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A case study on synthesis in preliminary design
Computers chem. Engng, Vol. 21, Suppl., pp. $53-$58, 1997 © 1997 Elsevier Science Ltd All rights reserved Printed in Great Britain
Pergamon PII:SO098-1354(97)00025-2
0098-1354/97 $17.00+0.00
A Case Study on Synthesis in Preliminary Design D. Murray Laing* Eric S. Fraga t Department of Chemical Engineering, University of Edinburgh, Edinburgh EH9 3JL, United Kingdom Abstract. In preliminary design, the space of design alternatives can be large. Automated synthesis tools may be used interactively to explore the design space, starting with a broad but coarse search and gradually progressing to more focussed and detailed searches. Recent developments in the search procedure used by the cHiPs process synthesis package enable the generation of partial solutions, solutions which although not feasible can be useful in the analysis of the synthesis problem. This enables one to use the tool as a device for exploration and experimentation. Furthermore, it provides a framework upon which the synthesis procedure can be expanded to provide automatic techniques for identifying suitable recycle structures. This paper briefly describes the approach for generating partial solutions. It demonstrates the use of the resulting tool in preliminary design through the presentation of a case study for the design of a Hydrofluoric acid plant, showing how the synthesis tool can be applied iteratively. The result is a process flowsheet suitable for more rigorous study.
considering reactor conversions in the range of 90% to 99% in steps of 3%. The results from such a run will help Preliminary design is characterised by the use of shortidentify the general location of the optimum. Subsequent cut models and simplified analysis. The goal is to quickly runs use a finer discretisation over a narrower range (e.g. reduce the, potentially large, space of design alternatives reactor conversion of 98.5% to 99.0% in steps of 0.1%). to a small set of candidate designs which merit more deIn this way the design space can be explored systematitailed attention. However, even with shortcut models, it is cally without encountering problems with computing reoften difficult to explore the full design space manually. source limitations. Alternatively, to employ a rigorous automated synthesis procedure over the full design space may not be possible SYNTHESIS OF PARTIAL SOLUTIONS due to computing resource limitations. It may also be difINTRODUCTION
ficult to ascertain a suitable superstructure without a pr/or/knowledge of the appropriate process flowsheets. In this paper we present a case study that demonstrates how an automated synthesis tool, such as CHIPS (Fraga and McKinnon, 1994), can be used effectively in preliminary design. The CHIPS synthesis package is used with shortcut models to interactively explore the design space in a systematic fashion. CHIPS uses an iterative dynamic programming (IDP) algorithm to search a discretised space of design alternatives. The engineer can control this search by specifying the discretisations employed. The result of the search is a set of designs, each of which consists of a set of units and their design parameters along with the interconnections between the units, including recycle streams. Unlike many other synthesis procedures, the search procedure is able to identify the N best solutions, for any value of N. Greater insight into the nature of the optimum can then be gained by inspection of the differences and commonalities between the top ranked designs. The general strategy employed when using a discrete programming based synthesis procedure is one of gradual refinement. Initially, coarse discretisations are used to explore a broad range of design alternatives. For example, *Current address: AspenTech UK Ltd, Sheraton House, Castle Park, Cambridge CB3 0AX, United Kingdom, email: laing@atuk, aspentec, com.
tAutber to whom all correspondenceshouldbe addressed. Current address: Departmentof Chemical & BiochemicalEngineering,University CollegeLondon,LondonWC1E 7JE, United Kingdom,email: e. f r a g a @ u c l , ac. uk.
The synthesis procedure implemented by the CHIPS package is based on the use of dynamic programming with implicit enumeration. The mixed integer nonlinear problem is converted to a fully discrete problem through the careful use of discretisations applied to continuous quantities such as stream flows and unit operating conditions. The result is a graph which encapsulates the set of possible solutions represented by the discretization. The resulting graph is traversed recursively using dynamic programming (DP) and branch & bound (B&8) techniques to minimize computation (Fraga, 1996a). By encoding problem definitions uniquely using strings, a hash table can be used to store problem solutions which can then be accessed later in a search (the discretisation approach leads to multiple occurrences of subproblems within the search space) (Fraga, 1996b). This combination of dynamic programming with a hash table provides an efficient search procedure which can generate a ranked list of the best N solutions for a given problem, where solutions differ in structure from each other (the structure of each solution is described by a string encoding which can be compared easily to other solutions). Recently, the ability to generate partial solutions has been added to the search procedure (Fraga, 1996c). Using a heuristic based classification system for ranking incomplete solutions, the user may be presented with solutions that do not achieve all of the targets given or are infeasible with respect to some of the constraints. The ranking system is customizable by the user and can therefore be tailored for the type of problem. One possible ranking
S53
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PSE '97-ESCAPE-7 Joint Conference
m. ,,,.. ~
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glm
~,._(? t ] j m m H
--m
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~*
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J
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I -
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Figure 1: Graphical browser for the cost table showing partial solutions
(from most desirable to least) is shown here: 1. 2. 3. 4. 5. 6.
