VAPORIZATION THROUGH POROUS MEMBRANES M. E. F I N D L E Y University of Missouri
at
Rolla, Rolla, Mo.
Mixtures may b e evaporated from one interface of a nonwettable porous membrane with diffusion through the vapor-filled pores and condensation a t the other interface of the membrane, by a sufficiently higher temperature on the mixture side maintained by a heat supply to the mixture and heat removal from the condensate equal to the latent heat transferred with vapor plus heat transferred by conduction. This permits essentially infinite-stage flash evaporation at constant liquid pressures, either with diffusion through noncondensable gases in the pores, or with vapor flow a t a lower pressure than liquid pressures, but with liquids excluded from pores by surface tension.
Paper, glass fiber, and diatomaceous earth-containing
membranes can b e used for this type of transfer, and better membranes appear to b e feasible. Calculations indicate possible economical performance, especially a t high temperatures, if high temperature, long life, and low cost membranes are obtainable.
N EVAPORATING
solutions or mixtures, heat consumption is
I reduced by using a n increased number of effects or stages, each of which must normally be at a different pressure from the others. However, if evaporation-condensation is reduced to the essentials only, as in “flash” evaporation, the only requirement is solution, vapor, and condensate separated and at suitable temperatures (2, 4). These rcquirements can be met by a solution layer, vapor in a pore, and a condensate layer. Thus a single pore, with liquids excluded, can act as a small single stage of flash evaporation. On this basis a porous membrane could act as a n infinite-stage flash evaporation system. T h e purpose of this investigation was to study the possibility of this type of evaporation. Some of these results have been included in a patent application on evaporation and mass transfer through membranes with temperature and vapor driving forces. Experimental
Conventional Evaporation. The basic principles and requirements involved in evaporation are relatively simple. T h e requirements for a single effect of evaporation are a liquor section, a vapor section, and, if vapors are to be condensed, a section for condensing and collecting condensate separated from liquor. Finally it is necessary to provide means of adding heat to the liquor and removing heat from the condensate. I t is possible in stagewise flash evaporation, such as the “vaporreheat” method (4), to add heat to the liquor outside of the evaporator and to supply a coolant directly into an evaporator for condensation and heat recovery. A flash evaporator stage may contain only a liquor section, a vapor space, and a condensate section with the necessary inlets and outlets. Similarly a single vapor-filled pore leading from a hot liquor surface to a cooler condensate surface may act as a n evaporation stage.
Evaporation through a Porous Medium. Assume that a hot solution, 3 in Figure 1, is placed in contact with one side of a porous medium or porous membrane, 1, of sufficient thickness, that a sufficiently cooler liquid, 4, iy placed in contact with the other side, and that liquids are held out of the pores at surfaces 5 and 6 by surface tension forces. Then if the vapor pressure at the hot solution surface, 5 , is greater than the vapor pressure at the cooler liquid surface, 6, evaporation will occur at the solution surface and vapors, M , will diffuse or flow through the pores to the cooler surface, where they will 226
l&EC PROCESS DESIGN A N D DEVELOPMENT
Figure 1 . Schematic diagram of evaporation through porous membranes
condense. Latent heat will be transferred as in conventional evaporation. If noncondensable gases are present, the vapors must diffuse through the membrane or medium, but if noncondensables are eliminated, vapors will flow through the membrane, with the difference in vapor pressures supplying the pressure drop. Both liquids may be a t any convenient pressure higher than the vapor pressure, so long as surface tension forces prevent their entry into the pore vapor spaces. No entrainment will occur, no changes in pressure are required for liquids, and the pressure and temperature of evaporation are limited only by the liquid temperatures and the possibility of noncondensables being present. Scaling will be unlikely against a nonwettable surface, liquid flows from pore to pore (or “stage” to “stage”) are