Ind. Eng. Chem. Res. 1993,32, 315-334
315
Studies in Chemical Process Design and Synthesis. 10. An Expert System for Solvent-Based Separation Process Synthesis Jean-Christophe Brunet and Y. A. Liu* Department of Chemical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 -021 1
This paper describes a knowledge-based approach for the preliminary design of solvent-based separation processes. Our approach incorporates efficient tools for problem representation and simplification, feasibility analysis of separation tasks, and heuristic synthesis and evolutionary improvement. It leads to an Expert system for SEParation synthesis (EXSEP), which requires only basic input data such as component K-values and expected component recoveries in the overhead and bottom products. EXSEP generates within seconds many feasible and economical flowsheeta in terms of the separation factor, solvent flow rate, and number of theoretical stages. We apply EXSEP to several industrial absorption, stripping, and extraction problems, and compare resulting flowsheets and component recoveries with those from the literature and from rigorous computer-aided design (CAD). In most cases, EXSEP gives very similar and even better flowsheets. With ita menu-driven decision tools and window-baaed explanation facilities operating on personal computers (PCs),EXSEP is convenient and user-friendly. It can be easily used by practicing chemical engineers and in undergraduate design teaching. 1. Introduction
Process synthesis or flowsheet development is the most critical step in the design of chemical plants. It is commonly recognized that over 70% of the total cost of a design project is fixed by decisions made in the synthesis step. The preaent work deals with the subject of separation process synthesis, that is, the development of efficient and economical flowsheets for the separation of multicomponent mixtures into desired products. This synthesis problem becomes very complex when multicomponent feeds and multicomponent produds exist. Estimating the component recoveries in product streams resulting from a potential separation is a formidable task, especially since we cannot carry out rigorous simulations using commercial computer-aided design (CAD) software systems prior to having a preliminary separation flowsheet that is yet to be synthesized. In addition, we may need to consider multiple separation methods as well as the possible use of nonsharp separations for which a thermodynamic feasibility analysis of potential separations must be performed. To our knowledge, very few efficient and user-friendly, computer-aided tools exist today for separation process synthesis. Recently, there has been a significant interest in applying the emerging science of artificial intelligence (AI) to solving chemical engineering problems (Quantrille and Liu, 1991; Samdani, 1992a,b;Shaw, 1992). According to Barr and Feigenbaum (1981), AI is the part of computer science concerned with designing intelligent computer systems, that is, systems that exhibit characteristics we associate with intelligence in human behavior. The objective of the present work is to develop and demonstrate an AI approach that uses facts, rules, and heuristics to guide the split sequencing and preliminary design of multicomponent separation processes using energy and solvents (i.e., mass-separating agents, MSAs). Our approach leads to a prototype, user-friendly Expert system for SEParation synthesis, called EXSEP, applicable to ordinary distillation, absorption, stripping, and extraction. There have been very few previous studies on the development and applications of AI approaches to synthesize multicomponent separation processes using solvents or MSAs, and a review of the published literature is available
* To whom correspondence should be addressed.
(Quantrille and Liu, 1991). Notable studies are those by Barnicki and Fair (1990,1992). These authors have proposed the concept of a general expert system for liquidmixture and gas/vapor separations. They recommend a rule-based approach to perform the tasks of method selection, split sequencing, and preliminary design of multicomponent separation processes. Currently, they have a prototype expert system operational, called SSAD (Separation Synthesis ADvisor) for liquid-mixture separations, and the corresponding system for gas/vapor separations has yet to be encoded. SSAD is developed by using a commercial expertrsystem development tool, called KEE (Knowledge Engineering Environment). Barnicki and Fair observe that, with its extremely large memory overhead, KEE is not capable of efficiently aiding in the development of many chemical engineering expert system such as SSAD. In particular, KEE has too many features, most of which are unnecessary for the separation synthesis application. Therefore, SSAD executes sluggishly in the KEE environment. The other notable study is that by Wahnschaft et al. (1991), who describe the ideas underlying the current development of a separation process designer, called SPLIT. This work combines a system of multiple sources of separation knowledge into an integrated system, called a blackboard in AI, with a mathematical optimization software. The resulting prototype expert system is implemented on a commercial expert-system development tool, d e d Knowledge Craft. This work is continuing and the published report emphasizes the application to am* tropic distillation problems. In the following sections, we describe the chemical engineering, AI, and user’s perspectives of EXSEP applied to absorption, stripping, and extraction problems. 2. Chemical Engineering Perspective of EXSEP
In this section, we first introduce the component assignment matrix that EXSEP uses to represent the problem of solvent-based separation process synthesis. We describe the technique of stream bypass for simplifying the synthesis problem. We then discuss the feasibility analysis of separation tasks and heuristic synthesis of flowsheet solutions. 2.1. Problem Representation and Simplification. A. Component Assignment Matrix (CAM) for Problem
0888-5885f 93/2632-0315$04.00/0 0 1993 American Chemical
Society
316 Ind. Eng. Chem. Res., Vol. 32, No. 2, 1993 Table I. Product Smcifications in Example lao vapor liquid overhead: bottom: component p l (mol/h) p2 (mol/h) K value H2 85.59 0.0 50 5.72 1.43 2.80 C3HB 0.751 0.639 1.2 C4Hl0 0.994 1.556 0.9 n-C4H,o 0.013 1.327 0.37 i-C5H12 0.0 1.98 0.24 C5H12+ "The feed stream is at 30 "C and 345 kPa. K-values listed are the Henry's law constanta in the presence of a lean oil a~ the solvent (molecularweight = 160; specific gravity = 0.83). Data taken from Nelson (1969).
