (1961). Christiansen, L. J., Fredenslung, A,, AlChEJ., 21, 49 (1975). Connolly. J. F., J. Chem. Phys., 36, 2897 (1962). Cukor, P. M., Prausnitz, J. M., J. Phys. Chem., 76, 598 (1972). Fredenslung, A., Grausm, L., IUPAC, 4th International Conference on Therrnodynamics at Montpelier, France, Vol. IV, p 36, Aug 1975. Gould, R. F., Ed., "Physical Properties of Chemical Compounds", Adv. Chern. Ser. No. 15, 518 (1955). Grayson, H. G., Streed, C. W., Sixth World Petroleum Congress in Frankfurt/Main Section VII, paper 20, June 19-26, 1963. Hildebrand, J. H., Scott, R. L., "The Solubility of.Noneiectrolytes", 3rd ed. p 426, Dover Publications, New York, N.Y., 1964. Johns, I. E., McElhill, E. A., Smith, J. O., J. Chem. Eng. Data, 7 (2), 277 (1962). Prausnitz, J. M., Chueh, P. L., "Computer Calculations for High-Pressure Vapor-Liquid Equilibria", Prentice-Hall, Englewood Cliffs, N.J., 1968. Reid, R . C., Sherwood, T. K., "The Properties of Gases and Liquids", 2nd ed. McGraw-Hill Co.. New York, N.Y., 1966. Reid, R. C., Prausnitz, J. M., Sherwood, T. K., "The Properties of Gases and Liquids", 3rd ed, McGraw-Hill Co., New York, N.Y., 1977. Simnick, J. J., Lawson, C. C., Lin, H. M., Chao, K. C.. AlChE J., 23, 469 (1977). Weast, R. C.. Ed., "Handbook of Chemistry and Physics", 54th ed, Chemical Rubber Co., Cleveland, Ohio, 1973.
Receiued for reuiew June 6, 1977 Accepted November 28,1977
Funds for this research were provided by the Electric Power Research
Institute (RP-367-1)and the National Science Foundation.
