Analysis of Gas Separation by Permeation in Hollow Fibers C. Richard Antonson, Robert J. Gardner, Carl F. King, and Daniel Y. KO’ Contribution No. 5 11. Jackson Laboratory, Organic Chemicals Department, E. 1. du Pont de Nemours and Company, Wilmington, Delaware 19898
Gas separation by permeation in hollow fibers was analyzed. The high-pressure feed was on the tube side while the low-pressure permeate was drawn off on the shell side. Flow of feed and permeate was countercurrent. The effects of design parameters, operating variables, physical properties, flow patterns, and broken fibers on device performance (productivity, enrichment ratio, recovery of fast gas) were analyzed. Design parameters included fiber length, fiber outer diameter, and fiber hollow. Operating variables were feed pressure, feed flow, feed composition and pressure ratio. Physical properties were fast gas permeability and selectivity. It was shown that tube-feed, countercurrent flow is superior to various other combinations of shell-feed, tube-feed, countercurrent flow. Broken fibers manifest themselves as increases in the apparent permeability of the slow gas with little change for the fast gas.
Separation of gases by permeation through polymer membranes has generated considerable interest in recent years. Although the process has been known for over a century, recent advances are making it economically competitive in several areas. Applications which have received attention include recovery of hydrogen from refinery streams and ammonia plants, helium separation from natural gas and other streams, as well as sulfur dioxide removal from flue gases. While a considerable amount of gas permeation study and modeling has been published, relatively little information is available on permeation analysis of a commercial permeator, particularly a hollow fiber device. Permeation of gases through polyethylene membranes in film form was studied (Stern et al., 1971). Effects of pressure on pure gas permeabilities have been reported (Stern and Fang, 1972; Rodicher and Kroll, 1973). More recently, application of “free-volume’’theory to modeling of mixture gas permeation through experimental flat films was described (Fang and Stern, 1975). Pan (1973) and Walawender (1972) studied the effects of flow pattern and process variables in film devices. Blaisdell (1973) developed models for tube bundles made of silicone rubber. However, none of the above studies included the pressure drop either in the feed or permeate side of the membrane. I t is essentially this pressure drop in a commercial hollow fiber permeator which differentiates the current study from those carried out previously. The objective of this study is to analyze the effects of design parameters, operating variables, flow patterns, and broken fibers on device performance.
Hollow Fiber Devices Most studies employ polymeric membranes in film form. An alternative to film membranes is a device wherein the membrane is in hollow fiber form. Such devices have been developed and commercialized by Du Pont (Maxwell, 1967); other companies have also been active in this area (Mahon, 1966; Schingnitz, 1973; Yamamoto, 1973). The advantages of hollow fiber devices are: (1)the membrane surface area per unit device volume is orders of magnitude higher than that achievable with film membranes; ( 2 ) the hollow fibers do not require any support, whether the feed flows inside or outside of the fiber tubes; and (3) the hollow fibers themselves form the pressure vessel if the feed (high pressure) flows through the bore of the fibers. Partially compensating for the high surface-to-volume ratios are the generally lower permeabilities observed with hollow fibers. This is similar to the situation with film and fiber devices for reverse osmosis desalting
(Lynch, 1972; Probstein, 1973). Additionally, the pressure drop along the fiber bore is not negligible thus reducing the driving force available for gas permeation. A schematic of a single fiber in the device is shown in Figure 1.A typical device (Du Pont, 1969) and fiber specifications are given in Table I. The hollow fibers, which are made of polyester, are potted in epoxy a t both ends. After curing, both epoxy pots are cut to expose the fiber ends. High-pressure feed gas flows down the bore of the fiber (tube side) with permeate being drawn off on the low-pressure side (shell side). Residue exits the permeator a t the far end. Pressure drop takes place on the tube side while pressure on the shell side is constant. A 300-600 psi difference between feed and permeate pressure is typical. Flow of feed and permeate is countercurrent. Fiber length is divided into active and inactive sections, the latter being that length of fiber in the epoxy pots at either end where permeation does not occur; the pressure drops in the inactive sections can be significant. Model Development. The dimensionless equations governing the tube-side feed device are shown below. The basic permeation equations are derived in Appendix I. The summary equations for shell-side feed device are shown in Appendix 11. For tube side, z > 0
For shell side, z
>0 (4)
Equations 1 and 2 are the tube-side material balances for the fast and slow permeating gases, respectively. Equation 3 is the Poiseuille type equation for the pressure drop in the fiber bore. The differential length is measured from the residue end along the active fiber section. The tube-side boundary conditions a t the feed end are q1(z = 1) = x1 q2(2
= 1) = (1 - X , )
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 4, 1977
(5) (6)
463
t
Residue
k-Active 'Pot Length
Length-
__/1J 5
Pot Length
Figure 1. Single hollow fiber. Table I. Device and Fiber Soecifications
Active length ( L )= 14.6 f t Pot length (A) = 0.75 ft Device diameter = 11.4 in.