Complete Solution found. At least one product achieved. No outputs feasible. No utilities available for processing stream. Stream is almost a valid process output. No technology available to process stream.
Each subproblem encountered in the search procedure is classified according to the hierarchy. When comparing alternative solutions for a subproblem, the hierarchy level is considered first. If solutions are in the same level, the one with the better cost/profit is chosen. If they are at different levels in the hierarchy, the one with a lower level is chosen. For each subproblem, N solutions are recorded and this set may include solutions at different levels in the hierarchy.
Furthermore, the search procedure has been extended to make use of the extra information available. Certain subproblems encountered during the search procedure may be solved iteratively, attempting to recycle unprocessed streams. This provides an automated procedure for identifying suitable, albeit not necessarily optimal, recycle structures. The underlying algorithm is described in more detail in (Fraga, 1996c). THE HF CASE STUDY
The case study considers the preliminary design of a Hydrofluoric acid (HF) plant. The definition of a synthesis problem consists of one or more feed streams, a set of process technologies (unit models) which can be used, and a list of allowable outputs for the process. The list of units may include limits on the number of occurrences of each. The outputs are described in terms of composition and flow constraints or in terms of desired physical properties (vapour pressure, for example). See (Fraga, 1996a) The use of a hierarchy and enabling the generation of for an example of an input file for the CHIPS system. "infeasible" solutions is particularly useful in the early In defining the choice of unit models to be used in the stages of design when less is understood about the process. When the search procedure terminates, the user can search procedure, the user may have a choice between browse the table of subproblems and associated partial rigorous and short-cut models. To use rigorous models solutions (Figure 1 shows the graphical interface for the would slow the synthesis execution and inhibit the user system which facilitates this procedure). With a better experimentation which we want to encourage, especially understanding of the process, and by using the system it- during the initial design stages. The emphasis therefore is eratively, tightening or loosening constraints or targets as on the use of short-cut or approximate models which can desired, the user is eventually guided to a set of feasible be solved in reasonable time. For example, the Fenske, or complete solutions to the synthesis problem. Underwood & Gilliland equations are used for distillation
$55
PSE '97-ESCAPE-7 Joint Conference column design and the Kremser equation is used for absorber design (Coulson and Richardson, 1985). The Appendix describes the unit models in more detail. Simple physical property models are used.
Vapour ? Effluent
1 Flu°rspar--~-~----~-
] D1]
HF
I
Table 1: Material costs Material
CaF2 H2S04
H2S207 HF
Solid
Value $/kmol
Effl?uent
I
7.0 4.5 9.2 18.0
I
Excess
H2SO4
Figure 2: Best process generated initially. The feed for the process is 100 kmol/hr of Fluorspar (composition: 94% CaF2, 2% CaC03, and 4% Si02) and the specification for the Hydrofluoric acid product is that it be _> 98% HF. The material costs used are shown (the HF stream) along with three or more other streams. The streams noted above as waste (solid and light inerts) in Table 1. are separated into constituent components in the extreme case. As all the solutions generate the same valid product Initial Design stream, the best ranked solution is the one with the least Normally for synthesis we require specifications for all number of distillation columns (lowest cost). the acceptable or desired products. At the start of design, while we can define specifications for the main product, ~- Vapoureffluent defining acceptable byproducts and waste streams is difH SO4 Makeup ficult without some preliminary design work. However, as described above, the CHIPS synthesis package is able --I~ HF to generate partial solutions to a synthesis problem. A Fluorspar partial solution is a process which has output streams that " ' - ~ ' ( ~ " ~ ' 1 Reactor
]
~
I------~-
do not match any specified products and for which no further (profitable) downstream processing could be found to convert them to products. For the first synthesis run this feature is used to identify potential waste or byproduct streams. At the early design stages, it is useful to explore a broad range of alternatives while keeping the computation time reasonably short. A coarse discretisation of the stream flows and unit design parameters is used to achieve this. The only product specification given is that for the primary product, Hydrofluoric acid. As this run is only generating partial solutions, the costings are not as important as identifying a range of design alternatives, associated products, and the list of streams which could not be processed.
i
Solid
Effluent
] Excess
H2SO4
Figure 3: First complete process flowsheet, including automatically identified recycle streams (profit=
8.77M$/yr).
A ranked list of five solutions was requested from the synthesis tool. The flowsheet for the top ranked solution is shown in figure 2. In addition to the principle product, Hydrofluoric acid, three streams which can be processed no further are identified (marked by a '?' in the figure). Two of these streams can be considered to be waste streams, one of solids and one of light inerts. The remaining stream contains Sulphuric acid which is a primary reactant in the process and therefore a candidate for recycling.
