Efficient optimization of simulated moving bed processes

Toumi, Abdelaziz; Engell, Sebastian; Diehl, Moritz; Bock, Hans Georg; Schlöder, Johannes P.

doi:10.1016/j.cep.2006.06.026

Cited by 77 publications

(32 citation statements)

References 35 publications

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“…Well-developed direct solution strategies, e.g., single or multiple-shooting methods and simultaneous approaches, which have been proven to be highly efficient for continuous processes and CSS optimization of SMB (Dünnebier et al (2000), Kawajiri and Biegler (2006), Toumi et al (2007)), can not be used to address this type of issue directly. In this section, a multistage startup concept will be introduced briefly followed by the detailed problem formulation.…”

Section: Optimal Startup Operation Of Smbmentioning

confidence: 99%

“…However, both procedures are based on the equivalent TMB model and the "triangle theory" neglects the effect of axial dispersion and mass transfer resistances. To overcome these limitations, the model-based mathematical optimization methods have been developed (Dünnebier et al (2000), Kawajiri and Biegler (2006), Toumi et al (2007)). They consider a rigorous SMB model, involve a detailed cost function and use efficient Newton-based solution strategies.…”

Section: Css Operation and Conventional Startupmentioning

confidence: 99%

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Optimal startup operation of simulated moving bed chromatographic processes

Kawajiri

Raisch

et al. 2010

IFAC Proceedings Volumes

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SMB represents one of the widely established periodic adsorption processes and its periodic and nonlinear dynamics presents a significant challenge to the formulation and solution of the optimal startup issue. A multistage startup concept allowing to adjust operating conditions stage-wise is proposed. The startup problem is then formulated aiming at driving the system towards the reference cyclic steady state (CSS) in an optimum manner. A tailored decomposition algorithm is developed to tackle the resulting optimization problem and guarantee numerical tractability. The feasibility of the solution approach is demonstrated on a binary separation with nonlinear competitive isotherms. It is found that the new startup policy dramatically reduces transient time and desorbent consumption. The startup performance in terms of product concentration and purity is also evaluated quantitatively.

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Section: Optimal Startup Operation Of Smbmentioning

confidence: 99%

Section: Css Operation and Conventional Startupmentioning

confidence: 99%

Optimal startup operation of simulated moving bed chromatographic processes

Kawajiri

Raisch

et al. 2010

IFAC Proceedings Volumes

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show abstract

“…The optimal control problem, given by the objective (4) and constraints (1) and (2), is strictly convex. Hence, the first order optimality conditions are sufficient to define a unique solution (y * , u * ).…”

Section: The Optimality Conditionsmentioning

confidence: 99%

“…For example, a small α will yield a good approximation, yet require a large control effort. Our research on the control of periodic PDEs is motivated by the abundance of such processes in a variety of chemical engineering applications, such as 'simulated moving bed processes' [1] and 'pressure swing adsorbers', which find widespread use in the pharmaceutical and food industry. This article is structured as follows.…”

Section: Introductionmentioning

confidence: 99%

One-Shot Multigrid for the Optimal Neumann Boundary Control of Time-Periodic Partial Differential Equations

Abbeloos¹,

Diehl²,

Vandewalle³

2009

AIP Conference Proceedings

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Abstract. We present a one-shot multigrid method for the optimal Neumann boundary control of time-periodic, linear, parabolic partial differential equations. We focus on optimal control problems of the so-called tracking type, i.e., we try to steer the PDE solution such that it matches a prescribed periodic trajectory, or segment thereof, as closely as possible.To that end we derive the optimality condition of such problems. We develop a one-shot multigrid method for solving the resulting coupled system of forward and backward time-periodic differential equations. Numerical examples are presented to illustrate the behavior of the multigrid algorithm.

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“…There are two main approaches to the discretization, the sequential approach, in which only the decision variables (control parameters) are discretized, [3][4][5][6][7][8] and the simultaneous approach, in which both decision and state variables are discretized. [9][10][11][12][13] Direct methods enable easy incorporation of powerful numerical integration routines for systems of ordinary differential equations (ODEs) or differential-algebraic equations (DAEs) and of nonlinear programming (NLP) routines for optimization. Thus both the sequential and simultaneous approaches have been successfully applied to a wide range of problems, and both are in active use.…”

mentioning

confidence: 99%

Rigorous Global Optimization for Dynamic Systems Subject to Inequality Path Constraints

Zhao

Stadtherr

2011

Ind. Eng. Chem. Res.

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A new approach is described for the rigorous global optimization of dynamic systems subject to inequality path constraints (IPCs). This method employs the sequential (control parameterization) approach and is based on techniques developed for the verified solution of parametric systems of ordinary differential equations. These techniques provide rigorous interval bounds on the state variables, and thus on the path constraints and objective function in the dynamic optimization problem. These techniques also provide explicit analytic representations (Taylor models) of these bounds in terms of the decision variables in the optimization problem. This facilitates the use of constraint propagation techniques that can greatly reduce the domain to be searched for the global optimum. Since IPCs are often related to safety concerns, we adopt a conservative, innerapproximation approach to constraint satisfaction. Through this approach, the search for the global optimum is restricted to a space in which continuous satisfaction of the IPCs is rigorously guaranteed, and an ǫ-global optimum within this space is determined. Examples are presented that demonstrate the potential and computational performance of this approach.

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Efficient optimization of simulated moving bed processes

Cited by 77 publications

References 35 publications

Optimal startup operation of simulated moving bed chromatographic processes

Optimal startup operation of simulated moving bed chromatographic processes

One-Shot Multigrid for the Optimal Neumann Boundary Control of Time-Periodic Partial Differential Equations

Rigorous Global Optimization for Dynamic Systems Subject to Inequality Path Constraints

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