Fiber outer diameter ( D o )= 36 p Fiber inner diameter (Di)= 18 p
Numerical Solution. For numerical stability, the usual approach to handle this split value problem is not to start integration from the feed end. That is, rather than guess permeate mole fractions at the feed end and attempt to match the no-flow condition on the shell side a t the residue end, the tube-side flows and pressure a t the residue end were iterated until integration of eq 1-3 matched the given feed conditions. The procedure for adjusting the residue Conditions has been described previously (Fan, 1966).For simplicity, let q3 = PT. New guesses of the residue conditions (gi"+l) can be computed from the current value ( g i n ) by expanding a Taylor series about the current feed conditions (qin(z = 1))resulting from gin and extending it to the desired feed conditions ( q i ( t = 1))as shown in eq 9. qin+l (2 = 1) = q i " ( z = 1)
Equation 7 shows the pressure a t the feed end of the active section which is related to the feed pressure via the pressure drop across the pot (inactive) section a t constant flow rates. However, since eq 4 requires tube-side flow conditions a t the residue end, this problem becomes a split boundary value problem and is best to integrate from the residue end. Thus, it is necessary to guess the initial conditions a t the residue end, namely
The partial derivatives in the expansions were directly evaluated by differentiation of eq 1-3 with respect to the residue condition guesses and integration of the resulting set of differential equations. For this system, nine additional equations were generated (eq 10).
g l = 41, z = 0 g2 = q 2 , z = 0 g3 = q 3 = PT, z = 0
Initial conditions of the shell-side mole fractions are determined by the ratio of permeation rates
The above model uses several assumptions: (1)permeation involves three mass transfer steps for each gas-ibsorption solution onto the membrane, diffusion in the membrane, and desorption from the membrane surface. Henry's law applied to the gas-membrane interphase; (2) permeability coefficients for both gases are independent of gas pressure and depend only on fiber characteristics and temperature; (3) permeability coefficients for components of a permeating gas mixture are the same as those for the pure components; Le., components permeate independently of each other; (4) pressure drop in the fiber bore follows Poiseuille's equation for laminar flow with a parabolic velocity profile; (5) negligible axial diffusion and isothermal operation; and (6) mixture viscosity is based on mole fractions. We are aware of the fact that some of the above assumptions, particularly (2)-(4), may not be valid for other nonporous polymeric membranes or asymmetric membranes. Gas pressure was shown to have significant effect on permeabilities for permeation of some gases through polyethylene membranes (Stern et al., 1971, 1972; Rodicher, 1973). Coupling and/or iteration effects of permeabilities in gas mixtures have also been studied (Fang, 1975). Some of our recent experimental results with different types of fibers also indicated that the fast gas was "slowed down" by the slow gas and slow gas was "speeded up" by the fast gas. Furthermore, in some cases, Poiseuille's equation (eq 3) predicted smaller pressure drop than that determined experimentally if we had used fiber I.D. measured by photographic method. These problems deserve further study and research and will be the subject of further publication together with experimental data. However, for the fibers employed, the above listed assumptions have been found to be adequate in most situations. 464
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 4, 1977
where h,,(z = 0 ) = 1 when i = j ; 0 when j # j ; h,, = dddg,. Although initial guesses of residue conditions were usually based on experience, convergence was generally obtained even with poor initial guesses. Moreover a match to the feed conditions within f0.5% could usually be obtained in no more than five iterations. Such rapid convergence indicates the Taylor series expansion used to adjust the residue condition guesses yields a reasonable approximation. Through use over a period of years the above approach has been found to be both stable and adaptable to different flow patterns as will be discussed. Several recent papers have handled the split boundary conditions associated with gas permeation somewhat differently. Pressure drop was not considered on either side of the membrane; hence only two differential equations were needed to describe the process. These two equations were combined so as to yield the permeate mole fraction as the independent variable. Area required for separation was computed after the primary equation was solved and the resulting profiles stored. Blaisdell and Kammermeyer (1973) eliminated the split boundary condition by a change of variable (not applicable here), while Pan and Habgood (1973) circumvented it by specifying the desired residue mole fraction rather than desired recovery (split). Although making the permeate mole fraction the independent variable is a good approach because it reduces the number of equations by one, it was not employed here because the dimensions of the device were fixed. Such an approach would have required an additional iteration to match the device area. Discussion A. Effect of Process Variables. The following types of variables affect the process: (1) design parameters-fiber dimensions, device dimensions; (2) operating variables-feed pressure, feed flow, feed composition, shell pressure, temperature; (3) physical properties-viscosities, permeabilities. In dimensionless form, all of the above were combined into seven constants-C1, Cp, C3, Cq, Cg, pr, and xl. The ratio of fast gas permeability to slow gas permeability ( C p ) is termed the selectivity. Principal measures of permeator performance are: enrichment ratio (fast gas concentration in the per-
1.00 1
I
I
I
I
I
I
I 4000
-
F3000
-
LL
-182 c
-
[0 r
..
