Development of Heat-Integrated Evaporation and Crystallization

Ind. Eng. Chem. Res. 2001, 40, 2827-2841

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Development of Heat-Integrated Evaporation and Crystallization Networks for Ternary Wastewater Systems. 1. Design of the Separation System Gautham Parthasarathy† and Russell F. Dunn* Nylon Plastics and Polymers, Solutia Inc., 3000 Old Chemstrand Road, Cantonment, Florida 32533

Mahmoud M. El-Halwagi‡ Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849

This paper considers the optimal design of an evaporation and crystallization network for separation of a ternary wastewater stream with two salts and is the first part in a two part series on evaporation and crystallization networks. A crystallization and evaporation design is compared with previous work on condensation within the framework of a heat-induced separation network design. Detailed mathematical expressions are listed for complete material and energy balances, pinch equations, and unit sizing and cost of the evaporation and crystallization network. Some generic structures are proposed for heat integration of a typical evaporation and crystallization network. Several graphical insights are listed that allow one to use the representation of evaporation and crystallization operations on a ternary triangular composition diagram and to avoid mathematical complexity. Graphical insights enable reduction of the search space and allow solution of the problem in a computationally efficient manner. A graphical solution strategy and algorithm are described to converge to the optimal design. The solution algorithm requires the identification and bounding of certain critical design variables. A case study is solved to demonstrate the broad applicability and value of the proposed approach. 1. Introduction Crystallization has been extensively studied as a unit operation and finds broad application in various industries1 including (1) separation (e.g., separation of pxylene from o- and m-xylene), (2) concentration (e.g., concentration of fruit juice), (3) solidification (e.g., modification of the appearance of sugar), (4) purification (e.g., separation of an essential amino acid, L-isoleucine, from a fermentation broth), and (5) analysis (e.g., determination of the molecular structure). Crystallization operations play a vital role in product recovery and are capable of producing very high purity products from impure solutions. Crystallization generally requires less energy for separation as compared to distillation or other commonly used methods of purification. Another important application of crystallization is in its value in lowering pollution.2 For instance, crystallization can be used to separate salts from aqueous effluent streams so that these streams may be recycled and reused in the process. It has been observed that there were less established design techniques for crystallization systems as compared to distillation and other separation techniques. In response to this shortcoming, significant work has gone into developing systematic design methodologies for crystallization systems. Melt crystallization manufacturing systems have been opti* To whom correspondence should be addressed. E-mail: [email protected]. Tel: 850-968-8216. Fax: 850-9688732. † E-mail: [email protected]. Fax: 850-968-8732. ‡ E-mail: [email protected]. Tel: 334-844-2064. Fax: 334-844-2063.

mized and mathematically characterized.3 Systematic procedures were formulated for the separation of binary and ternary mixtures via extractive crystallization.4,5 A methodology to generate phase diagrams from solubility product data was developed along with a synthesis procedure for fractional crystallization processes to obtain pure solids from conjugate salt solutions.6 A design technique for suspension crystallization was studied and a computer algorithm was developed for crystallizer design including mass and population balances, crystallization kinetics, and operating conditions.7 Crystallization paths, analogous to residue curve maps in vapor-liquid equilibrium systems, for melt crystallization processes were introduced.8 An approach for generating equilibrium-based fractional crystallization processes was described.9 A systematic procedure for solids mixture separation based on solubility was presented.10 A methodology for the identification of alternative process designs for fractional crystallization from solution was described.11 Guidelines were described for separation of two and three solute mixtures and for bypassing regions of multiple saturation via solvent addition (removal) and cooling (heating).12 A general method for the calculation of various types of phase diagrams for aqueous electrolytic systems was developed and applied toward simulation and optimization of fractional crystallization processes.13 The retrofit of an existing fractional crystallization process to improve product recovery was considered.14 A method to synthesize fractional crystallization process flow sheets was presented and a network flow model was developed from equilibrium data for a candidate set of potential operating point temperatures.15 This flow model represented the potential separation flow sheets. A network

10.1021/ie000831d CCC: $20.00 © 2001 American Chemical Society Published on Web 05/26/2001

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Ind. Eng. Chem. Res., Vol. 40, No. 13, 2001

Figure 1. Problem definition for the evaporation and crystallization separation network for a ternary stream.

flow model for synthesizing crystallization sequences for multicomponent systems was also presented.16 Heat integration of the energy flows in a typical evaporation and crystallization system is not addressed. It has been identified that the major component of the operating cost of an evaporation and crystallization process lies in the heat duty to be added for evaporation and removed in cooling/heating the crystallization block.16 Although crystallization is a heat-induced separation network (HISEN), the previously developed solution methodologies for the design of volatile organic compound (VOC) condensation HISENs17-19 cannot address all aspects of the uniqueness of the evaporation and crystallization operation. The following section describes the problem statement for the design and heat integration of an evaporation and crystallization network. 2. Problem Statement for a Separation Network Crystallization can be classified as a HISEN because it employs indirect contact energy separating agents (or ESAs) such as coolants and refrigerants to effect phase change separations. The problem statement involves designing an evaporation and crystallization network for a ternary wastewater stream consisting of water and two salts. The separation network can consider both cooling and evaporative crystallization. The problem is represented in Figure 1. For the process under consideration, there is a wastewater stream, i, containing the species of interest (i.e., salts A and B). The total initial flow rate of the wastewater source, Fi, is known along with the composition of the two salts (zAi and zBi for salts A and B, respectively) and the supply temperature . Corresponding to the input stream, there are TFeed i three resultant streams exiting the interception (i.e., evaporation and crystallization) block. These are listed as follows: (1) a salt stream from the crystallization block with total flow rate, Salti, and composition of salt Salt ; (2) a pure water stream from the evaporation A, zi,A block with total flow rate, Soli; (3) a mother liquor stream from the crystallization block with total flow ML and rate, MLi, and composition of the two salts (zi,A ML zi,B for salts A and B, respectively).

