Studies in Chemical Process Design and Synthesis. 10. An Expert

Transcription

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
@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
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)
<0
Dev # 0
(lle)
We note that, in practice, the deviation (Dev) can never
drop to zero.
We choose to develop three additive component functions, with each of them contributing to the desirable solution characteristics such that
CS(DeV,N,S) = fl(Dev) + f 2 ( N )+ f 3 ( S )
(12)
dCS(Dev,N,S) - dfl(Dev)
aDev
dDev
(13a)
dCS(Dev,N,S) =-df2(N)
dN
dN
(13b)
dCS(Dev,N,S) = -df3(S)
as
dS
(134
A careful consideration of all of the above desirable
solution characteristics,eqs lla-l3c, leads to the following
form for the heuristic evaluation function, CS(Dev,N,S)
(Brunet, 1992):
CS(Dev,N,S) = exp
I
In eq 14, the presence of the logarithm reflects the additive
nature of component functions fl to f 3 according to eq 12.
For In VI), we choose the inverse function In (l/Dev) or
-In (Dev) for fi(Dev). This satisfies the requirement that
fl(Dev) increases as the deviation (Dev) decreases, eq lle.
For In (f2)and In (f3),we include parabolic functions in
f2(N) and fs(S)to satisfy the property of having a maximum at the optimum values, Noptand So t, respectively.
Also, to satisfy the other properties that 6S(N+1) > 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,
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
)
_
,
_
,
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
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
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<Xsl for any calculation to occur
~
m,
xopc<m
-
&$)O
N
-
___
m<xopc
1.8
case3
No more solutions are expected in the studied range
m<u
Xsl Xopt Xst
xst XOPl Xsl Xmin
I,
Nb+
k i n Xopt
Solutions may exist for X> 15 .W h a number of stages
still higher than 5. You should increase Xsl.
Xst Xal
NILE
Nopt
-
--
Xmin Xopl Xsl Xst
b
Crrse.5
The optimal X Xopt=l.6 should be smaller than Xst=l.5
because Xopt ought to be where N is greater than 5.
XminXst Xopt Xsl
to be studied. It should be greater than 1.7. You should decrease Win
L
Q
l
?
E
m>=xopt
The minimum value Xmin=l.5 should be smaller if you want to use
the optimal value Xopt=l.4.
Xopl Xmin Xst Xsl
The initial value of X, Xmin=l.6 is too high. Only solutions
with N smaller than 5 will be generated.
Xst Xmin Xopl Xsl
Figure 12. (a) Diagnosis of the range size of flowsheet search cases 1-4. (b) Diagnosis of the range size of flowsheet search cases 5-8.
A.2. Range Size of Flowsheet Search. There are 24
possible combinations of the 4 characteristic separation
factors Xmin,Xopt,Xst, and Xsl. Figure 12 shows the
structure of the diagnosis clause and displays the eight
most important cases. For example, if Xmin(the lower
limit) is higher than XsI(the upper limit), no calculation
occurs (case 2). As the user can change the values of the
four characteristic separation factors, errors like this one
could occur. EXSEP takes care of them.
One of the most important among the eight cases is
when X,,is higher than XsI(case 4). This means that the
upper limit is smaller than the value of the separation
factor when the number of theoretical stages becomes
optimum. In such a case,feasible solutions may exist with
a separation factor higher than the upper limit and a
number of theoretical stages still higher than the optimum,
as illustrated previously in Figure 5b.
B. Selection of the Best Solution. Each feasible
solution is stored in an independent database. Inside the
database, the separations are indexed with their respective
CS (coefficient of separation) factors, eq 14. To obtain the
best separation, EXSEP displays the solution that has the
highest CS factor (best solution), and asks the user to
accept or reject this selection. If the user rejects the 80lution EXSEP suggests,EXSEP displays the solution with
the second highest CS factor, and so on.
