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A novel superstructure and optimisation scheme for the synthesis of reaction-separation processes
European Symposium on Computer Aided Process Engineering - 10 S. Pierucci (Editor) 9 2000 Elsevier Science B.V. All rights reserved.
i165
A Novel S u p e r s t r u c t u r e and O p t i m i s a t i o n S c h e m e for the S y n t h e s i s of R e a c t i o n - S e p a r a t i o n P r o c e s s e s Patrick Linke § Vipul Mehta # and Antonis Kokossis + + Department of Process Integration, University of Manchester Institute of Science and Technology, PO Box 88, Manchester, M60 1QD, United Kingdom # Bayer AG, Corporate Technology, ZT-TE 7.1, 51368 Leverkusen, Germany A design tool is presented that allows simultaneous consideration of reaction and separation in isothermal and non-isothermal multiphase systems. The approach incorporates previous achievements in the area of multiphase reactor network synthesis with the representation being described in form of a superstructure of generic reactor/mass exchanger units and multi-purpose separators. The functionalities provided by the synthesis scheme are exploited by stochastic optimisation techniques. In contrast to past methods, the synthesis tool is applicable to general systems involving reaction and separation and is guided by the basic phenomena of reaction, mass transfer, and phase equilibria. Implementation of the methodology enables the development of targets and screening procedures that help the engineer to assess the system performance and review promising design options. The steps to generate the superstructure along with its modelling components are explained and two examples illustrate the efficiency of the approach. 1. INTRODUCTION Simultaneous consideration of reaction and separation in design can in many cases lead to a superior process performance. For most industrially relevant systems, the synthesis problem is characterised by a larger number of feasible design options and the models describing the phenomena are highly non-linear. Due to the complex design trade-offs, heuristics and graphical design approaches are highly likely to yield under-performing processes. Performance guarantees can be delivered by optimisation-based approaches. To date, such approaches have been proposed for special cases of the synthesis problem, including the synthesis of homogeneous, isothermal reactor-separator-recycle systems 1'2'3, the design of a reactive distillation column 4, and homogeneous reactor network synthesis considering intermediate separations 5'6. In order to address a more general synthesis problem, Papalexandri and Pistikopoulos v suggested the use of generic heat/mass exchange units to generate superstructures that are subsequently formulated as MINLPs. However, their representation of the reactor units poses a severe limitation to the approach if applied to multiphase reacting and reactive separation systems, as common mixing patterns cannot be represented by the units or combinations of these. Moreover, previous approaches make use of deterministic optimisation techniques and are hence severely limited by the nonconvexities in the mathematical formulations.
1166 A compact representation for multiphase reaction systems has been developed by Mehta and Kokossis 8'9 that allows to simultaneously address all possible mixing and contacting patterns between streams of different phases as well as temperature policies. The network superstructures are synthesised using a robust stochastic optimisation framework. Following this philosophy, a targeting and design tool for general reaction-separation systems is developed, which is not restricted to conventional process configurations but additionally facilitates all possible novel design options embedded in the network superstructures. 2. S Y S T E M R E P R E S E N T A T I O N The proposed system representation accounts for multiphase reaction and separation operations by introducing (i) generic multiphase reactor / mass exchanger units and (ii) multi-purpose separator units. The multiphase reactor / mass exchanger unit builds upon the compact representation of multiphase reactors introduced by Mehta and Kokossis a. It can either take the functionality of a reactor, a mass exchanger, or a combined reactor/mass exchanger unit by introducing decision variables indicating the existence of diffusional links between the different phases and reactions. If representing a reactor, one such unit consists of a homogeneous reactor compartment per phase present in the system. A reactor compartment of one phase exchanges mass via diffusional links with reactor compartments belonging to the same generic reactor unit but to a different phase. Temperature effects are incorporated by imposing temperature profiles on the reactor compartments or through a unit-based representation with all possible intermediate direct and indirect heat exchange 9. Mass exchanger units are realised by not considering reaction inside the compartments. By default, the mass exchanger units are modelled using a rate-based approach. As for the reactor units, all different mixing and contacting patterns can be realised by a single mass exchanger unit, e.g. for the case of a membrane unit, a single