The initial mass load of water in the stream is denoted by WNominal, where

WNominal ) Fi(1 - zAi - zBi )

(1)

The initial mass load of salt A in the stream is denoted by UNominal, where

UNominal ) FizAi

(2)

The initial mass load of salt B in the stream is denoted by VNominal, where

VNominal ) FizBi

(3)

It is desired to design a network based on evaporation and crystallization that can reduce the mass load of water and the two salts in the input stream to predefined levels at minimum cost. Thus, the final mass loads in the stream for water, salt A, and salt B are given as

WFinal e RWNominal

(4)

UFinal e βUNominal

(5)

VFinal e γVNominal

(6)

0eRe1

(7)

0eβe1

(8)

0eγe1

(9)

where

This reduction in mass load is based on process considerations that can be technical (e.g., to meet composition requirements of units accepting resultant created sources), environmental (e.g., to satisfy discharge standards), and operational (e.g., to stay away from plugging and corrosion limits). The separation of the species of interest from the wastewater streams is accomplished via evaporation and crystallization using a set of energy separating agents ESA {E|E ) 1, 2, ..., NE} consisting of two sets,

Ind. Eng. Chem. Res., Vol. 40, No. 13, 2001 2829

COOLANT {C|C ) 1, 2, ..., NC} and HOT {H|H ) 1, 2, ..., NH}, of candidate coolants and heating media, respectively. The temperature of each coolant, tCCool, and the cost of the coolant (given in $/kJ removed), COOLANT_COSTC, are known. The temperature of each heating media, tHHot, and the cost of the heating medium (given in $/kJ removed), HOT_COSTH, are known. The objective of the design task is to minimize the total annualized cost of evaporation and crystallization and to identify optimum strategies for evaporation and crystallization of the wastewater sources to meet prespecified separation tasks. 3. Comparison of Evaporation/Crystallization and VOC Condensation It may be noted that the design of a HISEN for evaporation and crystallization is different from the design for condensation of VOCs. Listed are some of the unique features of the HISEN for evaporation and crystallization. 1. In the case of VOC condensation, for a given input gaseous source assuming constant pressure, the target composition can be achieved at a unique value of T*. As will be described subsequently in the solution procedure, there are several values of TCryst that can achieve the same separation task for evaporation and crystallization. Iteration is required over all possible before converging to the optimal value values of TCryst i of TCryst . i 2. In VOC condensation, there are two output streams for every input stream. The two output streams are the residual gaseous source (following condensation) and the condensed VOC. In evaporation and crystallization, there are three output streams for every input stream. The three output streams are the pure water stream (from the evaporation block), salt stream, and mother liquor stream (from the crystallization block). 3. In the case of VOC condensation, there is no solvent analogous to water in evaporative crystallization. Some water is removed in a dehumidification step in VOC condensation. However, the amount of water removed is generally small and does not contribute to the economics of the process. In evaporation and crystallization, the removal of water via evaporation may be a major contributor to the economics of the process and may require greater external utility compared to the crystallization. 4. In the case of VOC condensation, the input gaseous stream is being either continuously cooled (to dehumidify it or to condense VOCs) or continuously heated (in heat integration). In the case of evaporation and crystallization, the input feed stream is initially heated to the evaporation block operating temperature. Following evaporation and creation of the pure water stream, the residual liquor may be cooled (in the case of cooling crystallization) to the crystallization block operating temperature. 4. Design Challenges The aforementioned problem poses several design challenges. Because of the interactions among the water and salts, the solid-liquid equilibrium governing the evaporation and crystallization of the species of interest is nonideal and possibly nonlinear, thereby complicating the computational aspects of the design problem. Thus, the final design must account for the nonideal interac-

tions existing between the species of interest. In addition, there exist several questions that must be addressed. (i) How much of the water should be evaporated in the evaporation block? (ii) Should interception (i.e., mass separation) be used to remove one or both salts? (iii) If a single salt is to be removed, which salt should be targeted for removal? (iv) How much of each or both salts should be removed via interception? The final design should achieve the desired reduction in mass loads of water and two salts at minimum cost. The previously developed methodologies for VOC condensation do not directly apply to this problem as indicated in the previous section. The following section considers the typical structure for the evaporation and crystallization network. 5. Structure of the Evaporation and Crystallization Network A generic network structure is developed to achieve the required separation task (refer to Figure 2). There are two main blocks, namely, evaporation and crystallization. Each of these blocks could consist of single or multiple units. Analogous to the structure for VOC condensation,17-19 the following structure can be proposed for heat integration of a separation network consisting of evaporation followed by cooling crystallization (refer to Figure 3). There are two heat exchangers for heat integration. Self-integration of a stream with itself is allowed, with the external utility being used to overcome the temperature driving force ∆Tmin.20 A value for ∆Tmin can be arbitrarily selected or the optimal value determined by iterating over different values of ∆T and trading off fixed and operating cost. For the scope of this paper, the value of the temperature driving force is fixed at ∆Tmin and is the same for all exchangers being considered. The input feed stream gets preheated to the evaporation block operating tempera) in the heat exchanger termed as Heat ture (TEvap i Integration 1. The external heating utility provides the heat required for evaporation in the evaporation block. The residual liquor from evaporation is sent to the crystallization block. An external cooling utility is used to supply the cooling required to the crystallization block, which results in the creation of the salt stream ) and mother liquor stream (at (at temperature TCryst i ). The cold mother liquor stream is temperature TCryst i then recycled and reused for heat integration. The heat exchanger termed Heat Integration 2 is used to cool the pure water stream via heat exchange with the cold mother liquor. If this heat exchange does not completely condense the pure water stream, an additional exchanger is used with external cooling utility. Some of the features behind selecting the proposed structure are summarized as follows: 1. Analogous to the structure proposed for VOC condensation,17-19,21 the proposed structure would seek to maximize heat integration. This includes self-integration of a stream with itself (e.g., the mother liquor stream and the condensed solvent-rich stream). 2. An external heating utility is used exclusively to provide the heat duty required for the evaporation block. This is so because none of the streams present in the evaporation and crystallization network is at temper. atures higher than TEvap i

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Figure 2. Generic structure for the evaporation and crystallization network for a ternary stream.

Figure 3. Proposed structure for a heat-integrated evaporation and crystallization network.

3. An external cooling utility is used exclusively to provide cooling for the crystallization block as well as to cool the pure water stream, if necessary. 6. Mathematical Formulation of the Separation Problem In this section, the design problem is formulated as an optimization program whose objective is to minimize cost subject to constraints of materials and energy balances, thermodynamic limitations, and technical and environmental requirements. The following subsections describe the constraints for material and energy balances, pinch equations, and unit sizing and cost. The constraints describing the evaporation and crystalliza-

tion network are given below for the ith stream being intercepted. 6.1. Evaporation Block.

Overall Material Balance Fi ) Soli + Ri

(10)

Component Material Balance for Salt A Resi FizAi ) Rizi,A

(11)

Component Material Balance for Salt B Resi FizBi ) Rizi,B

(12)

Resi Resi , and zi,B are the flow rate and composiwhere Ri, zi,A


tion salts A and B, respectively, in the residual liquor stream from the evaporation block. In general, the compositions of salts A and B in the residual liquor can be given by a solubility temperature relationship of the form

A similar expression (excluding the last two terms) can be derived for the enthalpy of the recycled mother liquor.

