any modification of the optimal working conditions; then, we have computed the maximal value of the economic criterion that could be reached by modification of the three remaining decision variables: preheater temperature output ( t 3 ) , bypass (A%
X3).
Results are presented by means of curves; one can find in Vincent’s thesis (1971) numerical values, along with results for other perturbations. Catalyst Activity Decay. T h e decay of the catalyst activity leads t o a modification of t h e mathematical expression for the reaction rate R(g,t). TT’hatever this modification, the work of optimization remains the same, our method not being based on t h e form of R. K e have chosen to simulate this decay by t h e simpler manner which consists of multiplying R by a coefficient a varying from 1 t o 0.5. Figure 3 shows that the economic criterion of the optimally designed sequence is very sensitive to catalyst decay; however, one ran maintain this criterion a t an acceptable level by modifying t3, and AS. Composition at Input. Reaction rate along the reactors depends on t h e composition of t h e feed mixture. Figure 4 shows t h e effect of a variation in t h e percentage of SOz. One can see that the adjustment of t 3 , Az, and A 3 is most
appreciable when the percentage of SO2 is decreasing (it has been supposed equal to 7.8 in this project). Total Flow Rate. T h e sequence of reactors has been optimized to produce 50 tons/day of sulfuric acid. Figure 5 shows the results obtained when the production varies from 25 to 75 tons ’day, with and without adjustment of t3, Al, and x3.
Conclusion
I n a preceding paper we showed that the optimal sequence of reactors was very sensitive to a small variation of preheating temperature (t3). In this paper, we have shown t h a t this sequence is also very sensitive to other perturbations. Severtheless, our method, slightly modified, allows the engineer t o control the reactors to obtain the maximum of the economic criterion, in spite of these perturbations. The method can be implemented on a small process computer. Literature Cited
llaleng6, J. P., Vincent, L. X, Ind. Eng. Chem. Process Des. Decelop., 11(4), 465 (1972). Vincent, L. M,, these Docteur-Inghieur, Universith de Nancy, 1971. RECEIVED for review July 22, 1971 ACCEPTED June 15, 1972
Separation of Binary Mixtures of CO and H, by Permeation Through Polymeric Films F. P. McCandless Department oj” Chemical Engineering, Montana State Tniversity, Bozeman, Jlont. 69715
The pure gas permeability coefficients of various polymeric materials to carbon monoxide and hydrogen were determined, and the most promising of these were tested as separation membranes using binary rnixtures of the gases. The effect of temperature, pressure, and feed composition on permeation rate and permeate compositions was determined. Polyimide, Dacron, Parylene C, and caprolactam films proved to be the most effective. Depending on permeator conditions, actual separation factors varying from 14 to about 70 and fluxes varying from 0.03 to 1.3 scfd/ft?were observed. The actual separation and flux were somewhat lower than would b e predicted on the basis of the pure gas studies, assuming Fick’s law. All materials tested were selective for hydrogen. Mathematical models of the two limiting cases of ideal permeation stages-i.e., no-mix and perfect-mix stages-were formulated. These models used the experimental flux and permeate compositions which were determined as a function of feed composition f o r various temperatures and pressures. These models were used to compare the surface area requirements and separation which would result for various stage cuts. In addition, a brief comparison of polyimide and Dacron was made for the two-stage separation of CO and Hz. This study showed that the membrane area requirements and the size of the interstage streams vary widely, depending on membrane material, operating temperature, and on the type of flow in the stage. A comparison of the models with a theoretical model assuming Fick’s law was also made.
T h e r e has been a growing interest the past few years in membrane processes as alternatives to conventional separation techniques. This interest continues to -grow because membrane process equipment and methods of operation are inherently much simpler than traditional separation methods. This is especially true of the separation of gaseous mixtures such as CO and HP, which require cryogenic temperatures 470 Ind.
