n NB
X I , X?
constant solvent water flux through membrane, gmol/sq cm sec operating pressure, atm product rate per given area of film surface, g/hr product rates per given area of film surface for feed systems A1-H20 and A2-H20 respectively, g/hr product rate for the mixed solute system per given area of film surface, g/hr pure water permeation rate per given area of film surface, g/hr feed flow rate, cc/min effective area of film surface, sq cm initial and final volumes respectively of the feed in a concentration process quantities defined by Equations 8 and 9 respectively mole fraction of solute in the bulk solution, and the concentrated boundary solution on the high pressure side of the membrane, and in the product solution on the atmospheric pressure side of the membrane respectively constants osmotic pressure corresponding to mole fraction X A of solute, atm
literature Cited
Agrawal, J. P., Sourirajan, S., IND.ENG.CHEM.PROCESS DES. DEVELOP. 8, 439 (1969).
Agrawal, J. P., Sourirajan, S., IND. ENG.CHEM.PROCESS DES. DEVELOP. 9, 12 (1970). Kimura, S., Sourirajan, S., AZChE J . 13, 497 (1967). Kimura, S., Sourirajan, S., IND.ENG. CHEM. PROCESS DES. DEVELOP. 7,197 (1968a). Kimura, S., Sourirajan, S., IND. ENG. CHEM. PROCESS DES. DEVELOP.7,548 (196813). Ohya, H., Sourirajan, S.,IND.ENG.CHEM.PROCESS DES. DEVELOP. 8,131 (1969a). Ohya, H., Sourirajan, S., AZChE J . 15, 829 (1969b). Sourirajan, S., Znd. Eng. Chem. Fundamentals 3, 206 (1964). DES. DEVELOP. Sourirajan, S., IND.ENG.CHEM.PROCESS 6, 154 (1967). Sourirajan, S., “Reverse Osmosis,” Logos Press, LondonAcademic Press, New York, 1970. Sourirajan, S., Agrawal, J. P., Ind. Eng. Chem. 61 (11), 62 (1969). Sourirajan, S., Govindan, T. S., Proceedings of First International Symposium on Water Desalination, Washington, D. C., 1965, Vol 1, p p 251-74, Office of Saline Water, U. S. Dept. of Interior, Washington, D. C. Sourirajan, S., Kimura, S., IND. ENG. CHEM. PROCESS DES. DEVELOP. 6, 504 (1967). Timmermans, J. “Physicochemical Constants of Binary Systems in Concentrated Solutions,” Vol 4, p 282, Interscience, New York, 1960 Wolf, A. V., Brown, M. G., in “Hand Book of Chemistry and Physics,” 50th Edition, R. C. Weast, Ed., p D-171, The Chemical Rubber Co., Cleveland, Ohio, 1969. RECEIVED for review March 30, 1970 ACCEPTED July 13, 1970 Issued as NRC No. 1155’7,
Kinetics of Isothermal Sorption of Ethane on 4 A Molecular Sieve Pellets Edward
F.
Kondis’ and Joshua S. Dranoff
Department of Chemical Engineering, Northwestern University, Euanston, Ill. 60201
A
study of the isothermal adsorption and desorption of ethane on pure crystals of 4A molecular sieve has recently been reported by Kondis and Dranoff (1970). Their investigation was carried out with crystal powder and pellets formed from crystal powder alone (containing no clay binder). The results showed that sorption was truly reversible and was controlled by diffusion of ethane within the micropores of the sieve crystals. The present study was undertaken to extend those results to commercially useful sieve pellets made with appropriate clay binders for physical strength. Previous studies have indicated that differences do exist in the sorption processes involving commercial particles. I n fact, Habgood (1958) showed that adsorption of methane on
’ Present 108
address, Mobil Oil Corp.. Paulsboro, N.J. 08066.
Ind. Eng. Chern. Process Des. Develop., Vol. 10, No. 1, 1971
such pellets was drastically different than on pure crystals. I n addition, Antonson and Dranoff (196910) found differences in diffusion rates for sieve pellets and beads. The results suggest that some changes in the crystals must occur in the preparation of various types of sieve particles that affect their subsequent performance in sorption processes. This study was aimed a t uncovering some possible explanations for the differences suggested above and a t finding a suitable mathematical description of sorption on sieve pellets. Materials and Methods
The constant pressure technique used in this work to study sorption kinetics consisted of the measurement of weight gained or lost as a function of time by a small
The kinetics of ethane sorption by commercial 4A molecular sieve pellets has been investigated in a constant pressure microbalance system under isothermal conditions. Results show that micropore diffusion of ethane i s the rate-limiting process, but diffusivities are much lower than for pure sieve crystals. Differences are apparently due to hightemperature steaming which must occur during pellet preparation, and not to heat stress or the presence of clay binder. Experimentally determined diffusivities can be used to predict fixed bed performance quite well.