Representation. The CAM is a convenient tool for representing the problem of synthesizing multicomponent separation sequences (Liu et al., 1990). As an illustration, Table I specifies an absorption problem, designated as example l a (Nelson, 1969). In the first column, the components in the feed mixture are H2 and C3H8to C5H12+. The problem is to remove 99% of iC5 and 100% of C5+, both of which are absorbed by an oil (C8 or CJ. The second and third columns are the flow rates (in moles per hour) of each component in the overhead and bottom products, respectively. The last column is the K value of each component. Equation 1gives the CAM for example la. The CAM is a P X C matrix, where P is the number of products and C is the number of components. The ijth element of this
E l
solvent
CAM 1
EI
H2
C3
iCs
C4
iC4
"+ I
1.43 0.639 1.556 1.327 1.98 i5.59 5.72 0.751 0.994 0.013 0
(1)
matrix corresponds to the molar flow rate of the j t h component in the ith product. The components are in columns and the products are in rows. To say that the flow rate of H2to the overhead product P2 is 85.59 mol/h, we simply write 85.59 in the first column and the second row. We sort the component columns from left to right in decreasing order of K values and arrange the product rows from top to bottom in increasing order of K values. We define the K value of the jth product as the weighted average given by eq 2, Rj = CKiFij/CFij (2) where K i is the K value of component i and Fij the flow rate of component i in the j t h product. To account for the use of solvent, we add the solvent to the CAM. It comes before product P1 in the first row, because the solvent for absorption is usually chosen for having a K value much smaller than those of products. If we call "oil" the solvent component, "oil" goes to the right of the C,+ column in the CAM, since it has the smallest K value among all the components. Equation 3 gives the CAM for example l a with solvent. CAM 2 H2 soivemIo 0
P2
C3
iC4
C4
iC5
Cg+
oil
o
kI 1
o
o
1.43
0.639 1.556 1.327 1.98
185.59 5.72
o
0.751 0.994
o
0.013 0
(3)
0
The C A M is very useful to represent the potential splits. In EXSEP, we test the feasibility of the split between the overhead and bottom products, P2 and P1, as represented by the horizontal line in CAM2. Every product above the split line (i.e., P1 and the solvent) will go to the bottom,
0 0
V
0.00009 0.0043 73.1399 0.0001 0.8633 0.5377 0 0 0
(5)
Ind. Eng. Chem Res., Vol. 32, No. 2, 1993 317
represents a significant amount of the product. In section 4.2D,we shall present EXSEP results, indicating that stream bypass does have a favorable effect on reducing the number of theoretical stages for the extraction problem represented by eqs 5 and 6. 2.2. Feasibility Analysis of Separation Tasks. For solvent-based separations, the goal of separation process synthesis or preliminary flowsheet design is to find the number of theoretical stages (A9 and solvent flow rate (L) in order to achieve the desired component splita between the overhead and bottom products, such as those specified in Table I for example la. First, let us comment briefly on our approach to achieving this goal in EXSEP, particularly for developing separation flowsheets accurately and efficiently. An important challenge arises when addressing the accuracy of an expert syetem for separation design. Without carrying out rigorous, multistage and multicomponent equilibrium calculations and mass/energy balances, how do we determine if a prehinary flowsheet design is indeed thermodynamically feasible to achieve the component splits? Another challenge associated with developing expert systems is the incorporation of quantative or "deep" knowledge into the systems. Systems using only qualitative or "shallow" knowledge tend to be inaccurate, and in the presence of new situation, they may be unreliable. However, systems using deep knowledge often require numerical models, which are cumbersome and run too slowly to be practical. In this work, we demonstrate that a proper balance between accuracy and efficiency in expert systems for separation process synthesis can be obtained through shortcut design techniques. Specifically,in order to quantitatively evaluate the thermodynamic feasibility of component splits, EXSEP uses the Kremser equation (Kremser, 1930) to estimate the component recoveries in the overhead and bottom products. In addition, EXSEP applies heuristia to find the economically optimum number of theoretical stages and solvent flow rate. A. Key Component. To quantitatively estimate the component splits in the overhead and bottom products, it is rmessary to first select the key component. Nelson (1969, p 853) gives an example of absorption, where the lowest-boiling (Le,, lightest) component is chosen as the key component. Henley and Seader (1981, p 472) define the key component as "the heaviest component to be stripped to a specific extent". In Figure 1,we illustrate how to choose key components in two examples of absorption and stripping. For absorption (Figure la), component D is the lightest component to be absorbed to a specific extent. Approximately 70% of the amount of D entering the column goes to the bottom, whereas only 2% of C is absorbed into the bottom. Thus, D is the key component. For stripping (Figure lb), D is the heaviest component to be stripped to a specific extent (60%) and is the key component. B. Shortcut Feasibility Analysis. After we have chosen a key component, we calculate a dimensionless parameter, called separation factor, to characterize the separation. We use the general notation X to represent the separation factors for all eolventcbased separations, and the specific notationa A, S,and E to denote the separation factors for absorption, stripping, and extraction, respectively. In Figure 2, we illustrate the definitions of molar flow rates of feed, solvent, and product streams of absorption, stripping, and extraction columns, together with the corresponding separation factors. B.l. Kremser Equation. The Kremeer equation is a practical, shortcut design model for a variety of equilib-
K In thaw produa
Klnthabonom
(nrlpplng
Figure 1. Key components in (a) absorption and (b) stripping.
rium-staged separations, such as absorption, stripping, extraction, leaching, adsorption, ion exchange, etc. (Wankat, 1988). For absorption, the Kremser equation is
For the Kremser equation to be valid, the following conditions must be met: constant molal overflow ( L / V is constant), isothermal and isobaric operation, negligible heats of absorption, and a straight equilibrium line; i.e., Henry's law applies: Yi = Kizi + bi (bi = constant) (8) In section 4.3, we shall discuss the validity of the Kremser assumptions in applying EXSEP to a number of industrial separation problems. We use the Kremser equation to find the design conditions of absorption columns, such as the number of theoretical stages (N)and solvent flow rate (L).Specifically, for a given absorption problem, we normally know the feed-gas flow rate V as well as the mole fractions of component i (e.g., the key component) in the feed gas and overhead product, ~ iand, yi,wt, ~ respectively. For preliminary design purpoeea, we may assume that the mole fraction of component i (e.g., the key component) in the solvent, zih, is fmed (perhaps z i h = 0). Therefore, the only remaining free design variables in the Kremser equation are the number of theoretical stages (N)and solvent flow rate (L).The latter variable appears implicitly in the defining equation for the absorption factor, A = L/KiV. Determining the values of N and L is an economic decision. A high value of N (more equilibrium stages) leads to a low solvent flow rate L, thus reducing the operating
