Ind. Eng. Chem. Res. 1995,34,2436-2449
2436
Design of Micellar-Enhanced Ultrafilters John H. Markels: Scott Lynn, and C. J. Radke* Department of Chemical Engineering, University of California, Berkeley, California 94720
A systematic calculational procedure is developed for the design of micellar-enhanced ultrafilters to treat aqueous streams contaminated with organic pollutants. Flat plate, spiral wound, hollow fiber, and tubular modules are evaluated for performance (reduction in organic concentration and volume reduction of the retentate) and cost (capital and operating). Membranes having a 5000 molecular weight cutoff (MWCO), which reject all micelles, and 50 000 MWCO membranes, which do not, are used as examples. The surfactant considered is hexadecyl(=cetyl)pyridinium chloride (CPC), and the organic pollutants are chlorobenzene, trichloroethylene, tetrachloroethylene, and toluene. The goal is to design an ultrafiltration system to reduce the concentration of a pollutant from its saturation value in water to the Environmental Protection Agency pretreatment standard for municipal sewage. A combined osmotic-pressure and foulingresistance model quantifies the ultrafiltration permeate flux. Also important are the molar solubilization ratios of the respective organics in aqueous CPC solutions, the osmotic pressure of the surfactant as a function of concentration, and the intrinsic rejection behavior of the membranes for surfactant monomers and micelles. An equilibrium-staged configuration operating countercurrently is proposed for the ultrafiltration system. For treatment of 7.6 m3 per day [ZOO0 gallday] of wastewater saturated with chlorobenzene, the optimal design consists of a 3 equilibrium stage system using 18 tubular 50 000 MWCO modules in the first stage operating at 207 kPa [30 psig], 2 spiral wound 50 000 MWCO modules in the second stage operating a t 207 kPa [30 psigl, and 2 spiral wound 5000 MWCO modules operating at 1034 W a [150 psigl in the final stage. The optimum volume concentration ratio is 6; the surfactant concentrate leaves the ultrafilter at 17 kg/m3, and the crossflow velocity is 2 m/s in each stage. This design eliminates the need for prefiltration of the total feed and minimizes capital and operating costs.
Introduction Micellar-enhanced,ultrafiltration (MEUF) has been proposed as a method for removing dissolved organic contaminants from aqueous process streams (Leung, 1979; Dunn et al., 1985; Bhat et al., 1987; Gibbs et al., 1987; Smith et al., 1987) and for concentrating the oilladen product of surfactant soil-washing operations (Ellis et al., 1985; Gannon et al., 1989; McDermott et al., 1989; Wilson et al., 1989). In both cases, the hydrophobic organic contaminants partition between the bulk water and the micelle interior. This solubilization process not only increases the solubility of the organic relative to its saturation concentration in pure water (important in soil-flooding applications), but it also increases the effective size of the organic solutes with respect to ultrafiltration (UF)because micelles can be rejected by some ultrafiltration membranes (McBain and Jenkins, 1922). No design methodology for MEUF currently exists. In fact, other than a general investigation of the effects of concentration polarization in MEUF (Dunn et al., 19871, very little has been published concerning the performance of MEUF as a unit operation. We describe a procedure for model-based design of a multistage, countercurrent,feed-and-bleedUF system to reduce the concentration of an organic pollutant from its saturation value in water t o the EPA standard for municipal sewage disposal. The procedure combines a predictive model for permeate flux (Markels et al., 1995) with knowledge of the intrinsic membrane rejection characteristics (Markels et al., 1994),solubilization equilibria
* To whom correspondence should be addressed.
’ Current address:
Merck & Co., Inc., P.O. Box 4, WP 2870, West Point, PA 19486.
(Amos, 19921, module geometry, and process economics. The design framework presented here is useful in general, though issues specific to the ultrafiltration of micellar surfactant solutions are discussed for the first time.
