Ind. Eng. Chem. Res. 2009, 48, 1543–1550
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NSGA-II for Multiobjective Optimization of Pervaporation Process: Removal of Volatile Organics from Water Gopal R. Nemmani,† Satyanarayana V. Suggala,*,‡ and Prashant K. Bhattacharya§ Department of Chemical Engineering, Bapatla Engineering College, Bapatla, India, Department of Chemical Engineering, J.NTU College of Engineering, Anantapur, India, and Department of Chemical Engineering, Indian Institute of Technology, Kanpur, India 208016
Pervaporation is fast emerging as a viable technique for the removal of VOC from wastewater. In our previous study (Satyanarayana, V. S.; Bhattacharya, P. K. Ind. Eng. Chem. Res. 2003, 42, 3118) we have carried out the minimization of the treatment cost for a fixed toluene removal fraction from multicomponent wastewater by single-stage pervaporation using shell and tube module without recycling permeate. In the present work, two objective optimization problem of minimization of the treatment cost with simultaneous maximization of percent removal of toluene is studied using an evolutionary algorithm of NSGA-II. The previously available model (Satyanarayana, V. S.; Bhattacharya, P. K. Ind. Eng. Chem. Res. 2003, 42, 3118) is employed including fiber diameter as an eighth decision variable. The study reveals that attractive trade-offs are available between the two objectives. Further, vacuum and condensation cost is found to be the major contributor to the treatment cost for the entire range of Reynold’s number and the contribution is found to be more dominating with decrease in Reynold’s number. 1.0. Introduction Removal of VOCs from air and water streams has been a global problem and billions of dollars are spent annually to remove these environmentally hazardous pollutants. With conventional separation techniques facing problems in removing VOCs from wastewater, the clean-technology alternatives like reverse osmosis, membrane contactors, and pervaporation are now being explored. In this regard, pervaporation,2 considered to be under clean technology, is fast emerging as a viable unit process; particularly, when the process is overcoming its basic disadvantages of low flux and selectivity because of advent of newer materials, membrane preparatory techniques, and module designs. Industries, hitherto reluctant, now seriously consider membrane processes as alternatives3 to their existing conventional processes like adsorption, distillation, advanced oxidation, and biological treatment, etc. Such utilities of the processes have drawn the attention of many for the removal of VOCs from wastewater as recently there has been significant improvements in the context of membrane materials,4,5 module designs,6,7 hybridizations,8-10 and boundary layer formation,11,12 etc. Pervaporation is proving to be a better alternative (especially for multicomponent mixtures1) than reverse osmosis and membrane contactors; the former facing the limitation of high osmotic pressures and, in the membrane contactors, the VOCs are just transferred from one phase to another. Peng et al.13 have reviewed the pervaporation-studies on the removal of VOCs from wastewater. Pervaporation is a membrane-based separation process in which a given feed mixture is brought in contact with a nonporous perm-selective barrier on one side with vacuum being applied on the other side to collect the permeate as vapor enriched with the preferentially permeating component on the down stream side. The vapor collected is often condensed and removed as liquid. * To whom correspondence should be addressed. E-mail: svsatya7@ gmail.com. Tel: +91-9849509167. Fax: +91-8554-272098. † Bapatla Engineering College. ‡ J.NTU College of Engineering. § Indian Institute of Technology.