318 Ind. Eng. Chem. Res., Vol. 32, No. 2, 1993
@D
EkimcUon Factor
Mpping Factor
Abmptfon Factor
L
A
=K,V
Figure 2. Schematic diagrams of absorption, stripping, and extraction columns and corresponding separation factors. Table 11. Kremrer Equation for Abeorption, Stripping, and Extraction Columne absorption stripping separation factor A =LJKiV S KiVJL x i,in . . - x .i p u t AN'' - A Y LIII . . - Y . r,out =-SN+' - S Kremser equation =yi,m . . - K . xI . .i,in ANtl - 1 xi,in - Yi,in/Ki SNt'- 1
extraction
E =KiS/L
x i,in . . - x .i,out
Xi,in
- Yi,in/K
EN+' - E EN+' - 1
=-
x r,in , . - x .r,wt
no. of theor etagee,
xi,in
- Yi,in/Ki
Xfl N= no. of theor etagee,
h A
Y..i,in - Y , i,out
N=
x=1
-1 N =
N=
- Kixi,in = Yi,in -
Yi.out
component recovery,
Yi,out
XZ1 Cyic component recovery,
XI1
Yi,out
- Kixi;m)( =
Yijn
xi.out
-)
+ NKixi,in %,out
N+1
(94 Yi,in
+Wni,in
In E
-1
- xi,out
- Yi,in/Ki = Xi,in -
(xi,h
or when A = 1 (9b) N+l Knowing the recovery of each component, we can quantitatively assess the technical feasibility of achieving the desired component splits between the overhead and bot=
Xi,in
-1 N=
xi,in
cost and keeping the subsequent solvent-recovery capital cost at minimum. However, the absorber itself will need more stages to offset the lower solvent flow rate. Conversely, a low N leads to a high L. This smaller column reduces the absorber capital cost, but increases the solvent-recovery cost. A key goal in absorber design is to identify the tradeoff between Nand L. In section 2.3,we shall describe the heuristic rules and search strategy that EXSEP u e s to find the economically optimum combinations of N and L values. Once we determine the appropriate values of N and L (and hence A), we use the Kremeer equation again to estimate the mole fraction of any component i in the overhead product, yi,out:
Yi,out
In S
I
-
$)( -)
%,out
(
= Xi.in -
xi,in
-% EN+' ) - 1 (E)
+ NCyi,in/Ki) Xijn + N C y i , i n / K i ) xiout = N+l N+1 tom products in a preliminary flowsheet. Table I1 summarizes the relevant relationships for the shortcut feasibility analysis of absorber, stripper, and extractor designs based on the Kremser equation. B.2. Rules for Feasible Component-Recovery Ratios. The component-recovery ratio (d/bIi is the molar fraction of component i going to the overhead product (di) divided by that going to the bottom product (bJ. In EXSEP,we use the following rules to calculate the component-recovery ratios: If di = 0, then (d/b)i= 0.02. We always assume that at least 2% of a light component goes to the overhead product. If bi = 0, then (d/b)i= 49.0. We always assume that at least 2% of a heavy component goes to the bottom product If di # 0 and bi # 0, then (d/bIi = di/bi. For a preliminary flowsheet to be feasible, we require that the deviation between the specified and actual recovery ratios for every component to be less than 10%. Thia impliea the following condition:
=
Zi,in
ispecified
2.3. Heuristic Synthesis of Separation Flowsheets. A. Heuristics for Economically Optimum Designs.
Ind. Eng. Chem. Res., Vol. 32, No. 2,1993 319
L
Arnin
/
I
Aopt
Ast
As1
A=L/KV Figure 4. Position of an absorption flowsheet solution (indicated by the black dot) in a plot of N (number of theoretical stages) versus A (absorptionfactor) and illustrations of four characteristic separation factors.
20
I
I
I
I
--
e
.Q
l
\
\
I
0
2
,
I
I
8 .6 Numbrr of Thmmtkol Stom 4
I
to
1 00
Figure 3. Illustration of the heuristics for the number of theoretical stages for absorption and extraction columns (Keller (1982),pp 50 and 74).
A.l. Optimum Number of Theoretical Stages. Keller (1982, p 50) presents a heuristic chart (Figure 3a) where the X-axis is the number of theoretical stages of an absorption column. The first Y-axisis the ratio of the solvent flow rate to the amount of CHI recovered in an absorption column. The second Y-axisis the energy (work) required to pump the solvent. For a number of theoretical stages, N,of about 5, both the solvent flow rate and energy required are minimum. This observation leads to the following design heuristic for absorbers (Keller (1982), p 49): Heuristic 01. It is almost always profitable to have at leaat five theoretical stagea in an absorption column if high (greater than M%) recoveries of absorbing components are desired, unless their solubilities are extremely high (Keller (1982), p 49). In addition, it is obvious that the taller a column, the more expensive it is to build. N should be at least 5, but not much greater. This suggests an optimum value of 5 for the number of theoretical stages, and the same observation applies also to stripping columns. Thus, in EXSEP, we set an optimum number of theoretical stages of 5, Nopt= 5, for both absorption and stripping columns. Figure 3b shows a practical correlation of the extraction factor versus the number of theoretical stages (Keller
(1982), p 74). This correlation illustrates the following design heuristic for extractors: Heuristic 0 2 . (a) For extraction, favor the use of 5-10 theoretical stages in order to attain a reasonably low, solvent-recovery cost. Decreasing the number of theoretical stages increases the amount of solvent needed (Keller (19821, p 75). (b) The number of theoretical stages appears to have been optimized at 5-7 in many petroleum-refinery operations (Hanson, 1971). (c) Mixer-settler batters for extraction are built with up to five theoretical stages (Reissinger and Schriiter, 1978). In EXSEP, we set an optimum number of theoretical stages for extractors, No,, = 5 and 5 I N I10. A t . Optimum Separation Factors. For absorption, we use an optimum absorption factor of 1.4 (Aopt= L/KiV = 1.4) to generate initial flow sheeta. This is based on the following design heuristic: Heuristic 03. For isothermal absorbers targeting high recoveries (>90-99%) of absorbing components, favor an absorption factor (A = L / K i V )between 1 and 2, with an optimum value Aoptbeing 1.4. Higher values of L (increased solvent flow rate), and hence larger A values, raise the solvent-recovery cost. Lower values of L, and thus smaller A values, require more theoretical stages and increase absorber costa (Douglas (198% p 77; Treybal(1980), p 291). For stripping, we favor an optimum stripping factor of 0.71 (S?pt= K i V / L = l/AOpt= 1/1.4 or 0.71) and follow the design heuristic: Heuristic 0 4 . In the design of stripping towers, the optimum value of the stripping factor will be in the range of 0.5-0.8 (Perry and Green (1984), p 14-29). For extraction, the recommended value of the optimum extraction factor varies according to literature sources: Heurktic 0 5 . For extractions targeting high recoveries (90-99%) of extracting components: (a) favor an extraction factor (E = KiV/L)between 1 and 1.25; or (b) choose of 1.3 (Cusack et al., a minimum extraction factor (Emin) 1991); or (c) use an optimum extraction factor of approximately 2 (see Figure 3b) (Keller (1982), p 74). In EXSEP, we start with a minimum extraction factor (E-) of 2 to generate initial flowsheeta, and use a smaller Emin value if necessary. B. Heuristic Search of Flowsheet Solutions. B.l. Characteristic Separation Factors. Figure 4 illustrates the position of an absorption flowsheet solution in a plot of N versus A. To find this solution, EXSEP starts the calculationswith the absorption factor equal to a minimum value called A- (e.g., A- = 1.0). Then, from left to right on Figure 4, EXSEP incrementa A (e.g., increasing A from