Background Applications. Whether surfactant is added to an industrial waste stream to solubilize the organic contaminants or injected into the ground to wash polluted soil, it must be substantially recovered in a reusable form for the solubilization-basedprocess to have utility (Leung, 1979; Dunn et al., 1985; Ellis et al., 1985; McDermott et al., 1989; Brant et al., 1990; Kandori and Schechter, 1990). We propose a process, illustrated in Figure 1, that includes separation and reuse of the surface-activeagent employed. Major steps include the following: 1. mixing of a concentrated surfactant solution with an aqueous waste in order t o solubilize the organic contaminant into the micellar surfactant “phase” 2. micellar enhanced ultrafiltration of the aqueous surfactant/organic mixture to separate the major fraction of the bulk aqueous phase, leaving a concentrate of surfactant solution with the solubilized organic solute 3a. liquid-liquid extraction of the concentrated surfactanliorganic stream by a lower molecular weight organic solvent, or “extractant” (necessaryfor nonvolatile pollutants only) 3b. distillation to separate the extractant from the contaminant 4. steam stripping to separate the surfactant and the solubilized extractant in the aqueous phase leaving step 2 or 3a. The recovered surfactant is recycled directly
0888-5885/95/2634-2436$09.00/00 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34,No. 7, 1995 2437
. I c S
=
I I
(AQ-U~O-US)
surfactant contaminant
=
I
i , , EXTRA^ EXTRACTION
E
(Iscycle Extractant
u
Aqueous R e c o vSeur e r fda c t a n t
~
~
ORGANIC CONTAMINANT
Table 1. Membrane Parameters
to step 1; the extractant is recycled t o step 3a if the optional extractioddistillation operations are necessary. For the sake of clarity, our discussions are limited in two respects. First, we consider the treatment of polluted aqueous streams rather than surfactant recovery from soil leachate, and there are some differences between the two. For the treatment of an aqueous process waste, for example, the solubilization operation pictured in Figure 1occurs in a tank or an in-line mixer. In a soil-washing process, on the other hand, solubilization occurs external to the separation scheme. Important differences in UF design for the two applications are pointed out as the discussion proceeds. Second, we do not consider the effect of the UF design on the optional extractioddistillation sequence, but assume that the pollutant is suffhiently volatile t o allow the concentrated retentate to be processed directly in the steam stripper. Performance of the ultrafiltration step is central to the process. The purely experimental approach to design used traditionally is unsatisfactory because it is expensive, lacks generality, and teaches little about the physical processes that control performance. We describe here a more alternative, based on a physically consistent permeate flux model that applies over the entire operating range. Design Procedure. This paper is divided into three parts. In this section we introduce a model for predicting permeate flux in crossflow M E W (Markels et al., 1995) and describe a method for quantifying the intrinsic rejection of surfactant from micellar solutions by UF membranes (Markels et al., 1994). A simple description of micellar solubilization is given that, along with membrane rejection coefficients and a mass transfer model, is used to predict the pollutant concentration permeating an ultrafilter. The mode of operation for the UF system and the proposed process configuration are also described. Next the design model is briefly discussed, starting with the characteristics of the various module geometries ( e g . , spiral wound, tubular) and how they are distinguished in the model. The procedure for calculating the various flow rates, surfactant concentrations, and organic concentrations is presented, followed by an overview of the economic analysis.
type I1
@S
1.0
0.88
Ri
0.80
0.75 0.4 1.0 0.85
RL ,’R! R? R,’ ( W a d m ) MWCO surfactant solution properties MW (g/mol) II(S) in 0.01 M NaCl at 30 “C (Wa) S (kg/m3) Sam (kg/m3) p (m P a 4
D (cm2/s)
e (g/cm3)
Steam
Figure 1. Schematic flow diagram of the process.
type I
membrane propertiesa
a
not applicable 1.0
not applicable 1.7 107 5000
4.5 x 105 50000
values for CPC 358.01 -0.003668 0.01209S2 8.0 10-553 2.592 10-7s4 0.5 kg/m3 c S c 220 kg/m3 (Markels, 1993, Chapter 3) 0.3 (&sen, 1978) 1.225 (Dunn et al., 1985) 1.5 x (Hartley and Runnicles, 1938) 1.0
+
+
+
Markels et al., 1993.
We conclude with the results from an example design for the removal of chlorobenzene from water. This includes an evaluation of the process configuration (module geometry, number of equilibrium stages, membrane molecular weight cutoff for each stage, and prefiltration provisions) and the operating conditions (surfactant concentration, degree of volume reduction of the retentate stream, transmembrane pressure drop, temperature, and crossflow velocity) for each stage. The assumption of differential crossflow ultrafiltration is verified by an ordering criterion, derived from an extended form of the model that accounts for variations of velocity and concentration in the axial direction. Flux Model. The model for predicting permeate flux for the ultrafiltration of micellar solutions of the cationic surfactant hexadecyl(=cetyl)pyridiniumchloride (CPC) using 5000 and 50 000 molecular weight cutoff (MWCO) poly(ether sulfone)UF membranes is described in detail elsewhere (Markels et al., 1995). The model relates the permeate volumetric flux, V,, to an osmotically corrected pressure driving force, AP - n, and a fouling-corrected flow resistance, Rm’:
This simple expression is extremely effective in predicting permeate flux over a wide range of applied transmembrane pressure drop (AI’),crossflow velocity (Vz), and surfactant mass concentration at the membrane surface, S, (Markels et al., 1995). It is identical in form to that proposed by Nabetani and co-workers for albumin ultrafiltration (1990). As indicated in the model, there appears to be no gel-layer resistance in the CPC micellar system. However, because of the large repulsive interactions between the like-charged micelles, the concentrated surfactant solutions are highly nonideal and large osmotic pressures result. The osmotic pressure as a function of surfactant concentration for CPC solutions in 0.01 M NaC1, measured by membrane osmometry, is given in Table 1 (Markels et al., 1995; Markels, 1993, Chapter 3). Concentration polarization reduces flux by the establishment of an osmotic pressure difference (An)across the membrane of opposite sign to the applied pressure drop. For the highly rejecting membranes considered, uAll n(&),where u is the Staverman reflection coefficient.
