I n d . E n g . Chem. Res. 1988, 27, 2078-2085
2078
Perry, R. H., Chilton, C. H., Eds. Chemical Engineers’ Handbook, 5th ed.; McGraw-Hill: New York, 1973. Peters, M. S.; Timmerhaus, K. D. Plant Design and Economics for Chemical Engineers, 3rd ed.; McGraw-Hill, New York, 1980. Powers, G. J. “Heuristic Synthesis in Process Development”. Chem. Eng. Prog. 1972, 68, 88. Rossiter, A. P. “Design and Optimization of Solids Processes Part 3-Optimization of a Crystalline Salt Plant Using a Novel Procedure”. Chem. Eng. Res. Des. 1986, 64, 191. Rossiter, A. P.; Douglas, J. M. “Design and Optimization of Solids Processes Part 1-A Hierarchical Decision Procedure for Process Synthesis of Solids Systems”. Chem. Eng. Res. Des. 1986a, 64, 175. Rossiter, A. P.; Douglas, J. M. “Design and Optimization of Solids Processes Part 2-Optimization of Crystallizer, Centrifuge and Dryer Systems”. Chem. Eng. Res. Des. 1986b, 64, 184. Sherwood, T. K.; Pigford, R. L.; Wilke, C. R. Mass Transfer; McGraw-Hill: New York, 1975; p 223.
Siirola, J. J.; Rudd, D. F. “Computer-Aided Synthesis of Chemical Process Designs”. Ind. Eng. Chem. Fundam. 1971,10,353. Siirola, J. J.; Powers, G. J.; Rudd, D. F. “Synthesis of System Designs 111: Toward a Process Concept Generator”. AIChE J . 1971, 17, 677. Sohnel, 0.;Matejckova, E. “Batch Precipitation of Alkaline Earth Carbonates, Effect of Reaction Conditions on the Filterability of Resulting Suspensions”. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 525. Treybal, R. E. Mass Transfer Operations, 3rd ed.; McGraw-Hill, New York, 1980. Wakeman, R. J. “The Performance of Filtration PostTreatment Process 1. The Prediction and Calculation of Cake Dewatering Characteristics”. Filtr. Sep. 1979, NovlDec, 655.
Received f o r review February 10, 1988 Revised manuscript received June 30, 1988 Accepted July 31, 1988
SEPARATIONS Adsorptive Drying of Toluene Sudhir Joshi and James R. Fair* D e p a r t m e n t of Chemical Engineering, T h e University of T e x a s a t A u s t i n , A u s t i n , T e x a s 78712
The adsorption of water from toluene was studied using the following desiccants: activated alumina, 3A molecular sieves, and 4A molecular sieves. Water isotherms were measured, mass-transfer rates were studied by means of batch-type kinetics experiments, and breakthrough data were determined by means of flow experiments using fixed beds of the desiccants. A linear driving force mass-transfer model was found to fit the breakthrough results, with equilibrium and mass-transfer parameters determined from the isotherm and kinetics experiments. The results showed that intraparticle diffusion offers the controlling resistance to the transport of water. In the process industries, it is often necessary to dry fluids before they can be processed further. Such concerns as hydrate formation, catalyst poisoning, and corrosion require that the fluid streams contain exceedingly small amounts of water. Adsorptive drying is a logical method, though not the only method of water removal. Liquid drying by adsorption is an important unit operation and despite its scant coverage in the literature is practiced extensively in industry, often empirically. The objective of this work was to study the adsorptive removal of water from hydrocarbons with limited water solubility. This study was to be experimental as well as mechanistic. A mathematical model utilizing the mechanistic characteristics of the process was needed which could be useful in designing commercial drying systems. Toluene was chosen as a model compound, representative of hydrocarbon liquids requiring water removal in processing operations.