4. User’s Perspective of EXSEP
In this section, we discuss EXSEP from the user’s
perspective. The simple menu and window systems incorporated in EXSEP make it very easy to use by practicing chemical engineers and in undergraduate design
teaching. We describe here the system and file requirements of EXSEP, and illustrate the applications of EXSEP to a number of industrial separation problems involving absorption, stripping, and extraction. Detailed
user’s manuals for EXSEP are available for solventcbased
separations in Brunet (1992)and for ordinary distillation
in Quantrille and Liu (1991).
Table IV. Comparison of Several Flowsheet Solutions for
Example la
solution technique
A
N L (mol/h)
traditional shortcut method (Nelson, 1969) 1.50 8
55.50
EXSEP
1.45 9.2
50.75
1.50 8.6
55.50
1.55 8.1
57.36
4.1. System and File Requirements. EXSEP can run
on almost any IBM-PCs (AT, XT, or PS/2) using MS
DOS. It was developed for a VGA monitor and works
better with this type, but it can also work on CGA, EGA,
and even Hercules Monochrome monitors. The executable
version EXSEP.EXE is in compiled Prolog. Its relatively
small size (280 kB)makes it usable from a floppy disk. It
does not require an extended memory. One megabyte of
RAM is entirely sufficient. It solves the examples presented below in less than 1 s of CPU time with a 286,
8MHz processor. This makes EXSEP an efficient expert
system for IBM-PC. To run, EXSEP needs three fixed
system files: (1)EXSEP.EXE (282 kB), (2) MAIN.IDB
(65.5 kB), and (3) MENU.AR1 (2.6 kB). EXSEP also
needs two user-provided data fdes: (1)*.DAT (0.5 kB)(for
problem input) and (2) DEFAULT.* (0.1 kB)(default data
files).
From a user’s viewpoint, it is fairly easy to provide the
two input data files in Prolog. For instance, an input file
named ABSORB.DAT may represent the Prolog input
file for example l a shown in Figure 9; a default data file
for defining the heuristic search conditions for an absorption problem, named DEFAULT.FAC, may correspond to the following Prolog file (note: in Prolog, comments appear preceded by 5%):
optimal-A (1.4).
% optimum absorption factor Aopt (~1.4)
minimum-A (1.35). % minimum absorption factor A,,, (=1.35)
% maximum absorption factor A,,
limit-A (1.6).
(golvent) (=1.6)
optimal-N (5).
% optimum number of theoretical stages
Nopt (=5)
% incremental size of absorption factor in
step (0.06).
heuristic search
error (0.1).
% specified component-recovery ratios,
d/b’s; see eq 8.
To increase AS1from 1.6 to 2.0, for example, we need to
edit the DEFAULT.FACfde with a word processor or an
editor to change the Prolog fact, limit-A (1.6).
4.2. Illustrative Examples. A. Example la: Absorption of Natural Gas by Lean Oil. Example l a is
a six-component absorption problem in petroleum refining
(Nelson, 1969). The problem is to absorb 99% (molar) of
iC5 and 100% of C5+ with an oil from a feed mixture of
H2 (85.59%) (molar), C3 (7.15%), iC4 (1.39%), C4 (2.55%),
iC5 (1.34%), and C5+ (1.98%), resulting in the overhead
and bottom products specified in Table I. Figure 9 shows
the user’s input file for EXSEP, and eq 3 gives the corresponding CAM.
For this problem, Nelson (1969) uses the Kremser
equation as we do in EXSEP, but he follows a traditionul
shortcut method. He starts by assuming eight theoretical
stages ( N = 8) and then iteratively finds the corresponding
absorption factor (and hence the solvent flow rate) to
match the component flow rates in the overhead and
bottom products. In EXSEP, we do not need to assume
the number of theoretical stages. EXSEP can quickly give
multiple feasible combinations of the number of theoretical stages, absorption factor, and solvent flow rate that
yield the specified component recoveries within an acceptable error tolerance. For example, Table IV compares
the flowsheet solution obtained by the traditional shortcut
method according to Nelson (1969) with several solutions
resulting from the heuristic search by EXSEP over the
range, A- (=1.35) < A < A,, (=1.60), with an incremental
size, AA = 0.05. EXSEP gives not only a solution that is
consistent with that obtained by Nelson, but also additional feasible solutions.