For successful commercialization of the process, the effects of the process variables on performance are important. Lipski and Cote14 have set up a mathematical model to study the effect of process variables like Reynold’s number, thickness of the fiber, and configuration of the modules on treatment cost. The model was then extended by Ji et al.,15 considering the effect of down stream pressure and variable volumetric feed flow rate in the fiber for multicomponent mixtures. Further, they also carried out single objective optimization of treatment cost for binary system as a function of process conditions using Powell’s conventional optimization technique. Later on an evolutionary algorithm of real coded simple genetic algorithm was used by Satyanarayana et al.1 to determine the optimal conditions of the process. This was done for multicomponent mixture separation with single objective optimization (minimization) of treatment cost. However, for VOC separation both objectives, that is, minimization of treatment cost and maximization of VOC removal are important. Therefore, the present work is carried out with the objective of multiobjective optimization problem utilizing previously1 developed mathematical model. The basic concept of the multiobjective optimization16 is to find a set of solutions which are called a nondominated set as none of the solutions are supposed to dominate any other solution in the set and there is no single solution which is the best with respect to all the objectives in the entire search space. In other words as we move from one point to the other of the nondominated solutions in the objective function space at least one of the objectives must be improving with simultaneous deterioration of at least one of the other objectives. This is also called the Pareto optimal solutions or Pareto optimal set. If the Pareto optimal set is such that if any other solution in the entire Table 1. Genetic Parameters maximum number of generations maximum population size random seed probability of cross over probability of mutation distribution index for cross over distribution index for mutation
10.1021/ie8005319 CCC: $40.75 2009 American Chemical Society Published on Web 01/08/2009
70.00 800 0.0625 0.60 0.06 5.00 80.00
1544 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 Table 2. Properties of Feed Componentsa heat heat of Henry’s diffusion capacity vaporization Constant coefficient (J/(mol · k)) (kJ/mol) (k · Pa · m3/mol) ×10-9 (m2/s) toluene 1,1,2 trichloroethane methylene chloride water a
157.44 145.0 128.35 34.25
37.56 37.65 28.54 43.76
0.7358 2.1115 0.1181
1.97 2.56 2.57
Temperature 30 °C.
function value in the randomly chosen gene pool and the most nondominant and isolated gene attaining highest fitness function value. Further, to get the next generation of population, the cross over and the mutation are carried out as is followed with simple genetic algorithm. The procedure is repeated for set-number of generations to arrive at the Pareto solutions. As the present work being an extension of the previous1 work in order to carry out multiobjective optimization, it was decided to utilize same decision variables; namely, volumetric rate (Reynold’s number) of the feed, downstream pressure, membrane thickness, concentration of the feed for same module configuration (tubular membrane module of cross-flow type) with poly(dimethylsiloxane) (PDMS) membrane. Similarly, toluene, trichloroethane (TCE), and methylene chloride (MC) are chosen as VOCs. It may be mentioned that diameter was not included in the previous1 work as a decision variable. Since, diameter is an important variable to affect the process performance; in the present work, it (diameter) is included as the eighth decision variable. 2.0. Theory and Numerical Simulation
Figure 1. (a) Removal percent versus treatment cost Pareto solutions for removal of toluene from water; (b) removal percent versus various costs of Pareto solutions in panel a for removal of toluene from water.
search space is dominated by at least one solution in the set then it is called the global Pareto optimal set.16 Earlier a number of multiobjective optimization problems have been set up in core chemical engineering in the areas of reaction engineering,17-20 mass transfer,21 and process control,22 etc. Bhaskar et al.23 have done an excellent review of multiobjective optimization tasks, specifically in the domain of chemical engineering. Most of such problems are solved using evolutionary algorithms like nondominated sorting genetic algorithm (NSGA-II). Therefore, the present work also employs NSGA-II to solve the proposed two-objective optimization problem (i.e., minimization of treatment cost and maximization of removal percent of organic) to obtain the Pareto optimal solutions. NSGA-II is based on the Darwinian principle of survival of the fittest. Hence, it is also based on the three basic operations of reproduction, crossover, and mutations. A fixed set of population is randomly chosen over the entire search space and classified into several nondominating fronts of decreasing dominance. These fronts are assigned progressively decreasing values of fitness. The individual fitness of a member in a front is calculated based on a dummy-fitness (assigned to the front in which it is) and also on the density of population around it. This helps to maintain the spread of the solutions in the decision variable space. This leads to each member having its fitness