Previous Work Burfield and co-workers (Burfield et al., 1977,1978,1981, 1984; Burfield and Smithers, 1978, 1980, 1982, 1983) studied static and dynamic drying of laboratory solvents and reagents using several adsorbents activated aluminas, silica gels, molecular sieves, and ion-exchange resins, together with several chemical agents. Temperature of activation was shown t~ have a strong impact on the moisture
holding capacity of molecular sieves and ion-exchange resins. The 4A molecular sieves, when regenerated at 130 “C, had 7.3% w/w water holding capacity from p-dioxane. This capacity increased to 18.5% w / w when regenerated at 250 “C (Burfield et al., 1978). Most organic molecules have effective diameters in excess of 4 A. For toluene, the effective diameter is about 12 A based on a Lennard-Jones potential constant. This effectively excludes most of the hydrocarbons from the main adsorption space in the micropores of 3A and 4A molecular sieves. In such cases, if water is the only adsorbate, Basmadjian (1984) concluded that moisture uptake isotherms theoretically might be independent of the nature of the solvent and thus yield one common isotherm from all nonadsorbable solvents on a particular molecular sieve. This isotherm might then be related thermodynamically to the vapor adsorption isotherm by equating the fugacities of all three phases. Thus, the calculated vapor isotherm should represent the generalized moisture uptake isotherm on a particular molecular sieve from all nonadsorbable solvents. Actually, many of the reported moisture uptake isotherms from liquid solvents differ substantially from the calculated vapor isotherm (Goto et al., 1972; Selin et al., 1964; Stuchkov, 1975; Varga and Beyer, 1967). The data reported by these authors on 4A molecular sieves were compiled and analyzed by Basmadjian (1984). A diversity
0888-588518812627-2078$01.50/0 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2079 Table I. Adsorbent Characterization" adsorbent 3A molecular 4A molecular sieves sieves nominal size, in. dp, ft x 102 Lp, ft X lo2 pP, W t 3 PB, lb/ft3 Vp, ft3/lb X lo3 aptft-' R,, ft x 103 eP tB
'Il6
0.5 1.204 68.7 43 (44) 8.73 969 3.09 0.6 0.374
1 1.989 71.3 42.7 (45) 8.94 499 6.01 0.638 0.401
' I16
0.544 1.056 69.6 43.7 (43) 9.51 923 3.25 0.662 0.372
SAhiPLtNG POINT
, 7
H-152 alumina
'18
'10
1.03 2.296 71.1 44.1 8.65 474 6.32 0.615 0.379
1.069 82.4 (86.1) 46.3 (46) 7.76 (7.4) 558 5.37 0.64 (0.6) 0.438
N
" Values in parentheses indicate manufacturers' data. of solvents including hydrocarbons, halogenated hydrocarbons, alcohols, ethers, and lower ketones was studied. The data showed deviations from the ideal vapor isotherm. These deviations were small at or near the solubility limits but grew larger at lower concentrations. The most important observation was that the isotherms were markedly different for different solvents, stressing that the nature of the solvent does have a significant effect on the equilibrium concentration of water on 4A molecular sieves. This observation contradicts the generalized isotherm concept. Teo and Ruthven (1986) used the Chakravorti model (1973) to present an analytical solution to breakthrough assuming an irreversible isotherm. The agreement between experimental data and model results was good. Goto et al. (1986) used the analytical solution to breakthrough proposed by Rasmuson and Neretnieks (1980) for a linear isotherm, in order to compare their experimental benzene drying data on ion-exchange resins. The model results compared well with those determined experimentally. Basmadjian (1984) utilized available breakthrough data to predict pore and surface diffusivities. He found that, as opposed to the diffusivities in sorption of water vapor, which cluster around cm2/s for pore diffusion and lo4 cm2/s for surface diffusion, the solid-phase diffusivities in liquid moisture sorption were spread over the ranges 104-104 cm2/s for pore diffusion and 10-7-10-8 cm2/s for surface diffusion. He found no apparent correlation with either the bulk liquid diffusivities or the degree of saturation. Most pore diffusivities were found either to approach or to exceed the liquid diffusivity values, making clear that the surface diffusion predominated. Basmadjian (1984) reported a surprisingly simple linear relation between the logarithm of pore diffusivity and the logarithm of the water activity coefficient. This suggests that mass transfer within the solid is heavily influenced by solvent properties such as polarity, molecular size, and water solubility. Basmadjian also reported substantial film mass-transfer resistances in liquid drying operations, accounting for up to 70% of the total resistance. Several other authors (Ruthven, 1984; Teo and Ruthven, 1986; Prasher and Ma, 1977) have concluded that for liquid-phase adsorption intraparticle transport offers the controlling resistance to mass transfer. Breakthrough data presented by Goto et al. (1972, 1986) also confirm that intraparticle diffusion was controlling.
Experimental Work Materials. Adsorbents used in this study were l/a-in. and lIl6-in. 3A and 4A Linde molecular sieve extrudates and 'Is-in. Alcoa H-152 modified activated alumina beads. The adsorbents were supplied by the indicated manufac-
d FEED
B BALLVALVE N NEU)LEVALE
T THERMOCOUPLE
Figure 1. Equipment layout.
turers. A detailed account of determination of the physical characteristics of adsorbents is given elsewhere (Joshi, 1987). The physical properties are listed in Table I. The toluene used was reagent grade and was supplied by Fisher Scientific Company. Moisture Measurement. An anodized aluminum hygrometer (Parametrics System 1)was used to analyze the liquid stream for water content. Detailed descriptions of the unit and the other moisture detection methods considered are given by Joshi (1987). Dynamic Equipment. A flow diagram of the equipment used is shown in Figure 1. Several workers have used an upflow configuration for liquid-phase adsorption to achieve better flow distribution and to flush entrapped gas. In the present work, it was feared that any flushed gas might accumulate in the sample cell and form two phases, which could lead to erroneous hygrometer readings. Therefore, the adsorption step was carried out in downflow. For visual checking of gas exclusion during adsorption, the adsorber was made of beaded glass pipe sectionsjoined together by Viton pressure seal couplings. Column inside diameters of 3.0 and 1.0 i d were used. Liquid was fed to the adsorbent bed via a perforated plate distributor and a 6-in. depth of 1/8-in. glass beads. (For the 1-in. bed, a course wire mesh replaced the distributor plate.) The length of adsorbent bed was varied from 6 to 1 2 in. Isotherm Measurement. The shaker bottle method was used; it is quite simple and with proper precautions yields good results without the fear of contamination from atmospheric moisture. A major advantage of the method is that many samples can be equilibrated at the same time and then analyzed in rapid succession. The adsorbents were not crushed to a powder for two reasons. First, the moisture uptake from ambient air is small when the particles are large. Fine powders are susceptible to rapid moisture uptake from ambient air during transfer (from hot oven to liquid in bottles). The second reason is that molecular sieve pellets are not homogeneous materials. They are formed by mixing binder with zeolite microcrystals to form pellets. As much as 25-30% of the pellet weight can be binder. It was feared that, if the pellets were crushed before regeneration, the material transferred to different bottles for isotherm determination might not
2080 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 Table 11. Constants for Isotherm Equations" adsorbent 3A molec. sieves (Treg= 220) 3A molec. sieves (Tmg= 220) 4A molec. sieves (T, = 220) 4A molec. sieves (Trw= 180) 4A molec. sieves (Trw= 220) 4A molec. sieves (Tmg= 180) H-152 alumina (T,eg= 220)
size, in.