mass exchanger can represent well-mixed, co- and counter-current units as well as cross flow. Equilibrium based models such as equilibrium stages can easily be adopted for the mass exchangers. The mass transfer links between the different phases can be established or deactivated. For two-phase systems, this allows to account not only for multiphase reactors but also for homogeneous reactors to be present in the network. If more phases are present, more combinations exist, e.g. for the case of a gas-liquid-liquid system with one reacting liquid phase, a single multiphase unit can represent (i) a three phase reactor, (ii) a homogeneous reactor and an absorber/stripper, (iii) a reactive extraction unit, (iv) a gas-liquid reactor, or (v) an absorber/stripper. The multi-purpose separator units split existing streams of one phase into a number of streams of the same phase but of different compositions. These units allow to represent the many different unit operations that are commonly used to separate process streams into the desired products or intermediates. Additionally, by not restricting the feasibility of the separations, the units can be employed to identify the most beneficial separations and guide the choice of proper unit operations or give incentives for development of new separation technology such as solvent design. When representing unit operations, the tasks that are performed by the separator units are chosen according to the separation order of the mixture and the components present in the inlet streams. One such unit is associated with a single unit operation, e.g. distillation,
1167 crystallisation, or absorption. The individual tasks and the number of tasks performed by a unit are decision variables. If more than two tasks are performed, a single separator unit represents a sequence of simple separators featuring one feed and two products. The sequences are represented by task vectors and all different sequences can be realised by partitioning the vector. The separator units perform sharp splits between key components; however, additional degrees of freedom for the sloppiness of the splits can easily be introduced. It should be noted that the main aim here is to screen and scope beneficial interactions between reaction and separation. In this context, the sharp splits are in most cases sufficient to investigate the trade-offs present in the system. To allow comparison of design alternatives on a common basis, costs need to be associated with the separator units. Real costs can either be realised through regressed cost models or short-cut equipment sizing procedures. Approximate costs of splits between ke~ components can be calculated as a function of feed flowrates and compositions ~. Alternatively, if short-cut sizing methods such as the Underwood method for distillation design exist for a particular unit operation, these models can directly be employed in conjunction with approximate equipment cost models. The search space for the separations can alternatively be extended to include all combinatorially possible separations between the components present in the system. This allows to search for the most beneficial separations in terms of the system performance enhancement regardless of feasibility considerations. The designer can introduce biases so that separations known to be unrealistic can be excluded from the search. If the identified most beneficial separations can effectively be carried out by conventional technology, e.g. by distillation, this particular unit operation can confidently be employed for subsequent synthesis studies, associating one type of the multi-purpose separator units with the separation orders of the unit operation. Although the identified separations might not be known to be achievable by conventional technologies, they can be used to give incentives for the development of novel separation techniques such as the design of novel solvents. 3. R E A C T I O N - S E P A R A T I O N S U P E R S T R U C T U R E A superstructure of multiphase reactor/mass exchanger units and multipurpose separator units is generated featuring all novel and conventional structural alternatives that can be realised by combinations of generic units. In each phase (or state) present, a network of intraphase streams exists that realises all feasible connections between the different units employed in the representation. Convective links between different phases are established via an interphase stream network of all feasible connections between units of different phases. The interphase streams are associated with equipment used for converting the state of streams such as reboilers, condensers, pumps, compressors, throttles, or turbines. Two of the many possible designs that can be obtained from the superstructure are illustrated in Figure 1. A layout of a reactive distillation system integrated with a separation sequence is shown in Figure la. A sequential arrangement of reactors and separators is shown in Figure lb. It should be noted that the representation is not restricted to any particular system, but instead can be applied to a variety of reaction, separation or combined processes such as extraction and reaction, reactive crystallisation, and membrane networks amongst others.