∫tt CPi,w(ti) dti + t L Yi,u(tCryst )i∫t CPi,u (ti) dti ∑ i u)A,B

hi(ti) - hi(tCryst )) i

i

Cryst i

i

Cryst i

Solid-Liquid Equilibrium Resi Resi (zi,A , zi,B ) ) Ψi(TCryst ) i

(13)

6.2. Crystallization Block. Similar material balances can be developed for the crystallization block as well.

Overall Material Balance Ri ) Salti + MLi

(14)

Component Material Balance for Salt A Resi ML Salt ) Saltizi,A + MLizi,A Rizi,A

(15)

Component Material Balance for Salt B Resi Salt ML Rizi,B ) Salti(1 - zi,A ) + MLizi,B

(16)

where Salti is the flow rate of the salt stream from the ML ML , and zi,B are the flow crystallization block and MLi, zi,A rate and compositions of salts A and B, respectively, in the mother liquor stream from the crystallization block. In general, the composition of the species of interest in the mother liquor can be given by a solubility temperature relationship of the form

Solid-Liquid Equilibrium ML ML , zi,B ) ) ξi(TCryst ) (zi,A i

(17)

6.3. Enthalpy Balance. Let us develop the enthalpy expression for the hot salt-laden stream as its temperature is cooled from its supply temperature, TSi , to some arbitrary temperature, Ti, which is below the temperature at which crystallization begins to occur in the liquid phase. Assuming that the heat of crystallizaCryst , remains tion of the salt u (S) crystallizing out, Hi,u constant over the crystallization range, the enthalpy change (e.g., kJ/kg of salt-free liquid stream) can be evaluated through

∫TT CPi,w(Ti) dTi + L (Ti) dTi + ∫TT ∑ Yi,u(Ti) CPi,u u)A,B S Cryst - Yi,u(Ti)]Hi,u + ∑ [Yi,u u)A,B

Hi(Ti) - Hi(TSi ) )

i

S i

i

S i

S S - Yi,u(Ti)]CPi,u (Ti) dTi ∫T ∑ [Yi,u u)A,B Ti S i

(18)

T i ) ti +

6.4. Pinch Equations. Once the evaporation and crystallization task has been converted into a heatexchange problem, the pinch diagram can be used to minimize the separation cost. Because of the nonlinearity of the enthalpy vs temperature composite curves (particularly that for the hot salt-laden sources), thermodynamic feasibility has to be guaranteed at each temperature level.20 This can be achieved by dividing into k the entire temperature range from TSi to TCryst i intervals. The temperature value on the hot scale corresponding to the end of the kth interval is denoted by T h i,k where k ) 1, 2, ..., k. Similarly, the temperature value on the cold scale corresponding to the end of the kth interval is designated as hti,k where k ) 1, 2, ..., k. Note that the hot source is assumed to be at a supply , while the cold recycled mother temperature of TSource i liquor is heated to a final outlet temperature of tout i . Cumulative energy lost by the ith hot source until an arbitrary temperature, Ti,k, within the kth interval is given by H H (Ti,k,Fi) ) φi,k-1 (T h i,k-1,Fi) + FWater [Hi(Ti,k) φi,k i h i,k-1)] k ) 1, 2, ..., k (21) Hi(T H is the cumulative enthalpy exchanged by the where φi,k hot source until an arbitrary temperature, Ti,k, is reached within the kth interval, and

T h i,k-1 e Ti,k e T h i,k

(22)

H (T h i,0,Fi) ) 0 φi,0

(23)

and the total energy lost by the hot source is given as H (T h i,K,Fi) ) FWater [Hi(TSi ) - Hi(TCryst )] φi,k i i

(24)

refers to the amount of water present in where FWater i the ith source. We can also write an equivalent set of equations for the cold recycled mother liquor. Hence, the cumulative energy gained by the ith cold recycled mother liquor stream until an equivalent temperature, ti,k, within the kth interval can be expressed as follows: C C φi,k (ti,k,MLi) ) φi,k-1 (thi,k-1,MLi) + MLWater [hi(ti,k) i k ) 1, 2, ..., k (25) hi(thi,k-1)]

where

where CPi,w is the specific heat of water for the ith L is the specific heat of the uth salt in the source, CPi,u S is the specific heat of the ith liquid source, and CPi,u uth salt in the ith solid source. A minimum allowable temperature difference is always necessary between the hot source and the recycled mother liquor that can be given as

∆Tmin 1

(20)

(19)

ht i,k-1 e ti,k e ht i,k

k ) 1, 2, ..., k

(26)

Equation 25 may be mapped onto the hot temperature scale by using eq 19 to yield C C (T h i,k-∆Tmin h i,k-1-∆Tmin φi,k 1 ,MLi) ) φi,k-1(T 1 ,MLi) +

[hi(T h i,k - ∆Tmin h i,k-1 - ∆Tmin MLWater i 1 ) - hi(T 1 )] k ) 1, 2, ..., k (27)

2832


where C φi,0 (T h i,0-∆Tmin 1 ,MLi) ) 0

(28)

and the total energy gained by the cold recycled mother liquor is given as C (T h i,k-∆Tmin φi,k 1 ,MLi)

)

MLWater [hi(tCryst ) i i

-

Int2 ∆Tlog mean,i )

log

To guarantee the thermodynamic feasibility of heatinduced separation, the cold stream must be above the hot stream at each temperature on the pinch diagram. This requirement is identical with stating that, at any enthalpy level, the temperature of the cold recycled stream must be less than that of the hot composite stream less ∆Tmin 1 . One way of ensuring this is by requiring that within any temperature interval the least vertical distance between the cold and hot composite streams is nonnegative. Thus, the following equation may be written:

min h i,k T h i,k-1eTi,ke∆T k)1,2,...,k

C {φi,k (Ti,k-∆Tmin 1 ,MLi)

)

-

hi(TFeed )] i

Int1 ∆Tlog mean,i )

(

(40)

Int3 ) UInt3 AInt3 ∆Tlog QInt3 i i i mean,i

(41)

where λ is the latent heat of condensation for the ith source. Int3 Int2 ∆Tlog - tCool mean,i ) Ti C

(42)

and fixed cost is evaluated through

) FCOSTInt3 (AInt3 ) FCOSTInt3 i i i

-

)

Cool ) UCool ACool ∆Tlog QCool i i i mean,i

(43)

Cool ∆Tlog mean,i

(

TEvap - tCool i C

TCryst - tCool i C

)