EXSEP has several kinds of windows to display flowsheet solutions. Figure 13a shows a window that compares
the specified and actual component-recovery ratios, corresponding to the flowsheet solution ( A = 1.50, N = 8.6,
and L = 55.5 mol/h) displayed in Figure 13b. In the latter
window, EXSEP also provides a diagnosis for the solution:
“L is higher than the optimum value. The minimal solution for N is greater than the optimum of 5 [case 31.” We
have previously discussed the implications of this diagnosis
on the quality of flowsheet solutions in Figure 5a and
Figure 11 (case 3). Figure 13c displays the window for the
range size of flowsheet search, “the range of absorption
factor is 1.35-1.60”, together with the diagnosis: “solution
may exist for A > 1.6, with a number of stages higher than
5.0. You should increase As..” The reader may refer to
Figure 5b and Figure 12 (case 4) of our previous discussion
of this diagnosis on the range size of flowsheet search.
Figure 13d shows the window for the best heuristic flowsheet solution based on CS ranking, eq 14. Figure 13e
displays the flowsheet-summary window. The first column
shows the names of the separators. The second column
gives the amount of feed bypass to directly form a part of
the overhead or bottom product. The column “Stream
Flow In” shows the inlet molar flows to the absorption and
solvent-recovery columns, and the last two columns specify
the component flows in the overhead and bottom products.
Table V compares the component recoveries for example
l a obtained from (1)EXSEP’s heuristic search, (2) Nelson’s traditional shortcut method, and (3) rigorous CAD
simulations by DESIGN I1 (ChemShare Corporation,
1985), corresponding to EXSEP’s flowsheet solution, A =
1.50, N = 8.6, and L = 55.5 mol/h. EXSEP’s solution
proves the necessary and reliable specifications of design
variables for the preliminary flowsheet prior to carrying
Table V. Comparison of Component Recoveries for Example la Obtained from EXSEP’s Heuristic Search, Nelson’s
Traditional Shortcut Method, and Rigorous CAD Simulations: A = 1.50. N = 8.6, and L = 55.5 mol/h
EXSEP
Nelson (1969)
CAD
percent
vapor
percent
vapor
percent
vapor product
absorbed
feed
vapor product
absorbed
Droduct
absorbed
(mol/h)
(%)
(mol/h)
(%I
component
(mol/g)
85.59
0
85.55
0.1
H,
85.59
5.87
18
7.15
5.73
20
5.73
20
C,
0.80
42
1.39
0.75
46
0.75
46
iC,
0.93
64
2.55
0.99
61
0.99
61
c,
1.34
99
8.5 x 10-3
0.03
98
8.5 X
iC5
99
1.1 x 10-3
100
1.1 x 10-3
100
0.04
98
c,+
1.98
2.5 x 10-3
0
oil
0
0
d
e
ROCUsymwda
morr(-
WAmrnd
81
nmr
BbmRah
1 . w nz
7.18C3HB
1.38WlO
Z.1UHlO
1.MC6HlZ
i.mcwiz+
81
Onmnd =a
o3.m nz
8.73 C3H8
0.76WHlO
O.WC4HlO
0.03 lcsHlZ
O.LU'XHIZ+
0.0 oll
1.71 nz
1.42C3H8
0.M IC4HlO
1.1UHlD
1.31 KXHlZ
1.31 IClHlZ
1.MChlZc l.MChll+
1.6 dl
0.0 oll
1.71 HZ
1.UCW8
0.84 IUHlO
1.68UHlO
1.71 HZ
1,42C3Hl
O.MC4HlO
1.MUHlO
1.31 C8HlZ
i.~chiz+
1.8
0.0
dl
nz
O.OC3H8
0.0Cull0
O.OC4HlO
0.0lClHlZ
O.OChlZ+
1 . 8 dl
Figure 13. EXSEP's windows for displaying flowaheet solutiona for example la: (a) window for the procese feasibility analysb; (b) window
for the p r o a s heuristic analysis and explanation (diagnoeie);(c) window for the range size of flowaheet search; (d) window for the beat flowsheet
solution; and (e) window for the flowsheet summary.