In 0 2. c
-> -
w
..
rE
u
0
3
82000 a
1000
0
-161;
-
-14
l0,OOO Feed Flaw (SCFH)
5000 2
I
I
I
I
I
3
4
5
6
7
Pressure R a t i o
(Pr)
8
Figure 2. Effect of pressure ratio and feed concentration; fast gas recovery = 50%; Pf= 500 psig; 1, X1 = 0.90; 2, X I = 0.50; 3, X I= 0.01. Table 11. Physical Properties Gas = hydrogen Pel = 200cB /.ll = 0.0088 CP
Gas = methane Pez = 5 cB /.lz= 0.011 CP
meate/fast gas concentration in the feed), permeate productivity (SCFH), and recovery of the fast gas. Except where stated, the analyses employ typical physical properties for hydrogen and methane as shown in Table I1 as well as device and fiber dimensions as shown in Table I. Throughout this discussion one should bear in mind the fundamental differences between the two types of applications mentioned above: upgrading hydrogen streams in refineries and recovering helium from natural gas. In the former, the feed typically contains between 50 and 80% hydrogen while in the latter, the feed is less than 1%helium. Selectivities are in the same range for both applications. However with hydrogen, the feed can be easily upgraded to acceptable levels in one device, while with helium, devices in series on the permeate stream would be required to produce product of acceptable quality. In other words, hydrogen requires a singlestage plant while helium requires a multi-stage plant. Thus with hydrogen, the emphasis is on productivity in order to reduce the number of devices while with helium, product quality (enrichment ratio) is also important in order to reduce the number of devices via reduction in number of stages. Most of the analyses were carried out for a feed composition of 50% fast gas and thus were typical of hydrogen upgrading. However, some exceptions will be noted. From eq 8, the enrichment ratio achievable under limiting conditions (zero recovery, zero pressure drop) can be computed. Three of the above parameters (pressure ratio, pr,selectivity, Cs, and feed mole fraction, x ~ affect ) the basic separation. Their effects have been described by Pan and Habgood (1973) for film devices; with fiber devices the effects are similar. Briefly, the enrichment ratio asymptotes to a limiting value given by eq 11as the pressure ratio is increased; the rate of approach is faster with higher feed mole fractions.
Figure 3. Effect of feed flow and feed pressure: pr = 34.5; X1 = 0.5; 1, Pf= 500 psig; 2, P f = 700 psig.
This is especially important for helium recovery because it means that very high pressures are required to realize the full potential of the membrane. Running at a lower pressure ratio means poorer quality product and hence more stages to reach acceptable helium levels. Figure 2 shows the fractional approach to the limiting enrichment ratio at a constant recovery of 50% for the fast gas; the feed flows were varied to maintain this recovery. As the selectivity increases, lower pressure ratios will yield the same enrichment ratio. Although not shown, it should be noted that, at fixed feed flow, lower feed mole fractions lead to higher enrichment ratios and lower productivities, while lower pressure ratios result in lower enrichment ratios and lower productivities.