320 Ind. Eng. Chem. Res., Vol. 32, No. 2, 1993
Ami, by incrementa of 0.05) and performs the feasibility analysis for each incremental step. This incremental process continues until the absorption factor reaches ita upper limit called A,,, (e.g., Ad = 2.0; sl stands for solvent because this limit depends on the solvent). In Figure 4, A, is the optimum absorption factor based on heuristics (Aopt= 1.4). We also define ASt (for Ltage), which is the value of the absorption factor when the number of theoretical stages is exactly equal to the optimum number of theoretical stages Nopt(4,for absorption). We call these factors (Ami,,A,, A,, and AnJthe four characteristic separation factors. In the same way, we define S-, , S S , and Sk(for lean gas) for stripping and E-, E, E, and E d for extraction. These factors, except Xnt(i.e., AOt,Snt,and E,J, are normally constant and set according to heuristica in EXSEP. However, the flexibility of EXSEP enables ita user to change those values to suit an exceptional problem statement. B.2. Flowrheet Solutions. We use the heuristics for both the optimum number of theoretical stages (heuristics D1 and D2) and the optimum separation factor (heuristica D3-DS) to search for flowsheet solutions, even though these two groups of heuristics may seem related to each other. Indeed, we can optimize separately the number of theoretical stage^ N and the absorption factor A. Consider, for example, a potential solution represented by the black dot in Figure 4. This flowsheet candidate has an absorption factor A close to and d e r than A, (=1.4) and also smaller than & (at which N = N, = 5), and has anumber of theoretical stages N close to N (=5). If EXSEP finds this preliminary design thermc$ynamically feasible in achieving the specified component recoveries, then it accepts this flowsheet as satisfactory, because both A and N are close to their optimum values. When the separation is thermdynamically infeasible, EXSEP imposes a new value of A being equal to A,,, (=1.4). This may lead to better component recoveries and result in a feasible separation, but may also increase the number of theoretical stages N above ita optimum value Nopt(6). To summarize, EXSEP considers a flowsheet as satisfactory if it is thermodynamically feasible, and if (a) A N Aopt,N No t, and A IAnt(at which N = Nopt= 51, or (b) A = A , !=1.4) and N 1 Nopt(=5). BJ. Range Size of Flowsheet Search. The existence of a potential flowsheet solution depends not only on the size of the search space (i.e., from the minimum absorption fador Aminto the limitingabmrption factor for the solvent, Ad), but also on the relative positions of the four characteristic separation factors. If A,,,is smaller than Ami,, no calculation will OCCUT as EXSEP starts imcrementing from Ad,, to A& There are eight important combinations of relative positions of the four characteristic separation factors, and EXSEP considers each combination and gives explanationsconcerning the locations of poeeible solutions in the search apace. We shall discuss these combinations later in Figure 12 when we describe the AI perspective of EXSEP. Let us look at an example. Figure 5a displays the explanation on an EXSEP window of a flowsheet solution for example la (absorption) with N = 8.6 and A = 1.5. EXSEP explains that "L is higher than the optimum value", since A > A, ( 4 . 4 ) and L = AKjV > Lo EXSEP also explains &at T h e minimal solution o!r N is greater than the optimum of 5", because N > Nopt(=5). Figure 5b displays the range size of flowsheet search "1.36-1.6", Le., from A- = 1.35 to Ad = 1.60. This figure also shows that A,t (the absorption factor at which N =
r)
Solution: N=8.6 Ar1.5 Y is higher tlran he optimum due. The minimal soluiYbn forA! is greater then the optimum of 5 '
b)
-
Range: 1.35 1.6 !SoIuiYbn may w3t &A> 7.6, wib'r a number of
stages still higher &an 5 You should immase A d Amin=l.35 Aopt4.4
Figure 5. Example of EXSEP's explanations for example la ( a b sorption): (a) a flowsheet solution; and (b) the range size of flowsheet search.
Nw = 5) is greater than 4 (=1.6). Since EXSEP searches for flowsheet solutions in the range of Ami, to Ad, it will stop the search at Anl,where the corresponding number of theoretical stages is still higher than the optimum number of theoretical stages. Thus, a solution may exist with N exactly being equal to ita optimum value of Nopt (4)and A being equal to Aat, and this solution may be better than another solution inside the search space between Aminand A,, with N greater than 5. As a result, Figure 5b displays the explanation on an EXSEP window that "Solution may exist for A > 1.6, with a number of stages still higher than 5. You should increase A&" To a m , if 4 < A&, there may exist other feasible and possibly better flowsheeta with N greater than 5. In that case, the explanation facility in EXSEP advises the user to increase A,,. B.4. Heuristic Ranking of Flowsheet Solutions. EXSEP can generate many feasible flowsheet solutions, depending on the incremental size of the separation factor used in the heuristic search. Each solution has its intrinsic quality, which varies with the separation factor (S), the number of theoretical stages (N),and the average percentage of deviation (denoted by Dev) between the actual and specified component-recovery ratios. We have developed a heuristic evaluation function, denoted by CS(Dev,N,S),for the coefficient of separation, to rank flowsheet solutions according to the heuristica for economically optimum designs presented in section 2.3A. First, we seek flowsheet solutions with N equal to the optimum value N if possible, or with N being slightly greater than Nwt.%or example, we prefer six stages over four stages,because the construction coet will not be much different, whereas the economy of solvent and the performance with six stages are better. This deeirable solution characteristic requires that
(dCS(De;,N,S))
N-N-1
=O
( W
and CS(N+l)
> CS(N-1)
(lib)
Next, we try to find flowsheet solutions with a separation factor (e.g., stripping factor) equal to the optimum value So,, if possible, or with S being slightly smaller than Sop, (to minimize the solvent flow rate). Thia desirable solution requirement may be expressed by (aCSm;,N,S))
s=so,
=O
(W
1
Ind. Eng. Chem. Res., Vol. 32, No. 2, 1993 321 s=o.71, Dev=l%
JIOO,
2000
1,oo
,
.
.
.
.. .
...
..........i ...........,........i...........i. ........i. .........i. ...... . .......i............+....................... . . :. :. . .. . . . .
. . . , . .. . ...........i................................:............................................ ~
. ..
+
. .. . .. .. . : ................ . . . ,. ... .. .. . i
:
i
:
,
.
...
1
. : . . .. .. :
:
......................
i
and CS(S+l) < CS(S-1)
(1W
Lastly, we favor the flowsheet solution with a minimum average percentage of deviation between the actual and specified component-recovery ratios, and we want CS(Dev,N,S) to increase as the deviation (Dev) decreases. This desirable solution characteristic suggests that dCS(Dev,N,S)
CS(N-1) and CS(S+l) < CS(S-1), we use the arctangent functions in f 2 ( N ) and f3(S).