out the rigorous simulations of a solvent-based separation
process using a commercial CAD software system such as
DESIGN 11, PRO 11, or ASPEN PLUS. The reeulb sum-
marized in Table V indicate that component recoveries
given by EXSEP are very cloee to those obtained by a
rigorous simulation. EXSEP tends to slightly overestimate
Components
I
Top Exsep
=
B o t EXSEP
Top DesII
Top Exp.
Bot DesII
Bot Exp
.
1
Figure 14. Comparison of component recoveries for example lb obtained by EXSEP from rigorous Simulations (DESIGN 11)and from actual
experimental data (Sherwood and Pigford, 1952).
the absorption of light components and underestimate the
absorption of heavy components. This tendency results
from the assumption that at least 2% of light components
goes to the bottom product, and at least 2% of heavy
components appears in the overhead product.
B. Example lb: Absorption of Cracking Oil Gas
by Lean Oil. Example lb deals with a 19-plate refinery
absorber operating on cracking oil gas (Sherwood and
Pigford (1952), pp 211-214). A lean oil (molecular weight
= 285) enters the top of the column at 31.3 "C and 4.96
X lo5 Pa. An ll-component mixture (1841 mol/h) of H2S
(2.4%) (molar), H2 (6.5%), CHI (35.0%), C2H4 (3.79'01,
C2H6 (20.5%), C3H6 (7.270)~C3H8 (13.1%), C4H8 (3.5%),
C4H10 (4.7%), C5H12 (2.6%), and CsH14 (0.8%)enters the
bottom of the column at 24 "C and 4.96 X lo5 Pa. The
column operates at 4.96 X lo5 Pa. The plate efficiency is
approximately 30%. The molar flow rate of the lean oil
is 728.34 mol/h. The lean oil contains traces of H2S
(0.06%), C3H8 (0.01%), C4H8 (0.1%), C4H10 (0.19'0)~and
c5H12 (170)The number of theoretical stages predicted by EXSEP
(N = 5.02) is close to and consistent with the value
Sherwood and Pigford give (N= 6.33). The lean-oil flow
rate provided by EXSEP (L= 709 mol/h) is also satisfactory compared to the amount fed to the industrial
column (L= 728 mol/h). Thus, EXSEP gives good preliminary design variables, N and L. For this example,
EXSEP chooses a small absorption factor, A = 0.85, instead of the heuristic optimum, A,, = 1.40 (heuristic 03).
This choice reflecta EXSEP's ability to automatically reject
those values of the absorption factor that result in an
unrealistically low number of theoretical stages, N < 5
(heuristic Dl), as found in this example.
Figure 14 compares the component-recovery ratios,
sorted in decreasing K-value order, for the results from
EXSEP (first series), those from DESIGN I1 (second series), and those from the actual industrial absorber reported by Sherwood and Pigford (third series). A cut
appears between C3H8and C4H8. Thus, C4H8is the key
component. This figure shows that when compared to
rigorous simulations, EXSEP gives satisfactory recoveries
of the key component, but it slightly underestimates the
absorption of the components lighter than the key.
C. Example 2: Steam Stripping for Absorber
Solvent Recovery. To examine the validity of the
STRIPPING module, we investigate the solvent recovery
of our previous absorption problem (example la). The
recovery process is inspired by an example in Smith (1963,
p 470), where steam is used to recover an oil that serves
as the solvent to absorb heavy Components from a mixture
of methane to pentane. Specifically, the bottom product
from the absorber of example l a becomes the inlet stream
to a steam stripper. We use the stripper design variables
(number of theoretical stages, N = 5; and steam flow rate,
V = 80.61 mol/h) obtained by EXSEP to run a rigorous
CAD simulation with DESIGN 11.