(45)

and fixed cost is evaluated through

) FCOSTCool (ACool ) FCOSTCool i i i

(46)

For the Evaporation Block. The total heat duty is given by

(34)

Evap ) UEvap AEvap ∆Tlog QHot i i i mean,i

(47)

where

Once the area of the heat exchanger is evaluated, its , can be evaluated: fixed cost, FCOSTInt1 i

FCOSTInt1 ) FCOSTInt1 (AInt1 ) i i i

)

Cryst (TEvap - tCool - tCool i C ) - (Ti C )

log

(33)

tInt1 ) i

(44)

where

(32)

where

- TFeed ) - (TEvap i i Int1 Ti - TFeed i log Evap Ti - tInt1 i

) Soliλ QInt3 i

For the Crystallization Block. The total heat duty is given by


(TInt1 i

(39)

-

6.5. Unit Sizing and Fixed and Operating Cost Equations. There are up to three heat exchangers, an evaporation block, and a crystallization block for each input stream. For Heat Integration 1. The total heat duty is given by

FWater [hi(tInt1 ) i i

)

(38)

For External Cooling in Heat Integration 3. If the pure water stream is not condensed via heat exchange in heat integration 2, the remaining task of condensation is accomplished via use of an external cooling utility. The total heat duty is given by

φi,kH(Ti,k,Fi)} g 0 (31)

QInt1 i

TInt2 - tCryst i i

) FCOSTInt2 (AInt2 ) FCOSTInt2 i i i

(29)

C Cool H (T h i,k-∆Tmin ) φi,k (T h i,k,Fi) + QHot φi,k 1 ,MLi) + Qi i (30)

(

TInt1 - tInt3 i i

and fixed cost is given by

hi(tout i )]

where MLWater refers to the amount of water present in i the ith mother liquor stream. Because the overall energy balance has to be satisfied, then

(TInt1 - tInt3 ) - (TInt2 - tCryst ) i i i i

(35)

Evap ∆Tlog mean,i )

Evap Int1 ) - (tHot ) (tHot H - Ti H - ti

log

(

)

Evap tHot H - Ti Int1 tHot H - ti

(48)

For Heat Integration 2. The total heat duty is given by

Once the area of the heat exchanger is evaluated, its , can be evaluated: fixed cost, FCOSTEvap i

QInt2 ) MLWater [hi(tCryst ) - hi(tInt3 )] i i i i

(36)

) FCOSTEvap (AEvap ) FCOSTEvap i i i


(37)

The total fixed cost for the entire evaporation and crystallization network for the ith input feed stream is given by

where

(49)


FCOSTi ) FCOSTInt1 + FCOSTInt2 + FCOSTInt3 + i i i + FCOSTEvap (50) FCOSTCool i i The operating cost of evaporation is primarily attributed to the cost of external heating and is given by

OCHot ) QHot i i HOT_COSTHθi

(51)

The operating cost of crystallization is primarily attributed to the cost of external cooling and is given by

) QCool COOLANT_COSTCθi OCCool i i

(52)

The operating cost of the coolant used in Heat Integration 3 must be included as Int3 COOLANT_COSTCθi OCInt i ) Qi

(53)

The total operating cost for the entire evaporation and crystallization network for the ith input stream is given by

OCi ) OCHot + OCCool + OCInt i i i

(54)

The total annualized cost can now be calculated for the ith source as

TACi )

FCOSTi + OCi τi

(55)

where τi refers to the years of depreciation. Having listed the problem constraints, the objective function, aimed at minimizing the total annualized cost of evaporation and crystallization, is given as

,TEvap ,Fi,zAi ,zBi ,R,β,γ, min {TACi[TCryst i i COOLANT_COSTC,HOT_COSTH]} (56) where TACi is the total annualized cost of the evaporation and crystallization network to reduce the mass load of water and the two salts in the input feed streams to the desired target output mass loads. This problem cannot be solved globally using commercial optimization packages. In addition to the nonconvexity of the problem, it has an inner minimization program (eq 31). These complications call for the development of a graphical solution strategy based on graphical insights to solve this problem. 7. Graphical Insights to the Evaporation and Crystallization Problem The above optimization problem is mathematically intensive. A graphical approach is proposed to solve the problem at hand. The approach is focused on representing the ternary system on a triangular composition diagram as in Figure 4. The vertexes of the triangle represent the pure species (namely, water and salts A and B). The solid-liquid equilibrium at different tem, TCryst2 , and TCryst3 for the ith source, peratures, TCryst1 i i i is represented as shown in Figure 4. There is a unique ) that corresponds to the composition (for a given TCryst i , the eutectic composition. If a source is cooled to TCryst i eutectic composition represents the least possible water composition in the mother liquor following crystalliza-

Figure 4. Triangular composition diagram representing the solid-liquid equilibrium at different temperatures.

tion. It must be noted that the final mother liquor composition will lie somewhere on the solid-liquid equilibrium line (but not necessarily at the eutectic composition). The exact location of the mother liquor composition will be decided by the separation requirements to be satisfied by the interception operation. Some useful insights can be deduced from the graphical representation. Referring to Figure 5, there are two zones in the triangle separated by the line joining the water vertex to the eutectic composition at a tempera. ture TCryst i If the initial feed location, F (with known flow rate and composition constraints), is in zone I (II), it is not possible to separate salt A (B) as a pure species at the . To meet the target reduction in temperature TCryst i mass load for salt A (B), both salts A and B have to be separated. Also, to get salt A (B) to crystallize at the , enough water must be evaporated so that given TCryst i the residual liquor from evaporation lies below the straight line joining the eutectic composition to the pure salt B (A) vertex. In this case, the mother liquor composition will correspond to the eutectic composition at that temperature. The evaporation and crystallization operations at different temperatures can be followed on the triangular composition diagram. Some rules relating separation and mixing of streams on the triangular composition diagram can be invoked. These include the following insights. 1. When two streams are mixed, the resultant stream will have a composition on the straight line joining the two streams. The exact location of the resultant stream will be decided by the relative amounts of the initial streams being mixed. In Figure 6, two streams, 1 and 2, are mixed to result in stream 3. It may be noted that mixing follows the lever arm principle. 2. When evaporation is carried out from a given source and the resultant water is pure, the operation can be represented as a straight line joining the pure water vertex to the feed location on the triangle. The residual liquor stream, following evaporation, will lie on this straight line on the other side of the feed location. The exact location of the residual liquor is a function of how much water is evaporated from the initial feed source. In Figure 7, upon evaporation of pure water from the feed F, the resultant liquor composition is at point 1 on the triangle. 3. A crystallization operation generating a pure salt as the final product may be represented by a straight

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Figure 5. Insights on the feed location of the triangular composition diagram.