Eng. Chem. Process Des. Develop., Vol. 1 1 ,
No. 4, 1972
when separated by condensation, distillatiou, or adsorption. Selective permeation has shown great promise for the separation of gases, but in the past it has not been economic because of the very large membrane surface areas required to carry out industrial-scale separatiorl (Feller and Steiner, 1950). HoJyever, recent advances in membrane technology
TO PERYF*TE HEAWRYENT
I
m
Figure 1. Details of permeation cell (A) Filter paper, (B) membrane,
(C)gasket, (D)porous S.S. plate Figure 2. Apparatus for permeability measurement
through the use of hollow fiber membrane modules permits the assembly of a very large number of small-diameter hollow plastic tubes in units TT hich have a high surface area per unit volume (about 10,000 ft2/ft3) (Michaels, 1989). This breakthrough could easily make some gas separations b y membrane methods economical. As a result, when i t is desired to separate the components of a gas stream, gas permeation should be considered along n ith the traditional separation methods. This paper presents the results of an investigation of various polymeric materials in the separation of carbon monoxide and hydrogen, a system which has considerable industrial importance. .Although several authors (Weller and Steiner, 1950) have included both of these gases in pure gas permeation studies, none have dealt with the separat:on of mixtures of the two. Honever, it should be noted that a proprietary permeation process has been developed which utilizes hollow fiber membrane modules and which can be used t o separate hydrogen from other gases, including carbon monoxide (Atkinson, 1970). Apparently, this process is being successfully applied in commercial plants. Experimental
A diagram of the permeability cell is shown in Figure 1. It nab fabricated from two stainless steel blank flanges, in. thick and 41/2 in. in diam. Two cavities mere machined in the flanges for the gas inlet and membrane support. T h e membrane was supported b y a porous stainless steel disc backed with a filter paper. The cell was sealed by a silicone rubber gasket and clamped shut by eight equally spaced bolts. The gasket opening, and hence exposed membrane, was 2 in. in diam. A 1.0-nil pipet which had a n S-shaped bend near the bottom was connected to the outlet from the membrane support. I n operation, the test cell was mounted in a constanttemperature enclosure and connected to the rest of the permeability apparatus shown in Figure 2. The constant-temperature air bath was made from a piece of 12-in.-diam asbestos pipe, sealed at the bottom and with a tight-fitting asbestos board lid. The wall, top and bottom, mere further insulated n ith aluminum-backed glass fiber. A 500-W heater n a s mounted in t h e bottom part of t h e enc'osure, and t h e test cell n a s shielded from the heater by another p ece of aluminum-backed glass fiber. The input to the heater was controlled b y a variable transformer and a Thermistemp temperature controller. The thermistor probe v, as mounted near the test cell while a thermocouple for temperature measurement was mounted a t the gas inlet to the cell. Feed gas n as supplied from cylinders through a needle metering valve and then through a 30-ft coil of l/*-in. stainless steel tubing to ensure that the gas was a t the same temperature as the
(A) Test cell, (B) constant-temperature enclosure, (C)gas inlet, (D) pressure gage, (E) heat exchanger, (F) back-pressure regulator, (G)baffle, (H) 500-W heater, (1) thermistor probe, (J) thermistemp temperature controller, (K) thermocouple probe, (1) rubber septum, (M) gas measurement pipet
test cell. The pressure in the cell was controlled b y a Grove Mighty Mite back-pressure regulator. The permeate gas rate was measured by timing the rise of a short plug of silicon oil in the pipet. During operation, the pipet was connected to the test cell through the lid by a short length of in. tubing. A swagelock tee containing a silicone rubber septum n a s connected to the bottom of the measuring pipet during the binary tests to permit periodic sampling of the permeate for analysis on a chromatograph. The S-shaped curve in the pipet prevented the silicone oil from falling nto the test cell when it was not in operation. T o test a membrane material, the assembled cell was placed in the constant-temperature enclosure and allowed to reach the desired temperature. The high-pressure side of the cell was thoroughly purged with the gas to be tested and then pressurized. A gas rate of about 10 l./hr (STP) nas maintained through the high-pressure side of the cell, thus maintaining a constant gas compoqition throughout a run. The permeating gas was allowed to vent to the atmosphere through a n oil seal while the system reached equilibrium. To measure the rate of gas permeating through the membrane, the connection to the pipet was tightened and the rise of silicone oil in the capillary 1~as timed. Sampling for gas analysis was done using a gas-tight syringe. The carbon monoxide used LT-as C. 1'. grade (Matheson Co.) while the hydrogen as commercial grade supplied by I1&R Oxygen Co., Billings, Norit. The accuracy of permeation measurements using a similar apparatus has been reported to be of the order of +5% (Stern et al., 1963). Gas Analysis
