Optimization of VARICOL SMB processes using hybrid modeling and nonlinear programming
•The VARICOL process is represented by a hybrid model.•The discrete-time dynamics is described by a timed transition Petri net.•The hybrid representation considerably simplifies the optimization of the VARICOL productivity.•The optimum productivity can be as high as twice the productivity of a conve...
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| Published in: | Computers & chemical engineering Vol. 71; pp. 1 - 10 |
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04.12.2014
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| Abstract | •The VARICOL process is represented by a hybrid model.•The discrete-time dynamics is described by a timed transition Petri net.•The hybrid representation considerably simplifies the optimization of the VARICOL productivity.•The optimum productivity can be as high as twice the productivity of a conventional SMB process.
The Varicol process exhibits continuous and discrete-time dynamics and can be represented by a hybrid model, where the continuous-time dynamics is described by mass-balance partial differential equations, whereas the discrete-time dynamics is described by a timed transition Petri net (TTPN). This hybrid model allows to simplify the solution of a normally difficult Mixed-Integer Non-Linear Programming problem for maximizing the productivity of a Varicol process subject to constraints on the desired purities of the extract and the raffinate components. Indeed, the coverability tree of the TTPN can be constructed to generate a set of candidate integer parameters, and the corresponding nonlinear problems are solved for a subset of candidates selected on the basis of an approximate evaluation using the (true moving bed) triangle theory. The optimal solution is the Varicol configuration (column sequence) for which the productivity is maximal. A repeatability and a robustness analysis show the feasibility of this approach. |
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| AbstractList | •The VARICOL process is represented by a hybrid model.•The discrete-time dynamics is described by a timed transition Petri net.•The hybrid representation considerably simplifies the optimization of the VARICOL productivity.•The optimum productivity can be as high as twice the productivity of a conventional SMB process.
The Varicol process exhibits continuous and discrete-time dynamics and can be represented by a hybrid model, where the continuous-time dynamics is described by mass-balance partial differential equations, whereas the discrete-time dynamics is described by a timed transition Petri net (TTPN). This hybrid model allows to simplify the solution of a normally difficult Mixed-Integer Non-Linear Programming problem for maximizing the productivity of a Varicol process subject to constraints on the desired purities of the extract and the raffinate components. Indeed, the coverability tree of the TTPN can be constructed to generate a set of candidate integer parameters, and the corresponding nonlinear problems are solved for a subset of candidates selected on the basis of an approximate evaluation using the (true moving bed) triangle theory. The optimal solution is the Varicol configuration (column sequence) for which the productivity is maximal. A repeatability and a robustness analysis show the feasibility of this approach. The Varicol process exhibits continuous and discrete-time dynamics and can be represented by a hybrid model, where the continuous-time dynamics is described by mass-balance partial differential equations, whereas the discrete-time dynamics is described by a timed transition Petri net (TTPN). This hybrid model allows to simplify the solution of a normally difficult Mixed-Integer Non-Linear Programming problem for maximizing the productivity of a Varicol process subject to constraints on the desired purities of the extract and the raffinate components. Indeed, the coverability tree of the TTPN can be constructed to generate a set of candidate integer parameters, and the corresponding nonlinear problems are solved for a subset of candidates selected on the basis of an approximate evaluation using the (true moving bed) triangle theory. The optimal solution is the Varicol configuration (column sequence) for which the productivity is maximal. A repeatability and a robustness analysis show the feasibility of this approach. |
| Author | Torres Zúñiga, Ixbalank Vande Wouwer, Alain |
| Author_xml | – sequence: 1 givenname: Ixbalank surname: Torres Zúñiga fullname: Torres Zúñiga, Ixbalank email: ixbalank@gmail.com organization: Laboratory for Research on Advanced Processes for Water Treatment, Unidad Académica Juriquilla, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Blvd. Juriquilla 3001, 76230 Querétaro, México – sequence: 2 givenname: Alain surname: Vande Wouwer fullname: Vande Wouwer, Alain email: alain.vandewouwer@umons.ac.be organization: Service d’Automatique, Faculté Polytechnique de Mons – UMons, Bd. Dolez 31, B7000 Mons, Belgium |
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| Cites_doi | 10.1205/026387603765444500 10.1002/aic.690440307 10.1016/j.cej.2005.06.008 10.1081/SS-100100622 10.1016/S0021-9673(03)00557-0 10.1016/j.ces.2004.04.009 10.1016/S0098-1354(03)00159-5 10.1016/j.compchemeng.2003.11.006 10.1109/5.24143 10.1016/j.ces.2010.11.022 10.1109/41.334574 10.1016/S0967-0661(01)00053-3 10.1016/S0021-9673(02)01802-2 10.1016/j.chroma.2008.10.075 10.1021/ie0302894 10.1016/S0021-9673(97)00048-4 10.1016/j.compchemeng.2007.04.009 10.1016/j.seppur.2008.10.050 10.1016/j.compchemeng.2003.11.003 |
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| Keywords | Simulated moving bed Separation Process control Chromatography Optimization Tree(graph) Continuous time Non linear programming Modeling Partial differential equation Conservation law Moving bed reactor Hybrid model Robustness Petri net Productivity Moving bed Process planning Mixed integer programming Time response Timed system Engineering design Continuous process Repeatability Discrete time Feasibility Non linear effect |
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| Snippet | •The VARICOL process is represented by a hybrid model.•The discrete-time dynamics is described by a timed transition Petri net.•The hybrid representation... The Varicol process exhibits continuous and discrete-time dynamics and can be represented by a hybrid model, where the continuous-time dynamics is described by... |
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| SubjectTerms | Applied sciences Chemical engineering Chromatography Computer science; control theory; systems Computer simulation Control system analysis Control theory. Systems Exact sciences and technology Inventory control, production control. Distribution Liquid-liquid and fluid-solid mechanical separations Mathematical models Mathematical programming Nonlinear dynamics Nonlinear programming Nonlinearity Operational research and scientific management Operational research. Management science Optimization Process control Productivity Programming Separation Simulated moving bed |
| Title | Optimization of VARICOL SMB processes using hybrid modeling and nonlinear programming |
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