constants
isotherm Langmuir Langmuir Langmuir Langmuir Langmuir Langmuir Freundlich
'I16 'I8 '116 'I16 '18 lI8 lI8
TOPg
b b b b b b k
= 0.0186 = 0.0178 = 0.01186 = 0.00733 = 0.0255 = 0.018 = 0.002
qs = qs = qn = qn = qs = qn =
0.160 0.135 0.140 0.138 0.140 0.120 l / n = 0.7
25 25 25 25 25 25 25
a Treg = regeneration temperature in "C; b in ppm-'; qe in gram of water/gram of dry adsorbent; k in gram of water/gram of dry adsorbent/ppm water concentration; Topa= operating temperature in OC.
0
200 300 400 500 WATER CONCENTRATION@pmw)
100
0
600
Figure 2. Water isotherm for 1/16-in.3A molecular sieves (25 "C, toluene solvent).
conform to the same zeolite-to-binder ratio in all the samples because of uneven settling due to nonuniform sizes and to density differences of the crushed particles. A known quantity of standardized wet liquid was transferred to glass bottles. To these was added the regenerated adsorbent in varying quantities to vary the adsorbent-to-liquid ratio. The bottles were then sealed and shaken in a constant-temperature shaker bath for 48 h. The difference between the initial and the final liquid concentrations determined the moisture uptake by the solid phase. A detailed description is available elsewhere (Joshi, 1987). Batch Kinetics. Correlations that predict liquid water diffusivity on the basis of adsorbent structure appear not to have been developed. The empirical correlation of Basmadjian (1984), mentioned earlier, did not take structure into account. It was therefore thought prudent to determine diffusion coefficients directly from batch kinetics experiments. In these experiments, a known weight of regenerated desiccant was added to a known quantity of liquid in a conical flask. The flask was then stoppered with a probe and the mixture agitated by a magnetic stirrer. The liquid-phase concentration was monitored continuously.
200 300 400 500 WATER CONCENTRATION@pmw)
100
600
Figure 3. Water isotherm for 1/16-in.4A molecular sieves (25 "C, toluene solvent).
0
200 300 400 500 WATER CONCENTRATION@pmw)
100
600
Figure 4. Water isotherm for '/8-in. H-152 activated alumina (25 "C, toluene solvent).
2o
I
Results and Discussion Isotherms. Equilibrium data at 25 OC were obtained on all adsorbents. The adsorbenh were regenerated at 220 "C in a convection oven. The isotherms for molecular sieves were best represented by the Langmuir relationship: q*(C) =
q,bC
1 + bC
(for molecular sieves)
(1)
The isotherms for activated alumina were best represented by the Freundlich equation: q * ( C ) = kC1/" (for activated aluminas) (2) The results are presented in Figures 2-4 and Table 11. Additional isotherm data are available (Joshi, 1987).
0
100
200
300
400
500
600
WATER CONCENTRATION@pmw)
Figure 5. Comparison of water isotherms on '/&n. 4A molecular sieves and 1/8-in. H-152 activated alumina (25 "C, toluene solvent).
Water isotherms on l/s-in. H-152 activated alumina and 1/16-in.4A molecular sieves are shown in Figure 5. The
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2081 Table 111. Measured and Best Fit Pore Diffusion Coefficients in Adsorbents'
4
adsorbent 3A molec. sieve 4A molec. sieve 4A molec. sieve H-152 alumina
(measd), pellet size, in. cm2/s 1IlR 3.27 X 10" li;B 7.10 x 6.80 X l/8 7.30 X
0, (best fiti, cmZ/s 4.30 X 8.28 x 10" 8.28 X 8.00 X 10"
"Bulk diffusion coefficient, water in toluene, is 6.19 cmz/s.