The CO-H2 mixtures ivere analyzed using a thermal conductivity gas chromatograph operating a t the following conditions: Column = 8 ft X in. stainless steel packed n i t h 30/60 mesh LIolecular Sieve 13X Column temp = 80°C Detector temp = 125OC Carrier flo~v= 30 cc/min Detector current = 200 X I For gas samples containing less than 15% CO, helium was used as the carrier gas while argon n n s used for mixtures Ind. Eng. Chem. Process Des. Develop, Val. 1 1 , No. 4, 1972
471
Table I. Hydrogen Permeabilities and Ratio of Permeabilities for Different Materials Ratio o f permeability coeff. Membrane material
'
P H ~ ' (30°C)
P H ~ ' (1 OOOC)
PH,/PCO
3OoC
1 OOOC
Polyoxb~c 1.8 x ... 4.3 . . . Polyethylene 2 . 0 X 10-9 ... 5.3 . . . Polystyrene 1.1 X 10-9 1 . 1 X 10-8 1 2 . 0 5.8 Polyvinyl chloride 8.0 X 5 . 5 X 10-9 12.9 4 . 5 25.4 1 4 . 1 ParyleneXCad 2 . 8 X 10-10 1 . 2 X 10-9 Cellulose acet'atee 1 . 3 X 10-9 4 . 4 X 10-9 3 7 . 2 25.8 37.8 30.8 Polysulfonef 1 . 4 X 10-9 3 . 7 X 10-9 Polyvinyl fluorideB 6.0 X 8 . 4 X 10-lo 66.7 1 2 . 0 Mylarh Type S 1 . 4 X 10-lO 8 . 7 X 10-lO 74.0 51 . O Polyimidei 2,O X 10-10 7 . 5 X 10-10 74.0 55.6 Parylene C c J 1 . 4 X 1OT10 8 . 4 X 10-10 110.0 52.5 1 . 2 X 10-9 115.0 3 7 . 6 Caprolactamk 1 . 5 X 8 . 3 X 10-lo 110.0 50.0 Dacronh,' 1.3 x Cellophane" 8x 1X ... ... a Units of permeability coefficients are cm3(STP) cm/sec. cm2. cm Hg. * Polyethylene oxide. Union Carbide Reg. trademark. d Poly(para-xylylene). e DuPont 100 CA-43. f Union Carbide Sulfone 47. DuPont Tedlarh. DuPont Reg. trademark. i DuPont Kapton,h a copolymer of an aromatic tetrabasic acid and an aromatic amine. 1 Poly(monoch1oro-para-xylylene). k Allied Chemical and Dye Co., Amorphous nylon film. 1 DuPont amorphous polyester film. m DuPont. Q
containing more than 15% CO. This proved to be necessary to obtain good sensitivity because of the very large difference between the thermal conductivity of CO and H?. I n both cases the chromatograph was calibrated using known gas mixtures in the composition range expected for the samples. Duplicate analyses of gas samples of known compositions indicated an accuracy of about fly0of the absolute amount present. Results
P u r e Gas Permeation Studies. A number of polymeric materials were tested using pure CO and HZa t a pressure difference of 50 psi and temperatures of 30" and 100°C and t h e pure gas permeabilities calculated. This was done to screen available materials to determine which would be most promising for a CO-H2 separation system. T h e
permeability coefficients and their ratio, which gives a n indication of the selectivity of t h e material for a particular gas and the separation which may be obtained (Stern and Walawender, 1969), are shown in Table I. As can be seen from Table I, Parylene C, caprolactam film (an amorphous nylon), and Dacron all exhibit similar characteristics in the CO-H2 system, both in selectivity (as indicated by the ratio of permeability coefficients) and absolute permeability. However, a t the higher temperatures, the selectivity of caprolactam film is significantly lower than the other two. I n comparison, the polyimide film exhibits the greatest selectivity a t the higher temperatures The Polyox film and polyethylene both fused to the filter paper membrane backing a t 100°C TThile the permeability of cellophane to CO was too low to be measured in the equipment as used. I n addition, the cellophane became very brittle and was very easily ruptured after several hours operation a t 100°C. From these data, it appears that of the materials tested, polyimide, Parylene C, caprolactam film, and Dacron would have the best potential for use in a permeation system for the separation of CO and Hf. -1s a result', these materials were further studied in the separatioii of binary mixtures of the two gases. Binary Tests. I n all of the binary tests, a gas rate on the high-pressure side of the cell was maintained at about 10 1./ hr (STP) while the maximum measured permeation rate was about 0.002 L/hr (Parylene C a t 500 psi, 115°C). a result, the data closely approximate point or local fluxes and permeate compositions and justifies the assumption of constant composition on both sides of the membrane for subsequent calculations. Preliminary binary tests were run with the polyimide film and a 50% CO, 50% H ? feed mixture. These tests were made to obtain a qualitative feel for the effects of temperature and pressure on the separation, and choice of film used iii these tests was rather arbitrary. The results of these tests are shown in Table 11. (Sotwithstanding the preliminary nat'ure of these measurements, it is iiiterest,iiig to contrast these data with the behavior of a n ideal system because they seem to indicate deviation from ideality.) The degree of separation which may be obtained in a membrane process is indicated by the actual local or point separation factor which is defined as:
Table II. Performance of Polyimide Film in Tests with 50% H2, 50% CO Feed AP, psi
Temp, OC
50
40 63 84 101 122 23 51 80 110 37 71 119 23 83 106
100
300 5CO
472
Permeate flux, ft3(STP)lft2(dayl
3.1 X 4.6 x 6.8 x 9.8 X 12.9 x 3.8 x 7.2 x 12.8 x 25.2 X 18.9 X 40.1 x 92.1 x 21.1 x 10-2 89.0 X 127.7 x
Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 4, 1972
% co
Obsd separation factor, Equation 1
Ideal separation factor, Equation 2
3.1 3.6 4.4 4.5 5.0 2.3 3.1 3.8 4.9 2.3 3.2 4.5 1.4 3.1 3.7
31.2 26.8 21.8 21.2 13.7 42.5 32.2 25.3 19.4 42.5 30.2 21.2 70.5 31.2 26.0
38.3 33.0 28.1
Composition,
... t . .
...
... .
I
.
...
...
...
...
... 41.4
...
PHz/pCO
71.5 61.6 54.1 ... ... ...
...
...
... ... t
.
.
... ... 44.0 ...