sample of adsorbent exposed to a gas stream of constant composition in a flow system. This “single particle” approach was preferred to the more traditional fixed bed technique because of its greater sensitivity, both in the accumulation of experimental data and the differentiation of mathematical models. Experiments were run a t three temperatures with dilute mixtures of ethane in helium and with commercial and specially made laboratory sieve pellets. The experimental data were compared with theoretical model curves to determine effective diffusivities of ethane. Equilibrium data were also obtained from the total amounts of ethane picked up by the adsorbent under various conditions. Equipment. The principal apparatus was a “ThermoGrav” microbalance (American Instrument Co.). I t consists essentially of a small sample holder connected to a fine calibrated spring, the motion of which is followed by an electrical transducer and recorded continuously. The sample holder was contained within a Pyrex vessel or sample tube through which gas was circulated. The equipment was arranged so that the sample tube could be easily submerged in either an electrical furnace or an oil filled constant temperature bath. The furnace was used for sample regeneration while the bath served t o maintain system temperature a t predetermined levels during adsorption or desorption experiments. The apparatus was completed by the addition of a manifold and monitoring devices for gas flow control. Capillary flow meters were used for gas flow control and measurement, with calibration by means of wet test or bubble meters. Materials. The gases used in this study were research grade ethane and helium, both 99.99 mole 7% pure. The principal impurity in the ethane was ethylene. This material is very strongly adsorbed by 4A sieves and steps had to be taken to avoid contamination of the adsorbent sample by it. The solid adsorbents used were commercial 4A pellets supplied by Linde and other pellets made for this study in this laboratory. The Linde pellets were Xe-inch diameter and had an average length of 0.274 cm. and a density of 1.1grams per cc. A macropore size distribution furnished by the manufacturer showed that about 75% of the macropores in these pellets were between 0.3 and 0.8 micron in diameter. For some experiments these pellets were crushed by hand to smaller size (28 to 32 mesh). The specially prepared pellets were made from a mixture of pure 4A crystal powder (weight average particle size of 1.39 microns) with 20% by weight (on an as-received basis) of Georgia-kaolin clay. The mixture was hand packed into a section of !;-inch Tygon tubing which was then sealed at both ends and subjected to a pressure of 30,000 psi in a hydrostatic press. The resulting pellets
were quite similar in appearance to the Linde pellets but had a density of 1.15 grams per cc. They also differed from the commercial pellets in the technique by which they were initially calcined. Procedure. The usual pattern followed in these experiments was to regenerate a given adsorbent sample and then carry out an adsorption-desorption cycle, with continuous monitoring of the sample weight as indicated by spring deflection. Regeneration was accomplished by heating the sample up t o 500°C. (at a rate of 20‘C. per minute) and maintaining it a t that temperature under a helium purge until a constant weight was reached. This normally required about 1 hour for the sample sizes used (0.25 to 6 grams). Thereafter, the sample was allowed to cool under helium purge to room temperature and then the sample tube was immersed in a constant temperature bath to bring the sample t o the desired temperature for the adsorption experiments. The absence of contamination during this procedure was indicated by constant sample weight. When thermal equilibrium was reached, as indicated by temperature within the sample tube, an adsorption run was initiated by replacing the helium stream by a predetermined mixture of ethane and helium. The feed was maintained until the sample was saturated as indicated by constant weight. Desorption was then carried out by changing the feed gas to pure helium and running until the sample weight returned to its initial value. A graph of the fraction of ethane sorbed or desorbed as a function of time was then constructed directly from points on the recorded spring deflection-time traces after a correction was made for the effects of buoyancy and (or) drag of the flowing gas stream on the sample holder. These corrections were determined experimentally to be from 1 to 5% of the total change in weight of the sample during such experiments. Equilibrium loading data were also extracted directly from the final sample weights during adsorption. The basic Thermo-Grav apparatus was modified somewhat as the result of a number of preliminary experiments made to test the response of the system. The original sample tube was replaced by a smaller diameter vessel and a specially designed sample holder was constructed. This consisted of an annular basket of brass wire mesh having inside and outside diameters of 5/h and ’/* inch, respectively. The use of these along with sufficiently high gas flow rates and small adsorbent samples made it possible to eliminate effects of mass transfer limitations from the bulk gas stream to the adsorbent surfaces and to achieve sharp step changes in gas composition within the tube. In addition, a major experimental problem due to sample contamination by impurities in the ethane feed was eliminated by placing a small amount (about 200 mg.) of 4A sieve in the bottom of the sample tube. This material, Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 1, 1971
109
1.0
is pictured as the exact reverse of this process, with the adsorbed phase concentration a t the crystal surface maintained a t the value of zero, in equilibrium with the ethanefree gas stream. This model may be represented mathematically by the following partial differential equation system for a spherical particle of radius a.