For ready reference, the pervaporation process and cost model1 utilized for the present work is presented in the Appendix 1 and Appendix 2, respectively. Including the bore diameter as one more decision variable, the two-objective unconstrained optimization problem can be described as follows: minimum annual treatment cost (q, Re, l, D, p, xtol, xTCE, xMC) maximum toluene removal fraction (q, Re, l, D, p, xtol, xTCE, xMC) subject to 2.77 × 10-3 < q < 5.77 × 10-3 20 < Re < 7000 5 × 10-5 < D < 8 × 10-4 5 × 10-6 < l < 10-4 0.2 < p < 4.0 2 × 10-6 < xtol < 9.8 × 10-5 2 × 10-6 < xTCE < 9.7 × 10-5 2 × 10-6 < xMC < 4.01 × 10-3 Further, the removal percent of toluene is defined as Gtol 100 qtolCtol
(1)
The tubular membrane is simulated by solving the overall (eq A.14) and component (eq A.15-A.17) continuity equations, element by element of the shell and tube module. The permeate compositions are obtained by simultaneous solution of the flux equations (eq A.4 and A.5) at each element of the module. The total flux of toluene is obtained by summing the flux for each individual element. The removal percent of the toluene is estimated according to eq 1. This procedure is continued for an exit concentration of toluene in retentate equal to 10% of its initial concentration. The previous study1 reveals that genetic parameters are not affecting the optimal solution. Therefore, fixed genetic parameters given in Table 1 are chosen for study for which properties of the components are given in Table 2. 3.0. Results and Discussion The objective of the present work is to study two-objective optimization using NSGA-II for VOC separation from multicomponent aqueous solutions providing Pareto optimal solutions. This is presented in three parts: (1) Pareto optimal study in objective function space, (2) Pareto optimal study in decision variable space, and (3) sensitivity analysis.
Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1545
Figure 2. (a-h) Values of the decision variables (q, Re, D, l, p, xtol, xTCE, xMC) on the Pareto solutions in Figure 1a for removal of toluene from water.
3.1. Pareto Optimal Study in Objective Function Space. Figure 1a and 1b represent the Pareto optimal study in objective function space. Figure 1a is the plot of removal percent versus treatment cost. The objective function space clearly shows that there exists a tradeoff between the two objectives (i.e., minimization of treatment cost and maximization of removal percent of toluene). The removal percent versus treatment costcurve is in two segments. The lower segment corresponds to turbulent region and the upper segment corresponds to the
laminar region. The treatment cost is lower in turbulent region compared to that in laminar region which is in contrast with the single objective optimization study.1 Further, it may be inferred that for the given range of decision variables, the removal percentage varies from 72.6 to 73.8 and total cost varies from $2.80 × 104 to $1.07 × 107 per year. Though the range of removal percentage appears to be small, the increase in the removal of toluene is approximately 7 tons/year corresponding
1546 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 Table 3. Sensitivity Analysisa q × 103 ) l × 106 ) D × 104 ) p) xMC × 103 )
case I
II
III
2.77 3 8 0.3 4
2.57 -
2.97 -
IV V
VI
2 -
-7 -
10 -
VII VIII IX X XI 9 -
0.2 -
0.6 -
2
3
a For all cases II to XI: Re ) [20 2100]; xtol ) [2 × 10-6 9.8 × 10-5]; xTCE ) [2 × 10-6 9.7 × 10-5].
to the feed volumetric flow rate of 2.8 m3/s, for an approximate initial concentration of toluene equaling 7.8 × 10-5 mole percent. To get deeper insight about the objective function space, a plot (Figure 1b) is made between the removal percent versus various costs. It is clear from the figure that when the removal percent varies from 72.6 to 73.4 the vacuum and condensation cost increases from $1.78 × 104 to $6.69 × 106, whereas the feed pumping cost varies from $3.14 to $1.37 × 104, membrane replacement cost varies from $7.04 × 102 to $1.37 × 104 and the initial cost varies from $7.45 × 103 to $5.63 × 105. This reveals that the total cost is dominated by the vacuum and condensation cost over the entire range of Pareto solutions whereas the membrane replacement cost and the feed pumping cost are comparably insignificant. This is in contrast with single objective studies carried out earlier1 as it was concluded that different costs dominate in the treatment cost in different regions
Figure 3. (a-e) Effect of decision variables (q, D, l, p, xMC) on the Pareto set.