Figure 6. Coefficient of Separation versus number of theoretical stages: stripping factor S =, S , = 0.71; deviation between actual and specified component-recovery ratios Dev = 1%.
Although the CS function given by eq 14 may seem somewhat complex mathematically, it does provide a quantitative parameter for a reliable ranking of flowsheet solutions according to the heuristics for economically o p timum designs presented in section 2.3A, or their quantitative expresaions, eqs lla-llc. As an illustration, Figure 6 shows a plot of CS(N), keeping the stripping factor S = Sop,= 0.71 and the percentage of deviation between the actual and specified component-recovery ratios Dev = 1% We notice that CS is maximum when N = Nopt= 5 and that CS(N=6) > CS(N=4), thus satisfying the desirable characteristics for economically optimum flowsheet solutions, eqs l l a and llb. This example clearly indicates we can confidently apply the CS(Dev,N,S) function to heuristically rank the flowsheet solutions. The higher the CS value, the more economical is the flowsheet solution. After finding all feasible flowsheet solutions, EXSEP calculates their respective CS values and sort the solutions in decreasing CS order. Then, EXSEP identifies the "best" solution according to the highest CS ranking.
.
3. Artificial Intelligence Perspective of EXSEP EXSEP is written in Prolog (Proaramming in h i c ) , an AI computer language (Quantrille and Liu, 1991). In this section, we describe EXSEP from the AI perspective. We discuas the three-part strategy ("plan-generatetest") used for the heuristic search of flowsheet solutions. In particular, we describe the knowledge representation and program structure in each of the three parts of the search strategy. We also introduce the explanation and diagncais facilities of EXSEP. 3.1. An Overview. A. Search Strategy. EXSEP usea a "plan-generate-test" search strategy (Quantdle and Liu, 1991) for heuristic flowsheet synthesis. Plan: Data acquisition and knowledge representation. EXSEP obtains data from a file. These data include facts, rules, and heuristics (called "knowledge" in AI). They are added to the database, and the problem statement is converted to a CAM to facilitate list processing by Prolog. Generate: Feasible solution generations. A flowsheet solution is defined by the number of theoretical stages, solvent flow rate (or separation factor), and actual component-recovery ratios. The "generate" stage is mostly performed by the Kremser c l a m (section 3.3B). Test: Feasible solution ranking and best solution selection. In the "test" stage, EXSEP ranks the feasible solutions according to the heuristic function, CS defined by eq 14,
322 Ind. Eng. Chem. Res., Vol. 32, No. 2, 1993
I
MAIN Module
synthesizegrocess
I
I
'
report
II
definition windows
I main menu I I
12
choice of separation
1
Methods=[od] I
aboliaLand
[ printCAM1 "
I
retract facts
'I
.I
svnth-lnem-
er seplvdbn or exit E S E P
I3
Methods=[dga] I
Methods=[~]
I
Methods=[lle] 1
split
for the top and the
Figure 7. Overview of current EXSEP modules. Table 111. PurDose of Key Clauses and Indewndent Modules in EXSEP Shown in Figure 7 clause/module purpose 1. key clauses drives program; coordinates entire program run [O]" develops EXSEP's window and menu systems; inputs data via file or keyboard initialize [ l ] carry out the plant-generate-test search for synthesizing the separation flowsheet synthesize-process [2] reports the final flowsheet results to the user report [ 81 terminates the program execution terminate [9] 2. independent modulesb performs feed-stream bypass to directly form a part of the overhead or bottom BYPASS [2.2] product analyzes the thermodynamic feasibility of potential splita for ordinary distillation, SST [3.1] sets up a separation specification table (SST), and identifies feasible splits heuristically ranks the feasible splits and develops the separation sequence for SPLIT [3.2] ordinary distillation ABSORB [4.1],STRIPPING [5.1],and LLE [6.1] perform the plan-generate-test search for synthesizing the separation flowsheeta for absorption, stripping, and liquid-liquid extraction (LLE),respectively ~
Numbers within brackets refer to the branches and steps in Figure 7 that show the links between clauses/modules. bFigure 7 does not include an independent module in EXSEP called UTILITY that supports all other modules with frequently-used list and numerical processing tools or 'utility" relations.
and displays the heuristically optimum solution. The user can override the EXSEP recommendation and choose other feasible solutions. This user-interrupt capability permits the evolutionary synthesis of additional separation flowsheets. Note that the "generate* stage actually performs some of the "testing" to increase the efficiency of the flowsheet search. Thus,there is some overlap between the generator and the tester. B. Modular Programming. To facilitate the continuing development of EXSEP for the selection, sequencing, and design of a variety of separation processes, we have adopted a modular approach to AI programming for EXSEP. Figure 7 gives an overview of currently available modules in EXSEP, including the central program driver and control, called MAIN, as well as a number of key clauses and independent modules. Table 111lists the objectives achieved by the key clauses and independent modulues in EXSEP. We note that independent modules SST (for geparation mecification table) and SPLIT are applicable to or-
dinary distillation only, and they are discussed elsewhere (Quantrille and Liu, 1991). In the following, we describe how the MSA-based (i.e., solvent-based) modules, namely ABSORB, STRIPPING and LLE, work, and what their common structure is. 3.2. Plan Stage. Figure 8 shows the overall structure of the MSA modules. This structure is common to all three modules. We use X as a generic term for the separation factor. It can be A (absorption factor), S (stripping factor), or E (extraction factor). To help the reader follow our discussion, we label the branches and steps in Figures 7-11 by numbers within brackets. A. CAM Representation. In branch [2] of Figure 8, the user enters the input data for the synthesis problem through a queation/answer session or through a Prolog file, and EXSEP performs the list processing to convert the problem data to a CAM. For example, Figure 9 illuetratea the problem input for example l a represented by CAM3 of eq 3. The Prolog fact henry("2',50.0) in Figure 9 says, "the Henry's law constant of component H2is 60.0"; the
Ind. Eng. Chem. Res., Vol. 32, No. 2, 1993 323
)
_
,
_
,
m _s a _ b, a P et d _ s e p (i L b t lC l T co p ~wT o pp C L=l s f B _
actual calculations
evaluaW for the p m duds. LLisl is the so.
rtsdlidproduas lmm high lo W K ' s CLLiStisSOhd
-
-
3.2
start incrementing X for(XminJlg or X s a l Xlg or Xsl is the upper limtt for X.