Figure 6. Representation of mixing of two sources on the triangular composition diagram.

Figure 7. Representation of evaporation of pure water from a given source on the triangular composition diagram.

Figure 8. Representation of crystallization from a given source on the triangular composition diagram.

line. This line will join the pure salt vertex to the point (on the composition triangle) representing the feed to the crystallization block and extend on the other side until it intercepts the solid-liquid equilibrium at the crystallization operating temperature. In Figure 8, point 1 refers to the residual liquor from evaporation and point 4 refers to the mother liquor composition. It may be noted that the mother liquor composition does not correspond to the eutectic composition at the tempera-

ture of the crystallization block. This is the case when a single salt is crystallized out as a pure species. If a mixture of salts is crystallized out, the mother liquor composition (which will correspond to the eutectic composition at the crystallization block temperature) is joined to the feed via a straight line. The line is then extended on the other side until it intercepts the side of the triangle corresponding to the binary salts A and B mixture. The amount of product crystallized out can


crystallized out corresponding to the lever arm 3-5, and the mother liquor composition corresponds to the eutectic composition (point 5). Also, a mixture of salts is separated out whenever the residual liquor lies below the line joining vertex B and point 5. 9. Insights into the Design of the Evaporation and Crystallization Network

Figure 9. Design of the evaporation and crystallization network using the triangular composition diagram.

be obtained from the appropriate lever arms. In Figure 8, point 5 corresponds to the mother liquor composition, while the binary salt mixture crystallized out is given by point 3. 8. Solution Approach to the Separation Problem The problem can be solved as follows. The problem definition gives us the values of the initial mass loads of water and the two salts in the ith feed source as well as the required reductions in terms of R, β, and γ. From this information, the minimum amount of water to be separated (via evaporation) and salts A and B to be separated (via crystallization) can be determined. The challenge lies in determining the optimal design of the minimum cost evaporation and crystallization network that would accomplish this task. The solution methodology includes application of graphical insights to design the network within the ranges specified for certain critical variables as described subsequently. The critical variables are bounded based on problem insights. Before describing the steps to be followed to converge to the minimum cost solution, the following analysis using the triangular composition diagram is useful in the design of the network. For a given crystallization temperature, , there are three possibilities of design as shown TCryst i in Figure 9. 1. The residual liquor from evaporation of the feed source F is located at point 1 on the triangle. The amount of water evaporated corresponds to lever arm F-1. The residual liquor is sent to the crystallization block. Pure salt B is crystallized out corresponding to the lever arm 1-4, and the mother liquor composition corresponds to point 4. Also, the mother liquor is not at the eutectic composition. 2. The residual liquor from evaporation of the feed source F is located at point 2 on the triangle. The amount of water evaporated corresponds to lever arm F-2. The residual liquor is sent to the crystallization block. Pure salt B is crystallized out corresponding to the lever arm 2-5, and the mother liquor composition corresponds to the eutectic composition (point 5). 3. The residual liquor from evaporation of the feed source F is located at point 3 on the triangle. The amount of water evaporated corresponds to lever arm F-3. The residual liquor is sent to the crystallization block. A mixture of salts A and B (at point A/B) is

From the equations given previously for the evaporation and crystallization network (i.e., eqs 10-17), it may be observed that there are 2 degrees of freedom. Three critical variables define the scope of the separation network. These are (1) mass load of water evaporated ), and (3) (Soli), (2) crystallization temperature (TCryst i mass loads of salt A and/or B separated out via crystallization. Fixing two of these values will result in the third value getting fixed. All intermediate mass flows and compositions of all species of interest will be fixed. Because the target in many environmental applications is to reduce the discharge of the salts (or pollutants) to desired limits, the crystallization temperature and mass load of water evaporated may be selected as the degrees of freedom. In other words, for a given mass load of water evaporated from an initial feed stream with known flow rate and composition, the separation target for both salts will be satisfied at a unique crystallization temperature. It may be noted that the final crystallization temperature will correspond to the value at which the desired separation target of the limiting salt (either A or B) is satisfied, which implies overseparation of the other salt. The cost of separation is a function of the cost of evaporation and the cost of crystallization. If more water is removed in the evaporation block, this results in a higher cost of evaporation. However, because of higher concentrations of the salts in the residual liquor, the separation target for both salts can be met at a higher crystallization temperature, leading to lower cooling duty and, subsequently, a lower cost of crystallization. Thus, there is an inherent tradeoff between the cost of evaporation and the cost of crystallization, with the optimal network operating at minimum total cost of evaporation and crystallization. 10. Design with the Heat-Induced Pinch Diagram For a known water evaporation load and given a that satisfies the crystallization temperature TCryst i separation targets for both salts, all of the flows are defined for the evaporation and crystallization network. The structure of the evaporation and crystallization network to be considered was described previously. All intermediate temperatures can be defined once the minimum temperature driving forces have been fixed. The heat-induced pinch diagram can be developed for the evaporation and crystallization network as shown in Figure 10. Note that the minimum external heating and cooling utilities can be obtained from the plot. Knowing these duties, one can estimate the operating and fixed costs of the evaporation and crystallization network. Notwithstanding the similarity of the heat-induced pinch diagram with thermal pinch diagrams for heat-exchange networks, important differences are to be noted. First,

2836


Figure 10. Heat-induced pinch diagram for the evaporation and crystallization network.

the diagram is driven by separation tasks; hence, composition must be mapped into temperature via phase equilibrium expressions. Because of the separation objectives, a stream may be cooled beyond its target temperature. Therefore, self-integration may be used. A detailed discussion of these issues can be found in the literature.20 11. Parameter Bounding for Critical Variables The difficulty lies in the wide range of search values for TCryst and Soli. This section discusses insights to i identify the allowable values of these variables. The can be bounded based on the allowable values of TCryst i following insights. is the operating temperaThe upper bound on TCryst i ture of the evaporation block i.e.

TCryst,Upper ) TEvap i i

(57)

Note that, at the upper bound, the entire separation task will be achieved by means of evaporation exclusively and the evaporation block functions as an evaporative crystallizer. can be On the other hand, the lower bound on TCryst i obtained by choosing the highest temperature when the following constraints are activated: Technical (e.g., as dictated by materials of construction or other process considerations)

g TProcess TCryst i i

(58)

iteratively varied over a relatively limited range given by

TCryst,Lower e TCryst e TCryst,Upper i i i

(61)

Bounds on the allowable values of the water evaporation load can be determined. The upper bound on Soli is the maximum amount of water present in the ith feed source, i.e.