,-.
limiting enrichment ratio =
CP
(XlCZ - x1+ 1)
(11)
The effects of feed flow and feed pressure on productivity are shown in Figure 3. As one might expect, increasing the feed flow leads to higher productivities and enrichment ratios but lower recoveries. However, as shown, if the feed flow is increased too far, the pressure drop inside the fibers becomes excessive,thus reducing the driving force and the productivity. Higher feed pressures alleviate the situation because of lower linear velocities and lower pressure drops. Figure 4 shows the effect of fast gas permeability (Pel) and selectivity (C2) on productivity and enrichment ratio at fixed feed flow. Increasing the fast gas permeability increases the productivity; the decline in enrichment ratio is a result of increased slow gas permeation a t the residue end where its shell-side partial pressure is high. Increasing the selectivity at fixed Pel means that Pea has decreased. Increased enrichment ratio is the obvious result; decreased productivity results from less slow gas in the permeate. Device design parameters usually include: fiber outer diameter (Do),fiber inner diameter (Di), active length ( L )and pot length (A). The ratio of Di to Do squared is the fiber hollow. Clearly pot length should be as small as possible, consistent with maintaining the mechanical integrity of the device. Productivity increases with increasing fiber hollow a t fixed outer diameter because it benefits from both decreased pressure drop and wall thickness. The upper bound on fiber Ind. Eng. Chem., Process D e s . Dev., Vol. 16, No. 4, 1977
465
,
Tube Feed
20
L
I. -@
c 4
2.-@
c
& 3.@ -*-
Shell Feed c-
4.
@
c-
7
5.-@
6.I*O
c-
c_
(0
-c
Figure 6. Flow patterns: tube feed; shell feed.
//
__1' Perm I Oe0a b i l i t y o f 200 Fast Permeating 300 Gas (cB) 400
12
-
Figure 4. Effect of permeability and selectivity: Qf = 6000 SCFH; XI = 0.5; p s = 0.029; 1, Cz = 10;2, Cz = 40; 3, Cz = 100.
I
Fiber A c t i v e L e n g t h I F t I
Figure 5. Effect of fiber active length-constant feed flow rate: pr = 34.5; Pf = 500 psig; Q f = 6000 SCFH; X I = 0.5.
hollow is determined by the mechanical strength required to withstand the high differential pressures across the fiber. The effect of fiber outer diameter at fixed fiber hollow, device dimensions, and pack density (fiber volume/total volume) is also easily understood. As the outer diameter decreases, pressure drop and number of fibers increase, while fiber wall thickness decreases. However, the detrimental effect of increased pressure drop does not overcome the dual beneficial effect of increased number of fibers and decreased fiber wall thickness. Thus for this application, the fiber outer diameter should be as small as possible. The effect of active length is shown in Figure 5 for a fixed superficial residence time (rDi2LN/4Qf).As fiber active length is increased, the gains in productivity are not linear as one would expect with film devices where pressure drops are not significant. Each additional foot of fiber gives less than a proportional gain in productivity because it is operating a t a lower pressure. On the other hand, fixed costs associated with the pot ends make very short fiber devices expensive. Thus device length is determined by the economics of the fabrication process as well as mechanical considerations. B. Effect of Flow Pattern. Different flow patterns can be used in permeator designs. Equations 1-8 can be readily altered to represent different flow arrangements. As an example, equations for shell-side feed countercurrent flow are summarized in Appendix 11. Where split boundary conditions arose, the method outlined earlier was employed. Six flow 466
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 4, 1977
2000
3000
I
4000
I
5000
F e e d Flow ( S C F H )
Figure 7. Effect of flow pattern; numbers correspond to cases shown in Figure 6; pr = 34.5; Pf= 500 psig; X I = 0.5.
patterns were considered; they are shown schematically in Figure 6 and described below. (1)Tube feed with countercurrent permeate flow; this is the case which has been the basis for all previous discussions. ( 2 ) Tube feed with cocurrent permeate flow; no split boundary conditions. (3) Tube feed with permeate flow away from the fiber (Weller, 1950); no split boundary conditions because permeation a t each point along the fiber is governed only by the mole fractions inside the fiber. (4) Shell feed with countercurrent permeate flow down the inside of the fiber; split boundary conditions similar to case 1. ( 5 ) Shell feed with cocurrent permeate flow down the inside of the fiber; the only split boundary condition involves the pressure inside the fiber a t the feed end. (6) Shell feed with countercurrent permeate flow at the feed end and cocurrent permeate flow a t the residue end; the numerical problems are severe because the point at which flow splits inside the fibers is not known; it must be found iteratively such that pressure drop is the same in both directions. Figures I and 8 show the effects of flow pattern on enrichment ratio and recovery of fast gas at different feed flows. Changes in productivity were small. Within the tube-feed flow patterns (cases 1-3), countercurrent flow is superior to cocurrent with outward flow lying between the two. The same was true within the shell-feed flow patterns (cases 4-6). Case 6 not only is a combination of co- and countercurrent flow but
I
Y
400 -
o
20 2000
3000 Feed
4000
5000
Flow (SCFHI
0.2 0.4 0.6 0.e 1.0 F R A C T I O N A L DISTANCE FROM F E E D E N 0
Figure 9. Pressure differentials between feed and permeate sides and/or gas pressure in fiber bore: A = pressure profile or pressure difference for tube-side feed; B = pressure difference for shell-side feed; C = pressure profile for shell-side feed; feed pressure = 500 psig; permeate pressure = 0 psig.