-
2438 Ind. Eng. Chem. Res., Vol. 34,No. 7,1995
The effect of surfactant fouling on and within the membrane on flux can be modeled as a modified membrane resistance (Rm’) because the fouling resistance, which has both a reversible adsorption component and an irreversible pore-blocking component, is essentially a constant for filtration of solutions above the critical micelle concentration (cmc)(Markels et al.,1995; Markels, 1993, Chapter 4). In UF, the solute concentration in the permeate, CP, is generally related t o the solute concentration a t the ,, by an intrinsic rejection coefmembrane surface, C ficient, R, where R 1- Cp/Cm. For most applications, membranes are chosen so that R is unity, i.e., the membranes are nonleaky and Cp is zero. As we show, however, less resistive, large-pore membranes that exhibit some monomer and micelle leakage can be used to advantage even when the criterion for pollutant concentration in the permeate is very stringent. Therefore, it is especially important that the intrinsic membrane rejection characteristics be known in MEW. This is complicated by the fact that both micelles and monomers are present in solution and an equilibrium exists between them. A detailed study of rejection in surfactant ultrafiltration has been described (Markels et al.,1994; Markels, 1993, Chapter 2). A brief overview of the physical picture used is repeated here. It is convenient to consider two types of pores: “small” pores that reject micelles completely and monomers partially and “large” pores that partially reject both monomers and micelles. Characterization of such a membrane requires five parameters: the intrinsic monomer rejection coefficient for the small ( R i ) and large (RL) pores, the intrinsic micelle rejection coefficient for the small (Rr) and large (RY) pores, and the fraction of the total permeate flow through small pores (as). On the basis of this, membranes are classified as type I membranes, which contain only small, micelle-rejecting pores, and type I1 membranes, which contain some of each type of pore. Using an unstirred batch UF cell operating a t constant flux, Markels et al. (1993) found that Filtron NOVA 5000 and 50 000 MWCO membranes are types I and 11, respectively, for CPC ultrafiltration. The membrane rejection characteristics that they determined, as well as the modified hydraulic resistances, are used here in the design calculations and are listed in Table 1. For practical purposes the type I membranes have a total surfactant rejection coefficient of essentially unity. As illustrated further below, this is not true for the type I1 membranes, through which surfactant leakage is important.
Micellar Ultrafiltration Design The present analysis is based on treatment of 7.6 m3/ day 12000 gal/dayl of water saturated with chlorobenzene at 25 “C. The process must reduce the chlorobenzene concentration in the permeate sufficiently that the water can be discharged to a nonhazardous wastewater treatment facility, such as a municipal sewer. Table 2 contains the Safe Drinking Water Act Maximum Contaminant Levels for several organics of interest. These are pretreatment standards for the commodity organic chemicals industry and correspond to the maximum allowable monthly average concentrations of the pollutant in the pretreatment water. In addition t o producing a clean permeate, the volume of the contaminated fraction should be reduced sufficiently t o offset, to the extent required by economics, capital and operating costs in the downstream stripping operation. This
Table 2. Organic Contaminant Physical Characteristics Kb pretreatment stdsa Osat (for CPC) contaminant (max monthly av) kg/m3 (kg/m3) (m3/kg) chlorobenzene 142 x 0.47b 4.16 trichloroethylene 26 x l.lOb 1.78 tetrachloroethylene 52 x O.Eb 7.13 toluene 28 x 0.49 3.65
US EPA 40 CFR, Subpart F, Commodity Organic Chemicals, July 1, 1992, Edition, Pretreatment standards for existing sites, p 278. Amos, 1992. Seidell, 1991.