w = X I X until X> =Xlg (or Xsl
kremser~CUist,[LG],V,~KConstTapUaSBotLW)
fact flow(P1,"2',85.59) says, "the molar flow rate of component H2in product P1 is 85.59 mol/h". We see that it is very simple and straightforward to represent the input data through a Prolog file. B. Split Determination. In branch [3] of Figure 8, EXSEP identifies the desired split and key component, and creates the appropriate lists representing the feed and product specifications. For example l a represented by CAM3 of eq 3, EXSEP creates the following lista (Sstands for solvent): List = list of products = [Pl, [PZ, SI] C3, iC4,C4,iC5, C5+, CList = list of components = [H2, oil] TopList = list of products in the overhead = [Pl] TopClist = list of components in the overhead = [H2, C3, iC4,C4, iC51 BotList = list of products in the bottom = [P2, S] BotClist = list of components in the bottom = [H,, C3, iC4,C4, iC5, C5+, oil] These lists constitute the independent variables (called arguments in Prolog) of the functional relationship (called functor), ma-based-sep, specified in branch [l] of Figure 8. 3.3. Generate Stage. A. Generating Multiple Flowsheet Solutions. Let us refer to Figure 8. To generate multiple separation flowsheets, EXSEP uses an incremental procedure ([3.2] in the figure). The starting point of the procedure depends on the minimum separation factor, X-, [3.1], given by heuristics (e.g., A- = 1.0 for absorption). The end point of the procedure is specified by Xd (for Eolvent in absorption and extraction; d e d Xk for lean gas in stripping). This upper limit is ale0 given by heuristics (e.g., A,, = 2.0 for absorption). EXSEP obtains Xmh,Xll, and AX from a default data file for characteristic separation factors ([2] in the figure), called DEFAULTSAC (see section 4.1), which representa design heuristics D3-D5, and can be modified by the user.
Each incremental step corresponds to a separation factor X. With the feed flow rate and K value of the key component, EXSEP finds the solvent flow rate by Lsolvent = KkeycompVfedX (case of abeorption) (15) On the basis of the sortad lists of producta (LList), components (CLList),overhead product (TopList) and bottom product (BotList),EXSEP evaluates the feasibility of the separation charactmized by all these independent variables [3.3]. To generate several solutions, the program always fails after the Kremser clause [3.4], and it backtracks to the incremental step [3.2]. This backtracking continues until the incremental step itself fails, Le., when X = Xn1 (or X ). Then, the heuristic search is finished. B. Bremser Clause. To evaluate the split feasibility, EXSEP calls the Kremser clause. Figure 10 shows the logic structure of the Kremser claw. The first instruction [l] of the Kremser clause is to calculate the number of theoretical stages, N. If EXSEP cannot evaluate N (when the Kremser equation has a negative logarithmic argument), the system backtracks to increment X [2]. When EXSEP can evaluate N,the first heuristic is teated, [3] or [12]. EXSEP enters branch [3] if heuristics concerning the number of theoretical stages, N,are satisifed-the number of stages N must be greater than a given value Nopt(=5 for absorption). EXSEP teats if X is smaller than the optimum value (e.g., A, = 1.4 for absorption). If X satisfies this condition f4],the EXSEP calculates the component-recovery ratios [4.1] and checks if they correspond to the specifications (an error of 10% is allowed). If they do [5], EXSEP explains the situation [5.1]. Then, the program stores the separation in the data base [6.2], and increments the X factor to try to find another solution. If the component-recovery ratioe are not satisfactory (61, and the separation is not feasible, then EXSEP f o r a X to be greater than the actual value and seta it equal to the optimum separation factor Xopt[6.1]. This corresponds to an increase of the solvent or lean-gas flow rate. Doing
324 Ind. Eng. Chem. Res., Vol. 32, No. 2, 1993 QuestioniAnswer Session How nuny products ire in the syatem ? 2. How nuny components are in the ryatem ? 6. What is the name of product 1 ? pl. of product 2 ? p2.
What is the name
What is the name of component I What is the MIW of component 2 What is the name of component 3 What is the M ~ ofCcomponent 4 What is the nome of component 5 Whaf is the name of component 6
? "2'. ? 'C3HS'.
? 'ICJHIO'. ? 'CJAIO'. ? 'ICSHU'. ? 'CSH12+'.
What Whit What What What What
is the Henry's law constant of component H2 ? SO. is the Henry's law constant of component C3H8lZ.80. is the Henry's law constant of component lC4HlO ? 13. is the Henry's law conatant of component C4H10 ? 0.9. is the Henry's law constant of component lCSHl2 ? 037. is the Henry's law conatant of component CSH12+ ? 0.24.
What What What What What What
is the flow of component H? in p l ? 8559. is the flow of component C3H8 in pl ? 5.72. is the flow of component IC4HIO in p l ? 0.751. is the flow of component NCQHIO in pl ? 0.994. ir the flow of component lCSHl2 in pl ? 0.013. is the flow of component CSH12-i in p l ? 0.0.
h l o g File: 'ABSORB.DAT". hemy('H2'.50.0). hcmy('C3H8'.2.8). hcmy('lC4HlO', 1.2). hcnry('C4HI0',0.9). bemy('ICSH12',0.37). hemy('C5H I2 + ',0.24). flow@I ,'W2',8S 59). flow@I,'C3H8',5.72). flow@ 1.'IC4H 10'.0.75 I). flow@1,'C4H IO' ,0994). f l k @ l .'ICSH12'.0.013). flow@I .'CSH 12+ ',O). flow@2.'H2'.0). flow@2.'C3H8',1.43). flow@2,'IC4H10',0.639). flow@2,'C4HIO',1.556). flow@2. 'ICSH12'. 1.327). flow@2.'CSH12+ ',1.98). molc_fnction(rolvea.'H2',O). mdc_fnction(rolvent,'C3H8',O).
mole_fnction(rolvent.'IC4HlO',0). mok_fnction(mivent, 'C4HIO',@. mok-hction(rolvent. 'IC5H 12' ,O) mok_hction(rolvent, ' CSH I2 + ',Q.
.
initid-l_ut([pl .p21). initirl_componenu(['H2','~H~','lC4HlO',
'CQHIO'.'ICSH12'.'CSH12+'D. What is the flow of component H2 in p2 ? 0.0. What is the flow of component C3H8 in p2 ? 1.43. What is the flow of component IC4HlO in p2 ? 0.639. What ir the flow of component C4H10 in p2 ? 15%. What ir the flow of component ICSH12 in p2 ? 1327. What is the flow of component CSHI2+ in p2 ? 1.98.
so,lvcnt(oil). key_component(dga,'IC5Hl2~. % d p = dilute p' abrotption plitqrOduct(pl).
What ir the name of the solvent ? oil. What ir the mole What ia the mole What ia the mole What is the mole What ir the mole What is the mole
fnction of H2 in oil ? 0. fraction of C3H8 in oil ? 0.
fraction of IC4H10 in oil ? 0. hction of C4H10 in oil ? 0. fnction of ICSH12 in oil ? 0. fnction of CSHI2+ in oil ? 0.