of the process. In the laminar region the capital cost was dominating and in the turbulent region feed pumping cost was dominating. 3.2. Pareto Optimal Study in Decision Variable Space. Volumetric feed rate, membrane thickness, downstream pressure, Reynold’s number, diameter of the fiber, and feed organic concentration (toluene, TCE, MC) are the decision variables chosen to study their effect on the Pareto optimal solutions. Their effect on the Pareto is given in Figure 2a-h. Among these variables volumetric rate, diameter, membrane thickness, down stream pressure, and methylene chloride concentration are ineffective on the Pareto in the laminar region. On the other hand, Reynold’s number, toluene concentration, and trichloroethane concentration are affecting the Pareto. Similar types of trends were reported in the literature for beer dialysis.21 Figure 2a is a plot of removal percent versus volumetric feed rate. The volumetric feed rate is varied between the lower limit 2.77 × 10-3 m3/s and 5.77 × 10-3 m3/s. It is clear that the Pareto solutions lye at the lower bound. It is because of this fact that the treatment cost decreases with decrease in volumetric feed flow rate and the removal percent of toluene, as defined by eq1, increases. Figure 2b is a plot of removal percent versus Reynold’s number. The Reynold’s number is varied from 20 to 7000. Two sets of optimal solutions are obtained. The upper bound (turbulent zone) solutions correspond to lower treatment cost and lower removal percent. The solutions to the lower bound
Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1547
Figure 4. (a-e) Effect of decision variables (q, D, l, p, xMC) on Reynold’s number corresponding to the points in Figure 3.
(laminar zone) correspond to higher treatment cost and higher removal percent. The removal percent versus the Reynold’s number curve is not surprising in the lower bound region, that is, in the laminar zone. This may be attributed to the fact that increase in Reynold’s number increases the volumetric rate on the tube side and hence decreases the removal percent, as per eq 1. On the other hand, the increase in Reynold’s number increases the organic flux by virtue of increased mass transfer coefficient. Therefore, the removal percent increases. But the previous effect is dominating and hence the removal percent decreases overall. As explained in section 3.1, the decrease in removal percent decreases the treatment cost by decreasing the cost of vacuum and condensation cost which is dominating in the treatment cost. However, at higher Reynold’s number, that is, in the range of 5000-7000, the increase in Reynold’s number increases both the removal percent and treatment cost. This is because in this range of Reynold’s number both downstream pressure and membrane thickness are not constant but decrease (Figure 2d and Figure 2e). Lower downstream pressure infers higher driving force, and lower fiber thickness provides lesser resistance to transport. Both these effects will increase permeation flux. Hence, there is increase in treatment cost and removal percent. Figure 2c is the plot of removal percent versus diameter of the fiber. The diameter is varied from 5 × 10-5 to 8 × 10-4
and the Pareto falls at higher diameter. As the diameter is varied from 5 × 10-5 to 8 × 10-4, the trends of the analysis performed are valid not only for the hollow fiber membrane module but also for the capillary membrane module. It is clear from the Pareto solutions in plots 2d and 2e that the downstream pressure and thickness are important variables in the turbulent region. Further, it is clear that the two variables lie at their lower bounds in the laminar region. It is because of this that these two variables complement each other in the contribution for the vacuum and condensation cost which is dominating in the treatment cost and removal percent of the VOC. Figure 2 panels f-h are the plots of removal percent versus feed organic concentrations of toluene, TCE, and MC, respectively. The figures clearly indicate that MC concentration is insignificant in the Pareto where there is a spread of Pareto for toluene and TCE. The similarities in Figure 2 panels f and g may be attributed to the similar permeabilities and liquid phase mass transfer coefficients of toluene and TCE at low pressures.15 The least Henry’s law constant of methylene chloride among these three components may be the reason for obtaining optimal solutions at the upper bound (Figure 2h) and in the turbulent region where the treatment cost and the removal fraction are to be at the lower values, the inlet concentrations of all components are understandably at their lower bounds.