analysis is concerned primarily with the design of the ultrafilter, so the economic analyses do not contain the costs of stripping. As we illustrate below, though, the optimum degree of concentration in the ultrafilter is largely independent of the stripping costs. We also assume that any residual surfactant exiting in the clean permeate is a financial loss, but that no environmental restriction is imposed. Table 2 contains values of the distribution coefficients ( K ) for several organic pollutants between the solution micelles and the bulk water phase for CPC, defined as osol
K = ounsol smic
[g]
where OSo1 is the mass concentration of the solubilized organic (averaged over the solution volume), Ounsolis the mass concentration of unsolubilized organic (in the bulk water), and Smicis the mass concentration of surfactant micelles, expressed as monomer. Systems with larger K values exhibit more efficient organic solubilization. K is only weakly dependent on surfactant concentration, and is assumed constant here (McBain and Hutchinson, 1955; Mukerjee, 1979; Dunn et al., 1985). Industrial UF operations can be run in either batch or continuous mode, with several possible variations of each (Cheryan, 1986). In this analysis we consider the “feed-and-bleed”mode of operation, shown schematically in Figure 2, because it is a continuous, steady-state operation. Q is the volumetric flow rate, and S and 0 are the surfactant and organic mass concentrations, respectively. Subscripts F, P, and R represent the bulk feed, bulk permeate, and bulk retentate. During startup of a feed-and-bleed operation the retentate stream is totally recycled, its concentration increasing while only dilute permeate is withdrawn. When the required concentration is reached in the recycle loop, a portion of the concentrated retentate stream is continuously drawn off. The feed rate is then reset at a value equal to the sum of the permeate and retentate product rates to establish the steady state. Because the operation is continuous, the feed tank, though useful as surge and for preparation of cleaning solutions, is unnecessary. A disadvantage of this configuration is that the process always operates with the highest concentration adjacent to the membrane, resulting in a lower average transmembrane flux than in a batch operation with retentate recycle. To counteract this, large-scale feed-and-bleed units often utilize several concentration stages in series. The retentate from the first stage is less concentrated than the final retentate, resulting in a higher flux and less membrane area. As shown in Figure 2 for two concentration stages, the stage 1 retentate feeds the second stage, where it is concentrated t o the final value. In the limit of infinite concentration stages, overall flux in the feedand-bleed mode equals that for a batch operation.
WASTE WAT E R
I
-
Ind. Eng. Chem. Res., Vol. 34,No. 7,1995 2439
S U R FACTAN T
I
-P
P E R M E AT E 4
1
OP
E
J
medium concentration
O R
concentration
Figure 2. Schematic of a feed-and-bleed ultrafiltration system. Two concentration stages are used to improve the average flux of the operation and to reduce membrane area.
Unsolubilized organics of interest are not rejected by ultrafiltration membranes. For a type I membrane that completely rejects micelles, for instance, the concentration of organic in the permeate (Op) is equal to the equilibrium concentration of unsolubilized organic above the membrane (Leung, 1979;Dunn et al., 1985). We assume that this equilibrium is established in the feed tank and that the concentration of unsolubilized organic in the recycle loop does not deviate from this value. The same holds for type I1 membranes, but under similar conditions, the organic concentration in the permeate from a type I1 membrane is higher than from a type I membrane because some swollen micelles permeate. With careful design, one can take advantage of the higher flow permeability of the large-pore membranes without sacrificing separation performance. Equilibrium Stages. If the permeate contaminant concentration cannot be reduced sufficiently using a single ultrafilter, additional surfactant may be added to the permeate, which is filtered again. The contaminant concentration in the permeate from the second ultrafilter is thereby reduced further. This is an equilibrium-staged operation similar to familiar solvent extraction using mixerhettlers, for example. To determine whether a single equilibrium stage is sufficient to reduce the contaminant concentration to the desired level, the total organic concentration in the feed to the process is calculated as the sum of the solubilized and unsolubilized portions which, for a stream initially saturated with pollutant, is
0, = Osat = or1 + o y l
(3)
Combining this with eq 2 t o eliminate 0;' gives
-OYl K = osat
0uFnso1smic
(4)
Assuming that a type I membrane is used, the minimum CPC concentration required to reach the chlorobenzene pretreatment standard, Op = = 142 x kgl m3 [142pg/L], is 788 kg/m3 from eq 4 since K = 4.16 (Table 2). This far exceeds the solubility we observe for CPC in water at 25 "C (CPC solutions become turbid a t approximately 220 kg/m3 at 25 "C in 0.01 M NaCl). Clearly, more than one equilibrium stage is necessary to achieve the required separation. As is evident from Figure 3, the extramicellar organic concentration decreases rapidly for increasing surfactant concentration
"E
-
0.024 I
1R
0.021
A-
I
I
I
I
I
I
I
I
I
4
I
Type I membrane Organic: chlorobenzene Surfactant: CPC
.-
0.015 C
2
0.012
0
0.006
Cmax in permeate = 1.42 x 10 0.003
kg/m
e O.O@@
0
100
200
300
400
500
600
700
800
Feed Surfactant Concentration, S, (kg/m3)
Figure 3. Reduction of extramicellar organic concentration as a function of total surfactant concentration for chlorobenzene in aqueous CPC. The ordinate represents the UF permeate concentration using a type I membrane.
