Advances in mathematical programming for the synthesis of process systems (original) (raw)
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Mathematical programming approaches to the synthesis of chemical process systems
Korean Journal of Chemical Engineering, 1999
This paper presents a review of advances that have taken place in the mathematical programming approach to process design and synthesis. A review is first presented on the algorithms that are available for solving MINLP problems, and its most recent variant, Generalized Disjunctive Programming models. The formulation of superstructures, models and solution strategies is also discussed for the effective solution of the corresponding optimization problems. The rest of the paper is devoted to reviewing recent mathematical programming models for the synthesis of reactor networks, distillation sequences, heat exchanger networks, mass exchanger networks, utility plants, and total flowsheets. As will be seen from this review, the progress that has been achieved in this area over the last decade is very significant.
This paper presents a review of advances that have taken place in the mathematical programming approach to process design and synthesis. A review is first presented on the algorithms that are available for solving MINLP problems, and its most recent variant, Generalized Disjunctive Programming models. The formulation of superstructures, models and solution strategies is also discussed for the effective solution of the corresponding optimization problems. The rest of the paper is devoted to reviewing recent mathematical programming models for the synthesis of reactor networks, distillation sequences, heat exchanger networks, mass exchanger networks, utility plants, and total flowsheets. As will be seen from this review, the progress that has been achieved in this area over the last decade is very significant.
Synthesis of reactor networks in overall process flowsheets within the multilevel MINLP approach
2001
This paper presents the superstructure-based mixed-integer non-linear programming approach to the synthesis of reactor networks in an equation-oriented environment. The model comprises a general superstructure in which the exact formulation of the recycle reactor (RR) and a continuous stirring tank reactor (CSTR) are embedded so as to enable a different feeding (cross flow, side stream), recycling and bypassing. The reactor arrangement is capable of representing several reactor systems such as a pure CSTR, a pure plug flow reactor, pure RR, their combinations and also a cross flow reactor. The superstructure is suitable either for an isothermal or non-isothermal, simple or complex reactor network. With the multilevel-hierarchical strategy, it is possible to postulate the superstructure at different levels of representation of flowsheet alternatives. Therefore, the superstructure is optimized more effectively and reliably. The approach has been applied to a complex non-isothermal reaction problem-an industrial example of the production of allyl chloride.
A systematic modeling framework of superstructure optimization in process synthesis
Computers & Chemical Engineering, 1999
A systematic framework is presented for the representation of superstructures and derivation of optimization models in process synthesis. The state task network (STN) and state equipment network (SEN) are proposed as the two fundamental representations of superstructures for process systems involving mass, heat and momentum transfer. The mathematical modeling of either of the two representations is performed with generalized disjunctive programming (GDP), and then converted systematically into mixed integer linear programs/mixed integer non-linear programs (MILP/MINLP) problems. The application of this methodology is illustrated with the synthesis of distillation sequences, with and without heat integration, which lead to MILP problems. It is shown that ad hoc models that have been reported in the literature can be systematically derived, and in the case of separation sequences with heat integration, a new improved model is derived. Numerical results for comparing alternative models are also presented.
A structural optimization approach in process synthesis—I
Computers & Chemical Engineering, 1983
mixed-integer linear programming approach is presented for performing structural and parameter optimization in the synthesis of processing systems. This approach is applied to the synthesis of utility systems that have to provide fixed demands of electricity, power for drivers and steam at various pressure levels. A superstructure that has embedded many potential configurations of utility systems is proposed, as well as its corresponding mixed-integer programming model. The application of the model is illustrated with a large example problem.
Logic-based MINLP algorithms for the optimal synthesis of process networks
Computers & Chemical Engineering, 1996
In this paper, the MINLP problem for the optimal synthesis of process networks is modeled as a discrete optimization problem involving logic disjunctions with nonlinear equations and pure logic relations. The logic disjunctions allow the conditional modeling of equations (e.g. if a unit is selected, apply mass/heat balances; otherwise, set the flow variables to zero). It is first shown that this framework for representing discrete optimization problems greatly simplifies the step of modeling. The outer approximation algorithm is then used as a basis to derive a new logic-based OA solution method which naturally gives rise to NLP sub-problems that avoid zero flows and a disjunctive LP master problem. The initial NLP sub-problems, that provide linearizations for all the terms in the disjunctions, are selected through a set-covering problem for which we consider both the cases of disjunctive and conjunctive normal form logic. The master problem, on the other hand, is converted to mixed-integer form using a convex-hull representation. Furthermore, based on some interesting relations of outer approximation with generalized Benders decomposition, it is also shown that it is possible to derive a logic-based method for the latter algorithm. The proposed algorithm has been tested on several structural optimization problems, including a flowsheet example showing distinct advantages in robustness and computational efficiency when compared to standard MINLP models and algorithms.
Industrial & Engineering Chemistry Research, 2002
In this paper, we employ the infinite dimensional state-space (IDEAS) paradigm to determine the globally minimum plate area for a liquid/vapor equilibrium based separation process (distillation) network. The IDEAS paradigm results in a convex (linear) optimization problem which accounts for all possible design alternatives. The obtained solution is thus guaranteed to be the global optimum over all networks. The power of the IDEAS paradigm is demonstrated in a case study on the separation of a nitrogen/oxygen mixture. The plate area for the IDEAS design is 58% lower than the plate area of the best conventional design.
Advances in Mathematical Programming for Automated Design Integration
1999
This paper presents a review of advances that have taken place in the mathematical programming approach to process design and synthesis. A review is first presented on the algorithms that are available for solving MINLP problems, and its most recent variant, Generalized Disjunctive Programming models. The formulation of superstructures, models and solution strategies is also discussed for the effective solution of the corresponding optimization problems. The rest of the paper is devoted to reviewing recent mathematical programming models for the synthesis of reactor networks, distillation sequences, heat exchanger networks, mass exchanger networks, utility plants, and total flowsheets. As will be seen from this review, the progress that has been achieved in this area over the last decade is very significant.
Multi-objective reactor network synthesis for industrial mass transfer limited processes
Computer Aided Chemical Engineering, 2006
This work describes a methodology for the synthesis of networks of multiphasic reactors, specially suited for processes where complex mecanistic models and a large number of unit types are present. The key concept consists on the decomposition and iteration of the original problem between two different representation levels (corresponding to smaller and less nonlinear problems), to avoid some of the numerical difficulties associated with the original one. This strategy was sucessfully applied to the aniline production phase of Quimigal S.A., allowing a systematic retrofit of this industrial process.
Reactor network synthesis for isothermal conditions
Acta Scientiarum. Technology, 2008
In the present paper, a computational systematic procedure for isothermal Reactor Network Synthesis (RNS) is presented. A superstructure of ideal CSTR and PFR reactors is proposed and the model is formulated as a constrained Nonlinear Programming (NLP) problem. Complex reactions (series/parallel reactions) are considered. The objective function is based on yield or selectivity, depending on the desired product, subject to different operational conditions. The problem constraints are mass balances in the reactors and in the considered reactor network superstructure. A systematic computational procedure is proposed and a Genetic Algorithm (GA) is developed to obtain the optimal reactor arrangement with the maximum yield or selectivity and minimum reactor volume. Results are as good as or better than those reported in the literature.