From this analysis we can be reasonably satisfied that the only additional product specifications required are those for the two waste streams. We do not want a Sulphuric acid product and would ideally expect such an output stream to be identified as a candidate for recycling. Adding the waste product specifications to the input for synthesis, the problem is solved again, this time with the automatic recycle mode in CHIPS enabled. The automatic recycle mode makes use of the extra information collected for each subproblem, identifying subproblems that could not be solved feasibly and which may be suitable for recycling.
The rest of the alternatives show similar structures in that the feed is processed by the reactor and the output of the reactor is separated using a series of distillation columns. The number of such columns differs in each of the alternatives: each has one valid output
The top ranked solution is shown in figure 3 As expected, the Sulphuric acid byproduct is identified as a suitable recycle stream and is in fact recycled to the reactor. This solution is the first "complete" solution and therefore we have an estimate of the profit.
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PSE '97-ESCAPE-7 Joint Conference
Vapour effluent
D2
H2SO4 Makeup FIuorspar Reactor
Solid Effluent
I
-----~
I
HF
t
HF'
D1 vl
®
'
A I
I D3
I
I
94
.F
Excess H2SO4 Figure 4: Process flowsheet generated using finer discretisation (profit= 8.26M$/yr).
Focusing on a Finer Discretisation The solutions generated in the previous run used a coarse discretisation. This is useful for exploring a broad range of alternatives. Having identified the general area of the search space in which we think a suitable optimum may lie, we can narrow the ranges for design variables and use a finer discretisation for a more detailed analysis.
profit.
Experimenting with Product Specifications
In the previous solution, column D4 only recovers a small amount of Hydrofluoric acid from the recycle stream. It is possible that it would be more economic not to perform this separation and to recycle the Hydrofluoric acid with the Sulphuric acid. To test this a lower limit Moving to finer discretisations allows us to consider is set on the flowrate for an H F product stream to force new aspects of the design. For example, for the H F study, small product flows to be recycled. we must take into account environmental constraints on It is known that the H F process described in the BUSS the vapour effluent: the proportion of Hydrofluoric acid in this stream must be small. In the previous solutions this patent (Buss, 1967) in fact uses an absorber as part of the does not appear to be a problem but the coarse discreti- separation process. The stripping solvent for this absorber sation used means that small yet important flows could is cold Sulphuric acid which is recycled to the reactor. In have been masked. To validate that the process will sat- all the previous solutions, the only separation unit present isfy the environmentalconstraint, a finer discretisation of has been distillation. However, figure 5 shows a process the flowrates is required. However, the size of the search that is substantiallydifferent from the ones in the previous space increases. To counterbalance this increase, the figures: an absorber is indeed present. Having removed ranges for some unit design parameters are correspond- the possibility of small H F product streams, the search ingly reduced. For example, in the initial runs, the kiln procedure now identifies that using an absorber instead of model is given five alternative conversions to try ranging one or more distillation columns is a better approach. from 95% to 99%. The optimal design uses a kiln with a conversion of 99%. For the new run the number of alter- Design information for final process native conversion is reduced to three centered around the The final process, shown in figure 5, consists of four previous optimum of 99%. main units with design information shown in Table 2. In figure 4, the top ranked solution using the finer discretisations is shown. It can be seen that additional sep- Performance issues The experiments discussed above were all performed arators are needed to meet the constraint on vapour effluent composition with a resulting reduction in the expected on a Pentium Pro 200 MHz computer with 64 MB of
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H2SO4 Makeup
Fluorspar ~
H2SO4 Makeup
I
Reactor
D1
Solid Effluent
~ "
Vapour effluent
.~ HF
HF+ H2SO4
I
D2
1
(~ •
I Excess H2SO4
Figure 5: Process flowsheet generated using zero H2S04 cost during search procedure (profit= 8.28M$/yr).
Table 2: Design information Unit Kiln
D1
D2
Parameters Volume 1246 m 3 Height 41 m Diameter 6 m Reflux Ratio 0.5 Nstages 15 Height 13.7 m Diameter 0.7 m Reflux Ratio 0.02 Nstages 15 Height 13.7 m Diameter 0.9 m
Nstages Absorber
Height Diameter
1 0.6 0.1
m m
memory running the Linux operating system, version 2.0.18. Table 3 shows the cpu time and memory requirements for each of the problems (identified by the figure number). The requirements are minimal (in terms of memory) and the amount of time is such that the user is encouraged to experiment. In later stages of design, there is scope for increasing the rigour of the models used within the synthesis procedure. On the order of 1000 unit model designs are performed in the largest problem presented here. Table 3: CPU and memory use Attempt 1 2 3 4
CPU time(s) 4.3 7.0 4.6 7.8
Memory(kB) 7900 9656 7440 9492
CONCLUSIONS At the preliminary design stage there can be a large number of potential design alternatives. Using an automated synthesis tool interactively and iteratively allows an engineer to direct the search and provides the initiative to experiment. The space of design alternatives can then be explored in a more systematic manner starting with a broad but coarse search, gradually refining and focusing in on particular alternatives. Including the possibility of generating partial solutions means that less decisions have to be made a priori, reducing the possibilities of misdirected searches leading to misinformed designs. The use of a cost table enables the
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PSE '97-ESCAPE-7 Joint Conference
user of the synthesis tool to browse the solutions to any The Kiln Reactor of the subproblems encountered during the search proThree parallel reactions are modelled for the kiln reaccedure. This can lead to a better understanding of the tor: choices available and the reasons for the specific choices made by the synthesis tool, promoting confidence in the results when appropriate.