1548 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009
3.3. Sensitivity Analysis. Sensitivity analysis is carried out with a base case picked up from the above Pareto optimal solutions in the laminar region. From the decision variable space, it is clear that the volumetric rate of feed, membrane thickness, bore diameter, down stream pressure, and methylene chloride concentration are nearly constant, whereas, Reynold’s number is found to vary over its entire range (including inlet concentrations of toluene and TCE). Hence, the reference cases II-XI are obtained by varying the volumetric rate, thickness, bore diameter, downstream pressure, and methylene chloride concentrations (Table 3). The values of these variables are varied one at a time near the base case values to obtain Pareto solutions. One may observe that for methylene chloride concentration the base case value is at its maximum solubility hence the sensitivity Paretos are obtained on lower side only. The other Pareto plots of percent conversion versus toluene concentration and TCE concentration are made but not shown for brevity. Sensitivity Pareto solutions shall be useful in identifying optimal feasible designs while analyzing the pervaporation process for the removal of VOC from wastewater. These plots not only present trade-offs available between percent removal and the treatment cost but also among Reynold’s number and other decision variables (q, l, D, p and xMC). If a pervaporation module of higher diameter is to be used in the process, then the design engineers can know what will be the treatment cost and Reynold’s number for a given target percent removal. These Pareto solutions are useful in reducing the designer’s choices and thereby making the design options less cumbersome. For example, for a given diameter of the hollow fiber and for a given cost the trade-offs between Reynold’s number and other variables (among volumetric rate, thickness of the fiber, toluene concentration, and trichloroethane) can be known. From Figure 3a it is clear that treatment cost marginally increases with increase in volumetric flow rate in the turbulent region but more sensibly in the laminar region. The Reynold’s number Pareto is not affected by change in volumetric flow rate (Figure 4a). This is because the change in total volumetric flow rate changes the number of tubes but not the inlet Reynold’s number in a given tube. Nevertheless, the present study generalizes the removal of organic pollutants in wastewater for a single-stage pervaporation process but without the recycle in a shell and tube-type module. 4.0. Conclusions The two-objective optimization study of simultaneous minimization of treatment cost versus maximization of percent removal of VOC (toluene) is carried out using the evolutionary algorithm of real coded NSGA-II for removal of VOCs from wastewater in a shell and tube-type module utilizing PDMS membrane. The optimization study is carried out on the basis of a previously derived mathematical model. It is concluded that attractive trade-offs are available between percent removal of toluene and annual treatment cost. Vacuum and condensation cost is observed to be dominating in the treatment cost under both laminar and turbulent regions. It is also found that the decision variables (thickness of fiber, downstream pressure, volumetric rate of the feed) are found to lie at their lower bound in the Pareto solutions, where as the diameter of the fiber is found to lie at its higher bound. Reynold’s number is observed to be varying in the entire range.