0
200 300 400 500 WATER CONCENTRATION @pmw)
100
600
Figure 6. Effect of regeneration temperature on the water isotherms on l/s-in. 4A molecular sieves (25 O C , toluene solvent).
superiority of sieves over activated alumina at low water concentrations is evident, but the reverse is true at high water concentrations. Regeneration temperature effects were studied by heating the 4A molecular sieves to 180 and 220 "C. The resulting isotherms are compared in Figure 6. An improvement of almost 10% in the maximum capacity was achieved by the increase in regeneration temperature. This observation compares well qualitatively with the results obtained by Burfield et al. (1978). They observed progressive reduction in moisture holding capacities of molecular sieves with reduction in regeneration temperature. Batch Kinetics. Relatively large adsorbent-to-liquid ratios (10-20 g of adsorbent/500 mL of liquid) initially used in the batch kinetic work proved to be unsatisfactory. The data obtained did not provide a constant value of diffusivity. The results oscillated, giving considerable scatter. Importantly, the scatter had a specific pattern. The deviations were all positive (the measured concentrations were higher than those calculated) in the early stages of drying, and the magnitude of deviations decreased with time. Therefore, the data obtained during the initial stages of drying typically represented lower diffusivities than those at the end of drying. The large time constant for hygrometer equilibration in a liquid medium was thought to be the source of inconsistency in the data. This seemed logical since the rate of change of concentration is fastest in the early stages of drying. I t was argued that lower solid-to-solvent ratios would reduce the initial rate of moisture uptake (in parts per million of water per unit time) considerably and give enough time for the instrument to equilibrate. This assumption proved to be correct. Solid-to-solvent ratios of 2-4 g of adsorbent/1000 mL of solvent were found to be optimum. The liquid-phase concentration of water as a function of time was recorded for all the adsorbents except '/,& 3A molecular sieves. Numerical solutions to the batch kinetics equations have been presented by Hashimoto et al. (1975). The diffusivities were calculated as functions of fractional approach to equilibrium, drying time, and isotherm parameters. Their results were presented for both Langmuir and Freundlich isotherms. In the present work, diffusivities in activated aluminas and molecular sieves were obtained by this approach. The external film mass transfer resistance was neglected based on use of the terminal settling velocity as the slip velocity. The intraparticle diffusivity is assumed to be constant over the concentration interval. Diffusivity values based on both surface diffusion and pore diffusion were tested.
X
The pore diffusivity was found to be constant, but the surface diffusivity was not. This does not mean, however, that pore diffusion is always the dominant mass-transfer mechanism. In fact, the intraparticle diffusivities in 4A molecular sieves and H152 alumina exceeded the liquidphase diffusivity of water in toluene. This suggests that the surface diffusion is the dominant mass-transfer mechanism. Even in the case of 3A zeolites, the best fit value of D, was only two-thirds of DL. Since expected tortuosities of multidisperse pellets are usually considered to be in the range 2-4; it can still be concluded that for the 3A material surface diffusion tends to dominate the mass-transfer process. The effective rate of diffusion of water into the 'I8-in. 3A pellets was quite low; this required longer contact times for adsorption and was accompanied by severe attrition of the pellets. This attrition made determination of the effective particle radius quite difficult. It was thus decided to assign to the lI8-in. 3A pellets the same diffusivity of water as obtained with 1/16-in.3A zeolite pellets. Since the pore diffusivity value is independent of particle size (as was proved for lIl6-in. and lI8-in. 4A molecular sieves in the current work and also shown by Teo and Ruthven (1986)),this is thought to be a reasonable assumption. The diffusivity values for liquid water on the adsorbents are given in Table 111. One should note that some of these values are higher than the measured value of 6.19 X cm2/s for the molecular diffusivity of water through bulk toluene (Lees and Sarram, 1971). The diffusivities for water in 4A molecular sieves and H-152 alumina were found to be about equal. The diffusivity in 3A molecular sieves was found to be half of that in 4A molecular sieves. Dynamic Experiments. Several combinations of bed diameter, bed length, liquid flow rate, and inlet water concentration were used for breakthrough experiments. A summary of the experimental conditions appears in Table IV. The temperature of adsorption was 25 "C. Flow velocities were typically in the range used by other workers (Goto et al., 1972,1986;Teo and Ruthven, 1986). Contact times of 5-10 min, as recommended by the desiccant manufacturers, were found to be impractical. To achieve such contact times would require either a very large adsorber or an unrealistically low liquid velocity. Short contact time did not appear to be a serious drawback, since the model developed from the experimental data would still be valid at longer contact times.
Model Development The following assumptions were made in the present work: isothermal operation, dilute solutions, constant linear liquid velocity through the bed, axially dispersed plug flow, negligible accumulation of adsorbate in the pores, single-adsorbate system, cylindrical pellets modeled as spheres, linear combination of mass-transfer resistances, volume-averaged concentration gradients, solid-phase concentration expressed pes unit of bulk volume.