CaF2 + H2S04
-4
2HF + CaS04 + 1-120
Although the approach may not lead to the global opCaCO3 + H2S04 ~ C02 + 1-120 + CaS04 timum, the insight achieved at this early stage of design Si02 + 4HF --+ SiF4 + 21-120 may prove to be invaluable for the later stages. The use of short-cut unit models and non-rigorous physical properties, as in this case study, make optimality a secondary The extent of first reaction is determined from a speciissue. Synthesis is used as a coarse sieve for the gener- fied conversion on the limiting reactant (normally CaF2). ation of good starting points for the rest of the, probably The other reactions are assumed to go to full conversion more rigorous, design process. of their limiting reactants (normally CaCOs & Si02 reAcknowledgements. This work was supported by spectively). The kiln has two product streams, a solids the Engineering and Physical Sciences Council of the stream consisting primarily of CaS04, and a gas stream United Kingdom (EPSRC grant numbers GR/K51594 & which includes the H F and any unreacted H2S04. An B/95/AF/2011) and E. I. du Pont de Nemours and Com- air intake is also included introducing more light inerts pany. The authors would also like to thank Professor J. W. (02, N2, and C02) into the vapour product. Ponton for his input.
The following correlation is used to determine the required residence time (Candido and Mathur, 1974): REFERENCES
V = F X(t)dt (1) Buss AG, 1967, Process for the Continuous Production of Hydrofluoric Acid, Patent 1216270 ( UK). dX k T r2(r~ - X)2(1 - X ) N Candido, D. and Mathur, G. P., 1974, An investigation d-? = () (2) into the kinetics of Reaction between Fluorspar and Sulphuric Acid, Ind. Eng. Chem. Proc. Des. Dev, 13, 20. k(T) = k 4 ~ o e x p ( E ( £ 1)) (3) Coulson, J.M., and Richardson, J. E, 1985, Chemical Engineering - Volume 2, Pergamon Press, Third Edition. Fraga, E. S., 1996a, The automated synthesis of comwhere V = reactor volume plex reaction/separation processes using dynamic proF = reactor feed rate gramming, Chem. Eng. Res. and Des., 74, 249-260. X ! = final conversion of CaF2, Fraga, E. S., 1996b, Discrete Optimization using String rc = mole of CaF2 per mole of Ca Encodings for the Synthesis of Complete Chemical Proin fluorspar feed. cesses, in State of the Art in Global Optimization: Comr~ = acid:spar ratio putational Methods & Applications, C A Floudas & P M k = rate constant Pardalos, Editors, 627-651. kas0, E, N, M = rate model constants Fraga, E. S. 1996c, The Use of Partial Solutions in Auto- The values for k45o, E, N, and M used are mated Process Synthesis, ECOSSE Technical Report, TRk45o = 0.247 1996-08, Department of Chemical Engineering, University of Edinburgh. E = 38263 2 Fraga, E. S. and McKinnon, K. I. M., 1994, CHIPS: A N --Process Synthesis Package, Chem. Eng. Res. and Des. 3 1 72, 389-394. U = Rathore, R. N. S., van Wormer., K. A. and Powers, G. 3 J., 1974, Synthesis Strategies for Multicomponent SepThe equipment costing uses the same correlation as the aration Systems with Energy Integration, AIChE J., 20, standard reactor model; the cost correlations for cHiPS 491-502. are taken from Rathore et al (1974). APPENDIX: UNIT MODELS The standard models available with CHIPS were not sufficient for this case study. Three new unit models were added:
Hydrofluoric Acid Absorption Column
The solvent used for this column is concentrated sulphuric acid which is introduced as a makeup stream. The model performs a simple mass balance based on specifications for recovery of H F to the acid stream and the Acid Blender ratio of acid to feed flowrates. The theoretical number of The acid blender model was written to handle the ex- stages is determined using the Kremser equation (Coulson pected recycle of sulphuric acid. Its basic function was to and Richardson, 1985). The column is then costed using ensure that its output had the correct ratio of 1-12804 to a similar correlation to the standard distillation model in CaF2. An oleum makeup (100% H2SzOr) is also intro- CHIPS. duced to eliminate water from the output stream.