In Figure 15, we compare the resulting component recoveries. The first set of bars represents the feed to the
column. For example, 100%of each component enters the
top of the column, whereas the steam enters the bottom.
The second set of bars represents the results given by
EXSEP. For example, 84% of the 1.98 mol/h of C6H12+
entering the column goes to the overhead, and the remaining 16% goes to the bottom. The third set of bars
corresponds to the result from rigorous simulations ( D E
SIGN 11).
We compare the EXSEP design and rigorous simulations by looking at the sizes of the bars, the feed in both
methods being the same. EXSEP gives a very good approximation of the actual component flow rates. It pro-
..................
..................
..................
.......................................
Steam C3 C4 C5+
Steam C3 C4 C5+ Steam C3 C4 C5+
H2 iC4 iC5 Oil
H2 1C4 1C5 Oil
HZ iC4 iC5 Oil
Components
Figure 15. Comparison of component recoveries for example 2 obtained by EXSEP and from rigorous simulations (DESIGN 11).
100
eo
60
40
20
a
9
Q,
u0
0
-2 0
-4 0
-60
-eo
-100
Benzene Phenol
Benzoic Water
Benzene Phenol
Benzoic water
Benzene Phenol
Benzoic Water
Components
I
I
Figure 16. Comparison of component recoveries for example 3a obtained by EXSEP and from rigorous simulations (DESIGN 11).
vides realistic design variables of the preliminary stripping
flow sheet. Indeed, the rigorous simulations indicate that
the separation given by EXSEP is feasible. Moreover, this
preliminary design by EXSEP is necessary, because the
user of any commercial CAD software system must have
an initial flowsheet prior t o ita rigorous simulations with
the software.
D. Example 3a. Extraction of Organic Compounds
from an Aqueous Effluent. To illustrate the application
of the LLE module and to demonstrate the effect of stream
bypass on the separation flowsheet design, we consider a
problem of extracting traces of benzene (BEN), benzoic
acid (BEC), and phenol (PHE) from an aqueous effluent,
using benzene as the extracting solvent (Simulation Sciences, 1987). Equations 5 and 6 give the CAMS for this
extraction problem with and without stream bypass, respectively.
For this problem, EXSEP searches for flowsheet solu)
tions over the range of extraction factors, Emin( ~ 2 . 0 <
E < EB1(=4.0), with an incremental size AI3 = 0.05. Table
VI compares the extractor design variables obtained by
EXSEP for two best solutions with and without stream
100
60
40
20
0
-2 0
-40
-60
-a o
-100
Figure 17. Comparison of component recoveries for example 3b obtained by EXSEP and by the Edmister method (Henley and Seader (198l),
p 479).
Table VI. Comparison of Several Flowsheet Solutions for
Example 3a
solution technique
E
N V (mol/h)
EXSEP
best solutions
without bypass
2
6.64
78.08
2
4.60
77.49
with bypass
alternative solution
without bypass
3.5
4
136.70
PRO I1 (Simulation Sciences, 1987)
2.58 4
135.25
without bypass
bypass at an extraction factor of E = Emin
= 2.0. Stream
bypass only slightly reduces the solvent flow rate, but it
lowers the number of theoretical stages by 30% from N
= 6.64 to 4.60. Thus, stream bypass can have a favorable
effect on reducing the stage requirement of a solvent-based
separation. Figure 16 compares the component recoveries
obtained by EXSEP for the best solution with stream
bypass (E = 2, N = 4.60, and V = 77.49 mol/h) and by
rigorous simulationsvia DESIGN II. As in absorption and
stripping applications, component flow rates predicted by
EXSEP for extraction problems are reliable.