Table 111. Results of Binary Tests
$There the compositions are taken a t the same position coordinates. For an ideal system in which Fick’s law is obeyed, i t varies with local composition and pressure difference (Stern and Walawender, 1969) according to the equation:
AP = 500 psi for all tests; all films nominal 1-mil thickness
Membrane material
Caprolactam
-
where r = ( p h / p L )is the ratio of the total pressure on the two sides of the membrane. As seen from Equation 2, CY (PHJ PCO) as r becomes large; that is, a t high-pressure differences. Thus, a t higher cell pressures, the actual separation factors should approach the ratio of pure gas permeabilities indicating that higher pressures would be more efficient. However, as shown in Table I, the observed separation factors are less than theoretical in all cases, and this difference appears to become greater a t higher pressures. I n addition, the total flus is only about 70-8070 (depending on temperature) of the flus which would be predicted using the pure component data. This indicates that there is some interaction between components of the binary mixture during permeation which effectively decreases the permeation of HP relative to CO. However, considering the analytical uncertainties and the sensitivity of LY to the values of composition, it is not known with certainty a t this time to what extent the indicated deviations are real or owing t o slight errors in analysis and flux measurement. At any rate, as will be shown in subsequent calculations, these slight deviations can make a significant difference in permeator requirements and so the tests do indicate t h a t design predictions based only on pure gas permeability data may be quite uncertain. Rather, experimental data obtained under anticipated conditions of commercial operation would be desirable. Subsequent tests Lvere made only a t a AP of 500 psi since this probably represents the lowest practical pressure of commercial interest. Various temperatures and feeds containing 0, 50, 75, 95, and 100% CO were investigated using the four most promising membranes. The results of these tests are shonn in Table 111. The maximum temperatures investigated using the Dacron and caprolactam films were lower than those for the other t130 because there appeared to be some film degradation a t the higher temperatures. On the other hand, the higher temperatures apparently had no adverse effect on the Parylene C and polyimide films. This is in line with their superior thermal characteristics as reported by the manufacturers. As can be seen from Table 111, separation is excellent with all four materials; honever, the Dacron and polyimide films appear to be superior to the other t n o in terms of selectivity and flus, especially a t the higher concentrations of CO. The selectivity of the Dacron is somewhat better than for the polyimide, but flus is greater with the polyimide film and even higher fluyes would probably be possible because the polyimide film could be operated a t a higher temperature. -1s stated previously, the cost of a permeation plant would probably be determined by the total membrane area required (Stern et al., 1965), but operating costs would depend largely on the number of stages required t o make a given separation. Hence, it appears that a meaningful side-by-side comparison of candidate membrane materials can only be made b y com-
Feed compbsitian, C O
% 0 50 75 95 100
Dacron
0 50 75 95 100
Parylene C
0 50 75 95 100
Poly imide
0 50 75 95 100
Temp, OC
Flux [ft3(STP)/ (ft2)(day)] X 102
Permeate composition,
% co 0 0 0
22 67 101 27 59 90 29 53 87 33 79 101 30 90
22.0 116.0 329.0 8.6 31 .O 89.3 4.1 12.0 36.8 1.4 8.7 22.9 0.1 8.7
1.1 2.4 3.7 1.8 4.7 7.9 31.6 39.4 50.8 100.0 100.0
28 75 25 40 72 25 50 75 30 51 75 31 77
50.6 142.0 17.1 26.3 66.0 9.4 16.9 35.0 2.4 3.5 7.6 0.4 2.5
0 0 1.6 2.0 2.7 3.0 5.0 7.5 29.0 30.9 35.2 100.0 100.0
39 82 104 33 83 115 37 79 104 37 75 104 26 104
64.8 180.0 332.0 21.2 109.0 247.0 11.5 34.5 72.9 4.3 9.7 21.7 2.0 13.7
0 0 0 2.0 3.2 4.6 5.9 9.6 13.2 43.8 49.0 55.4 100.0 100.0
25 50 83 23 83 106 30 60 103 34 53 117 49 116
61.1 98.1 209.0 20.5 94.8 134.0 11.9 22.4 49.9 3.1 5.7 20.2 1.9 8.9
0 0 0 1.4 3.1 3.7 5.0 7.0 8.2 33.8 32.8 41.5 100.0 100.0
Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 4, 1 9 7 2
473
I
POLYINIDE, 103 -0,100 Pbl
TOTAL PERMEATED STREAM
LAW
-PICKS
---YODEL
0
EXPERMENTAL U T 4
f E E D STR
I
HIN. WIN
00
8
VOLUME ELEMENT IN HlOH PRESSURE STREAM
+ z P
z 0
Figure 3. Single permeation stage with no mixing IO
z
0
paring area requirements and interstage stream volumes for the different materials. With this type of study in mind, two mathematical models were developed which represent the two limiting cases for a permeator-that is, perfect-mixing and no-mix models. Mathematical Models. T h e derivation of t h e model equations follows closely those reported in the literature (Stern and Kalawender, 1969) except t h a t experimentally determined flux and permeate compositions are used instead of assuming Fick’s law. No-Mixing Case. Consider t h e separation of a mixture of CO and H B in a simple permeation stage with no mixing on either side of the membrane as shown in Figure 3. A feed stream of H , , ft3/day containing a fraction W,, of CO is continuously fed to the permeator under pressure. The flux through the membrane a t any point depends on temperature, pressure, and gas composition on the high-pressure side and is designated as F ft3/ft2/day. The gas n-hich permeates through the membrane to the low-pressure side is enriched in Hz because of the nature of the membrane and the gas system. At the same time the high-pressure stream is enriched in CO as it flows parallel past the membrane. It is assumed that the permeate composition ( Y ) a t any point near the membrane is determined by the corresponding composition (n’)on the high-pressure side a t the same position coordinate, and that the permeate flows perpendicular to and away from the membrane before it is mixed. Thus, the gas composition on the lon-pressure side of the membrane is not affected by the composition of the total low-pressure stream. This is an ideal cross flow permeation stage with no mixing. A total material balance-a balance of CO on the highpressure side and a balance of CO on the low-pressure side over an element of volume vlhich contacts a membrane area AA-gives respectively the following equations in the limit as AA 4 0 :
13) \
dA
,
(5)
where dZld.4 represents the flus of CO only through the membrane a t any point. L and 2 then represent the total amount of gas and the total amount of CO, respectively, permeating through the membrane from the stage inlet to any point on the membrane, while H represents the volume rate of flow of the high-pressure stream remaining up to that point. The total permeated stream will be a t a rate of Lout containing a fraction CO of Yout. This results in a n exit high pressure stream of Hout with composition TT0,,. 474 Ind.