Figure 8. Effect of flow pattern; numbers correspond to cases shown in Figure 6; pr = 34.5;Pf= 500 psig; X I = 0.5. 4,000
also has a double-ended permeate take-off, thus reducing the parasitic pressure drop down the bore of the fiber. This makes it superior to cocurrent flow, but is not sufficient to make it better than countercurrent flow. In general, the performance of tube-feed flow patterns is better than shell-feed flow patterns. To understand this effect, profiles of the pressure drops in the fiber bore and pressure differentials across the fiber wall were plotted in Figure 9. As indicated, the pressure profile in the active fiber bore was markedly different in the tube-feed and shell-feed cases. Specifically, most of the pressure drop in shell feed occurs near the permeate take-off (feed end), while pressure drop in tube feed is almost linear with respect to length of the fiber. The resulting pressure differentials across the fiber wall (driving forces) for tube feed is greater than that for shell feed. Of the six flow patterns examined, tube-feed, countercurrent flow has both the highest enrichment ratio and the highest fast gas recovery a t all feed flows. Thus from a performance standpoint it is the preferred flow pattern. The results are consistent with previous investigations of gas permeation (Blaisdell, 1973; Pan, 1973; Walawender, 1972). C. Effect of Broken Fibers. Broken fibers can have a serious effect on device performance. When a break occurs with a tube-feed device, feed and residue are short-circuited into the permeate, thus reducing the enrichment ratio with a slight gain in productivity. T o monitor intrinsic fiber changes, a data reduction program was developed to compute permeabilities from field test data. The number of broken fibers could not be estimated with this program. Nevertheless it was necessary to understand how broken fibers would manifest themselves through the data reduction program. An analysis of the effect of broken fibers was in order. With broken fibers at the feed end, part of the feed leaks directly into the permeate. With broken fibers at the residue end, a portion of the residue leaks to the shell side and flows along the fibers affecting permeator performance before exiting at the permeate end. In short, leaks a t the residue end act as a sweep gas. Pan and Habgood (1973) analyzed the effect of a sweep in film devices. They found it to be beneficial insofar as it can increase productivity with little sacrifice in enrichment ratio in some cases. In effect the sweep gas lowers the shell-side partial pressure of the fast gas near the residue end, thus increasing permeation. Although results similar to
" t
-
2,000
m
,001
I
I
I
I
I 1 1 1 1
I
I 1 1 1 1 1 1 4 0
jZo2
E f f e c t of Broken Fibers on Apparent Permeability
-
P, = 3 4 . 5 PI = 500 osia
.01 B r o k e n F i b e r s ( % of T o t a l )
m
0. I
Figure 10. Effect of broken fibers on apparent permeability.