2082 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 Table IV. Conditions of the Dynamic Runs0 run adsorbent L, in. DIA, in. 1 2 3 4 5 6 I 8
52 53 54 55 56 59
lj16-in. 4A lIl6-in. 4A lIl6-in. 4A lIl6-in. 4A 1/16-in.4A l/s-in. 4A ‘js-in. 4A l/s-in. H-152 lj16-in.3A lIl6-in. 4A l/s-in. H-152 l/s-in. H-152 ‘Is-in. H-152 lIle-in. 4A
6.0 6.0 6.0 9.0 9.0 9.0 6.0 6.0
3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0
6.0 12.0 12.0 6.0 6.0 6.0
1.0 1.0 1.0 1.0 1.0 1.0
Trsg,“C
V, ft/h
Nb
T,,min
Cdet, ppm
Os, min
180 180 180 180 180 180 220 220 220 180 220 220 220 220
10.5 15.6 24.0 10.5 24.0 10.5 10.5 10.5 12.5 15.0 15.0 12.5 15.0 15.0
2.8 4.1 6.4
1.07 0.71 0.46 1.60 0.69 1.60 1.06 1.25 0.90 1.49 1.50 1.07 1.00 0.75
428 383 178 437 291 273 175 382 146 162 382 347 468 207
558 410 440 766 451 1180 1020 816 1647 1508 1109 707 539 839
2.8
6.4 5.5 5.5 4.6 3.2 4.0 6.6 5.5 6.6 4.0
“ L is bed length, DIA is bed diameter, Tregis regeneration temperature, V is superficial velocity, N b is Reynolds number, T,is contact time, Cidetis inlet water concentration, and OB is stoichiometric breakthrough time.
By use of these assumptions, the system can be represented by the following equations.
200 1
I
mass balance in the liquid phase:
ac -_ _ - Vsup _ -
iic + D i i ~1
at
a2
tg
az2
tB
aqav
at
(3)
mass balance in the solid phase: aqav/at = K(C - Cav)
(4)
where Qav
=
Q*(Cav)
(5)
The lumped overall mass-transfer coefficient expressed as combination of inverse resistances in the film and in the particle is
- -R P +- R,2 E - 3Kf 1 5 t S p 1
(6)
0
1000
2000
3000
TIME
Figure 7. Comparison of experimental and theoretical breakthrough curves for experiment 53 (1/16-in.4A molecular sieve, toluene solvent). Operating conditions are listed in Table 111. 400
with initial conditions
cav ( Z , O ) qav(2,0) =
=
300
cavinitia1
Q*(C,,i”itid)
(7) 200
and boundary conditions for t > 0,
at z = 0, C = Cinlet at z = L , aC/az = 0
(8)
This system of coupled partial differential equations was solved numerically by the method of lines. The axial dimension was discretized by using three-point central differencing with M node points. This gave rise to a system of 2M coupled ordinary differential equations. The Neuman boundary condition was discretized by two-point backward differencing. The resulting system of ordinary differential equations, isotherm equations, and the accompanying initial and boundary conditions was solved by using the DGEAR package developed by International Mathematics and Science Library (IMSL) based on the work by Hindmarsh (1974). Typically 48 node points were needed per foot of the column. For larger particle sizes where the mass-transfer zone was longer, 100 node points were used. For predicting the film mass-transfer coefficient, the Wilson and Geankoplis (1966) relationship was used: M K f = 1.09- (NR,)-o~66(Ns,)-O~66 (9) %
4
/I
.
I
”W -I
00
sTo1cHI0mTRIc
1000
2000
3000
TIME (min) Figure 8. Comparison of experimental and theoretical breakthrough curves for experiment 54 (ljs-in. H-152 activated alumina, toluene solvent). Operating conditions are listed in Table 111.
The axial diffusivity was predicted by using the correlation of Butt (1980): UdP = 0.2
DL
(7:)””
+ 0.011
-
(10)
Analysis of Experimental Breakthrough Data Experimental breakthrough data for typical experiments with l/s-in. H-152 alumina and 1/16-in.4A molecular sieves are shown in Figures 7 and 8 along with the predicted breakthrough curve. It is evident that in general the predicted breakthrough is in good agreement with the experimental data. The effective mass-transfer coefficients
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2083 Table V. Relative Mass-Transfer Resistances in the Film and in the Particle ~~
~
expt
adsorbent 'f18-in. 4A 'f16-in. 4A f la-in. 4A 'f8-in. 4A '/&. H152 '/&. H152 'fs-in. H152
1
2 3 6 8 54 55
'
R,, ft 0.003 25 0.003 25 0.003 25 0.006 32 0.005 37 0.005 37 0.005 37
V, ft/h 10.54 15.60 24.00 10.54 10.54 15.00 12.53
EXPERIMENTALDATA --.MEASURED -BEST FIT
I
400 600 800 TIME (h) Figure 9. Comparison of theoretical breakthrough curves obtained by using measured and best fit intraparticle diffusivity based on experiment 2 (1/18-in. 4A molecular sieve, toluene solvent). Operating conditions are listed in Table 111.