Table VI also lists an alternative flowsheet solution
obtained by EXSEP without stream bypass, and the extractor design variables specified as input data for rigorous
simulations of the problem by PRO I1 (Simulation Sciences, 1987), with both having the same number of theoretical stages, N = 4. A comparison of the two best solutions obtained by EXSEP with PRO I1 design specifications appears to suggest EXSEP solutions to be better
specifications for preliminary flowsheets, because for only
two to three more theoretical stages, the solvent flow rate
is cut by 42% from 135.25 to 79.5-78.0 mol/h. A precise
economic analysis would be able to choose between the
two. While the alternative solution obtained by EXSEP
is much closer to the PRO I1 specifications, it is not considered to be the best one by EXSEP due to the large
extraction factor, E = 3.5 > 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
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<maximum separation factor depending on the
Bean gas (1g) or solvent (51)
Xmln:minimum separation factor (from heuristics)
Xopt:optimum separation factor (from heuristics)
Xs<value of the separation factor when N = Nwt(st for &age)
y,,,,,, yl,ou; mole fraction of component i entering and exiting
the vapor phase, respectively
Abbreviations
CAM: component assignment matrix
CS: coefficient of separation, eq 14
ESA energy-separating agent
LLE: liquid-liquid extraction
MSA: mass-separating agent
Subscripts, Superscripts, and Bracket Notation
i: ith component
j : jth product
in, out: entering or exiting a separator
[ 1: reference of branches and steps in Figures 7,8, and 10
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New York, 1980.
Wankat, P. C. Separations in Chemical Engineering: EquilibriumStaged Separations; Elsevier: New York, 1988.
Wahnschaft, 0. M.; Jarian, T. P.; Westerberg, A. W. SPLIT A
Separation Process Designer. Comput. Chem. Eng. 1991, 15,
565-581.
~~
Received for review June 18, 1992
Revised manuscript receiued October 26, 1992
Accepted November 12,1992
Nonlinear Model Predictive Control Using Second-Order Model
Approximation
Sachin C. Patwardhant and K.P. Madhavan***
Systems and Control Group, Department of Electrical Engineering, and Department of Chemical Engineering,
Indian Institute of Technology, Powai, Bombay 400 076, India
A model predictive control (MPC) algorithm using a nonlinear discrete perturbation model for lumped
parameter systems has been proposed. The nonlinear ordinary differential equations (ODES)
representing the process are locally approximated using the terms up to second order in the Taylor
expansion. Using regular perturbation technique and certain simplifying assumptions, the resulting
equations are integrated over a sampling interval to obtain an approximate discrete model of the
system. The Morse lemma is used to identify the conditions under which the proposed approximation
will prove distinctly superior over the linear approximation. Under perfect model assumption, the
performance of the proposed algorithm is demonstrated by simulating regulatory control of two
continuously stirred tank reactors (CSTRs) characterized by zero steady-state gain with respect to
one manipulated input at the optimum operating point and attendant change in the sign of the
steady-state gain across the optimum. The MPC algorithm based on the proposed second-order
model is shown to improve the closed loop performance when compared to other nonlinear MPC
algorithms. Finally, it is shown that the proposed control algorithm is robust for moderate variations
in plant parameters.
1. Introduction
The ever increasing quest for improvement in the performance Of modern process plants and availability Of fast
computing power has given rise to the development of a
new generation of advanced control algorithms which can
identify the current optimal operating point Of a process
and effect the transition of the process to the new optimal
* T o whom all correspondence should be addressed.
Systems and Control Group, Department of Electrical Engineering.
Department of Chemical Engineering.
*
point in an acceptable and safe manner. The resulting
multivariable control problem with explicit constraint
handling requirements hes been successfully
model predictive control (MPC) techniques, such as dynamic matrix control ( D ~(cuder
~ ) and M~~
19w)
and model algorithmic control (MAC) (Richalet 'et al.,
1978). However, these control algorithms, developed
around linear Drediction models, may not be admuah for
handling stroigly nonlinear sys&ms-often encou&red in
the process industry. With the need being recognized, a
number of extensions of the m c & o r i b S , which employ a nonlinear prediction model, have been recently
proposed in the literature. On the basis of the approach
0888-5885193/2632-0334$04.0010 0 1993 American Chemical Society

Studies in Chemical Process Design and Synthesis. 10. An Expert

Transcription

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