at low surfactant concentrations; the benefit of adding more surfactant diminishes as its concentration increases. Therefore, an important design tradeoff exists between the concentration of surfactant used in each equilibrium stage and the number of stages used. Determination of a practical compromise is discussed below. As diagrammed in Figure 4,to include equilibrium stages in MEW, surfactant (eg.,stream & ~ ( 3 )is) added to the permeate of the first stage (which already has a lower pollutant concentration than the initial waste); the resultant mixture is ultrafiltered again in a second stage to reduce the polluant concentration in the permeate further (numbers enclosed in parentheses indicate the appropriate stage). The driving force for mass transfer is maximized by using a countercurrent configuration (Kandori and Schechter, 1990). Equilibrium staging is different from concentration staging discussed earlier to improve the average flux in feed-and-bleed operations. Each of the equilibrium stages illustrated in Figure 4 is a feed-and-bleed operation that might contain several concentration stages like those illustrated in Figure 2.
2440 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 Surfactant and Organic to Strlppor
Surf 80tan t from Strlppor
QR (1)
QR
1
QR
(4)
(2)
I ’
Q R ( ~ )
~ioan Pormoate .* * N
MI
MI
Figure 4. Equilibrium-staged, countercurrent, feed-and-bleed (dashed lines) configuration for micellar-enhanced ultrafiltration to treat organic-contaminated aqueous streams.
rooowrod rurfrctrnt from rtrlpplng
I
c
rurfrctrnt
rurfrctrnt
for UF rtrglng
for rolnJoctlon
Olrrn
Miorllrr
NACL’o
8wollrn Mlorllro
Figure 5. Schematic of process flows for treatment of a soil-washing product using the micellar-enhanced ultrafiltration process.
In the treatment of a contaminated water stream, the aqueous waste containing the highest organic concentration enters the first stage of the process at the left of Figure 4 and is mixed with the most saturated micelles (retentate from stage 2). The feed to each subsequent stage is a solubilized mixture of the permeate from the stage upstream and the retentate from the stage downstream. Fresh surfactant solution returns from the stripping operation to the final stage (N)at the right of the page (stage 3 for the case shown). The stage 1retentate is the concentrated product that feeds the stripper; the permeate from stage N is the rectified water product. This flowsheet must be modified somewhat for surfactant and contaminant recovery from a soil-washing process. As portrayed in Figure 5, complete countercurrent operation is not feasible in this case because, in order to clean the soil efficiently, the freshly recovered surfactant solution, rather than the retentate from the second stage, must be injected directly back into the soil to avoid reinjecting the organic contaminant. The surfactant is actually used for two distinct purposes here: to remove organic from the soil and to remove organic from the permeate of the first equilibrium UF
stage (Le., stage 2 in Figure 5). Therefore, if equilibration stages are required, some of the recovered surfactant solution must be diverted as feed to the downstream equilibration stages, as indicated in Figure 5. Though the mass balance equations differ slightly from those used in the present analysis, the design method for the MEUF portion of the soil-cleaning application is identical to the procedure presented here for rectlfylng aqueous wastes. Design Model. Inputs to the model are as follows: inlet waste flow rate, Qw; volume concentration ratio, VCR, of each stage (all equal); number of equilibrium stages, N,crossflow velocity in each stage, V, (all equal); exiting surfactant concentration to the stripper, &(I); membrane type for each stage, (I or 11);transmembrane pressure drop in each stage, hp; organic concentration in inlet waste stream, Osat;and membrane (h, w , L, rejection parameters, Rm’)and solution properties (IT, D, e, p, S,,,, K ) . The model equations and solution procedure, described in detail elsewhere (Markels, 1993, Appendix 7A), are discussed briefly below. The various module geometries, flat plate, hollow fiber, spiral wound, and tubular, have different mass transfer and energy utilization characteristics. These
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2441 characteristics, determined by the length (L), height (h), and width (w)of the retentate flow path and the crosssection geometry (circular or rectangular), impact the performance of the operation and its design (Wiley et al., 1985; Cheryan, 1986; Belfort, 1988). Module geometry is optimized on the basis of cost in the design procedure. The volume concentration ratio of stage i, given by is specified in the model and is equal VCR(i) Qw/&~(i), in each stage. Equal volume concentration ratios minimizes cost because retentate in this configuration is recycled (Markels, 1993, Appendix 7A). The inlet waste flow rate, Qw, is known, so the retentate flow rates for each stage are equal as well, followingthe