possible in any direction with a minimum of pumping, and finally, the evaporator may consist of only a thin layer of solution, a relatively thin porous medium, and a thin layer of condensate. Heating and cooling may be carried out outside the evaporation system, through a heat exchange surface parallel to the porous media, or by other methods. T h e only disadvantages over conventional evaporation other than the requirement of a porous medium would be the resistance to flow or diffusion through the medium, and the loss of heat by conduction through the medium, Q in Figure 1. Transfer through other phases than vapor by similar temperature driving forces should be possible, including other
liquid phases and possibly solid phases, with direction and required temperatures depending on the specific phase changes involved. However, such transfer might not be feasible because of higher heat conductivities and the resulting loss of heat without mass transfer. This method utilizes membranes similar in principle to those used in “vapor-gap” reverse osmosis ( 3 ) ,but driving forces are different and high pressures are not required. Infinite-Stage Flash Evaporation. O n e scheme of using evaporation through a porous medium to utilize effectively the possible advantages would be to maintain countercurrent flow of mixture to be evaporated and coolant, as shown in Figure 2. I n this way the latent heat of the mass transferred may be received by the condensate coolant at a temperature close to that at which it is removed from the mixture or solution, similar to a countercurrent heat exchanger. In this way the coolant outlet stream can be elevated to near the inlet solution temperature, and this allows retransfer of the heat to the solution by countercurrent heat exchange. This could elevate the solution feed and recycle to near the outlet coolant temperature. For each unit mass of solution circulated, the major energy requirement of heat would be only that required to elevate the unit mass through the heat exchanger AT and the AT across the medium in the evaporator. The maximum amount of moisture transfer per unit circulated would be approximately the quantity with latent heat equivalent to the solution enthalpy drop in the evaporator from inlet to outlet temperature, This assumes equal flow of heat capacity, so that AT in the exchanger and evaporator are constant. The minimum AT in the evaporator must be greater than the boiling point elevation throughout the evaporator, so that vapor pressure differences will be in the proper direction. The minimum AT in the heat exchanger will be 0. By the use of increasing areas of porous medium and heat exchange surface the AT values may
II I
1 I
HEAT
I
-IEAT EXCHANGER
I
111 I
KMBRANE :VAPORATOR
-
;ONDENSER
I
I I
EXCESS F O R COOLING +---
Th
h
I
>El
I I
I
1
I
PRODUCT ONDENSATE PRODUCT
Figure 2. Infinite-stage flash evaporation through porous membranes
be brought as close as desired to the minimums. Ifoperated with minimum A 7’values, in the evaporator and exchanger, as above, and with no heat conducted through the membrane, it can be shown that the process is almost reversible. (The only irreversibility would be due to sensible heat of the transmitted vapor from the solution temperature to condensate temperature and that due to mixing concentrated recycle solution with feed.) Thus the operation could conceivably approach the minimum available energy consumption for a n appropriate separation. ’The minimum heat consumption would depend on the source and sink temperature as in the Carnot cycle, but minimum available energy consumption would depend only on initial and final solution conditions. In most evaporators each effect is at a different pressure, and liqirids must be maintained at suitable pressures and levels by pumps, valves, and controllers. However, in the infinite-stage flash evaporation through porous media system suggested, the liquids involved could be at any convenient pressure higher than the highest boiling pressure, and the liquid sections would be completely filled. As liquid flows from one pore surface to another it is transferring from one ”stage” to another. T h e only vapor space is in the pores, ivhere pressure is determined by liquid temperature and noncondensables, and where liquid surface position is maintained by surface tension forces. This method may have capabilities of providing one of the simplest, smallest volume, most efficient evaporation systems possible. The