Eng. Chem. Process Des. Develop., Vol. 1 1 , No.
4, 1972
z
8 to
; W
!O
W , PERCENT
CO
i
IN HIGH PRESSURE STREAM
Figure 4. Comparison of model and experimental data with Fick’s law
S o w , a t constant temperature and pressure, F and Y are functions of Ti’ only, and these functional relationships can be determined from the experimental data since these data represent point fluses and permeate compositions because of the evperimental conditions in obtaining them. Assume that these are:
F
=
F(T)
(6)
Y
=
Y(Ti‘)
(7)
I n these equations, the permeator area, A , is the independent variable. Numerical integration yields values for H , Tt’, and Z for increasing values of area. Thus, a t the end of any particular step in the integration the resulting values and Zoutfor that particular value of the represent Hout, area. The composition and volume of the total low-pressure stream are then calculated from the simple material balances:
Yout
Zout =
__
Lout
(9)
Thus, Equations 3-9 together with the initial conditions represent a mathematical model completely describing the no-mix permeation stage. A computer program was written to simultaneously solve t,hese equations numerically. The program utilized a fourthorder Runge-Kutta integration method in conjunction with a n arbitrary function generator (Franks, 1970) to define F ( W ) and Y ( V )in terms of the experimental points. Figure 4 shows typical plots of the input of F and Y , these plots (dashed lines) being for polyimide a t 100°C. Also shown on the plots are bhe theoretical curves determined by solving the Fick’s law model (Stern and Walan-ender, 1969) using the experimentally determined permeability coefficients in the equations and using the same numerical integration routine. The curves obtained from Fick’s law are shown by the solid line. These plots further indicate deviat’ions from ideality of the CO-H2 system in the films tested, although a detailed study of these deviations was beyond the scope of this study.
T O T A L P E R M U T E D 8TRLAM
DACRON FEED 1000 SCFD,50 X C O
Ycur+Lour
FEED STRE
Hiw. WIN
Figure 5. Single permeation stage with perfect mixing
-
I PERFECT-MIX.
2
ac .c
2 f l C ' Y I X , 30.C
Perfect-Mixing Case. T h e other limiting case results
when t h e unpermeated gas has a t all points in the stage t h e same composition as t h e high-pressure product stream. The same assumption is made for the low-pressure side. A diagram of this perfect-mixing case is shown in Figure 5. T h e same material balances applied to this situation result in t h e following equations:
7
3 PERfECI-HIX,?J.C
I
1 NO'YIX. 78.C
e
.4
6
0
1.0
STAGE CUT
Figure 7. Comparison of perfect-mix and no-mix models for Dacron
Again, F and Y are functions of the high-pressure stream composition, as n-ell as temperature aiid pressure, and are determined from the experimental data. The solution of these equations required a trial-and-error procedure, assuming a value for the high-pressure side stage composition, To,,, and then calculating it from the material balance equations for various values of the area. This was accomplished on the digital computer using a Kegstein convergence technique (Franks, 19iO) again in conjunction with the arbitrary function generator which defined F aiid IT in terms of the esperiment'al points.