1168
Fig. 1 Special cases embedded in the network superstructure
4. NETWORK OPTIMISATION The network representation outlined above is used to formulate a mathematical model that is subjected to optimisation. This model facilitates the balances for each compartment in each phase as well as all separator units, stream mixers and splitters. The equilibrium relationships, which are required to model the mass transfer links, the kinetic models as well as the general regression models for costs or hydrodynamics may result in a highly nonlinear model. Optimisation variables include the component flows, the volumes of the reactor units, the temperatures within the network, the existence of units and streams, the type of reactor units, the relative flow directions of the phases, the types and tasks of the separator units, the sharpness of the splits performed. Any expression of these variables as well as the stream compositions can be used as an objective function for the optimisation problem. Profit, annualised cost, network yield or selectivity are examples for possible objective functions. The network is optimised using stochastic optimisation techniques in the form of simulated annealing which has previously been successfully applied in homogeneous and multiphase reactor network synthesisS'9'l~
5. EXAMPLES 5.1. Multiphase Denbigh reaction system The following series/parallel reactions occur in the liquid phase of the gas-liquid system: A+F A + 2F B+F B + 2F
----, ~ --, --,
B + G; D + 2G; C + G; E + 2G;
rl
- kl
r2
-- k2 CA CFCF
CACF
r3 = k3 CA CF r4
= k4CACFCF
(1) (2) (3) (4)
Component A is fed to the liquid phase where it reacts with component F to form the desired product B and by-product D. Product B further reacts to by-products C and E. The gas feed consists of reactant F and insoluble species H. The liquid phase components A, B, C, D, and E are non-volatile, whereas the solubility of by-product G is low. A multiphase
1169 reactor network synthesis study has been carried out for this system ll, establishing a target yield of 65%. The obtained designs feature co- and counter-current PFRs and a complex network of high flowrate recycle streams in the gas phase. The yield of the system is optimised allowing any combinatorially possible separation to be performed in (i) the gas phase only and (ii) in both phases present. In the former case, an improvement in terms of the performance target can not be observed for this system as compared to the results from the reactor network optimisation. The optimal separations aim at low concentrations of reactant F inside the reactor modules. However, the same effect is achieved via the excessive recycle flowrates observed in the reactor design study. In terms of structural complexity, less reactor units are generally observed when separators are present in the gas phase and the recycle flowrates are significantly reduced. As in the reactor design study, the reactor units consist of co- and/or counter-current PFRs. A significantly better system performance is observed when separators are additionally considered in the liquid phase. The yield for the system is consistently found to be above 95%, i.e. almost complete conversion of reactant A into the desired product. A typical design that achieves the target is shown in figure 2. Separations in the liquid phase aim at removing the desired product B from the network and completely recycling reactant A to the reaction zones. The by-products are found to be either partly recycled or completely removed. The reaction sections feature co-current and counter-current PFR units with side streams in the gas phase. CSTRs are occasionally present but always occur in conjunction with the PFR units. The separator units in the gas phase are not observed in most designs and a number of structures do not exhibit gas recycles and separators at all. This suggests that by choosing the proper process structure in the liquid phase, the previously identified bottleneck in the gas phase vanishes.
5.2. Production of Ethylbenzene The alkylation of benzene with ethylene is investigated. Gaseous ethylene (E) reacts with liquid benzene (B) to desired product ethylbenzene (EB). Four transalkylation reactions involve production of by-products diethylbenzene (DEB) and triethylbenzene (TEB). All reactions are assumed to be of first order with respect to each reactant. The multi-purpose separator units assume the functionality of distillation (separation order: B/EB/DEB/TEB) and the profit is to be maximised for a benzene feed of 10kmol/hr. Optimisation of the homogeneous system under the assumption that the liquid phase is saturated in ethylene yielded a profit target of around $730k/yr and sequential designs featuring a reactor, a direct separation sequence, and recycles of B, EB, and TEB. Reactor designs involve PFRs and in some rare cases CSTR/PFR combinations. These structures have been identified in earlier studies of this process 2'3. However, no information is gained on the interactions between liquid and gas phase. Optimisation of the multiphase system without consideration of the inter-phase stream network yields a slightly improved profit target. The optimal designs feature reactor-separator-recycle arrangements with intermediate reactant, by-product, and off-gas recycles as well as a direct separation sequence. Reaction zones are consistently found to be counter-current PFRs. Network optimisation of the general reaction-separation superstructure including the interphase stream network yields a target profit of around $860k for this process, an increase of around 20% as compared to the previous case. Optimal designs again feature
1170
I,
<
"- Liquid feed
-~ g
,.