above considerations were the basis for studies on the rates of heat and mass transfer through various types of porous and some nonporous media. The primary purpose of the study was to determine the possibility of the proposed method and the types of membranes or media which might be suitable. Procedure. ’The procedures used in this study for determining the rates of heat and mass transfer through porous media were developed primarily to obtain approximate evaluations of various types of media rather than to obtain accurate results on transfer coefficients. The basic procedure in runs 1 through 23 consisted of weighing a covered bottomless container with the membrane under study covering the bottom, and then filling this container with the desired liquid. The container was then placed so that the bottom membrane was in contact with the desired liquid in a relatively large pan or tray, in which the temperature remained relatively constant. From 10 to 30 minutes were allowed for the membrane to approach equilibrium. The container with the membrane was then emptied and refilled with a liquid at known temperature, and excess moisture was blotted off the membrane. T h e container was then weighed with the liquid contents, and replaced in contact with the liquid in the pan as timing was started. Bulk temperatures in the pan were measured during the run. After 10 to 30 minutes, the container was removed, excess moisture was blotted, the container was weighed, and the liquid temperature was measured. The change in weight and temperature, and the average of initial and final temperatures, all in the container, were then used for calculations of moisture transferred, M , and total heat transferred, q T , both on a unit area basis. Enthalpy transfer with the moisture was subtracted from qT to give qc, the heat transferred by conduction. Based on the average bulk temperatures, the over-all heat transfer coefficient for conduction heat, U , was calculated in B.t.u./ hr. sq. ft. F. Using vapor pressures of water, D, a t bulk temperatures and estimated activities, a, where necessary, the over-all mass transfer coefficients, K.hl, were calculated in lb./hr. sq. ft. inch Hq. I n runs 1 through 6 water was used on both sides of the membrane and a higher temperature was used in the container. In runs 7 through 23, salt solutions a t a higher temperature were used in the pan. In runs 7 through 13, a 7y0 salt solution was assumed to have an activity of water of 0.96. VOL. 6
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I n runs 14 through 23, a salt solution was used which had a boiling point elevation corresponding to a n activity of 0.945. Runs 24 through 27 were carried out using a different type of apparatus, which consisted of two chambers separated by a porous membrane with a glass plate and 3/s-inch gasket on the solution side and a brass plate and 3/s-inch gasket on the condensate side. T h e solution was heated with a n infrared lamp, while the condensate was cooled by convection to air from the brass plate. Holes in the thick gasket permitted tubing for filling and a thermometer on each side in runs 25, 26, and 27. Both chambers were filled and heating was commenced. When steady-state operation was attained, the condensate rate of accumulation was measured. I n run 26, a n attempt was made to remove noncondensable gases by steaming the membrane and bringing to a boil the solution and initial water fill for the condensate side. However, it appears unlikely that this was satisfactorily accomplished in run 26, since the results are similar to run 25. This was probably because of difficulties with the apparatus near the boiling point. R u n 27 was made on a type of membrane prepared with a view toward extended operations at higher temperatures. T h e membrane was prepared from a slurry of Owens-Corning glass fiber, type AA for glass paper, and a Teflon suspension, D u Pont 30B. Both the glass fiber and Teflon should be capable of operation at up to 500' F. T h e equations used were:
M
=
(W, - Wi)/At
qr
=
WiCp(Tcz
qC
= qT
-
Tci)/At
- M(HVTM - H L T C )
KIM= M/(apTM
-~TC)