0
200
used in the mathematical simulations were about 12-15% higher than those predicted by eq 6 using the measured values of intraparticle diffusivity. Figure 9 depicts the comparison of the two predicted breakthroughs with the experimental data of breakthrough run 2. The difference between the curves suggests that an apparent intraparticle diffusivity should be used in place of a diffusivity obtained from the batch kinetics experiments. Use of this apparent diffusivity, which in all cases was higher than the measured diffusivity, can be jusitified by the following arguments. The pore diffusivity, calculated from the measured batch uptake of water, is assumed to be constant over the concentration range encountered. The typical liquid-phase concentrations at equilibrium at the end of the batch uptake experiments were about 60-90 ppm water. The corresponding solid-phase concentrations were 5-9 g of water/100 g of adsorbent. With surface diffusion dominating intraparticle transport and since surface diffusivity increases with surface concentration, a higher particle diffusivity can be anticipated at higher surface concentrations. Also, into the higher intraparticle diffusivity were lumped any errors introduced by the general correlations for film mass-transfer coefficient and by the prediction of axial diffusivities. The best fit values of intraparticle diffusivities were used in all the mathematical simulations and appear in Table I11 along with the measured values. The best fit value for alumina was about 12% higher than the measured value. For 3A and 4A molecular sieves, the best fit values were almost 31% and 15% higher than the measured values, respectively. These deviations, though large, are within the limits of experimental error. The effective mass-transfer coefficients calculated from eq 6 provide some insight into the mechanisms of mass transfer from the liquid phase into a particle. Table V lists numerical values of the inverse of the two terms on the right-hand side of eq 6. Designated K[' and K,, they are
mass-transfer coeff Kf', l / h Kp, l / h 758 301 863 301 998 301 245 74 278 103 313 103 295 103
K,l / h
KIKf'
215 223 232 56 75 78 76
0.28 0.26 0.23 0.23 0.27 0.25 0.26
the inverse of the resistances to mass transfer offered by the film and the particle. The first three experiments were conducted over a wide range of liquid velocities. When the liquid velocity was increased by a factor of 2.27 in run 3 over that in run 1, the film-phase transfer improved by almost 31% but the overall effective mass-transfer coefficient improved by only 8%. As shown in the last column of Table V, some 70-75% of the total resistance to mass transfer resides in the particle. The design of an adsorber for the purpose of drying hydrocarbons with low water solubilities, as described here, involves the following steps: experimental determination of the water isotherm on the desiccant of choice; determination of the intraparticle mass-transfer coefficient with the aid of finite batch kinetics; prediction of the overall mass-transfer coefficient and the axial diffusivity, using appropriate correlations; use of mathematical simulation to predict the characteristics of the adsorber using the actual physical properties of the fluid plus the specified dynamic conditions. There is, to our knowledge, no available way to predict the water isotherm for a variety of commercially available desiccants from a liquid phase. The water isotherm or the equilibrium water holding capacity of the adsorbent must be determined experimentally. The evaluation of the physical properties and the dynamic conditions can be done routinely. The determination of the intraparticle mass-transfer coefficient using the finite batch kinetics is probably the most difficult and time-consuming step. In the usual industrial setting, the flow and composition of the feed stream to a dryer will not be constant. Variations of water content with time may also be encountered. Since the model requires a fixed inlet concentration and a fixed flow rate, it will only serve to provide an approximate breakthrough time of water. In a typical application, the adsorption step will be stopped when the water content of the effluent reaches a predetermined value, after which the regeneration is started. Under such circumstances, a conservative approach to design is suggested. As shown in Table I11 the intraparticle mass transfer coefficient is higher than the bulk diffusion coefficient of water for desiccants other than 3A molecular sieves. It may be advisable to use a readily available bulk diffusion coefficient to predict the breakthrough of water. The model will predict an earlier breakthrough if DLis used in place of Dp.For many practical applications, this will pose little problem since a conservative estimate is all that is needed. Figure 10 shows a comparison of breakthrough curves predicted using the best fit Dp and DL. It can be seen that the difference in the predicted breakthroughs is small and DL can be safely substituted to predict breakthrough. This circumvents the need to determine experimentally the value of Dp. Conclusions Fixed bed adsorptive drying of liquids was found to be an intraparticle mass-transfer rate-controlled process. The dominant mechanism of mass transfer was found to be the
2084 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 200 1
I
Nsc = Schmidt number, dimensionless q = solid-phase Concentration of water averaged over t h e
0
1000
2000
3000
TIME (d) Figure 10. Comparison of theoretical breakthrough curves obtained by using measured intraparticle diffusivity and by using bulk liquid-phase molecular diffusivity. Experimental data of 53 (1/16-in.4A molecular sieve, toluene solvent). Operating conditions are listed in Table 111.
surface diffusion of water. A linear driving force masstransfer model with a constant lumped effective masstransfer coefficient was found to predict the water breakthrough with a reasonable accuracy. Almost 7&75% of the total resistance to mass transfer resides in the particle. For the design of a system to dry liquids with limited water solubility, use of DL instead of D, should provide a conservative estimate of breakthrough, if 4A molecular sieves and H152 alumina are used. The smaller pore 3A sieves do not permit this conservatism, as shown in Table 111. For water-soluble solvents, used with adsorbents of the present work, substitution of DL for D, can lead to grossly optimistic breakthrough values. S u p p o r t i n g evidence for the latter solvent case has been provided b y Basmadjian (1984). Activated alumina H-152 was found t o have a higher water holding capacity than 4A molecular sieve at high water concentrations. The molecular sieves had a higher capacity for water in the low water concentration region.