Pergamon PII:SO098-1354(97)00025-2
0098-1354/97 $17.00+0.00
A Case Study on Synthesis in Preliminary Design D. Murray Laing* Eric S. Fraga t Department of Chemical Engineering, University of Edinburgh, Edinburgh EH9 3JL, United Kingdom Abstract. In preliminary design, the space of design alternatives can be large. Automated synthesis tools may be used interactively to explore the design space, starting with a broad but coarse search and gradually progressing to more focussed and detailed searches. Recent developments in the search procedure used by the cHiPs process synthesis package enable the generation of partial solutions, solutions which although not feasible can be useful in the analysis of the synthesis problem. This enables one to use the tool as a device for exploration and experimentation. Furthermore, it provides a framework upon which the synthesis procedure can be expanded to provide automatic techniques for identifying suitable recycle structures. This paper briefly describes the approach for generating partial solutions. It demonstrates the use of the resulting tool in preliminary design through the presentation of a case study for the design of a Hydrofluoric acid plant, showing how the synthesis tool can be applied iteratively. The result is a process flowsheet suitable for more rigorous study.
considering reactor conversions in the range of 90% to 99% in steps of 3%. The results from such a run will help Preliminary design is characterised by the use of shortidentify the general location of the optimum. Subsequent cut models and simplified analysis. The goal is to quickly runs use a finer discretisation over a narrower range (e.g. reduce the, potentially large, space of design alternatives reactor conversion of 98.5% to 99.0% in steps of 0.1%). to a small set of candidate designs which merit more deIn this way the design space can be explored systematitailed attention. However, even with shortcut models, it is cally without encountering problems with computing reoften difficult to explore the full design space manually. source limitations. Alternatively, to employ a rigorous automated synthesis procedure over the full design space may not be possible SYNTHESIS OF PARTIAL SOLUTIONS due to computing resource limitations. It may also be difINTRODUCTION
ficult to ascertain a suitable superstructure without a pr/or/knowledge of the appropriate process flowsheets. In this paper we present a case study that demonstrates how an automated synthesis tool, such as CHIPS (Fraga and McKinnon, 1994), can be used effectively in preliminary design. The CHIPS synthesis package is used with shortcut models to interactively explore the design space in a systematic fashion. CHIPS uses an iterative dynamic programming (IDP) algorithm to search a discretised space of design alternatives. The engineer can control this search by specifying the discretisations employed. The result of the search is a set of designs, each of which consists of a set of units and their design parameters along with the interconnections between the units, including recycle streams. Unlike many other synthesis procedures, the search procedure is able to identify the N best solutions, for any value of N. Greater insight into the nature of the optimum can then be gained by inspection of the differences and commonalities between the top ranked designs. The general strategy employed when using a discrete programming based synthesis procedure is one of gradual refinement. Initially, coarse discretisations are used to explore a broad range of design alternatives. For example, *Current address: AspenTech UK Ltd, Sheraton House, Castle Park, Cambridge CB3 0AX, United Kingdom, email: laing@atuk, aspentec, com.
tAutber to whom all correspondenceshouldbe addressed. Current address: Departmentof Chemical & BiochemicalEngineering,University CollegeLondon,LondonWC1E 7JE, United Kingdom,email: e. f r a g a @ u c l , ac. uk.
The synthesis procedure implemented by the CHIPS package is based on the use of dynamic programming with implicit enumeration. The mixed integer nonlinear problem is converted to a fully discrete problem through the careful use of discretisations applied to continuous quantities such as stream flows and unit operating conditions. The result is a graph which encapsulates the set of possible solutions represented by the discretization. The resulting graph is traversed recursively using dynamic programming (DP) and branch & bound (B&8) techniques to minimize computation (Fraga, 1996a). By encoding problem definitions uniquely using strings, a hash table can be used to store problem solutions which can then be accessed later in a search (the discretisation approach leads to multiple occurrences of subproblems within the search space) (Fraga, 1996b). This combination of dynamic programming with a hash table provides an efficient search procedure which can generate a ranked list of the best N solutions for a given problem, where solutions differ in structure from each other (the structure of each solution is described by a string encoding which can be compared easily to other solutions). Recently, the ability to generate partial solutions has been added to the search procedure (Fraga, 1996c). Using a heuristic based classification system for ranking incomplete solutions, the user may be presented with solutions that do not achieve all of the targets given or are infeasible with respect to some of the constraints. The ranking system is customizable by the user and can therefore be tailored for the type of problem. One possible ranking
S53
$54
PSE '97-ESCAPE-7 Joint Conference
m. ,,,.. ~
• m,...,-.
glm
~,._(? t ] j m m H
--m
ol.bm
~*
t
J
al lr k d Bs',.
I -
!
0 I,l
"•
Rosourcos ~ - - - - ~ 1
]
J ,m t~l.