) Fi(1.0 - zAi - zB1 ) SolUpper i

(62)

Note that, at the upper bound, all of the water present in the feed stream is evaporated, resulting in a mixture of salts A and B. The amounts of the two salts will correspond to the initial amounts present in the feed source. It may be noted that evaporation of all of the water present in the feed source may be cost prohibitive to achieve in practice. Hence, a practical upper bound may be established (e.g., 98% of the water present in the initial feed source). This practical bound may be established based on past operating experience and/or performance correlations for the evaporation block. On the other hand, the lower bound on Soli can be obtained by choosing the highest value when the following constraints are activated: In the case wherein the entire separation task has to be accomplished with crystallization and no evaporation

Soli ) 0.0

(63)

Process (e.g., other units or processes might require pure water that is generated from the evaporation block)

Refrigeration (cannot go below the temperature of the coldest refrigerant)

Soli g SolProcess i

TCryst g min (tref i c )

Water separation load (i.e., to satisfy the minimum water separation load defined by R given in the problem statement)

(59)

is given by Therefore, the lower bound on TCryst i

) max (TProcess , min (tref TCryst,Lower i i c ))

Soli g WNominl - WFinal (60)

Therefore, for the ith input feed stream, TCryst can be i

(64)

(65)

Therefore, the lower bound on Soli is given by

) max (0.0, SolProcess , WNominal - WFinal) (66) SolLower i i

Ind. Eng. Chem. Res., Vol. 40, No. 13, 2001 2837 Table 1. Selected Values of Soli and Corresponding Values of TCryst for a Feasible Design i case

Soli (kg/h)

TCryst i (°C)

I II III

21.73 28.32 35.32

-2.7 14.7 25.7

case

Soli (kg/h)

TCryst i (°C)

IV V

41.84 48.45

45.5 100

Therefore, for the ith input feed stream, Soli can be iteratively varied over a relatively limited range given by

SolLower e Soli e SolUpper i i

(67)

It may be noted that the optimal solution might require overseparation of water via evaporation. This is due to the tradeoff existing between the cost of evaporation and the cost of crystallization. The excess water obtained from evaporation has two main advantages. First, the total cost of separation may be lower at higher water evaporation loads. Second, the extra water generated (which is generally pure) can be used to replace freshwater currently being used in the process. Thus, the requirement for externally purchased freshwater is reduced as a consequence of the separation task. This results in lowering of fresh resource cost of and Soli can be the process. Thus, the values of TCryst i varied to converge to the optimal evaporation and crystallization network that will achieve the predefined separation tasks for all species of interest at minimum cost. 12. Solution Algorithm The solution algorithm to be used to converge to the minimum cost network is described subsequently. Generally, one of the three species of interest is the limiting component, and the remaining two are overseparated. Knowing the required minimum separation mass loads of water and the two salts, the following procedure can be implemented. 1. Select a mass load of water to be evaporated corresponding to the lower bound on Soli.

2. Select the upper bound on the crystallization . temperature TCryst i 3. Given the feed location on the triangle, move along the straight line joining the feed to the water vertex until the appropriate amount of water (from step 1) is evaporated. The graphical representation of evaporation was described previously. 4. Send the residual liquor to crystallization. 5. If the feed is in zone I and only salt B has to be separated, it is possible to achieve this with the given residual liquor. 6. If the feed is in zone II (I) and only salt B (A) has to be separated, it is essential to evaporate enough water to get the residual liquor below the line joining the eutectic to the pure A (B) vertex. This is to ensure crystallization of both salts. 7. If the feed is in zone I and both salts have to be separated, it is essential to evaporate enough water to get the residual liquor below the line joining the eutectic to the pure B vertex. This is to ensure crystallization of both salts. 8. Determine the amounts of salts A and/or B crystallized out using appropriate lever arms. The graphical representation of crystallization was described previously. 9. Verify whether the desired amounts of salts A and/ or B are separated out from the corresponding lever arms. If yes, this is a feasible design. If no, discard this design from further analysis. 10. Change the crystallization temperature, and repeat steps 5-9. has been reached 11. Once the lower bound of TCryst i or a feasible design has been achieved, select a new water evaporation load and repeat steps 2-11. 12. For each design scenario that is feasible from a separation target requirement, carry out the pinch analysis to determine the minimum heating and cooling utility demand. 13. Carry out equipment sizing and costing using the previously listed cost correlations. 14. Select the minimum total annualized cost option as optimal to achieve the predefined separation task.

Figure 11. Insights on the feed location on the triangular composition diagram.

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Figure 12. Representation of evaporation from the input feed stream on the triangular composition diagram.

Figure 13. Representation of crystallization from residual liquor on the triangular composition diagram.

13. Case Study The case study deals with a ternary wastewater system with two salts present in it. The salts are ammonium nitrate (salt A) and sodium nitrate (salt B). The initial flow rate and composition of the stream are given by Fi ) 107.07 kg/h, zAi ) 0.21, and zBi ) 0.327. It is desired to lower the mass loads of water and the two salts by the following: R ) 0.56, β ) 0.95, and γ ) 0.7. The reduction in mass load is to be achieved by means of an evaporation and crystallization network. Available for service are steam and a refrigerant, HFC134. Operating temperatures and cost data for the external utilities are provided in Appendix 1. The generic structure proposed for heat integration of an evaporation and crystallization based network can be applied. Overall heat-transfer coefficient and sizing/cost information is also provided in Appendix 1. It is desired to design an

optimal separation network to achieve the separation target at minimum cost. 14. Solution to the Case Study The solution algorithm described previously is implemented. The first step is to establish bounds on the and Soli. The lower bound on allowable values of TCryst i Soli is the minimum separation load of water as defined by the problem statement. The upper bound on Soli is the initial mass load of water. Thus, the bounds in kilograms per hour are

21.7 e Soli e 49.57 is the operating temperaThe lower bound for TCryst i ture of the refrigerant. Because ∆Tmin ) 5, we have the lower bound given by 270 K. The upper bound on TCryst i

Ind. Eng. Chem. Res., Vol. 40, No. 13, 2001 2839 Table 2. Flow Rates and Compositions of Salt Removed for Various Cases case

salt A (kg/h)

salt B (kg/h)

I II III

9.83 1.125 1.132

10.5 12.08 17.51

case

salt A (kg/h)

salt B (kg/h)

IV V

1.112 1.995

22.61 27.3

corresponds to the operating temperature of the evaporation block (384 K). Thus, the bounds in Kelvin are

