Suzhou Li

Using surrogate models for efficient optimization of simulated moving bed chromatography

Abstract A new approach of using computationally cheap surrogate models for efficient optimization of simulated moving bed (SMB) chromatography is presented. Two different types of surrogate models are developed to replace the detailed but expensive full-order SMB model for optimization purposes. The first type of surrogate is built through a coarse spatial discretization of the first-principles process model. The second one falls into the category of reduced-order modeling. The proper orthogonal decomposition (POD) method is employed to derive cost-efficient reduced-order models (ROMs) for the SMB process. The trust-region optimization framework is proposed to implement an efficient and reliable management of both types of surrogates. The framework restricts the amount of optimization performed with one surrogate and provides an adaptive model update mechanism during the course of optimization. The convergence to an optimum of the original optimization problem can be guaranteed with the help of this model management method. The potential of the new surrogate-based solution algorithm is evaluated by examining a separation problem characterized by nonlinear bi-Langmuir adsorption isotherms. By addressing the feed throughput maximization problem, the performance of each surrogate is compared to that of the standard full-order model based approach in terms of solution accuracy, CPU time and number of iterations. The quantitative results prove that the proposed scheme not only converges to the optimum obtained with the full-order system, but also provides significant computational advantages.

Optimization of simulated moving bed chromatography with fractionation and feedback: part I. Fractionation of one outlet.

A novel modification of simulated moving bed (SMB) technology, referred to as fractionation and feedback SMB (FF-SMB), has been introduced recently. This concept is based on fractionating one or both outlet streams and feeding the off-spec fractions back into the unit alternatingly with the original feed mixture. In this paper, the optimization problem of FF-SMB realizing one outlet fractionation is considered. A mathematical optimization framework based on a detailed process model is presented which allows to evaluate quantitatively the potential of this operating scheme. Detailed optimization studies have been carried out for a difficult separation characterized by small selectivity and low column efficiency. The results reveal that the proposed fractionation and feedback regime can be significantly superior to the classical SMB chromatography, in terms of both feed throughput and desorbent consumption. The effect of the feeding sequence on the performance of FF-SMB is also examined.

Optimization of startup and shutdown operation of simulated moving bed chromatographic processes

This paper presents new multistage optimal startup and shutdown strategies for simulated moving bed (SMB) chromatographic processes. The proposed concept allows to adjust transient operating conditions stage-wise, and provides capability to improve transient performance and to fulfill product quality specifications simultaneously. A specially tailored decomposition algorithm is developed to ensure computational tractability of the resulting dynamic optimization problems. By examining the transient operation of a literature separation example characterized by nonlinear competitive isotherm, the feasibility of the solution approach is demonstrated, and the performance of the conventional and multistage optimal transient regimes is evaluated systematically. The quantitative results clearly show that the optimal operating policies not only allow to significantly reduce both duration of the transient phase and desorbent consumption, but also enable on-spec production even during startup and shutdown periods. With the aid of the developed transient procedures, short-term separation campaigns with small batch sizes can be performed more flexibly and efficiently by SMB chromatography.

Reduced-Order Modeling and ROM-Based Optimization of Batch Chromatography

A reduced basis method is applied to batch chromatography and the underlying optimization problem is solved efficiently based on the resulting reduced model. A technique of adaptive snapshot selection is proposed to reduce the complexity and runtime of generating the reduced basis. With the help of an output-oriented error bound, the construction of the reduced model is managed automatically. Numerical examples demonstrate the performance of the adaptive technique in reducing the offline time. The ROM-based optimization is successful in terms of the accuracy and the runtime for getting the optimal solution.

Efficient Optimization of Simulated Moving Bed Processes Using Reduced Order Models

Abstract This paper explores the use of cheaper reduced order models (ROMs) to address computational challenges in the optimization of simulated moving bed processes. The trust-region framework is employed to manage ROMs constructed by proper orthogonal decomposition. The effectiveness of this new solution method is demonstrated on a separation example with nonlinear competitive Langmuir isotherm. It is shown that significant computational savings are gained with the ROM-based optimization strategy.

Optimization of simulated moving bed chromatography with fractionation and feedback incorporating an enrichment step

Abstract An enrichment step is proposed to simulated moving bed chromatography with fractionation and feedback (FF-SMB), a new variation of SMB, to concentrate recyclates before they are fed back into the unit. Effectiveness of this operation is evaluated by systematic optimization studies. Case studies reveal that enriching recyclates is advantageous to FF-SMB and provides further improvement in separation performance over the non-enriched case.

Optimal startup operation of simulated moving bed chromatographic processes

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.