where W = weight of water A = area of transfer p T M = vapor pressure of water at solution temperature P T C = avkrage vapor pressure of water a t Tc H = enthalpy t = time cp = specific heat T c = water temperature T M = temperature of solution or mixture a = activity of water in mixture M = water transfer per unit area q T = total heat transfer per unit area qc = heat transfer by conduction per unit area Subscripts 1 and 2 represent initial and final; V and L, vapor and liquid; and T M and T C , temperatures. Bars represent averages. Actually the values of U and K , are not independent, since U values were calculated based on heat conducted through the membrane, even though heats of vaporization had to be transferred through the liquid films. Likewise, the K, values were also a function of liquid film heat transfer resistances, because of their effect on surface temperatures. Table I gives the experimental results. O n the basis of run 21 on aluminum foil, if it is assumed that l / U = l/hv l / h c , and that hM = hc, the film heat transfer coefficients, then h, = hc = 2 Lr = 75 B.t.u./hr. sq. ft. O F. If the same values of hM and hc are assumed for any given run, the temperature drop through the films, A T p c and AT,,, can be-estimated as equal to ATFc = A T F M = qT/hc = qT/75. A better estimate of K M and U applying only to the heat and mass transfer across the membrane can then be obtained as follows:
+
M
228
l&EC PROCESS DESIGN A N D DEVELOPMENT
and
Table I1 gives estimated values for KMV and ULu for runs 19, 20, 22, and 23, and a comparison of the ratios of KA,/U and K M M / UM. In Table 11, the effects of liquid film concentration gradients are still included in the values of K M M . Discussion
Runs 7 and 17 illustrate an important point concerning the thickness of membranes. T h e temperature drop, T I Tz in Figure 1, across a membrane must be sufficient to establish the necessary pressure or concentration gradients for transfer and in order to maintain such a A T , the resistance of the membrane to heat transfer must be a sufficient fraction of the total resistance to heat flow. With no mass transfer, T I Tz = RM(T.w - Tp)/R.w RFlu R F C , where R = heat transfer resistance, F M refers to solution film, and FC refers to condensate film. If T I - Tz is to be greater than a certain minimum, the boiling point elevation, R,, will have to be greater than some minimum value for any given bulk temperature difference. Since Rnr is normally proportional to thickness, a certain minimum thickness is required for any given conditions. This probably explains why this type of transfer has not been appreciable in previous investigations with thin films (7, 5 ) , and why negative transfer (by osmosis) was obtained in run 7 . However, if membrane heat transfer resistance is sufficiently increased, as in run 17, transfer may be brought about. This demonstrates the desirability of carrying out the transfer through a vapor phase with high resistance to heat transfer. As membrane thickness is increased, resistance to mass transfer also increases. Thus for any given bulk temperature difference, there would exist some optimum membrane thickness for maximum mass transfer per unit area. In several runs, condensation was noted inside the membrane, specifically in all those using multiple-layer membranes and apparently inside single asbestos paper membranes. I n all membranes where resistance to diffusion or flow increases relative to resistance to heat flow by conduction, as the vapors travel through the membrane, there would be a tendency for latent heat to be conducted away, producing internal condensation, which might further decrease conduction resistance. Similarly internal adsorption of moisture might cause some swelling, reducing mass transfer, and increasing heat conduction. Cellulose paper membranes have been operated u p to 7 hours in run 24 without obvious difficulty of this type, while water repellant-treated asbestos paper quickly picks up moisture internally. This may be related to the manner in which water repellant is held by the fibers. Other types of membranes were tried unsuccessfully, primarily because of leaking or insufficient porosity. These included cloth, felts, and foamed polymers. With the apparatus and procedure used in runs 1 through 23, it was not feasible to eliminate noncondensable gases from the pores, and thus diffusion through noncondensables was the mechanism of transport. With the elimination of noncondensables in a n evaporation system, such as by steaming the membrane just prior to filling with deaerated liquids, it should be possible to obtain mass transfer by flow and rates should be considerably higher. This should increase the fraction of the heat utilized in mass transfer. Thus far this type of transfer has
-
+
+
-
Table 1.