What is the key component ?
'ICSEIU'.
What is the q l i t praduct ? pl.
Figure 9. Illustration of input data-loading options through a question/answer session or through a Prolog file: example la.
so enables the component-recovery ratios to meet the speoifications,but it yartificiallyuincreases the solvent flow rate which is contrary to the optimization of this parameter. Thus,if a solution exists for this impoeed solvent flow rate, it will not be an optimum solution. When component-recovery ratios do meet the specifications, the same procedure as [5]-(5.31 is applied in [7]-[7.3]. If they do not, EXSEP incrementa X [8]. Referring to [3], we note that if X is greater than X,, [9], then in [9.1] and in [lo]-[11.3], the same process is applied as in [6.21 and in [7]-[81. Returning to [l], we see that if N is smaller than Nopt[12], the column does not satisfy the design heuristics. However, EXSEP keeps trying to find a solution [12.2]. But when EXSEP finds a 'solution" [ 141,the program diagnoses it to be infeasible [14.1]. In [12.1], EXSEP stores the values of X when the branch [12] is entered the first time. This value X,,is the separation factor when the number of theoretical stages is optimum, and is used in the explanation process. Branches [4.1] and [9.1]-[12.2] of Figure 10 show that EXSEP also calculates the recovery fractions of all key and
nonkey components in the overhead and bottom products, following the relationships given in Table 11. C. Recovery Clause. After a flowsheet is generated for the choeen solvent-based separation, EXSEP simulates the solvent-recovery column. We can c h o w between two alternatives for the recovery clause. We choose to start a new simulation with another separation module, or we assume that the split is sharp and feasible. The latter corresponds, for instance,to the vertical dashed line in the CAM3 of eq 4 for example la. EXSEP then displays the split without requiring a feasibility analysis. 3.4. Test Stage. A. Explanation Facilities. A.1. Solution Position. EXSEP is able to explain or diagnoee the 'quality" of a flowsheet solution according to the deviations between the actual number of theoretical stages and separation factor and their respective optimum values based on heuristics. Figure 11 shows four possible configurations. Case 1 corresponds to branch [5] of the Kremser clause (Figure 10). In this case, EXSEP explains that the solvent flow rate is lower than the optimum and N higher than
Ind. Eng. Chem. Res., Vol. 32, No. 2, 1993 325
y, 121
store Xst only
1 IO
I -wpara(lon
14.2
I
Generic Form of the Kremser Clause
X can be A, S or E
I
Figure 10. Generic structure of the Kremser clause for absorption, stripping, and extraction.
I N
X - W V or kViL
case 1
X c a b A, Sor E II
\
Nopt
Case 4
N Nopt
I
I
XoptXst
Xsl or Xla
L* w t h m hop(imunv a u . Themwmrl cdutim tu N 1styaaerth.n Umopknum of Napl
Figure 11. Diagnosis of the quality of a flowsheet solution.
the optimum. Case 2 represents branch [SI in the Kremser clause (Figure 10). It occurs when we impose the separation factor X to be ita optimum value Xopt,which is equivalent to increasing the solvent flow rate. This is not an optimum solution because N is higher than the number of theoretical etagea correeponding to X, (0)on the graph for case 2 in Figure 11). Case 3 is a good configuration. Indeed,X and N are close to their optimum values. Case 4 is an unpractical configuration because N is too low and the solvent flow rate too high.
This explanation capability is based on the assumption that the four characteristic separation factors are in the following order: Xmin < Xopt < Xst < Xs1 (16) This is the best configuration for an efficient search. However, when the characteristic separation factors are not in this order, EXSEP analyzes the actual order, gives explanations, and advises on the range size of flowsheet search.
A
m
w
not have the limit X smaller than the optimal value: 1.O > 1.4
~
. Xmin
-m>u - case2 The upper limit Xsl is smaller than the lower limit Xmin: 2 you must have Xmin Emh= 2. Indeed, EXSEP is able to find many other alternative solutions in a matter
of seconds for which the user can further evaluate. This example demonstrates again how efficient EXSEP is to generate multiple flowsheet solutions, and how flexible it is when the user wants to reject EXSEP’s best solutions and search for alternative flowsheets. E. Example 3b. Extraction of DMA and DMF from a n Aqueous Solution. This example demonstrates the application of EXSEP to solvent-based separations where the added solvent contains also the original solute and solvent components present in the feed. We consider an aqueous solution containing 0.5% (mass) dimethylamine (DMA), 10% dimethylformamide (DMF), and 0.5% formic acid (FA). The extracting solvent is 99.73% methylene chloride (MC), plus traces of DMF (0.02%), and water (0.25%). This extraction problem comes from Henley and Seader (1981,p 479). The goal is to separate most of DMA, DMF, and MC into an extract (overhead) and most of FA and water into a raffinate (bottom). Wankat (1988)indicates that the Kremser equation used by EXSEP is applicable to most solvent-based separation problems in dilute mixtures based on component flow rates in mass units, rather than molar units. Thus, we may represent this extraction example by the following CAM according to the component flow rates (kilogramsper hour) given by Hanley and Seader: CAM 7
E eolvrnt
1:
MC
DMA
0.8975V
0 20 0
DMF
FA
H20
2
20
400
0. 25 0 0.0025V
0.002V
3660
1
(17)
Here, P1 and P2 are raffinate and extract products, respectively; V is the total solvent flow rate. In the CAM, we arrange the component columns from left to right in decreasing order of “average” K values (distribution coefficients): MC (40.2), DMA (2.21, DMF (0.8),FA (0.05), and H 2 0 (0.003).In particular, EXSEP uses a constant distribution coefficient of 0.8 for DMF. For this example, Henley and Seader consider the dependence of the distribution coefficient for DMF on ita
332 Ind. Eng. Chem. Res., Vol. 32, No. 2, 1993 Table VII. Comparison of Component Recoveries and Flowsheet Design Variables for Example 3b Obtained by EXSEP and by the Edminster Method (Henley and Seader (1981), p 479) EXSEP EDMISTER component" extract (kg/h) raffinate (kg/h) extract (kg/h) raffinate (kdh) MC 14094.5 0 9882.2 90.8 DMA 19.55 0.45 20 0 DMF 393.96 8.04 400.7 1.3 FA 0.4 19.6 0.3 19.7 H2O 71.7 3513.3 37.8 3557.2
N
E V (kg/h)
10 2.06 (av) 9.998
5 2.8 14.130
MC = methylene chloride, DMA = dimethylamine, DMC = dimethylformamide, FA = formic acid, and H20= water.