POLYIMIDE FEED 1000 SCFD, 5 0 % C O
I PLRfcCT-YIX,ac
.c
2 NO-MIX , W . C
.I
3 PERFECT-YIX,IOO F
4 H C - Y I X , 100 *C
Figure 6. Comparison of perfect-mix and no-mix models for polyimide film
Comparison of Perfect-Mix and N o - M i x Models. T h e equations for both models were solved using a Sigma 7 Computer for a 1000 scfd feed stream containing 50% H?, 50% CO over a range of areas for polyimide a t 100' and 5OoC, and Dacron a t 75' and 30'C. Details of the programs used in solving the equations can be obtained b y n-rit,ing the author. Thus, TITout, Hout; ITout,and Loutwere determined as a function of area for the two different films and temperatures. The bulk of data obtained from these calculations prohibits their inclusion in this paper. However, the performance of different permeator models can conveniently be compared by plotting the enrichment (defined as the mole fraction of the enriched species in the two streams) and area requirements for different stage cuts-that is, for the fraction of the high-pressure stream that is allowed to permeate. This is done in Figure 6 for polyimide and Figure i for Dacron. -1s can be seen from these plots, area requirements and the separation that results for different stage cuts is highly dependent on the t'ype of contacting and on permeator temperature. The no-mix permeator results in a significaiitly smaller area requirement and better separation than the perfect-mix model. I n addition, for the perfect-mis model the eiirichment of the CO in t e high-pressure stream is limited by equilibrium to values less t an about 96% even a t values of the stage cut approaching 1. For these reasons it appears that a permeator design which resulted in flow on the high-pressure side allproaching the no-mix model would be very advantageoub. A comparison of Figures 6 and 7 also s h o m that area requirements for the polyimide permeator are significantly lower than for Dacron a t about the same enrichment. This is mainly due t o the higher a s u m e d temperature for polyimide. The effects of temperature on single permeator requirements are not as clear cut, however, since separatioii efficiency is increased a t the lower temperatures even though are increased. This indicates that there mum temperature a t which to operate a permeator, or possibly that the optimum policy for tlyo or
f,
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 4, 1972
475
I8
POLYIMIDE FEED 1000 S C F D . 5 0 X CO 100 *C
I2
11
-
10
Figure 9. Two-stage permeator with interstage compressor
1 '
0
2 NO-MIX
2
.4
.e
STAGE CUT
Figure 8. Comparison of perfect-mix and no-mix models with corresponding Fick's law model
more permeators in series would be to operate them a t different temperatures. This will be the subject of a future study. The points of inflection in the curves for membrane area as a function of stage cut for the no-mix model are interesting since they appear to be prominent only in systems with a very high separation factor. As can be seen from Figures 6 and 7 , these inflection points correspond to the inflection points in the sigmoid-shaped enrichment curves for CO and Hz.This sigmoid curve results from rapid depletion of Hz in the high-pressure stream with increasing stage cut coupled with the relationship between flux and permeate composition as a function of the high-pressure composition (Figure 4). To see to what extent this behavior was owing to the experimental model, the Fick's law model for polyimide a t 100°C was plotted in the same fashion and compared with the corresponding experimental model. This comparison is shown in Figure 8. -4s can be seen, the Fick's law model shows the same inflection points, and indeed they seem to be more pronounced. This further points out possible deviations of the CO-H2 system from ideality. Figure 8 further illustrates the need for actual data for the binary gas system since the area requirements calculated from the experimental data model are significantly higher than those calculated using Fick's law. This of course reflects greatly the permeability in the actual system that is 7 0 4 0 % lower than would be predicted using the pure gas data. Comparison of a Series of Perfect-Mix Permeators with a No-Mix Model. As shown in t h e previous section, there is a significant difference in performance and area requirements between the perfect-mix and no-mix permeator models. I n the case of the former, the concentration of the gas on the high-pressure side is constant and a t a high concentration of the least permeable material-in this case CO. This means t h a t conditions are unfavorable for permeation and high area requirements and low separation efficiency result. On the other hand, in the no-mix 476 Ind.
Eng. Chem. Process Des. Develop., Vol. 1 1 , No, A, 1972
model, the high-pressure gas composition starts out a t a high concentration of the more permeable material and is gradually reduced along the path of flow. This means that the average concentration of the more permeable material on the highpressure side is much greater, and this results in lower area requirements and greater separation efficiency. This is entirely analogous to the behavior of back mix and plug flow chemical reactors (Levenspiel, 1962) and by this analogy it is obvious that a number of perfect-mix permeators connected in series should approach the performance of a no-mix permeator. T o obtain a quantitative feel for the approach of a number of perfect-mix permeators to one no-mix permeator, calculations were made using the perfect-mis model for up to eight permeators connected in series on the high-pressure side. For these calculations, polyimide a t 5OoC was arbitrarily chosen. The results