R1
as0 Sl
> EB EB
L
DEB
Liquid product (B)
Liquid product (ABCDE)
E > TEB
Fig. 2. Typical structure from the network optimisation for example 1
Fig. 3. Typical structure from the network optimisation for example 2
counter-current PFRs and a direct separation sequence; however, the reactor units are interconnected via intra- and inter-phase streams and show similarities with reactive distillation. A typical design is shown in figure 3. The improvements in profit stem from low component flowrates through the separation sequence with the separation of benzene being performed inside the reactor units. 6. CONCLUSIONS A general design tool for the synthesis of reaction-separation systems has been presented. The proposed network representation results in a rich and inclusive structure that embeds various mixing, phase distribution, and separation options. The stochastic optimisation scheme employed for network synthesis can handle the complexities resulting from kinetic expressions, phase equilibrium and mass transfer relationships. The proposed methodology can be used to analyse the problem trade-offs and to suggest incentives for the development of novel process structures. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
Pibouleau, L., P. Floquet, and S. Domenech, AIChE J., 1988, 34, 163. Kokossis, A.C. and C.A. Floudas, Chem. Eng. Sci., 1991, 46, 1361. Smith, E.M.B. and C.C Pantelides, Comp. Chem. Eng., 1995, 19, $83. Ciric, A.R. and D. Gu, AIChE J., 1994, 40, 1479. Balakrishna, S. and L.T. Biegler, Ind. Eng. Chem. Res., 1993, 32, 1327. Lakshmanan, A, Biegler, L.T., Ind. Eng. Chem. Res., 1996, 35, 4523. Papalexandri, K.P. and E.N. Pistikopoulos, AIChE J., 1996, 42, 1010. Mehta, V.L. and A.C. Kokossis, Comp. Chem. Eng., 1997, 21, $325. Mehta, V.L. and A.C. Kokossis, Comp. Chem. Eng., 1998, 22, S 119. Marcoulaki, E. and A.C. Kokossis, Comp. Chem. Eng., 1996, 20, $231. Mehta, V.L., Ph.D. thesis, UMIST, UK, 1998.
i165
A Novel S u p e r s t r u c t u r e and O p t i m i s a t i o n S c h e m e for the S y n t h e s i s of R e a c t i o n - S e p a r a t i o n P r o c e s s e s Patrick Linke § Vipul Mehta # and Antonis Kokossis + + Department of Process Integration, University of Manchester Institute of Science and Technology, PO Box 88, Manchester, M60 1QD, United Kingdom # Bayer AG, Corporate Technology, ZT-TE 7.1, 51368 Leverkusen, Germany A design tool is presented that allows simultaneous consideration of reaction and separation in isothermal and non-isothermal multiphase systems. The approach incorporates previous achievements in the area of multiphase reactor network synthesis with the representation being described in form of a superstructure of generic reactor/mass exchanger units and multi-purpose separators. The functionalities provided by the synthesis scheme are exploited by stochastic optimisation techniques. In contrast to past methods, the synthesis tool is applicable to general systems involving reaction and separation and is guided by the basic phenomena of reaction, mass transfer, and phase equilibria. Implementation of the methodology enables the development of targets and screening procedures that help the engineer to assess the system performance and review promising design options. The steps to generate the superstructure along with its modelling components are explained and two examples illustrate the efficiency of the approach. 1. INTRODUCTION Simultaneous consideration of reaction and separation in design can in many cases lead to a superior process performance. For most industrially relevant systems, the synthesis problem is characterised by a larger number of feasible design options and the models describing the phenomena are highly non-linear. Due to the complex design trade-offs, heuristics and graphical design approaches are highly likely to yield under-performing processes. Performance guarantees can be delivered by optimisation-based approaches. To date, such approaches have been proposed for special cases of the synthesis problem, including the synthesis of homogeneous, isothermal reactor-separator-recycle systems 1'2'3, the design of a reactive distillation column 4, and homogeneous reactor network synthesis considering intermediate separations 5'6. In order to address a more general synthesis problem, Papalexandri and Pistikopoulos v suggested the use of generic heat/mass exchange units to generate superstructures that are subsequently formulated as MINLPs. However, their representation of the reactor units poses a severe limitation to the approach if applied to multiphase reacting and reactive separation systems, as common mixing patterns cannot be represented by the units or combinations of these. Moreover, previous approaches make use of deterministic optimisation techniques and are hence severely limited by the nonconvexities in the mathematical formulations.