concentration in the water-rich (raffinate) product. They do not use the Kremser equation, but a more complex and iterative shortcut method, namely, the Edmister method. One feature of the Edmister method is to evaluate the extraction factor at different places in the extraction column, whereas the Kremser equation uses only a constant extraction factor throughout a column. In addition, the Edmister method requires an initial assumption of the number of theoretical stages in order to iteratively find the appropriate solvent flow rate (and hence the extraction factor) that matches the component-recovery specifications. Table VI1 compares the component recoveries and flow sheet design variables obtained by EXSEP and by the Edmister method (Henley and Seader (1981), p 479). The results from EXSEP utilize a heuristically optimum number of theoretical stages, N = No,, = 5, while Henley and Seader assume 10 theoretical stages and do suggest that "it would be worthwhile to calculate additional cases with leas solvent and/or few theoretical stages". Both solutions are valid, and a precise economic evaluation would decide on the best one. However, we prefer the Kremser equation and the heuristic search used by EXSEP, since they can give valid flowsheet solutions within seconds and offer significant advantages over a more complex iterative scheme like the Edmister method. 4.3. Validity of the Kremser Assumptions and Limitations of EXSEP. By using the stage-by-stage results from rigorous CAD simulations of the preceding examples, we could verify the validity of several simplifying assumptions for applying the Kremser equation in EXSEP. Figure 18a illustrates that we do not exactly have isothermal and isobaric conditions in our absorption or stripping examples. For extraction examples, this assumption is valid, as seen in Figure 18b. The Kremser equation requires that the molar overflow (L/ VI is constant throughout a separator column. With the constant K-value assumption, this also implies that the separation factor is constant, throughout a separator column. Figure 19 illustrates that these assumptions are not valid. Despite the fact that the assumptions required to use the Kremser equation are not exactly satisfied, the favorable results given by EXSEP for both flowsheet design variables and component recoveries in the preceding examples, when compared to those obtained from rigorous CAD simulations, do clearly suggest an important conclusion: EXSEP is indeed capable of giving good preliminary flowsheet designs regardless of the Kremser assumptions.
Our experience in applying EXSEP to a large number of solvent-based separation synthesis problems also identifies two main limitations on using EXSEP:
Isothermal and Isobaric Conditions
(a)
Absorption Exaaple (nelson, 1969) 350
35
(b)
18othormal and I8obaric Condition8 Extraction Bumpla (Pro11 mnual, 1987)
Figure 18. Checking the validity of the isothermal and isobaric assumptions: (a) example la (absorption) and (b) example 3a (extraction).
1. The components to be separated must be in dilute concentrations (< 10%). 2. The solvent or MSA cannot be a dominating component of the feed. An example of the second limitation is the stream stripping of sour water. EXSEP cannot effectively handle this problem, because the lean gas (solvent) is steam (water) and the main component of the feed is water (typically more than 90%). 5. Conclusions and Recommendations 1. EXSEP is now operating for four separation methods
ordinary distillation, absorption, stripping, and liquidliquid extraction. This is the first PC-based, quantitative expert system for multicomponent separations using both
Ind. Eng. Chem. Res., Vol. 32, No. 2,1993 333 V b r i f i c a t i o n of A-Con8tant Mvorption Example (Hellon, 1969) 0.65
7""
lecting the separation methods and solvents. Barnicki and Fair (1990,1992)have done excellent work in collecting and organizing the heuristic knowledge for these selection modules, particularly for liquid and gas/vapor mixtures. Much work remains to be done, however, in actually implementing the knowledge into a user-friendly expert system. Acknowledgment
1
2
3
4
5
6
7
i 9
8
' 1.4
N stage N a I
Verification of Elconstant Extraction Example (PRO11 manual,
1987)
1.)
.
I'
i
..i
......... ".i ..... . .1" 3.1 !
Figure 19. Checking the validity of the constant molar-overflow and constant separation-factorassumptions: (a) example l a (absorptiod)
and (b) example 3a (extraction).
energy and solvents. Currently, EXSEP is limited to dilute solvent-based separations and cannot effectively solve problems where the major feed component is also the solvent. 2. An advantage of EXSEP is ita ability to heuristically generate, in a matter of seconds, many feasible and economical flowsheet solutions in terms of the separation factor, solvent flow rate and number of theoretical stages. These solutions are accurate in meeting the specified component recoveries in both the overhead and bottom products, when compared with the results from rigorous simulations using commercial CAD software systems. Indeed, EXSEPs solutions provide the necessary and reliable specifications of design variables for preliminary flowsheets prior to their rigorous CAD simulations. 3. With ita menu-driven decision tools and windowbased explanation facilities, EXSEP is convenient and user-friendly. It can be easily used by practicing chemical engineers and in undergraduate design teaching. A user can also override EXSEP's recommendations and implement design changes to facilitate the evolutionary synthesis of alternative separation flowsheeta. 4. The knowledge representation and search strategy developed for EXSEP could be used for other kinds of separations such as leaching and adsorption. In particular, the modular programming structure of EXSEP makes it convenient for future expansions to include additional modules for the selection, sequencing, and design of a variety of separation processes. Perhaps the greatest challenges would be the developments of modules for se-
We dedicate this article to the memory of the late Professor Naonori Nishida, Science University of Tokyo, a coauthor of parts 1-4 of this series of studies in chemical process design and synthesis and a scholar internationally recognized for his review paper on process synthesis (Nishida et al., 1981). Y.A.L. is particularly thankful for the opportunity to have worked with Professor Nishida in 1975-1977 on the synthesis of heat exchanger networks and dynamic process systems, and greatly admired Professor Nishida's enthusiasm and wisdom for creative engineering design research. Professor Nishida's untimely death represents a great loss to the chemical engineering community, and we shall miss his enthusiasm and wisdom. Nomenclature A: absorption factor (L/K,V),dimensionless b,: constant in Henry's law, eq 8; or component-recovery fraction in the bottom product, dimensionless d,: component-recovery fraction in the overhead product, dimensionless Dev: average deviation between the actual and specified component-recovery ratios, %, eqs 11-14 E: extraction factor (K,V / L ) ,dimensionless Til: flow rate of component i in the jth product [mol/h] K : weighted-average K value of the jth product, eq 2 I(: K value, Henry's law constant or distribution coefficient of component i L: liquid flow rate, feed or solvent [mol/h] N: number of theoretical stages, dimensionless No,,: optimum number of theoretical stages, dimensionless PI:jth product S: stripping factor (K,V / L ) ,dimensionless V: gas or vapor flow rate, feed in absorption or lean gas in stripping; solvent flow rate in extraction [mol/h] X generic separation factor (can be A , S, or E ) x,,,", x,,~,,< mole fraction of component i entering and exiting the liquid phase, respectively X I or Xs