Acknowledgment This work was funded by the Separations Research Program at The University of Texas at Austin. The dessicants were donated by Union Carbide Corporation and The Aluminum Company of America. The authors are grateful for these contributions.
Nomenclature b = Langmuir equation constant, ft3/lb C = liquid-phase concentration of water, lb/ft3 C, = water concentration in t h e pore liquid averaged over the particle volume, lb/ft3 CaJnitid= initial water concentration in t h e pores in equilibrium with qavinitid,lb/ft3 Cinlet = water concentration in t h e feed, lb/ft3
D = axial diffusivity, ft2/h DL = liquid-phase diffusivity, f t 2 / h d, = equivalent spherical diameter of a cylindrical pellet, f t D, = intraparticle diffusion coefficient, ft2/h k = Freundlich equation constant K = overall mass-transfer coefficient, l / h Kf = film mass-transfer coefficient, f t / h
L
= bed length, f t
M = superficial liquid flow rate, l b / h r / f t 2 n = Freundlich equation constant N R =~ Reynolds number based o n particle diameter and superficial liquid velocity, dimensionless
particle volume, lb/ft3 qav = solid-phase concentration of water averaged over t h e bulk bed volume, lb/ft3 q, = solid-phase concentration of water averaged over t h e bulk bed volume at saturation, lb/ft3 q*(C,,) = solid-phase concentration of water averaged over t h e particle volume in equilibrium with t h e pore concentration C,,, lb/ft3 R, = radius of a sphere having t h e same surface-to-volume ratio as the cylindrical pellet, ft (equivalent spherical radius) R, = radius of sphere, f t t = time, h r u = interstitial velocity, f t / h V , = porosity, ft3/lb VaUp= superficial liquid velocity, f t / h z = axial dimension, f t
Greek Symbols tB
= surface-to-volume ratio of a particle, l / f t = bed void fraction, dimensionless
tp
= particle void fraction, dimensionless
cy,
p = liquid density, lb/ft3 p, = particle density, lb/ft3 p B = bulk density, lb/ft3 p
= liquid viscosity, l b / h / f t
Literature Cited Basmadiian,D. “The Adsomtive Drying - - of Gases and Liauids”. Adu. Dryiig 1984, 3, 307. Burfield. D. R.: Smithers. R. H. “Desiccant Efficiencv in Solvent Drying. Dipolar Aprotic Solvents”. J. Org. Chem. 1978,43, 3966. Burfield, D. R.; Smithers, R. H. “Desiccant Efficiency in Solvent Drying. Application of Cationic Exchange Resins”. J . Chem. Technol. Biotechnol. 1980, 30, 491. Burfield, D. R.; Smithers, R. H. ”Drying of Grossly Wet Ether Extracts”. J. Chem. Educ. 1982, 59(8), 703. Burfield, D. R.; Smithers, R. H. “DesiccantEfficiency in Solvent and Reagent Drying. Alcohols”. J . Org. Chem. 1983,48, 2420. Burfield, D. R.; Gan, G. H.; Smithers, R. H. “Molecular SievesDesiccants of Choice”. J . Appl. Chem. Biotechnol. 1978,28, 23. Burfield, D. R.; Hefter, G. T.; Koh, D. S. P. “Desiccant Efficiency in Solvent and Reagent Drying. Molecular Sieve Column Drying of 95% Ethanol: an Application of Hygrometry to the Assay of Solvent Water Content”. J . Chem. Technol. Biotechnol. 1984, 34A, 187. Burfield, D. R.; Lee, K. H.; Smithers, R. H. “Desiccant Efficiency in Solvent Drying. A Reappraisal by Application of a Novel Method for Solvent Water Assay”. J. Org. Chem. 1977, 42, 18. Burfield, D. R.; Smithers, R. H.; Tan, A. S. C. “Desiccant Efficiency in Solvent and Reagent Drying. Amines”. J. Org. Chem. 1981, 46, 629. Butt, J. B. Reaction Kinetics and Reactor Design; Prentice Hall: Englewood, NJ, 1980. Chakravorti, R. K. “Liquid Phase Adsorption in Batch and FixedBed Systems”. Ph.D. Dissertation, State University of New York, Buffalo, NY, 1973. Goto, C.; Joko, I.; Tokunaga, K. “Dynamic Drying of Liquids with Zeolite-A Synthesizedfrom Halloysite”. Nippon Kagakukai 1972, 1 I , 2070. Goto, M.; Matsumoto, S.; Yang, B. L.; Goto, S. “Dynamic Drying of Benzene with Ion-Exchange Resin”. J . Chem. Eng. Jpn. 1986, 9(5), 466. Hashimoto, K.; Miura, K.; Nagata, S. “Intraparticle Diffusivities in Liquid-Phase Adsorption with Nonlinear Isotherms”. J . Chem. Eng. J p n . 1975, 8(5), 367. Hindmarsh, A. C. “GEAR Ordinary Differential Equation System Solver”. Technical Report UCID-300001, 1974; Lawrence Livermore Laboratory, Berkeley, CA. Joshi, S. “Adsorptive Drying of Organic Liquids”. Ph.D. Dissertation, The University of Texas at Austin, 1987. Joshi, S.; Humphrey, J. L.; Fair, J. R. “AdsorptiveDrying of Organic Liquids-an Update”. Proc. 1986 Ind. Energy Tech. Conf., Houston, 1986; p 153. Lees, F. P.; Sarram, P. “Desorption into a Dry Gas for Drying Organic Liquids”. J . Chem. Eng. Data 1971, 41, 16.