Notation A ) area (m2) B ) module factor C ) concentration (kmol/m3) Cp ) specific heat capacity (kJ/kmol K) D ) Diameter (m) E ) dimensionless number E ) price of electricity ($/kWh) F ) fugacity (kPa) Fr ) fraction G ) total permeate flow (kmol/s) Hi ) Henry’s law constant (kPa m3/mole) H ) enthalpy (kJ/kmol) N ) permeation flux (kmol/m2 s) K ) overall mass transfer coefficient (m/s) kl ) mass transfer coefficient in the boundary layer (m/s) k ) heat capacity ratio L ) length of hollow fiber (m) LP ) permeability (kmol m/m2 kPa s) L ) membrane thickness (m) MC ) methylene chloride p ) downstream pressure (kPa) p° ) saturated vapor pressure (kPa) ∆p ) feed side pressure drop (kPa) q ) feed flow rate (m3/s) ri ) inner radius of hollow fiber (m) ro ) outer radius hollow fiber (m) R ) universal gas constant (J/mol K) Re ) Reynold’s number Sc ) Schmidt number Sh ) Sherwood number T ) temperature (K) TCE ) trichloroethane tol ) toluene t ) time period (h) U ) overall heat transfer coefficient (kJ/s m2 K) W ) energy consumption (kW) x ) mole fraction at feed side y ) mole fraction at permeate side z ) axial coordinate Greek Symbols γ ) activity coefficient F ) total concentration of the feed (kmol/m3) ∆ ) difference µ ) viscosity (kg/m s) η ) efficiency factor C e ) cost ($) Subscripts F ) feed side i ) organic compounds (i ) 1,2,3) j ) compounds (j ) 1,2,3 and water) m ) membrane P ) permeate side w ) water Superscripts L ) liquid phase org ) organic phase in permeate o ) saturated condition
Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1549 V ) vapor phase ∞ ) infinite dilution condition
LP,i,m (xiHi - pyi ⁄ F) LP,w (pwo - pyw) 1 dq )(A.14) 2π dz (Ei + 1) ln(1 + l ⁄ ri) F ln(1 + l ⁄ ri) i)1 3
∑
Appendix 1 Process Model. Mass Balance. Considering a small element of fluid of width dz in axial direction with surface area dA we have the overall mass balance as -F dq ) N dAm
q dx1 ) x1 2π dz
(A.1)
and the mass balance of the organic compound, (i ) 1, 2,..., i) d(qCi) ) -N dAm
(A.2)
q dx2 ) x2 2π dz
[∑
LP,i,m (xiHi - pyi ⁄ F) LP,w (pwo - pyw) + (Ei + 1) ln(1 + l ⁄ ri) F ln(1 + l ⁄ ri)
[∑
LP,i,m (xiHi - pyi ⁄ F) LP,w (pwo - pyw) + (Ei + 1) ln(1 + l ⁄ ri) F ln(1 + l ⁄ ri)
[∑
LP,i,m (xiHi - pyi ⁄ F) LP,w (pwo - pyw) + (Ei + 1) ln(1 + l ⁄ ri) F ln(1 + l ⁄ ri)
3
j)1
3
j)1
]
LP,1,m (x1H1 - py1 ⁄ F) (A.15) (E1 + 1) ln(1 + l⁄ri)
]
LP,2,m (x2H2 - py2 ⁄ F) (A.16) (E2 + 1) ln(1 + l ⁄ ri)
Rearranging eq A.1 and A.2, q
dCi CiN -N ) dAm F
(A.3)
q dx3 ) x3 2π dz
The permeation flux of organic species can be written as follows in terms of the overall mass transfer coefficient as
(
Ni ) Ki Ci -
) (
pi pyi ) Ki Ci Hi Hi
)
(A.4)
As the feed is a very dilute solution, neglecting liquid phase boundary layer resistance to mass transfer for water, it follows that
(
Nw ) Lp,w
) (
pwo - pw pwo - pyw ) Lp,w l l
)
i ) 1, 2, 3)
(where
(A.5)
(A.6)
Neglecting the vapor phase resistance in comparison to the liquid phase resistance and membrane resistance and applying the resistance in series model for overall mass transfer coefficient we obtain 1 1 1 ) + KiAml kl,iAFl LP,i,mHiAm
j)1
[ ] 2ri L
Cost Model. Capital Cost. The total capital cost may be estimated by em+C e mod + C e feedpump + C e vacuumpump + C e condenser) C e capital ) bmod(C (A.18) Assuming, a suggested price of $100/m2 for a commercial hollow fiber membrane, C e m ) 100Am
(A.7)
(A.8)
whereas, cost of $100/m for a typical hollow fiber membrane module may be taken and, hence,
LP,i,mHi Ei + 1
(A.20)
Further, the cost of feed pump may be estimated as (A.21)
Similarly, the cost of the vacuum pump was estimated as (A.9)
(A.10)
Therefore, Kil )
C e mod ) 100Am C e feedpump ) 26700(24 × 3600q ⁄ 50000)0.53
For Re > 4000,
1 1 1 ) + Kil kl,iri ln(ro ⁄ ri) LP,i,mHi
(A.19)
2
0.33
Sh ) 0.026Re0.80Sc0.33 Further, eq A.7 may be written as
LP,3,m (x3H3 - py3 ⁄ F) (A.17) (E3 + 1) ln(1 + l ⁄ ri)
Solving eq A.14 -A.17, the variation of flow rate, concentration of components along the axial direction of fiber for a given feed flow rate, and inlet concentrations of components may be obtained.