1166 A compact representation for multiphase reaction systems has been developed by Mehta and Kokossis 8'9 that allows to simultaneously address all possible mixing and contacting patterns between streams of different phases as well as temperature policies. The network superstructures are synthesised using a robust stochastic optimisation framework. Following this philosophy, a targeting and design tool for general reaction-separation systems is developed, which is not restricted to conventional process configurations but additionally facilitates all possible novel design options embedded in the network superstructures. 2. S Y S T E M R E P R E S E N T A T I O N The proposed system representation accounts for multiphase reaction and separation operations by introducing (i) generic multiphase reactor / mass exchanger units and (ii) multi-purpose separator units. The multiphase reactor / mass exchanger unit builds upon the compact representation of multiphase reactors introduced by Mehta and Kokossis a. It can either take the functionality of a reactor, a mass exchanger, or a combined reactor/mass exchanger unit by introducing decision variables indicating the existence of diffusional links between the different phases and reactions. If representing a reactor, one such unit consists of a homogeneous reactor compartment per phase present in the system. A reactor compartment of one phase exchanges mass via diffusional links with reactor compartments belonging to the same generic reactor unit but to a different phase. Temperature effects are incorporated by imposing temperature profiles on the reactor compartments or through a unit-based representation with all possible intermediate direct and indirect heat exchange 9. Mass exchanger units are realised by not considering reaction inside the compartments. By default, the mass exchanger units are modelled using a rate-based approach. As for the reactor units, all different mixing and contacting patterns can be realised by a single mass exchanger unit, e.g. for the case of a membrane unit, a single mass exchanger can represent well-mixed, co- and counter-current units as well as cross flow. Equilibrium based models such as equilibrium stages can easily be adopted for the mass exchangers. The mass transfer links between the different phases can be established or deactivated. For two-phase systems, this allows to account not only for multiphase reactors but also for homogeneous reactors to be present in the network. If more phases are present, more combinations exist, e.g. for the case of a gas-liquid-liquid system with one reacting liquid phase, a single multiphase unit can represent (i) a three phase reactor, (ii) a homogeneous reactor and an absorber/stripper, (iii) a reactive extraction unit, (iv) a gas-liquid reactor, or (v) an absorber/stripper. The multi-purpose separator units split existing streams of one phase into a number of streams of the same phase but of different compositions. These units allow to represent the many different unit operations that are commonly used to separate process streams into the desired products or intermediates. Additionally, by not restricting the feasibility of the separations, the units can be employed to identify the most beneficial separations and guide the choice of proper unit operations or give incentives for development of new separation technology such as solvent design. When representing unit operations, the tasks that are performed by the separator units are chosen according to the separation order of the mixture and the components present in the inlet streams. One such unit is associated with a single unit operation, e.g. distillation,
1167 crystallisation, or absorption. The individual tasks and the number of tasks performed by a unit are decision variables. If more than two tasks are performed, a single separator unit represents a sequence of simple separators featuring one feed and two products. The sequences are represented by task vectors and all different sequences can be realised by partitioning the vector. The separator units perform sharp splits between key components; however, additional degrees of freedom for the sloppiness of the splits can easily be introduced. It should be noted that the main aim here is to screen and scope beneficial interactions between reaction and separation. In this context, the sharp splits are in most cases sufficient to investigate the trade-offs present in the system. To allow comparison of design alternatives on a common basis, costs need to be associated with the separator units. Real costs can either be realised through regressed cost models or short-cut equipment sizing procedures. Approximate costs of splits between ke~ components can be calculated as a function of feed flowrates and compositions ~. Alternatively, if short-cut sizing methods such as the Underwood method for distillation design exist for a particular unit operation, these models can directly be employed in conjunction with approximate equipment cost models. The search space for the separations can alternatively be extended to include all combinatorially possible separations between the components present in the system. This allows to search for the most beneficial separations in terms of the system performance enhancement regardless of feasibility considerations. The designer can introduce biases so that separations known to be unrealistic can be excluded from the search. If the identified most beneficial separations can effectively be carried out by conventional technology, e.g. by distillation, this particular unit operation can confidently be employed for subsequent synthesis studies, associating one type of the multi-purpose separator units with the separation orders of the unit operation. Although the identified separations might not be known to be achievable by conventional technologies, they can be used to give incentives for the development of novel separation techniques such as the design of novel solvents. 