are shown in Table IV. As can be seen from Table IV for this case, eight equal size perfect-mix permeators in series closely approach the performance of one no-mix permeator with a total area equal to the sum of the perfect-mix units. This indicates that proper baffling on the high-pressure side of a permeator may be important to obtaining performance approaching the no-mix model. Two-Stage Requirements for Production of HighPurity Product Streams. A side-by-side comparison of different membrane materials can best be made by contrasting the total area and t h e number of stages required to effect a given separation. T h e area requirements are particularly important because this would probably deter. mine to a large extent the cost of a permeation plant. Likewise, interstage compression costs mould probably constitute the major operating cost. Thus, the optimum membrane material would be the one that would make the desired separation using the lowest total surface area, the fewest number of stages, and with the lowest possible gas volume to the interstage compressors. An extensive parametric study would be required to determine the optimum material and operating conditions; but it is interesting to briefly compare from this standpoint, the two most promising membrane materials found in this study. A two-stage permeator model, as shown in Figure 9, was used for this study. Area requirements and stream volumes and composition were calculated to produce 99% CO in the no-mix case and about 95% CO in the perfect-mis case. As pointed out previously, high-pressure product composition is limited to about 96% in the perfect-mix model by equilibrium considerations, depending on conditions and membrane material. The results of this brief study are shown in Table V. As
Table IV. Comparison of Performance of Several Perfect-Mix Permeators in Series with One No-Mix Permeator
Polyimide, 5OoC Feed: 1000 scfd, 50% H B , 5O%CO No. of 1
3800 3800 554.6
Area each permeator, ft2 Total area, f t 2 High-pressure H,, scfd product W,, fraction CO Low-pressure Lo,scfd product Yo,fraction CO ~~~~~
equal size permeators in series
1900 3800 514.7
0.828 445.4
950 3800 485.1
0.893 485.3
0.091
a 475 3800 473.5
4
2
No-mix model
3800 3800 457.2
0.939 514.9
0.960 526.5
0.086
0.087
0.083
0.981 542.8 0.094
~
Table V. Comparison of Two-Stage Permeators Basis: 1000 ft3/day feed, 50% H2, 50% CO, P = 500 psi (Areas are in ft2,stream rates are in fta/day)
Model
NO mix
Membrane materiol
Polyimide Dacron
Perfect mix
Polyimide Dacron
Temp, O C
AI
100 50 75 30 100 50 75 30
1,500 4,900 2,600 8,600 5,200 18,400 7,200 27,400
First stage Hz W1 11
426 438 435 456 178 264 297 317
0.991 0.990 0.990 0.990 0.951 0.950 0.939 0.950
574 562 565 544 822 736 703 683
Second stage Y1
0.135 0,116 0.122 0.087 0.402 0.340 0.314 0.291
can be seen, the area requirements vary widely, depending on temperature, membrane material, and flow characteristics in the reactor. Exact comparison cannot be made because stream rates and compositions are the dependent variables in the permeator and there is some variation in product quality and quantity. However, qualitatively i t can be seen that the perfect-mix model results in required membrane areas of four to five times t h a t required for t'he no-mix model at about the same separation, and that operation of the permeators a t lower temperatures requires up to about three times more area than a t the higher temperatures. I n addition, the quantity of the low-pressure stream from the first stage ( L l )is also very important because this stream must be compressed from atmospheric pressure to 500 psig before feeding to the second stage. As can be seen, for the no-mix case the volume of this stream is nearly constant for both membranes and all temperatures, but there is a \\-ide variation in this rate for the perfect-mix case. Also of significance is the fact that t'he interstage stream is much larger for the perfect-mix case. I n addition, it should be noted that the interstage stream is smaller a t the lower temperatures for both cases. Since there is such a striking variation in area requirements and interst'age stream size, these data indicate great, care must' be taken in choosing the operating conditions and in the permeator design. Summary and Conclusions
This study was by no means exhaustive in the testing of available polymeric materials for the separation of CO and Hz and probably other materials could be found which would be
Az
H2
500 5 4 . 5 1,300 51.7 800 54.6 1,900 4 0 . 3 . 900 297 1,800 240 1,100 204 3,200 196
Total
Wz
lo
0.998 0.992 0.994 0.990 0.969 0.959 0.965 0.953
519 510 510 504 525 496 499 488
Yo
AT
H,
W,
1,
Mole fraction H2, 1 - Y,
0.044 2,000 481 0.992 519 0.956 0.030 6,200 490 0.990 510 0.970 0.028 3,400 490 0.991 510 0.972 0.014 10,500 496 0.990 504 0.986 0.088 6,100 475 0.962 525 0.912 0.043 20,200 504 0.954 496 0.957 0.049 8,300 501 0.949 499 0.951 0.037 30,600 512 1.951 488 0.973