270 e

TCryst i

e 384

Once these bounds have been established, we select intermediate values for Soli. At each value of Soli, are selected until a feasible different values of TCryst i design is obtained. The different values of Soli and at each Soli are given in Table feasible values of TCryst i required to achieve 1. It may be noted that the TCryst i the separation target increases with increased evaporation of water, thus demonstrating the tradeoff between evaporation and crystallization. The subsequent analysis is for case II, which is the optimal scenario. The flow rates and compositions of species of interest were determined graphically. This information can also be obtained via simulation using ASPEN PLUS. Heat duties can be determined via simulation. The graphical procedure followed for case II is given in Figures 1113. Figure 11 represents insights based on the feed location. It may be noted that the input feed stream lies in zone I for the temperature of 14.7 °C. Thus, to separate both salts A and B, the residual liquor should lie below the line joining the pure salt B vertex to the eutectic composition. The operation of evaporation for case II is represented in Figure 12. The operation of crystallization is represented in Figure 13. The flow rates and compositions of salt removed in the crystallization block at different values of Soli are listed in Table 2. Once the intermediate flows and compositions have been determined, the intermediate temperatures can be fixed as depicted in Figure 14. The heat duties obtained

Table 3. Heat Duties and Total Annualized Cost of Separation Network for Various Cases case

QEvap (kW)

QCryst (kW)

QHE1 (kW)

QHE2 (kW)

QHE3 (kW)

TAC ($/year)

I II III IV V

14.1 18.2 22.2 24.9 27.7

10.41 8.33 7.06 4.57 0.89

8.76 8.76 8.76 8.76 8.76

4.77 6.01 4.42 2.75 0.32

0 2.86 8.82 14.55 21.1

130 023 125 840 143 020 149 724 150 241

from simulation and total annualized cost are both listed in Table 3. The optimal solution is given by case II with a total annualized cost of $125 840/year. The mass loads of various species of interest separated in kilograms per hour are given by

MassWater ) 28.32 MassA ) 1.125 MassB ) 12.083 It may be observed that water is overseparated but at a lower total cost of separation. This is due to the tradeoff between the cost of evaporation and the cost of crystallization. The excess water can always be used to replace externally purchased freshwater. 15. Conclusions This paper has introduced the problem of design and heat integration of an evaporation and crystallization network, for separation of species of interest from a ternary wastewater stream. Evaporation and crystallization is a HISEN. Most of the previous HISEN research focused on VOC condensation systems. A structure is proposed for heat integration of the evaporation and crystallization network. Detailed mathematical expressions are listed for complete material and energy balances, pinch equations, and unit sizing and cost. Several graphical insights are listed that allow the representation of evaporation and crystallization on a ternary triangular composition diagram and avoid

Figure 14. Intermediate temperatures and flows in the proposed evaporation and crystallization network for the optimal solution.

2840


mathematical complexity. Use of the diagram reduces the search space of the design and allows one to converge on the optimal design in a computationally efficient manner. An insight-based graphical approach coupled with a solution algorithm allows one to converge to the optimal design that also satisfies all separation requirements for all species of interest. A case study is included to highlight the broad applicability and value of the proposed methodology. Acknowledgment The authors acknowledge the support of Solutia Inc. toward this research. Appendix 1 Basis of Cost Calculations. The following equations were used to calculate the total annualized costs for the process.

fixed cost of the heat exchanger for heat integration ) 10000(area in m2)0.6 $ fixed cost of the evaporation block ) 150000(area in m2)0.6 $ fixed cost of the crystallization block ) 90000 (area in m2)0.6 $ UEvap ) 0.2 kW/m2‚K UInt1 ) 0.1 kW/m2‚K UInt2 ) 0.1 kW/m2‚K UInt3 ) 0.1 kW/m2‚K UCool ) 0.05 kW/m2‚K Depreciation over 5 years. Operating cost for external cooling using refrigerant HFC134 ) 100 $/MMkJ removed, operating temperature ) 265 K, operating cost for external heating with steam ) 30 $/MMkJ removed, operating temperature ) 467 K, and minimum temperature driving force, ∆Tmin ) 5 K. Nomenclature Ai ) area of the heat exchanger calculated, m2 CPSi,u ) specific heat of the uth salt in the solid phase for the ith source, kJ/kg‚K CPLi,u ) specific heat of the uth salt in the liquid phase for the ith source, kJ/kg‚K CPi,w ) specific heat of water for the ith source, kJ/kg‚K FCOST ) fixed cost, $ Fi ) total flow rate of the ith source, kg/h ) water flow rate in the ith source, kg/h FWater i Hi(Ti) ) enthalpy of the ith source at temperature Ti, kJ/ kg of the salt-free source hi(ti) ) enthalpy of the ith cold source at temperature ti, kJ/kg of the salt-free source Cryst Hi,u ) heat of crystallization of the uth salt in the ith source, kJ/kg i ) index denoting the wastewater source to be intercepted k ) index for temperature intervals in pinch calculation K ) total number of temperature intervals in pinch calculations MLi ) total flow rate of mother liquor from the ith source, kg/h

NC ) total number of coolants NH ) total number of heating media NE ) total number of ESAs OC ) operating cost, $/year Q ) total heat duty involved, kW QCool ) external cooling utility requirements for the intercepted source, kW QHot ) external heating utility requirements for the intercepted source, kW Ri ) total flow rate of the residual liquor for the ith intercepted source, kg/h Salti ) total flow rate of the salt stream for the ith intercepted source, kg/h Soli ) total flow rate of pure water for the ith intercepted source, kg/h T ) temperature of the hot source, °C t ) cold stream temperature, °C tCool ) operating temperature of the Cth coolant, °C C ) operating temperature of the Hth heating media, tHot H °C TSource ) initial temperature of the ith source, °C i ) feed temperature of the ith source, °C TFeed i ) operating temperature of the evaporation block TEvap i for the ith source, °C TCryst ) operating temperature of the crystallization block i for the ith source, °C Ti,k ) temperature of the ith hot source, °C ti,k ) temperature of the ith cold source, °C tref c ) cooling temperature of the cth refrigerant ) outlet temperature of the ith cold source, °C tout i T h i,k ) hot-scale temperature corresponding to the end of the kth interval, °C T h i,k ) cold-scale temperature to the end of the kth interval, °C TAC ) total annualized cost, $/year U ) overall heat-transfer coefficient, kW/m2‚K UNominal ) initial discharge of salt A from all terminal sources, kg/h UFinal ) final discharge of salt A from all terminal sources, kg/h u ) index denoting either salt A or B VNominal ) initial discharge of salt B from all terminal sources, kg/h VFinal ) final discharge of salt B from all terminal sources, kg/h WNominal ) initial discharge of water from all terminal sources, kg/h WFinal ) final discharge of water from all terminal sources, kg/h Yi,u ) composition (weight basis) ratio, given by composition of the uth salt divided by water composition, in the ith source zAi ) initial weight fraction of salt A in the ith source zBi ) initial weight fraction of salt B in the ith source Salt zi,A ) weight fraction of salt A in the salt stream from crystallization Resi zi,A ) weight fraction of salt A in the residual liquor of the ith intercepted source Resi zi,B ) weight fraction of salt B in the residual liquor of the ith intercepted source ML zi,A ) weight fraction of salt A in the mother liquor of the ith intercepted source ML ) weight fraction of salt B in the mother liquor of the zi,B ith intercepted source Sets COOLANT ) set of coolants COOLANT_COST ) set of cost of coolants ESA ) set of energy separating agents