3. R E A C T I O N - S E P A R A T I O N S U P E R S T R U C T U R E A superstructure of multiphase reactor/mass exchanger units and multipurpose separator units is generated featuring all novel and conventional structural alternatives that can be realised by combinations of generic units. In each phase (or state) present, a network of intraphase streams exists that realises all feasible connections between the different units employed in the representation. Convective links between different phases are established via an interphase stream network of all feasible connections between units of different phases. The interphase streams are associated with equipment used for converting the state of streams such as reboilers, condensers, pumps, compressors, throttles, or turbines. Two of the many possible designs that can be obtained from the superstructure are illustrated in Figure 1. A layout of a reactive distillation system integrated with a separation sequence is shown in Figure la. A sequential arrangement of reactors and separators is shown in Figure lb. It should be noted that the representation is not restricted to any particular system, but instead can be applied to a variety of reaction, separation or combined processes such as extraction and reaction, reactive crystallisation, and membrane networks amongst others.
1168
Fig. 1 Special cases embedded in the network superstructure
4. NETWORK OPTIMISATION The network representation outlined above is used to formulate a mathematical model that is subjected to optimisation. This model facilitates the balances for each compartment in each phase as well as all separator units, stream mixers and splitters. The equilibrium relationships, which are required to model the mass transfer links, the kinetic models as well as the general regression models for costs or hydrodynamics may result in a highly nonlinear model. Optimisation variables include the component flows, the volumes of the reactor units, the temperatures within the network, the existence of units and streams, the type of reactor units, the relative flow directions of the phases, the types and tasks of the separator units, the sharpness of the splits performed. Any expression of these variables as well as the stream compositions can be used as an objective function for the optimisation problem. Profit, annualised cost, network yield or selectivity are examples for possible objective functions. The network is optimised using stochastic optimisation techniques in the form of simulated annealing which has previously been successfully applied in homogeneous and multiphase reactor network synthesisS'9'l~
5. EXAMPLES 5.1. Multiphase Denbigh reaction system The following series/parallel reactions occur in the liquid phase of the gas-liquid system: A+F A + 2F B+F B + 2F
----, ~ --, --,
B + G; D + 2G; C + G; E + 2G;
rl
- kl
r2
-- k2 CA CFCF
CACF
r3 = k3 CA CF r4
= k4CACFCF
(1) (2) (3) (4)
Component A is fed to the liquid phase where it reacts with component F to form the desired product B and by-product D. Product B further reacts to by-products C and E. The gas feed consists of reactant F and insoluble species H. The liquid phase components A, B, C, D, and E are non-volatile, whereas the solubility of by-product G is low. A multiphase
1169 reactor network synthesis study has been carried out for this system ll, establishing a target yield of 65%. The obtained designs feature co- and counter-current PFRs and a complex network of high flowrate recycle streams in the gas phase. The yield of the system is optimised allowing any combinatorially possible separation to be performed in (i) the gas phase only and (ii) in both phases present. In the former case, an improvement in terms of the performance target can not be observed for this system as compared to the results from the reactor network optimisation. The optimal separations aim at low concentrations of reactant F inside the reactor modules. However, the same effect is achieved via the excessive recycle flowrates observed in the reactor design study. In terms of structural complexity, less reactor units are generally observed when separators are present in the gas phase and the recycle flowrates are significantly reduced. As in the reactor design study, the reactor units consist of co- and/or counter-current PFRs. A significantly better system performance is observed when separators are additionally considered in the liquid phase. The yield for the system is consistently found to be above 95%, i.e. almost complete conversion of reactant A into the desired product. A typical design that achieves the target is shown in figure 2. Separations in the liquid phase aim at removing the desired product B from the network and completely recycling reactant A to the reaction zones. The by-products are found to be either partly recycled or completely removed. The reaction sections feature co-current and counter-current PFR units with side streams in the gas phase. CSTRs are occasionally present but always occur in conjunction with the PFR units. The separator units in the gas phase are not observed in most designs and a number of structures do not exhibit gas recycles and separators at all. This suggests that by choosing the proper process structure in the liquid phase, the previously identified bottleneck in the gas phase vanishes.