Znd. Eng. Chem. Res. 1988,27, 2085-2092 Rasher, B. H.; Ma, Y.H. “Liquid Diffuaion in Microporous Alumina Pellets”. AIChE J. 1977, 23(3),303. Raemuson, A,; Neretnieks, I. ”Exact Solution of a Model for Diffusion in Particles and Longitudinal Dispersion in Packed Beds”. AIChE J. 1980,26(4), 686. Ruthven, D. M. Aincipks of Adsorption and Adsorption Processes; Wiley: New York, 1984. Selin, M. E.;Lavrukhin, D. S.; Kulemina, L. B. ”Adsorption by Synthetic NaA Zeolites From Alcohol Water Solutions”. Kolloid. Zh. 1964,26(4), 602. Stuchkov, G. ‘Maea Transfer during Liquid Phase Adsorption Drying of Chloromethane by Zeolites”. Khim Technol. (Kiev) 1975, 6, 40.
2085
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Received for review May 5, 1988 Revised manuscript received August 16, 1988 Accepted August 29, 1988
A Comprehensive Technique for Equilibrium Calculations in Adsorbed Mixtures The Generalized FastIAS Method James A. O’Brien* Department of Chemical Engineering, Yale University, New Haven, Connecticut 06520-2159
Alan L. Myers Department of Chemical Engineering, The University of Pennsylvania, Philadelphia, Pennsylvania 19104
A recent paper by Moon and Tien describes a n improvement to the FastIAS technique of multicomponent adsorption equilibria prediction, originally introduced by the present authors. In this paper, we extend the original FastIAS method to some additional cases suggested by Moon and Tien. We present a generalized technique for formulating adsorption equilibria calculations by the ideal adsorbed solution theory for arbitrary input specifications and illustrate it using the latter cases. T h e calculation involves the solution of a system of N nonlinear algebraic equations, of which N - 1 are always the same and only 1, a material balance, must be altered when different equilibrium specifications are made. We further refine the original formulation of FastIAS by taking advantage of the special structure of the equations involved. Overall, the improved technique performs almost twice as fast as the Moon-Tien procedure and is much simpler to implement and extend. Excellent initial estimates of the solution are given by considering the asymptotic low-pressure case which is analytically solvable for all of the specifications considered here. We identify the condition for an infeasible specification in one case. In an earlier work (O’Brien and Myers, 1985), we presented the initial development of a technique for making rapid adsorption equilibrium calculations using the theory of ideal adsorbed solutions (IAS) as originally described by Myers and Prausnitz (1965). IAS is a useful theory since (a) it requires no mixture data and (b) it is an application of solution thermodynamics to the adsorption problem, so it is independent of the actual model of physical adsorption. We briefly review the equations involved in IAS. The basic equation of IAS is the analogue of Raoult’s law for vapor-liquid equilibrium, i.e., Pyi = Pi”(T)Xi i = 1, ...,N (1) where Pi“ is the pressure which, for the adsorption of every pure component i, yields the same spreading pressure, T , as that of the mixture. Spreading pressure is defined, in turn, by the Gibbs adsorption isotherm (Ross and Olivier (1964) and references therein)
TA
dP
i = 1, ..., N
(2)
The function n:(P) is the experimentally measured adsorption isotherm of pure i. Finally, by requiring zero area change upon mixing at constant IT and T as the condition of ideality, we obtain the total amount adsorbed, n,,as (3)
As we have explained (O’Brien and Myers, 1985),there are N + 1degrees of freedom in this thermodynamic system, and therefore, fixing any N + 1 independent variables defines a unique equilibrium state. In principle, this is a straightforward calculation. Typically, we are interested in specifying the temperature, T, N - 1independent mole fractions (a description of one of the phases, in essence) and one other quantity such as the pressure, P, or the total number of moles of material adsorbed, n,. Other specifications are possible, and we present one example below in case 3. Note that, throughout all of the following, we have assumed that the temperature is always specified. Thus, we required only N additional specifications to be made. In practice, however, there are two computational difficulties with the procedure. Firstly, the value of IT which determines Pi” is the same for all components. Thus, we really don’t need eq 2, but its inverse expression for P ~ ( T )This . requires that Pi” be found by some iterative method. Secondly, the integral in eq 2 has typically been evaluated numerically (e.g., Myers (1984))since there has been no pure-component isotherm expression for nt(P;) which both correlates experimental data and permits analytical integration. In order to facilitate the use of IAS predictions in software for the design of adsorption processes, some method needed to be found to perform this kind of calculation at very high speeds. These concerns were addressed (O’Brien and Myers, 1985) by the original FastIAS technique. I t was based on a logical series-expansion extension to the Langmuir iso-
0888-5885/ 8812627-2085$0~50/0 0 1988 American Chemical Society