I
0.8 I
0.6 0.4
0.2
0.02
Porticle t y p e -sphere --cube
_.
1 i
I
0.05
0. I
0.2
0.5
i Dct/a2)"2 Figure 1 . Theoretical sorption curves for spherical and cubic particles which was regenerated a t the same time as the test sample, did not interfere with the sorption experiments but did serve as a pretreater to remove small amounts of impurity in the feed gas. These impurities were adsorbed strongly by the pretreater (along with minor amounts of ethane) before the feed contacted the sample proper. Use of this technique made possible reproducible adsorption-desorption cycles with no irreversible weight gain by the adsorbent in the sample holder. Experiments were made with this equipment a t temperatures of 25.2, 73.8, and 116.8"C. and with ethane concentrations during adsorption of 2 , 4, and 8 volume 56. These low concentrations were used to assure isothermal operation. The latter assumption was verified by experiments in which sieve pellets containing imbedded thermocouples were exposed to the feed gas in the sample tube. These showed peak temperatures which were less than 0.5" C. above the bath temperatures, which was considered satisfactory for this work. Further details of equipment and procedures are given by Kondis (1969). Mathematical Model of the Sorption Process
Before the experimental results are presented, the mathematical model which serves as the basis for the analysis of the data should be considered. I t has been shown previously (Kondis and Dranoff, 1970) that adsorption and desorption of ethane by 4A molecular sieve crystals in the absence of clay binders and under the same conditions as the present work may be described by a particle diffusion model which assumes: Micropore diffusion within the sieve crystals is the rate controlling process. Diffusion is described by Fick's law with a constant micropore diffusivity and a gradient in adsorbed phase concentration. Sorption equilibrium is maintained a t the exterior crystal surface. This model pictures the sorption process as a rapid equilibration of adsorbed phase solute molecules on the crystal surface with the surrounding gas phase, followed by slow diffusion of the adsorbed molecules to the interior of crystal. This process continues until the crystal is uniformly saturated with adsorbed solute a t a concentration in equilibrium with the gas phase composition. Desorption 110
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 1, 1971
where Qo represents the initial uniform loading of the crystal, and qs is the equilibrium concentration a t the crystal surface. If we assume Langmuir equilibrium, the latter is related to gas phase concentration as follows: q 9
= (KCTCJ / (1 + KC,)
(51
The solution to these equations is well known and takes the form given by Crank (1956):
where Q is the average concentration within the particle a t any time and Q1 represents the final average concentration. Thus, Equation 6 defines the fractional approach to equilibrium for an adsorption or desorption experiment. This solution is shown graphically in the semilog plot of Figure 1. Also shown on this graph is the solution for a cubic particle of side 2a. Clearly, there is no significant difference between these two curves. Furthermore, since microscopic observation of the 4A sieve crystals showed them to have a shape somewhere between that of a sphere and a cube, it was calculated that the crystals could be represented as spheres with negligible error. With known equilibrium loadings, this model contains one parameter, ( D e / a 2 ) Experimental . data may be fitted to the model and the appropriate value of this parameter found by a graphical matching procedure using Figure
0.8
--. R u n 47, 2 5 . 2 O C
c W 0
f
W
*\. '-. 10
30
50
100
tIn (sec.)"2 Figure 2. Comparison of theoretical and experimental ethane sorption data for Linde 4A pellets a t 25.2"C.
t"'
3
(sec.)"'
Figure 3. Comparison of theoretical and experimental ethane sorption data for Linde 4A pellets at 73.8"C.
Figure 4. Comparison of theoretical and experimental ethane sorption data for Linde 4A pellets at 116.8"C.
1 and an experimental graph of fractional sorption us. In ( t ) ' '. This superposition technique utilizes all of the data of a given experiment in the determination of the diffusion parameter. In view of the previous success in applying this model to the analysis of sorption data for pure 4A crystals in powder and pellet form, it was expected that it would also be applicable to commercial pellets. This implies the assumption that micropore diffusion will remain the rate limiting step for these particles as well.
Table I. &/a2 Values of Isothermal Sorption on 4 A Pellets Containing Binder
Results and Discussion
Sorption Kinetics with Commercial Pellets. Experimental sorption runs were first made with the >