superior to any of those tested. However, of t,he materials tested, Dacron and polyimide appear to be the most promising. It is interesting to note that in this study, ratios of the pure gas permeabilities ranged from about 4 t'o 110, and i t is possible that a material could be found which is selective for CO. This investigation has shown that design and membrane selection based on pure gas permeability data would be quite uncertain since small deviations from ideal behavior can make a large difference in membrane area requirements, especially in a system such as CO and H? where a high ratio of permeabilities is likely to result. Rather, experimental data on the flux and enrichment as a function of high-pressure stream composition for the actual system a t the anticipated conditions of operation is desirable. Mathematical models for no-mix and perfect-mix permeator stages were developed which utilize experimentally determined flux and enrichments. The models and computer solution techniques could be applied to any permeation system for which experimental data are available. A brief parametric study of the no-mix and perfect-mix models shows that the no-mix permeator is much more efficient and area requirements are much lower than for the perfect-mix case for the systems studied. For other systems with lower separation factors the difference would not be as great. The correspondence of an actual permeator to the ideal models would, of course, depend on the actual physical design of the permeator, and the comparison of the two models indicate that permeator design for correct flow characterist'ics would be very important. Other flow patterns are possible and, for example, a count'er flow model has been described (Oishi et al., 1961). Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 4, 1972
477
It was shown that a number (h’)of perfect-mix permeators in series approaches the performance of one no-mix permeator with the same total area. I n the extreme as N + the performance of the series of perfect-mix permeators should be identical to the no-mix model. However, with N = 8 the correspondence was quite close, and this indicates that proper baffling on the high-pressure side of the permeator would result in a performance approaching the no-mix model. Finally, the study of a two-stage permeator with both stages operating a t the same temperature indicates that the area requirements are much greater, the interstage stream that must be compressed is greater and enrichment is less for the perfect-mix case than the no-mix case, further emphasizing the need for correct flow characteristics in a permeator. Acknowledgment
The assistance of Chemical Projects International, Rome, Italy, and its Xanaging Director, R. G. Minet, in carrying out this research is gratefully acknowledged. Nomenclature
membrane area, ft2 flux through membrane, scfd/ft2 volume rate of high-pressure stream, scfd L volume rate of low-pressure stream (permeate), scfd P H ~PCO , = pure gas permeability coefficients, cm3(STP) . cm/sec . cm2 cm H g
A F H
= = = =
+
W = mole fraction CO in high-pressure stream Y = mole fraction CO in low-pressure stream or permeate dZ/dA = flus of CO only through membrane, a t any point mole fraction H2 product/ mole fraction CO
j
mole fraction Hz feed = actual local separation factor mole fraction CO (rrhere the compositions are measured at the same position coordinate) literature Cited
Atkinson, R., “‘Permasep’ Permeators for Hydrogen Separation,’’ Tech. Bull., E. I. DuPont de Nemours & Co., Inc., 1970. Franks, R. G. E., “ A Digital Computer Program for Simulating Unsteady State Processes,” Engineering Dept., E. I. DuPont de Nemours & Co., Inc., 1970. Levenspiel, 0. “Chemical Reactor Engineering,” Chap. 6, Wiley, Kew York, N. Y., 1962. RIichaels, H. S., Chem. Eng. Progr., 64 (12), 31-43 (1969). Oishi, J., Rlatsumura, Y., Hagashi, K., Ike, C., U.S. Atomic Energy Commission, Report No. AEC-TR-5134, 1961. Stern, S.A., Sinclair, T. F., Gareis, P. J., Vahldieck, K. P., Mohr, P. H., Ind. Eng. Chem., 57 (2), 49-60 (1965). Stern, S. A., Gareis, P. J., Sinclair, T. F., Alohr, P. H., J . A p p l . Polym. Sci., 7, 2035-51 (1963). Stern, S. A,, Walawender, W. P., Separ. Sci., 4(2), 129-59 (April 1969). Weller, S., Steiner, W. A , , Chem. Eng. Progr., 46 ( l l ) , 585-90 (November 1950). RECEIVED for review September 1, 1971 ACCEPTEDJuly 11, 1972
Kinetics of Silver-Catalyzed Ethylene Oxidation Peter 1. Metcalf,l and Peter Harriott Cornell University, Ithaca, N.Y. 14860
The kinetics of silver-catalyzed ethylene oxidation were studied using a differential reactor. Behavior of various inhibitors including ethylene oxide, carbon dioxide, water, and dichloroethylene was investigated at a number of reactant partial pressures. The rates of both ethylene oxide and carbon dioxide formation passed through maxima with increasing oxygen pressure. The inhibiting effects of carbon dioxide and water appeared to b e rapidly reversible and to follow a noncompetitive rate law. The inhibiting effects of ethylene oxide and dichloroethylene were only slowly reversible. These results were not completely consistent with Langmuir-Hinshelwood type rate expressions.
E t h y l e n e is easily oxidized with a silver catalyst. Two products are produced in this reaction: ethylene oxide and carbon dioxide.
0
CH?=CH?
+ 302
2C02
+ 2H20
(11)
Earlier studies by Bolme (1957), Buntin (1961), and Klugherz and Harriott (1971) have shown t h a t the reaction 1 Present address, E. I. du Pont de Xemours & Co., Inc., Wilmington, Del. 19898. To whom correspondence should be addressed.
478
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No.
4, 1972
is approximately first order in ethylene and three-halves order in oxygen a t low partial pressures of ethylene and oxygen. The rates of both reactions increase as the pressure of ethylene is increased, pass through maxima, and then decrease. A maximum in the rate of carbon dioxide formation with increasing oxygen pressure was suggested by Harriott (1971), but no maximum in the rate of ethylene oxide formation with increasing oxygen pressure has been reported. Buntin (1961) and Klugherz and Harriott (1971) found that the reaction products-ethylene oxide, water, and carbon dioxide-inhibit the reactions. liargolis et al. (1962) has shown t h a t various other elements more electronegative than silver-such as bismuth, sulfur, and chlorine-also inhibit the reactions.