5.2. Production of Ethylbenzene The alkylation of benzene with ethylene is investigated. Gaseous ethylene (E) reacts with liquid benzene (B) to desired product ethylbenzene (EB). Four transalkylation reactions involve production of by-products diethylbenzene (DEB) and triethylbenzene (TEB). All reactions are assumed to be of first order with respect to each reactant. The multi-purpose separator units assume the functionality of distillation (separation order: B/EB/DEB/TEB) and the profit is to be maximised for a benzene feed of 10kmol/hr. Optimisation of the homogeneous system under the assumption that the liquid phase is saturated in ethylene yielded a profit target of around $730k/yr and sequential designs featuring a reactor, a direct separation sequence, and recycles of B, EB, and TEB. Reactor designs involve PFRs and in some rare cases CSTR/PFR combinations. These structures have been identified in earlier studies of this process 2'3. However, no information is gained on the interactions between liquid and gas phase. Optimisation of the multiphase system without consideration of the inter-phase stream network yields a slightly improved profit target. The optimal designs feature reactor-separator-recycle arrangements with intermediate reactant, by-product, and off-gas recycles as well as a direct separation sequence. Reaction zones are consistently found to be counter-current PFRs. Network optimisation of the general reaction-separation superstructure including the interphase stream network yields a target profit of around $860k for this process, an increase of around 20% as compared to the previous case. Optimal designs again feature
1170
I,
<
"- Liquid feed
-~ g
,.
R1
as0 Sl
> EB EB
L
DEB
Liquid product (B)
Liquid product (ABCDE)
E > TEB
Fig. 2. Typical structure from the network optimisation for example 1
Fig. 3. Typical structure from the network optimisation for example 2
counter-current PFRs and a direct separation sequence; however, the reactor units are interconnected via intra- and inter-phase streams and show similarities with reactive distillation. A typical design is shown in figure 3. The improvements in profit stem from low component flowrates through the separation sequence with the separation of benzene being performed inside the reactor units. 6. CONCLUSIONS A general design tool for the synthesis of reaction-separation systems has been presented. The proposed network representation results in a rich and inclusive structure that embeds various mixing, phase distribution, and separation options. The stochastic optimisation scheme employed for network synthesis can handle the complexities resulting from kinetic expressions, phase equilibrium and mass transfer relationships. The proposed methodology can be used to analyse the problem trade-offs and to suggest incentives for the development of novel process structures. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
Pibouleau, L., P. Floquet, and S. Domenech, AIChE J., 1988, 34, 163. Kokossis, A.C. and C.A. Floudas, Chem. Eng. Sci., 1991, 46, 1361. Smith, E.M.B. and C.C Pantelides, Comp. Chem. Eng., 1995, 19, $83. Ciric, A.R. and D. Gu, AIChE J., 1994, 40, 1479. Balakrishna, S. and L.T. Biegler, Ind. Eng. Chem. Res., 1993, 32, 1327. Lakshmanan, A, Biegler, L.T., Ind. Eng. Chem. Res., 1996, 35, 4523. Papalexandri, K.P. and E.N. Pistikopoulos, AIChE J., 1996, 42, 1010. Mehta, V.L. and A.C. Kokossis, Comp. Chem. Eng., 1997, 21, $325. Mehta, V.L. and A.C. Kokossis, Comp. Chem. Eng., 1998, 22, S 119. Marcoulaki, E. and A.C. Kokossis, Comp. Chem. Eng., 1996, 20, $231. Mehta, V.L., Ph.D. thesis, UMIST, UK, 1998.