M, Lb./Hr. Sq. Ft. 0.032 0.032 0.025 0.029
Experimental Results
Av. QCl qT? B.t.u./Hr. B.t.u./Hr. TM, F. Sq. Ft. Sq. Ft. 31.9 92.5 65.4 91.4 103.3 124.1 58.4 100.5 86.5 98.4 60.4 92.0
Av. apTM, In. Hg 1.575 2.13 1.96 1.842
Av. Tc,
Av.
KIM, Lb./Hr. In. Hg Sq. Ft. 0.055 0.025 0.025 0.030
Bet."./?. PTC, ' F. In. Hg Sq. Ft. F. Membrane 78.7 0.992 2.3 Paper hot cup A 75 0.875 3.2 Paper hot cup A 76.6 0.923 2.4 Paper hot cup A 75.8 0.899 2.6" 2 layers paper hot cup A 108.7 2.50 5.48 0.028 140 137.3 4.9 0.083 224 5 Paper hot cup A 1.93 100 154 8.35 0.027 137 2.5 0.175 6 336 Paper hot cup A b 78.5 122.7 ... ... ..* 0 ... 7 5 layers uncoated cello- -Negl. phane 82.2 8.46 1. l l 448 156.2 0.383 860 0.052 6.1a 2 layers asbestos paper 8 silicone 86.7 3.72 124.3 1.28 1380 0.053 0.131 1520 36.7" 9 1 layer asbestos paper silicone 70.9 2.52 0.762 492 110.4 0.092 590 0.052 12.5a 2 layers asbestos paper 10 silicone 68.9 2.15 0.712 286 104.9 0.0084 293 0.006 7.9" 11 2 layers paper hot cup A 76.7 2.22 0.926 341 106.1 11.6 0.237 0.183 594 12 1 layer paper hot cup B 72.5 2.12 55 104.4 0.805 205 0.142 0.108 13 2 layers paper hot cup 1.730 B b 80 ... 3.86 126.2 1.03 0.226 l/lB-inch gum wood ... 0.080 14 veneer silicone b 1.05 80.4 3.79 ... 125.5 0.144 0.053 15 1 layer paper cup B ... b 74.5 ... 128 4.05 0.861 0.106 0.033 l/ls-inch gum wood 16 veneer b a 81.5 4.42 1.08 0.051 . . . 131.3 0.015 3 layers uncoated cello17 phane separated by glass fiber b 134.7 79.3 0.206 4.85 1.01 0.053 18 Paper plate 4.57 1.22 132.5 85.2 361 507 0.137 19 Paper plate 0.041 7.6 412 4.63 1.21 133 84.8 570 0.150 20 Paper plate 0.044 8.5 125.6 94.1 0 ... 980 Aluminum foil 980 ... 0 21 37.5 135 80.7 467 4.88 1.05 255 0.198 22 4.7 Glass fiber mat on 0.052 nylon water repellant 270 0.190 47 3 130.1 4.29 82.9 1.13 23 Glass fiber, diatom. 0.060 5.7 earth mat on nylon water repellant 0.197 (7 hour run) 24 water reBlotter pellant b ... 0.238 167 10.91 155 25 Blotter water re8.56 0.101 (2 :20 run) pellant b . . . 0.236 159.9 12.05 173.8 9.63 26 Blotter water re0.097 pellant (steamed) b C . . . 126.5 0.097 3.96 114.4 27A 2.94 0.096 Glass fiber Teflon b . . . 179.2 14.43 1.60 153.5 8.25 Glass fiber 27B Teflon 0.26 a Appeared t o have internal condensation or adsorption of moisture between layers or inside surfaces. Not suitable f o r heat transfer calculations. e A and B included in one 3-dav run. Exjt.
No. 1 2 3 4
+ + +
+
+
+
+ + +
++
Table II. Calculated Transfer Coefficients for Membrane Only A TFM
Exfit. NO. 19 20 22 23
ATFc,
OF. 6.8 7.6 6.2 6.3
KMM 0.059 0.067 0,069 0.005
UM 10.7 12.5 4.9 7.8
KMM/UM 5.5(10-3) 5.4(10-3) 14.1(10+) 10.9(10-3)
KM/U 5.4(10-3) 5.2(10-3) 11.1(10-3) 10.5(10-5)
not been demonstrated because of difficulties in steaming without causing internal condensation or excessive flexing. T h e apparatus used in runs 24 through 27 was used to attempt runs with noncondensables eliminated, which were unsuccessful. However, it was possible to establish that over somewhat longer periods u p to 3 days, the rates of mass transfer could be maintained. This apparatus also permitted evaluation of K M with lower driving forces. For a given set of bulk temperatures, the ratio of mass transfer coefficient to heat transfer coefficient would determine the fraction of the heat used effectively in mass transfer, and
the fraction lost by conduction through the membrane. T h e fact that the ratios in Table I1 are similar in magnitude indicates that calculations of heat consumption based on overall coefficients should be reasonably accurate, even if film coefficients a r e reduced considerably, and that the major heat transfer resistance is in the membrane, Based upon experimental observations and logical conclusions, the most suitable types of medium for this method of mass transfer would have:
A high resistance to heat flow by conduction A sufficient but not excessive thickness A negligible permeability to the liquids and nonvolatile components, or small-diameter, nonwettable pores High porosity A low adsorptivity of moisture A uniform thermal conductivity and porosity, or increasing porosity compared to conductivity in the direction of transfer Relatively straight-through pores, if possible None of the membranes studied had all the above characteristics, but improved characteristics should be possible in special membranes, prepared from porous ceramics, polymers, special paper, felts, tightly woven cloth, small-pore foams, or VOL. 6