definition of VCRW given above. The permeate flow rate from stage N is calculated from an overall mass balance. Beginning with stage N , the remaining feed and permeate flow rates are calculated from mass balances around the ultrafilter and feed tank, respectively. Permeate flux for each stage, V&), is calculated from a solute mass balance around the membrane, the flux model (eq 11, and a membrane intrinsic rejection equation (Markels et al., 1994) that relates the surfactant concentrations at the membrane surface and in the permeate (Markels, 1993, Appendix 7A). Standard correlations for the mass transfer coefficient are used. The required membrane area for that stage, the number of plates or tubes, and the recycle ratio are then calculated. Surfactant concentrations in the feed and retentate are determined from surfactant mass balances around the ultrafilter and feed tank. A general method is required for estimating the organic concentration in the permeate for a k n o w n condition a t the membrane surface. For a type I membrane, the organic in the permeate is a t the same concentration as the unsolubilized organic in the bulk solution above the membrane and is calculated directly from eq 2. The situation for a type I1 membrane, where some swollen micelles permeate, is more complicated. We assume that the extramicellar organic concentration, Ounsol,is a constant throughout the solution and in the membrane pores. Therefore, from eq 2, the solubilized organic concentration is proportional to the micellar surfactant concentration everywhere in the retentate. At the membrane surface, for instance, we write that
0E1= KOun"O'(S,
- )S ,,,
(5)
where KOunso1 is the constant for proportionality. The same is true in the leaky pores, so that the ratio of the solubilized organic concentration in the pore and at the membrane surface is the same as the ratio of the micelle concentrations there, or
We know from eqs 2 and 3 that 01 :=
OsatK(S, - S,,,) K(S, - S,,,) + 1
(7)
The solubilized organic concentration in the large pores is available from eqs 6 and 7, and the unsolubilized organic concentration in the large and small pores is determined by the equilibrium in the feed tank. There-
Table 3. Cost Factors Used in Economic Analysis operating factor = 0.83 cost of electricity = 0.08 ($/kW;h) cost of surfactant = 4.5 ($kg) dump efficiency = 0.6 membrane life = 1.5 (yrs) pump capital cost as a function of capacity factor ( C F Q A P f ) $(1980) = 3320.95 0.02144(CF) 1.23045 x lo-' (CF2) (Peters and Timmerhaus, 1980) captial charge factor: membrane module (7.5 yr life) = 0.133 capital charge factor: pumps (10 yr life) = 0.1 membrane module capital cost = 1264 ($/m2)= 117.4 ($/ft2) (Perry and Chilton, 1973) membrane replacement cost (hollow fiber) = 344 ($/m2)= 32 ($/ft2) (Cheryan, 1986) membrane replacement cost (other) = 173 ($/m2)= 16.1 ($W)(Cheryan, 1986)
+
+
fore, the total organic concentration in the permeate is given by
1
OP= [K& -OS" S,,,) + 1 +
Equations 7 and 8 are derived for a feed stream saturated with organic. For any equilibrium stage other than the first, Oaatis replaced by OF(^). Organic solute mass balances around the UF unit and the feed tank are then written for each stage. These coupled algebraic equations are solved simultaneously for the organic concentrations (Markels, 1993, Appendix 7A). Economics. Both fixed capital and operating costs are considered. Fixed capital costs consist of the purchase costs of the pumps and the ultrafiltration unit, including housings, valves, instrumentation, and other peripherals. Since the tanks illustrated in Figure 4 will be replaced in the process, where possible, by in-line mixers, the cost of tankage is not included. Before a MEUF process is built, it is necessary to verify that sufficient residence time can be provided in the mixers to attain solubilization equilibrium. Operating costs include electricity for pumping, makeup surfactant to replace surfactant lost from the process in the permeate stream of the final stage, depreciation, membrane replacement, and miscellaneous expenses (maintenance, supplies, taxes, and insurance). Assumptions utilized in the cost analysis are listed in Table 3. Standard correlations for the friction factor are used (Markels, 1993, Appendix 7B). The capital cost of the centrifugal pumps was calculated as a function of their capacity factor, defined as the product of the flow rate and the pressure difference across the pump (Peters and Timmerhaus, 1980). Yearly depreciation charges were calculated by multiplying the pump and membrane capital costs by their respective depreciation factors from Table 3. The miscellaneous operating expenses are taken as 10%of the fixed capital cost. Inflation was accounted for by applying the appropriate cost index ratios. The operating and capital costs presented are written as absolute dollars per year and dollars, respectively, required to treat the model waste stream of 2000 gdday. These can easily be related to throughput for scaling to different process duties.