For Re < 2100, kl can be calculated from Leveque equation: Sh ) 1.62Re0.33Sc0.33
]
Appendix 2
and N ) ΣNi + Nw
3
(A.11)
C e vacuumpump ) 4200(60GRTo⁄Po)0.55
(A.22)
where, To and Po are standard temperature and pressure. The cost of permeate condenser was calculated from the cost of carbon steel shell and tube condenser, where the condenser tube length was 3.66 m. Accordingly, for 0 < Acondenser < 22.30, C e condenser ) 1176.7 + 128.1Acondenser
(A.23)
where
where
4
LP,i,mHi Ei ) kl,iri ln(ro ⁄ ri)
j
(A.12)
Substituting eq A.11 into eq A.4, Ni )
LP,i,m(CiHi - pi) LP,i,m(CiHi - pyi) ) (Ei + 1)l (Ei + 1)l
∑ G [(∆H) + C
(A.13)
Further, substituting eq A.5, A.6, and (A.13) into eq A.1 and eq A.3, respectively, as
Acondenser )
j
j)1
U(∆T)F
V p,j(∆T)P]
(A.24)
The value of U was taken to be 9.52 × 10-3 kJ/(s · m2 · K) for streams condensed by ammonia. Treatment Cost. The treatment cost (TC) was estimatedon the basis of four aspects: (1) capital depreciation (CD), (2) maintenance and labor requirement (ML), (3) membrane replacement (MR), and (4) energy consumption (EC).
1550 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009
C e TC ) (Fr)CDC e capital + (Fr)MLC e capital + C e MR + C e EC (A.25) To cover depreciation and taxes (CD), a value of 15% of installed total capital cost was assumed. The annual maintenance and labor costs were taken to be 10% of the total capital cost. Further, a membrane life of 3 years was assumed. Therefore, ∉MR ) 100Am ⁄ 3
(A.26)
Energy consumption consists of pumping feed, vacuum pumping, and vapor condensation. Therefore,
[
∉EC ) (e)t
WF Wvacuum Wcondenser + + ηF ηvacuum ηcondenser
]
(A.27)
where, WF is power for the feed pump and it was taken as the product of flow rate q and flow pressure drop ∆p, WF ) q∆p
(A.28)
In pervaporation, downstream pressure was maintained by efficient condensation of permeate. The condensation temperature controls the downstream pressure. Due to limited solubility of organics in water, permeate may be obtained in two phases. Further, it was assumed that equilibrium was reached among vapor organics and aqueous phases, therefore,
p)
fiV ) fiL
(A.29)
Σpi(T) ) Σpoi γ∞i xi ) Σpoi yorg i
(A.30)
pw ≈ pwo
(A.31)
∑ p (T) + p (T) ≈ ∑ p (T)y i
org o i + pw(T)
o i
w
i
(A.32)
i
A vacuum pump was used to remove the inert gas and assumed to operate at 10% of the total operating time. The work done by the vacuum pump is therefore,
[(
po k RT Wvacuum ) 0.1G k-1 p
)
]
( )-1 k-
1 k
(A.33)
Further, energy balance on the condenser gives the energy consumption, 4
Wcondenser )
∑ [G (∆H) + C j
j
V P,j(∆T)P)]
(A.34)
j)1
Literature Cited (1) Satyanarayana, V. S.; Bhattacharya, P. K. Real coded genetic algorithm for optimization of process parameters for removal of volatile organics from water. Ind. Eng. Chem. Res. 2003, 42, 3118. (2) Strathmann, H. Membrane separation processes: Current relevance and future opportunities. AIChE J. 2001, 47, 1077. (3) Ruey-Shin, J.; Su-hsia, L.; Min Chih, Y. Mass transfer analysis on air stripping of VOCs from water in microporous hollow fibers. J. Membr. Sci. 2005, 255, 79.