those of Pan and Habgood were found in this study, clearly a large number of broken fibers is detrimental to product quality. The gas permeation model, including the effect of broken fibers, was employed to simulate device performance. The results thus generated were used in the data reduction program to compute apparent permeabilities. The results are shown in Figure 10. The amount of fast gas which broken fibers contribute to the permeate is small compared to the amount through permeation. Thus the apparent fast gas permeability is close to the true value. On the other hand, little slow gas permeates across the fibers, making the amount which leaks to the permeate side significant. The result is an apparent slow gas permeability which can be much higher than the true value. Summary Table I11 summarizes the effects of system parameters on device performance. Each row gives the general trend in performance with increases in that parameter, all other parameters being held constant. The trends are for typical operating conditions with a hydrogen-methane mixture. The base values around which perturbations were made are also given. Clearly the table is not all inclusive. As has been noted, interactions between parameters can be significant, resulting in reversal of the trends shown. Viscosity and pot length effects were not Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 4, 1977
467
Table 111. Summary of Effects Enrichment ratio
Recovery
Productivity Increases Increases Increases Increases
Decreases Decreases Decreases Increases
Increases Increases Increases Increases
Increases Increases Decreases
Decreases Decreases Increases
Increases Increases Decreases
Decreases Increases
Increases Decreases
Decreases Increases
of fast gas
Operating Variables Pressure ratio (pr),34.5 Feed pressure (P,), 500 psig Feed comDosition (XI).0.50 Feed flow-(Qf),6000 SCFH Design Parameters Active length (I,),14.6 f t Fiber hollow, 25% Fiber outer diameter ( D o ) ,36 p Physical Properties Selectivity (Cz), 40 Fast gas permeability (Pel),200 cB discussed because it is obvious that increases in these variables lead to detrimental increases in bore pressure drop. In analyzing the effect of flow pattern, it was shown that countercurrent flow is better than cocurrent flow, tube feed is better than shell feed, and tube-feed, countercurrent flow was the best design of the six considered. Finally, the effect of broken fibers manifests itself in the form of higher apparent permeabilities for the slow gas with little change in the apparent permeability of the fast gas. Acknowledgment We acknowledge the timely contribution of P. F. Tomlan, who suggested the method employed for solving the split boundary value problem. Appendix I Basic Equations for Gas Permeation. The present study considered permeation as the penetration of gases or vapors in the form of individual isolated molecules through nonporous membranes. The transmission of the gas consists of three consecutive steps as indicated by the following diagram.
Since membranes are very thin, the concentration gradient can be approximated by a linear relation dC C,-CT *dt -
t,
Combining the above equations gives u=-DH--”----pP,P -PTPT-Ps tm tm where P, = D H = permeability coefficient. For a mixture gas, the driving force for each component will be its partial pressure differential. Consider permeation taking place through the fiber wall and use the logarithmic mean radius for deriving permeation area. Equations 1 and 2 are easily obtained from the above equation. Appendix I1 GAS, SHELL-SIDE FEED, COUNTER
PERMEATE
SCHEMATIC PRESENTATION OF PERMEATION
TUBE- SIDE
SHELL-SIDE
RESIDUE
FEED
T u b e Side
Fast: z = 0:,
Y 1Tg3)
Y 1T -
For convenience, tube side indicates the high-pressure side and shell side represents the low-pressure side of the membrane. 1. In the tube side, the permeating component dissolves a t the surface. Assuming thermodynamic solubility equilibrium develops under isothermal condition and the solubility of gases in the membrane is generally very low, Henry’s law applies to the interphase behavior
H=%
Shell Side
PT
2. Transport of gases through the “nonporous” membrane can be described by Fick’s law of molecular diffusion dC u = -Ddt 3. Desorption of gases from the membrane surface onto the shell side also follows Henry’s law
Pressure: ps = constant Boundary Conditions Fast: q l s ( z = 1) = X I Slow: q p s
488
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 4, 1977
(2 =
1) =
xz
Pressure: p r
(2
= 1) = {I
+ ~ C ~ C ~ ( F-~g(l )X I + P 2 W 2 - g2))11'2
42 .~ = dimensionless QdQf
flow of slow gas on the tube side,