Results Module Geometry. The most common UF'module configurations are flat plate (FP), spiral wound (SW),
2442 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 Table 4. Flat Plate Geometry, Typical Design Results (sR(1) = 20 kg/m3;VCR = 5, N = 3) case areab (m2) Rec Smd (kg/m3) no. platesc recycled ratio Op(3) kg/m3) (A) typical FPO 233 200 35.7 1457 169 110 (B) h = 0.03 cm 25.1 440 208 140 36 110 (C) h = 0.01 cm 24.3 147 107 135 12 110
k
x
lo6
(ds)
3.6 5.4 7.8
APf (kPa) 2.1 25.0 221
a h = 0.1 cm, w = 11.94 cm, L = 50 cm, V, = 0.90 d s , AP = 517.1 kPa [75 psi], N = 3. Total for three stages. Equal in each stage. Average for three stages.
Table 5. Flat Plate Geometry, Typical Cost Results (&(I) = 20 kg/m3;VCR = 5, N = 3) capital costsa ($1000) case (A) typical F F (B)h = 0.03 cm (C) h = 0.01 cm
Pump 34 31 31
UF 45 32 31
total 79 63 62
deprec 9.3 7.3 7.2
operating costsa ($100O/yr) membr replace. misch energy 4.1 7.9 6.8 2.9 6.3 12.0 2.8 6.2 29.0
total 29 29 46
a Total for three stages. Maintenance, supplies, taxes, insurance. h = 0.1 cm, w = 11.94 cm, L = 50 cm, V, = 0.90 d s , AP = 517.1 kPa [75 psil, N = 3.
hollow fiber (HF), and tubular U"E5). The module types vary in geometry, operating pressure, and crossflow rate, leading to differences in energy efficiency, cleanability, mass transfer characteristics, and cost. An overview of the differences among them is given by Cheryan (1986). We consider variations on a base-case design for each module type to illustrate tradeoffs and to identify the configuration best suited for the specified = 20 kg/m3, duty. In the cases described below, VCR = 5 (for each stage and overall), and N = 3 equilibrium stages. 1. Flat Plate. Typical FP dimensions are h = 0.1 cm, w = 11.94 cm, and L = 50 cm with a recommended crossflow velocity of 0.9 mls and transmembrane pressure of 517 W a [75 psil. h = 0.03 cm and h = 0.01 cm are also common dimensions (Tutunjian, 1985; Wiley et al., 1985; Cheryan, 1986; Belfort, 1988). The flow channels are shallow, and particulates of diameter greater than one-tenth the channel height should be prefiltered to avoid blockage of the flow path. Flat plate UF systems typically operate in laminar flow. Model results for the typical flat plate module with a type I membrane are listed in Tables 4 and 5. Several variations of the typical design are listed as well. Unless otherwise specified in the first column, all input variables have the same values as the typical case. From Table 4 we see that flow is laminar and the organic concentration leaving in the exiting permeate kg/m3 is always below the target value of 142 x 1142 p&I. In the typical case (A), capital costs for the pumps and the UF unit are comparable. The operating cost contributions are all significant; the capital-related expenses tend to be high and the surfactant losses in the permeate from the final stage are low (not shown in the table: $750/yr). This illustrates the extremely high surfactant rejections exhibited by the 5000 MWCO membranes. For these type I membranes, the surfactant concentration in the permeate from the third stage depends solely on the value of the cmc and the monomer rejection coefficient, according t o S p = S c m c ( 1 - R I ) (Markels et al., 1994). The permeate flow rate is equal in each of the cases listed, so the surfactant losses are equal as well. Cases B and C utilize channels of smaller heights. In laminar flow, the mass transfer coemcient is inversely proportional to the cube root of the hydraulic diameter. Thinner channels therefore produce higher mass transfer coefficients, and the increased rate of surfactant transport from the membrane surface decreases the surfactant concentration at the membrane surface, S m . This increases transmembrane flux and reduces the required membrane area. Reducing S m is