(4) Panek, D.; Konieczny, K. Preparation and applying the membranes with carbon black to pervaporation of toluene from the diluted aqueous solutions. Sep. Purif. Technol. 2007, 57, 507. (5) Jou, J. D.; Yoshida, W.; Cohen, Y. A novel ceramic-supported polymer membrane for pervaporation of dilute volatile organic compounds. J. Membr. Sci. 1999, 162, 269. (6) Vane, L. M.; Alvarez, F. R. Full-scale vibrating pervaporation membrane unit: VOC removal from water and surfactant solutions. J. Membr. Sci. 2002, 202, 177. (7) Scott, K.; Lobato, J. Mass transfer characteristics of cross-corrugated membranes. Desalination 2002, 146, 255. (8) Noworyta, A.; Trusek-Hołownia, A.; Mielczarski, S.; KubasiewiczPonitka, M. An integrated pervaporation - biodegradation process of phenolic wastewater treatment. Desalination 2006, 198, 191. (9) Shah, M. R.; Noble, R. D.; Clough, D. E. Pervaporation-air stripping hybrid process for removal of VOCs from groundwater. J. Membr. Sci. 2004, 241, 257. (10) Oliveira, T. A. C.; Scarpello, J. T.; Livingston, A. G. Pervaporationbiological oxidation hybrid process for removal of volatile organic compounds from wastewaters. J. Membr. Sci. 2002, 195, 75. (11) Psaume, R.; Aptel, P.; Aurelle, Y.; Mora, J. C.; Bersillon, J. L. Pervaporation: importance of concentration polarization in the extraction of trace organics from water. J. Membr. Sci. 1988, 36, 373. (12) Cote, P.; Lipski, C. Mass Transfer Limitation in Pervaporation for Water and Wastewater Treatment. In Proceedings of the 3rd International Conference on PerVaporation in the Chemical Industry, Nancy, France, 1988; Bakish, R., Ed.; Bakish Materials Corporation: Englewood, NJ, 1988; pp 449–462. (13) Peng, M.; Vane, L. M.; Liu, S. X. Recent advances in VOCs removal from water by pervaporation. J. Hazard. Mater. 2003, B98, 69. (14) Lipski, C.; Cote, P. The use of Pervaporation for the Removal of Organic Contaminants from Water. EnViron. Prog. 1990, 9, 254. (15) Ji, W.; Hilaly, A.; Sikdar, S. K.; Hwang, S. T. Optimization of Multicomponent Pervaporation for Removal of Volatile Organic Compounds from Water. J. Membr. Sci. 1994, 97, 109. (16) Deb, K. Multi-objectiVe Optimization Using EVolutionary Algorithms. John Wiley & Sons: New York, 2002. (17) Rajesh, J. K.; Gupta, S. K.; Rangaiah, G. P.; Ray, A. K. Multiobjective optimization of steam reformer performance using genetic algorithm. Ind. Eng. Chem. Res. 2000, 39 (3), 706. (18) Gupta, R. R.; Gupta, S. K. Multi-objective Optimization of steam reformer performance using genetic algorithm. J. Appl. Polym. Sci. 1993, 73, 729. (19) Bhaskar, V.; Gupta, S. K.; Ray, A. K. Multi-objective optimization of an industrial wiped film poly(ethelene terephthalate) reactor. AIChE J. 2000, 46 (5), 1046. (20) Elliot, L.; Ingham, D. B.; Kyne, A. G.; Mera, N. S.; Pourkashanian, M.; Wilson, C. W. Multi-objective genetic algorithm for calculating the reaction rate coefficients for hydrogen combustion. Ind. Eng. Chem. Res. 2000, 42, 1215. (21) Yuen, C. C.; Aatmeeyata,Gupta, S. K.; Ray, A. K. Multi-objective optimization of membrane separation modules using genetic algorithm. J. Membr. Sci. 2000, 176, 177. (22) Fleming, P. J. Computer-Aided Control System Design of Regulators Using a Multi-Objective Optimization Approach. In Control Applications of Nonlinear Programming and Optimization; Di Pillo, G., Ed.; Proceedings of the Fifth IFAC Workshop, Capri, Italy, June 11–14, 1985; Pergamon Press: New York, 1986; p 47. (23) Bhaskar, V.; Gupta, S. K.; Ray, A. K. Applications of multi-objective optimization in chemical engineering. ReV. Chem. Eng. 2000, 16, 1.
ReceiVed for reView April 3, 2008 ReVised manuscript receiVed November 5, 2008 Accepted November 14, 2008 IE8005319