B pt ; J t . l , . jw ' P
Jt. r.,, I. wr
| , l ] q II I.qT! P
~ s 4 ke I
Figure 1: Graphical browser for the cost table showing partial solutions
(from most desirable to least) is shown here: 1. 2. 3. 4. 5. 6.
Complete Solution found. At least one product achieved. No outputs feasible. No utilities available for processing stream. Stream is almost a valid process output. No technology available to process stream.
Each subproblem encountered in the search procedure is classified according to the hierarchy. When comparing alternative solutions for a subproblem, the hierarchy level is considered first. If solutions are in the same level, the one with the better cost/profit is chosen. If they are at different levels in the hierarchy, the one with a lower level is chosen. For each subproblem, N solutions are recorded and this set may include solutions at different levels in the hierarchy.
Furthermore, the search procedure has been extended to make use of the extra information available. Certain subproblems encountered during the search procedure may be solved iteratively, attempting to recycle unprocessed streams. This provides an automated procedure for identifying suitable, albeit not necessarily optimal, recycle structures. The underlying algorithm is described in more detail in (Fraga, 1996c). THE HF CASE STUDY
The case study considers the preliminary design of a Hydrofluoric acid (HF) plant. The definition of a synthesis problem consists of one or more feed streams, a set of process technologies (unit models) which can be used, and a list of allowable outputs for the process. The list of units may include limits on the number of occurrences of each. The outputs are described in terms of composition and flow constraints or in terms of desired physical properties (vapour pressure, for example). See (Fraga, 1996a) The use of a hierarchy and enabling the generation of for an example of an input file for the CHIPS system. "infeasible" solutions is particularly useful in the early In defining the choice of unit models to be used in the stages of design when less is understood about the process. When the search procedure terminates, the user can search procedure, the user may have a choice between browse the table of subproblems and associated partial rigorous and short-cut models. To use rigorous models solutions (Figure 1 shows the graphical interface for the would slow the synthesis execution and inhibit the user system which facilitates this procedure). With a better experimentation which we want to encourage, especially understanding of the process, and by using the system it- during the initial design stages. The emphasis therefore is eratively, tightening or loosening constraints or targets as on the use of short-cut or approximate models which can desired, the user is eventually guided to a set of feasible be solved in reasonable time. For example, the Fenske, or complete solutions to the synthesis problem. Underwood & Gilliland equations are used for distillation
$55
PSE '97-ESCAPE-7 Joint Conference column design and the Kremser equation is used for absorber design (Coulson and Richardson, 1985). The Appendix describes the unit models in more detail. Simple physical property models are used.
Vapour ? Effluent
1 Flu°rspar--~-~----~-
] D1]
HF
I
Table 1: Material costs Material
CaF2 H2S04
H2S207 HF
Solid
Value $/kmol
Effl?uent
I
7.0 4.5 9.2 18.0
I
Excess
H2SO4
Figure 2: Best process generated initially. The feed for the process is 100 kmol/hr of Fluorspar (composition: 94% CaF2, 2% CaC03, and 4% Si02) and the specification for the Hydrofluoric acid product is that it be _> 98% HF. The material costs used are shown (the HF stream) along with three or more other streams. The streams noted above as waste (solid and light inerts) in Table 1. are separated into constituent components in the extreme case. As all the solutions generate the same valid product Initial Design stream, the best ranked solution is the one with the least Normally for synthesis we require specifications for all number of distillation columns (lowest cost). the acceptable or desired products. At the start of design, while we can define specifications for the main product, ~- Vapoureffluent defining acceptable byproducts and waste streams is difH SO4 Makeup ficult without some preliminary design work. However, as described above, the CHIPS synthesis package is able --I~ HF to generate partial solutions to a synthesis problem. A Fluorspar partial solution is a process which has output streams that " ' - ~ ' ( ~ " ~ ' 1 Reactor
]
~
I------~-
do not match any specified products and for which no further (profitable) downstream processing could be found to convert them to products. For the first synthesis run this feature is used to identify potential waste or byproduct streams. At the early design stages, it is useful to explore a broad range of alternatives while keeping the computation time reasonably short. A coarse discretisation of the stream flows and unit design parameters is used to achieve this. The only product specification given is that for the primary product, Hydrofluoric acid. As this run is only generating partial solutions, the costings are not as important as identifying a range of design alternatives, associated products, and the list of streams which could not be processed.
i
Solid
Effluent
] Excess
H2SO4
Figure 3: First complete process flowsheet, including automatically identified recycle streams (profit=
8.77M$/yr).
A ranked list of five solutions was requested from the synthesis tool. The flowsheet for the top ranked solution is shown in figure 2. In addition to the principle product, Hydrofluoric acid, three streams which can be processed no further are identified (marked by a '?' in the figure). Two of these streams can be considered to be waste streams, one of solids and one of light inerts. The remaining stream contains Sulphuric acid which is a primary reactant in the process and therefore a candidate for recycling.