especially important in the typical case (A) because the surfactant concentration at the membrane surface is above the turbidity boundary for CPC (ca. 220 kg/m3), raising concerns of increased resistance due to formation of a semisolid "gel" layer a t the membrane surface. Decreasing the channel height has two competing effects on cost. First, the hydraulic frictional losses in the module increase (to 25 kPdplate L3.6 psi/platel for h = 0.03 cm and 221 kPdplate [32 psYplate1 for h = 0.01 cm), which increases pumping costs. Conversely, the higher flux achieved allows the use of fewer plates to provide the specified permeate flow rate. This, in turn, reduces the recycle ratio necessary to maintain the specified crossflow velocity. The reduction in recycle flow rate is not enough, however, to offset the increased frictional losses, so the product Q M f (Le., the pumping energy) in the recycle loop increases with decreasing h. However, thinner channels do decrease the purchase cost of both the pumps and the membrane modules, and the results suggest that the intermediate channel height provides the best balance between capital and operating costs. As discussed in more detail below, a thinner channel requires the additional cost of a more rigorous prefiltration system. The optimal crossflow velocity for the flat plate geometry was also investigated. In laminar flow the mass transfer coefficient is proportional to the one-third power of the crossflow velocity, so the effect of increasing V, on membrane area is similar to the effect of decreasing h, but with less operational penalty in energy usage. When increasing V,, one essentially trades energy costs against membrane savings. For tubular and hollow fiber modules, which have relatively low maximum operating pressures, crossflow velocity is also limited by the fact that a large axial pressure drop (large V,) decreases the average transmembrane pressure drop available between the inlet and outlet of the module (Tutunjian, 1985). The characteristics of the flow in the retentate channel dramatically affect process performance. Solute mass transfer characteristics in ultrafiltration are much more favorable in turbulent than laminar flow because the mass transfer boundary layer thickness and the concentration at the membrane surface are decreased. A larger flow aperture is therefore beneficial because a higher Reynolds number can be achieved with a given crossflow velocity, assuming the boundary layer thickness is small relative t o the aperture thickness (Markels, 1993, Appendix 7 0 . We assume the transition Reynolds number is 2100 for all geometries investigated here. As inferred from Table 4, a crossflow velocity of 4.3 m l s is required to achieve Re = 2100 for h = 0.03
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1996 2443 Table 6. Spiral Wound, Hollow Fiber, and Tubular Geometries: Typical Design Results (&(I) = 20 klt/ms;
VCR = 5, N = 3)
case areaa (m2) (D)typical SWd 34.0 (E) typical SW, V, = 2.0 ds 5.85 (F)typical HFO 50.4 (G)typical TUBf 29.5
Smc (kg/ms) no. platesb recycle ratio Op(3) (10-8 kg/ms) k x loa (ds) APP (Wa) 3.3 2.8 338 10 149 110 1795 51 110 30 13.8 3600 152 2 Reb
898 20400
90 31
7600 103
57 202
110 110
4.2 25
10.3 4.8
a Total for three stages. Equal in each stage. C Average for three stages. Spiral wound: h = 0.11 cm, w = 165 cm, L = 66 cm, V, = 1.0 ds, AP = 1034 kPa [EO psil, N = 3. e Hollow fiber: h = w = 0.11 cm, L = 63.5 cm, V, = 1.0 ds,AP = 172.4 kPa [25 psil, N = 3. AP = 199.9 kPa [29 psi]. fTubular: h = w = 1.25 cm, L = 240 cm, V, = 2.0 ds,
Table 7. Spiral Wound, Hollow Fiber, and Tubular Geometries: Typical Cost RelrulfE ( S R (= ~ )20 kg/m8;VCR = I ,N = 3) operating costen ($lOOO/yr) capital costs" ($1000) pump UF total deprec. membr replace. miscb energy total case 9.8 31.7 79 9.3 3.9 7.9 36 43 (D)typical SWc 0.7 4.0 12.9 22.5 32 7.4 40 4.2 (E) typical SW, V, = 2.0 ds 7.2 34.8 95 11.6 5.8 9.5 31 64 (F)typical HFd 12.0 31.3 69 8.2 3.4 6.9 32 37 (0) typical TUBe ~~
~
a Total for three stages. b Taxes, insurance, maintenance. h = 0.11 cm, w = 165 cm, L = 66 cm, V, = 1.0 ds, AP = 1034 kPa [150 psil, N = 3. d Hollow fiber: h = w = 0.11 cm. L = 63.5 cm., V,- = 1.0 ds, AP = 172.4 kPa [25 psil, N = 3. e Tubular: h = w = 1.25 cm, L = 240 cm, V, = 2.0 ds, AP = 199.9 kPa [29 psi].
cm. The frictional losses in that case are nearly 207 kPa [30 psil, though, and the calculated $10 000 saved in capital expenditure is not worth the additional $200 000 in annual energy costs. As discussed below, other geometries are better suited to achieving turbulence with reasonable energy costs. 2. Spiral Wound. Spiral wound (SW) modules provide a relatively compact, inexpensive design and are generally more energy efficient than flat plates. Each module can be visualized as a wide flat plate that this rolled up. Typical geometry and operating characteristics are h = 0.11 cm (or 0.086 cm), w = 166 cm, L = 66 cm, V, = 100 cm/s, and AP = 1034 kPa [160 psil (Tutunjian, 1986; Wiley et al., 1986; Cheryan, 1986; Belfort, 1988). Like flat plates, they must be used with clean streams (