Ind. Eng. Chem. Res., Vol. 40, No. 13, 2001 2841 HOT ) set of heating media HOT_COST ) set of cost of heating media

Upper ) upper bound Water ) water

Greek Letters

Literature Cited

R ) factor indicating required reduction in water discharge β ) factor indicating required reduction in discharge of salt A γ ) factor indicating required reduction in discharge of salt B λ ) latent heat of water, kJ/kg Φi,k ) cumulative enthalpy exchanged by the hot (or cold) source until an arbitrary temperature, Ti,k (or ti,k), within the kth interval, kW ψ ) function representing solubility temperature relationship for the residual liquor ξ ) function representing solubility temperature relationship for the mother liquor θ ) number of hours per year τ ) years of depreciation, years ∆Tmin ) minimum allowable temperature driving force 1 between hot and cold streams, °C ∆Tlog mean ) log mean temperature driving force, °C Subscripts A ) salt A B ) salt B C ) coolants E ) ESAs H ) heating media i ) ith wastewater source k ) index for temperature intervals in pinch calculation u ) uth salt w ) water Superscripts A ) salt A B ) salt B C ) cold source Cool ) temperature of the coolant Cryst ) crystallization Evap ) evaporation Feed ) feed Final ) final discharge H ) hot source Hot ) temperature of heating media Int1 ) Heat Integration 1 Int2 ) Heat Integration 2 Int3 ) Heat Integration 3 L ) liquid Lower ) lower bound ML ) mother liquor min ) minimum Nominal ) nominal discharge out ) outlet Process ) process ref ) refrigerant Resi ) residual liquor S ) solid Salt ) salt Source ) source

(1) Kirk-Othmer. Encyclopedia of Chemical Technology, 4th ed.; John Wiley and Sons: New York, 1993; Vol. 7, pp 683-691. (2) Sharratt, P. N. CrystallizationsMeeting the Environmental Challenge. Trans. Inst. Chem. Eng. 1996, 74, 732. (3) Gilbert, S. W. Melt Crystallization: Process Analysis and Optimization. AIChE J. 1991, 37, 1205. (4) Rajagopal, S.; Ng, K. M.; Douglas, J. M. Design and Economic Trade-Offs of Extractive Crystallization Processes. AIChE J. 1991, 37, 437. (5) Dye, S. R.; Ng, K. M. Bypassing Eutectics with Extractive Crystallization: Design Alternatives and Trade-Offs. AIChE J. 1995, 41, 1456. (6) Berry, D. A.; Ng, K. M. Separation of Quaternary Conjugate Salt Systems by Fractional Crystallization. AIChE J. 1996, 42, 2162. (7) Palosaari, S.; Zuoliang, S.; Toyokura, K. Crystallization Design Chart and Computer Algorithm. Acta Polytech. Scand. 1996, 234, 1. (8) Slaughter, D. W.; Doherty, M. F. Calculation of SolidLiquid Equilibrium and Crystallization Paths For Melt Crystallization Processes. Chem. Eng. Sci. 1995, 50, 1679. (9) Fitch, B. How to Design Fractional Crystallization Processes. Ind. Eng. Chem. 1970, 62, 7. (10) Ng, K. M. Systematic Separation of a Multicomponent Mixture of Solids Based on Selective Crystallization and Dissolution. Sep. Technol. 1991, 1, 108. (11) Cisternas, L. A.; Rudd, D. F. Process Designs for Fractional Crystallization from Solution. Ind. Eng. Chem. Res. 1993, 32, 1993. (12) Dye, S. R.; Ng, K. M. Fractional Crystallization: Design Alternatives and Trade-Offs. AIChE J. 1995, 41, 2427. (13) Thomson, K.; Rasmussen, P.; Gani, R. Simulation and Optimization of Fractional Crystallization Processes. Chem. Eng. Sci. 1998, 53, 1551. (14) Cesar, M. A. B.; Ng, K. M. Improving Product Recovery in Fractional Crystallization Processes: Retrofit of an Adipic Acid Plant. Ind. Eng. Chem. Res. 1999, 38, 823. (15) Cisternas, L. A.; Swaney, R. E. Separation System Synthesis for Fractional Crystallization from Solution Using a Network Flow Model. Ind. Eng. Chem. Res. 1998, 37, 2761. (16) Cisternas, L. A. Optimal Design Of Crystallization-Based Separation Schemes. AIChE J. 1999, 45, 1477. (17) Dunn, R. F.; El-Halwagi, M. M. Selection of Optimal VOCCondensation Systems. Waste Manage. 1994, 14, 103. (18) Dunn, R. F.; El-Halwagi, M. M. Optimal Design of MultiComponent VOC-Condensation Systems. J. Hazard. Mater. 1994, 38, 187. (19) Richburg, A.; El-Halwagi, M. M. A Graphical Approach to the Optimal Design of Heat-Induced Separation Networks for VOC Recovery. In AIChE Symposium Series; Biegler, L., Doherty, M., Eds.; American Institute of Chemical Engineers: New York, 1995; Vol. 91, p 256. (20) El-Halwagi, M. M.; Srinivas, B. K.; Dunn, R. F. Synthesis of Heat-Induced Separation Networks. Chem. Eng. Sci. 1995, 50, 81. (21) Parthasarathy, G.; El-Halwagi, M. M. Optimum Mass Integration Strategies for Condensation and Allocation of Multicomponent VOCs. Chem. Eng. Sci. 2000, 55, 881.

Received for review September 20, 2000 Accepted April 13, 2001 IE000831D

Development of Heat-Integrated Evaporation and Crystallization

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