From this analysis we can be reasonably satisfied that the only additional product specifications required are those for the two waste streams. We do not want a Sulphuric acid product and would ideally expect such an output stream to be identified as a candidate for recycling. Adding the waste product specifications to the input for synthesis, the problem is solved again, this time with the automatic recycle mode in CHIPS enabled. The automatic recycle mode makes use of the extra information collected for each subproblem, identifying subproblems that could not be solved feasibly and which may be suitable for recycling.
The rest of the alternatives show similar structures in that the feed is processed by the reactor and the output of the reactor is separated using a series of distillation columns. The number of such columns differs in each of the alternatives: each has one valid output
The top ranked solution is shown in figure 3 As expected, the Sulphuric acid byproduct is identified as a suitable recycle stream and is in fact recycled to the reactor. This solution is the first "complete" solution and therefore we have an estimate of the profit.
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PSE '97-ESCAPE-7 Joint Conference
Vapour effluent
D2
H2SO4 Makeup FIuorspar Reactor
Solid Effluent
I
-----~
I
HF
t
HF'
D1 vl
®
'
A I
I D3
I
I
94
.F
Excess H2SO4 Figure 4: Process flowsheet generated using finer discretisation (profit= 8.26M$/yr).
Focusing on a Finer Discretisation The solutions generated in the previous run used a coarse discretisation. This is useful for exploring a broad range of alternatives. Having identified the general area of the search space in which we think a suitable optimum may lie, we can narrow the ranges for design variables and use a finer discretisation for a more detailed analysis.
profit.
Experimenting with Product Specifications
In the previous solution, column D4 only recovers a small amount of Hydrofluoric acid from the recycle stream. It is possible that it would be more economic not to perform this separation and to recycle the Hydrofluoric acid with the Sulphuric acid. To test this a lower limit Moving to finer discretisations allows us to consider is set on the flowrate for an H F product stream to force new aspects of the design. For example, for the H F study, small product flows to be recycled. we must take into account environmental constraints on It is known that the H F process described in the BUSS the vapour effluent: the proportion of Hydrofluoric acid in this stream must be small. In the previous solutions this patent (Buss, 1967) in fact uses an absorber as part of the does not appear to be a problem but the coarse discreti- separation process. The stripping solvent for this absorber sation used means that small yet important flows could is cold Sulphuric acid which is recycled to the reactor. In have been masked. To validate that the process will sat- all the previous solutions, the only separation unit present isfy the environmentalconstraint, a finer discretisation of has been distillation. However, figure 5 shows a process the flowrates is required. However, the size of the search that is substantiallydifferent from the ones in the previous space increases. To counterbalance this increase, the figures: an absorber is indeed present. Having removed ranges for some unit design parameters are correspond- the possibility of small H F product streams, the search ingly reduced. For example, in the initial runs, the kiln procedure now identifies that using an absorber instead of model is given five alternative conversions to try ranging one or more distillation columns is a better approach. from 95% to 99%. The optimal design uses a kiln with a conversion of 99%. For the new run the number of alter- Design information for final process native conversion is reduced to three centered around the The final process, shown in figure 5, consists of four previous optimum of 99%. main units with design information shown in Table 2. In figure 4, the top ranked solution using the finer discretisations is shown. It can be seen that additional sep- Performance issues The experiments discussed above were all performed arators are needed to meet the constraint on vapour effluent composition with a resulting reduction in the expected on a Pentium Pro 200 MHz computer with 64 MB of
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PSE '97-ESCAPE-7 Joint Conference
H2SO4 Makeup
Fluorspar ~
H2SO4 Makeup
I
Reactor
D1
Solid Effluent
~ "
Vapour effluent
.~ HF
HF+ H2SO4
I
D2
1
(~ •
I Excess H2SO4
Figure 5: Process flowsheet generated using zero H2S04 cost during search procedure (profit= 8.28M$/yr).
Table 2: Design information Unit Kiln
D1
D2
Parameters Volume 1246 m 3 Height 41 m Diameter 6 m Reflux Ratio 0.5 Nstages 15 Height 13.7 m Diameter 0.7 m Reflux Ratio 0.02 Nstages 15 Height 13.7 m Diameter 0.9 m
Nstages Absorber
Height Diameter
1 0.6 0.1
m m
memory running the Linux operating system, version 2.0.18. Table 3 shows the cpu time and memory requirements for each of the problems (identified by the figure number). The requirements are minimal (in terms of memory) and the amount of time is such that the user is encouraged to experiment. In later stages of design, there is scope for increasing the rigour of the models used within the synthesis procedure. On the order of 1000 unit model designs are performed in the largest problem presented here. Table 3: CPU and memory use Attempt 1 2 3 4
CPU time(s) 4.3 7.0 4.6 7.8
Memory(kB) 7900 9656 7440 9492
CONCLUSIONS At the preliminary design stage there can be a large number of potential design alternatives. Using an automated synthesis tool interactively and iteratively allows an engineer to direct the search and provides the initiative to experiment. The space of design alternatives can then be explored in a more systematic manner starting with a broad but coarse search, gradually refining and focusing in on particular alternatives. Including the possibility of generating partial solutions means that less decisions have to be made a priori, reducing the possibilities of misdirected searches leading to misinformed designs. The use of a cost table enables the
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PSE '97-ESCAPE-7 Joint Conference
user of the synthesis tool to browse the solutions to any The Kiln Reactor of the subproblems encountered during the search proThree parallel reactions are modelled for the kiln reaccedure. This can lead to a better understanding of the tor: choices available and the reasons for the specific choices made by the synthesis tool, promoting confidence in the results when appropriate.