= dimensionless flow of slow gas on the shell side for shell-side feed Q1 = flow of fast gas on the tube side, SCFH Q2 = flow of slow gas on the tube side, SCFH Qf = total feed flow, SCFH t = membrane thickness from the high pressure side, cm T = operating temperature, "C To = standard temperature, 273 K u = gas permeation flux, cm3 (STP)/cm2-s X1 = mole fraction of fast gas in the feed y1 = mole fraction of fast gas on the shell side Y1T = mole fraction of fast gas on the tube side for shell-side feed 2 = distance from residue end, f t z = dimensionless distance from the residue end, Z / L X = pot length, ft ~1 = viscosity of fast gas, CP 1r2 = viscosity of slow gas, CP ~2~ ~~
Guesses
Fast: g1 = q l S ( z = 0 ) Slow: g2 = q z s ( 2 = 0) Pressure: g3 = PT ( z = 0) Nomenclature C = concentration of gases in membranes, cm3 (STP)/cm? C1 = 2rPelLPfN/Qfln (DcJDi) C t = membrane selectivity, PeJPe2 CA = l28QfLPoT~l/.rrDl4NP~To c4
= X/L
C5 = viscosity ratio, pJp1 cB = permeability Pe X 10l2 D = diffusivity of gases in membranes, cm2/s Di = fiber inside diameter, ~r D,, = fiber outside diameter, p g l = dimensionless flow of fast gas a t the residue end, q1(z = 0) g2 = dimensionless flow of slow gas a t the residue end, q2(z = 0) H = Henry's law constant, cm3 (STP)/cm3 cmHg L = fiber active length, f t N = number of hollow fibers N B F = number of broken fibers p s = dimensionless shell-side pressure, Ps/Pf pr = pressure ratio, Pf/Ps PT = dimensionless tube-side pressure, PT/Pf P f = feed pressure, psi P, = shell-side pressure, psi PT = tube-side pressure, psi Po = standard pressure, 14.7 psi Pel = permeability of fast gas, cm3 (STP)-cm/cm2-scmHg Pe2 = permeability of slow gas, cm3 (STP)-cm/cm2-scmHg q = dimensionless flow of fast gas on the tube side, Q1/Qf 91s = dimensionless flow of fast gas on the shell side for shell-side feed
Literature Cited Blaisdell, C. T., Kammermeyer, K., Chem. Eng. Sci., 28, 1249 (1973). Du Ponf Innovation, 1, 1 (1969). Fan, L. T., et al.. "The Continuous Maximum Principle-A Complex System Optimization", pp 354-358,Wiley, New York, N.Y., 1966. Fang, S. M., Stern, S. A., Chem. Eng. Sci., 30 (8), (1975). Franks, R. G.E., "Mathematical Modeling in Chemical Engineering", pp 192-196, Wiley, New York, N.Y., 1966. Lynch,M.A.,Mintz,M.S.,J.A.W.W.A.,64(11),711 (1972). Mahon, H. I., U.S. Patent 3 228 876 (1966). Maxwell, J. M., et al., US. Patent 3 339 341 (1967). Pan, C. Y., Habgood, H. W., Fourth Joint Meeting of the Canadian Society of Chemical Engineering and the American Institute of Chemical Engineers, Vancouver, B.C., Sept 1973. Probstein. R. F., Am. Sci., 61 (3),280 (1973). Rodicher, H., Kroll, V., Chemtech, 21 (1973). Schingnitz, M., et al., German Patent 2 150 241 (1973). Stern, S. A., Fang, S. M., Jobbins. R. M., J. MacromoISci.-Phys., BS(l),(Mar
1971). Stern, S. A., and Fang, S. M., J. Polym. Sci., Part A-2, 10 (1972). Walawender, W. P., Stern, S.A.. Sep. Sci., 7 (5),553 (1972). Weller, S.,Steiner, W. A., J. AppI. Phys., 21, 279 (1950). Yamamoto, T., et al., Chem. €con. Eng. Rev., 5 (4) 22 (1973).
Received for reuieu: April 8, 1974 Resubmitted February 14, 1977 Accepted June 22,1977
Nitrate Removal from Waste Solutions by Solvent Extraction limo K. Mattila" and Tlmo K. Lehto Kemira Oy, Oulu Research Laboratory, 90 10 1 OuIu IO, finland
A process for recovering nitrate from waste nitrate solutions by solvent extraction with a mixture of water-insoluble secondary amine in an aliphatic kerosene diluent has been developed and demonstrated successfully in pilot-plant mixer-settler tests. Nitrate is recovered from the solvent by contacting it with a nearly saturated KCI-KN03 salt solution. KCI converts the amine to chloride salt form and transfers the nitrate to the salt solution. The recovered nitrate crystallizes easily from the salt solution as high-purity solid KN03 (>99% purity) and the mother liquid is returned to the stripping stage after dissolution of an equivalent amount of KCI.
Introduction Liquid-liquid extraction has proved to be a very promising method for the recovery of nitrates from nitrate waste solutions. It is generally known that suitable extractants for the removal of nitrates are certain high-molecular-weight, water-insoluble amines which act as liquid ion exchangers
(Kunin, 1973).The free-base form of the amine removes nitric acid from waste solutions by neutralization. The nitrate is then stripped back to the corresponding salt by using a suitable alkali, and the amine simultaneously converted back to its original free-base form is returned to the extraction. If the nitrogen compounds to be removed are in nitrate salt form, Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 4, 1977
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