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highly porous solids such as diatomaceous earth bonded into mats, sheets, or cakes. Suitable water repellancy should be obtainable by application and drying of fluorocarbon or other water-repellant suspensions or solutions. T h e cost, useful life, temperature range, and performance of such membranes will determine the feasibility of this potential method of evaporation. The use of evaporation through porous membranes would not necessarily be restricted to infinite-stage flash evaporation but could conceivably be useful in any process requiring vaporization and condensation. For example, in distillation, if porous media made up the vapor spaces and alternated between thin liquid layers, it might be possible to obtain considerably more "plates" per foot of height. Since gravity separations of liquid and vapor would not be necessary, columns could be horizontal. Evaporation or distillation with zero gravity might also be more feasible for the above reason. Calculations on lnflnite Effect Evaporation of Sea Water through Porous Membranes
Based upon coefficients of K.u = 0.055 for mass transfer and
U = 5.7 for heat transfer, well within the realm of possibility even with noncondensables present, calculations were made on the system shown in Figure 2 for saline water conversion, using 0.96 for the activity of water in sea water throughout, and assuming the following conditions: EVAPORATOR Condensate (coolant) entering. T -~ p lin Figure 2, 75' F. Solution leaving, T.&, 80' Fr' Solution entering, T,w, 212', 250°, 350°, 500' F. Condensate leaving, Tc2, 207', 245', 345', 495' F
-
RECOVERY HEATEXCHANGER Condensate entering, TCZ, 207', 245', 345O, 495' F. Solution leaving, T.vE?,202', 240°, 340°, 490' F. Condensate leaving, TCEI,85' F. Solution entering, T411,80' F. CONDENSATE COOLER Condensate entering, TCEI, 85' F. Sea water leaving, same as T M 180' , F. Condensate leaving, Tcl, 75' F. Sea water coolant and make-up entering, TMF,less than
75' F.
SOLUTION HEATER Solution entering, T.UE~, 202O, 240°, 340°, 490' F. Solution leaving, T M Z212', , 250°, 350°, 500' F. Heat supply as appropriate and economical, cost assumed to be 25 cents per 106 B.t.u. Considering an infinitesimal section,
dc
= Knr(apTAu- Prc)dA
do
= U(T.U
230
-
Tc)dA
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
These can be combined and reduced to
Thus, AC, the mass transfer, may be obtained by graphical or numerical integration from outlet solution to inlet solution temperatures, where
Q
C
CP AM
T.u A
-
conduction heat loss water flow at a given point specific heat latent heat of water at a given point Tc constant (5' F. used) = area of porous media from low temperature end = = = = =
O n this basis, the following heat requirements and areas were obtained at various inlet solution temperatures:
TMZ, ' F. 212 250 350 500 Heat required, B.t.u./ thousand pal. 1,317,000 909,000 477,000 277.000 Area of meGbrane, sq. ft./ (M gal./day) 12,250 9,260 6,800 3,820 Cost of heat only, cents/ M gal. 33 23 12 7 The above calculations indicate less consumption of heat a t high solution inlet temperatures for two basic reasons: first, the increasing efficiency of heat utilization, basic to thermodynamics, and second, the higher rate of increase of vapor pressure relative to temperature increase, which increases the AP driving force and thus mass transfer at higher temperatures while A T values for heat transfer remain constant. This increases the fraction of heat producing mass transfer. There is a slight effect of lower heats of vaporization a t high temperatures. Conclusions
If low cost, high temperature, long-life membranes with desirable characteristics can be obtained, this method could become an economical method of evaporation, as well as a n important possibility in the conversion of sea water. Considerable improvement over the above calculations should be possible, using more appropriate membranes and eliminating noncondensable gases. literature Cited
(1) Alexander, K. F., Z. Physik. Chem. 195, 165-74 (1950). (2) Guccione, E., Chem. Eng. 69, 122 (Dec. 10,1962). (3) Hassler, G. L., McCutchan, J. W., Advan. Chem. Ser., No. 27, 192-205 (1960). (4) Othmer, D. F., Benenati, R. F., Goulandris, G. C., Chem. Eng. Progr. 59, 63-8 (December 1963). (5) Wirtz, K., Z . Naturforsch. 3d, 380-6 (1948). RECEIVED for review June 13, 1966 ACCEPTED October 10, 1966 Work accomplished at Auburn University, Auburn, Ala., and at the University of Missouri at Rolla, Rolla, Mo.