CaF2 + H2S04
-4
2HF + CaS04 + 1-120
Although the approach may not lead to the global opCaCO3 + H2S04 ~ C02 + 1-120 + CaS04 timum, the insight achieved at this early stage of design Si02 + 4HF --+ SiF4 + 21-120 may prove to be invaluable for the later stages. The use of short-cut unit models and non-rigorous physical properties, as in this case study, make optimality a secondary The extent of first reaction is determined from a speciissue. Synthesis is used as a coarse sieve for the gener- fied conversion on the limiting reactant (normally CaF2). ation of good starting points for the rest of the, probably The other reactions are assumed to go to full conversion more rigorous, design process. of their limiting reactants (normally CaCOs & Si02 reAcknowledgements. This work was supported by spectively). The kiln has two product streams, a solids the Engineering and Physical Sciences Council of the stream consisting primarily of CaS04, and a gas stream United Kingdom (EPSRC grant numbers GR/K51594 & which includes the H F and any unreacted H2S04. An B/95/AF/2011) and E. I. du Pont de Nemours and Com- air intake is also included introducing more light inerts pany. The authors would also like to thank Professor J. W. (02, N2, and C02) into the vapour product. Ponton for his input.
The following correlation is used to determine the required residence time (Candido and Mathur, 1974): REFERENCES
V = F X(t)dt (1) Buss AG, 1967, Process for the Continuous Production of Hydrofluoric Acid, Patent 1216270 ( UK). dX k T r2(r~ - X)2(1 - X ) N Candido, D. and Mathur, G. P., 1974, An investigation d-? = () (2) into the kinetics of Reaction between Fluorspar and Sulphuric Acid, Ind. Eng. Chem. Proc. Des. Dev, 13, 20. k(T) = k 4 ~ o e x p ( E ( £ 1)) (3) Coulson, J.M., and Richardson, J. E, 1985, Chemical Engineering - Volume 2, Pergamon Press, Third Edition. Fraga, E. S., 1996a, The automated synthesis of comwhere V = reactor volume plex reaction/separation processes using dynamic proF = reactor feed rate gramming, Chem. Eng. Res. and Des., 74, 249-260. X ! = final conversion of CaF2, Fraga, E. S., 1996b, Discrete Optimization using String rc = mole of CaF2 per mole of Ca Encodings for the Synthesis of Complete Chemical Proin fluorspar feed. cesses, in State of the Art in Global Optimization: Comr~ = acid:spar ratio putational Methods & Applications, C A Floudas & P M k = rate constant Pardalos, Editors, 627-651. kas0, E, N, M = rate model constants Fraga, E. S. 1996c, The Use of Partial Solutions in Auto- The values for k45o, E, N, and M used are mated Process Synthesis, ECOSSE Technical Report, TRk45o = 0.247 1996-08, Department of Chemical Engineering, University of Edinburgh. E = 38263 2 Fraga, E. S. and McKinnon, K. I. M., 1994, CHIPS: A N --Process Synthesis Package, Chem. Eng. Res. and Des. 3 1 72, 389-394. U = Rathore, R. N. S., van Wormer., K. A. and Powers, G. 3 J., 1974, Synthesis Strategies for Multicomponent SepThe equipment costing uses the same correlation as the aration Systems with Energy Integration, AIChE J., 20, standard reactor model; the cost correlations for cHiPS 491-502. are taken from Rathore et al (1974). APPENDIX: UNIT MODELS The standard models available with CHIPS were not sufficient for this case study. Three new unit models were added:
Hydrofluoric Acid Absorption Column
The solvent used for this column is concentrated sulphuric acid which is introduced as a makeup stream. The model performs a simple mass balance based on specifications for recovery of H F to the acid stream and the Acid Blender ratio of acid to feed flowrates. The theoretical number of The acid blender model was written to handle the ex- stages is determined using the Kremser equation (Coulson pected recycle of sulphuric acid. Its basic function was to and Richardson, 1985). The column is then costed using ensure that its output had the correct ratio of 1-12804 to a similar correlation to the standard distillation model in CaF2. An oleum makeup (100% H2SzOr) is also intro- CHIPS. duced to eliminate water from the output stream.