Model reduction for linear simulated moving bed chromatography systems using Krylov‐subspace methods

Abstract

Simulated moving bed (SMB) chromatography is a well-established technology for separating chemical compounds. To describe an SMB process, a finite-dimensional multistage model arising from the discretization of partial differential equations is typically employed. However, its relatively high dimension poses severe computational challenges to various model-based analysis. To overcome this challenge, two Krylov-type model order reduction (MOR) methods are proposed to accelerate the computation of the cyclic steady states (CSSs) of SMB processes with linear isotherms. A "straightforward method" that carefully deals with the switching behavior in MOR is first proposed. Its improvement, a "subspace-exploiting method," thoroughly exploits each reduced model to achieve further acceleration. Simulation studies show that both methods achieve high accuracy and significant speedups. The subspace-exploiting method turns out to be computationally much more efficient. Two challenging analyses of SMB processes, namely uncertainty quantification and CSS optimization, further demonstrate the accuracy, efficiency, and applicability of the proposed methods.

Accelerating optimization and uncertainty quantification of nonlinear SMB chromatography using reduced-order models

“…For Φ(µ), the key is to compute u du,r (µ) and r du (µ) . This needs to compute a RB V du for the dual system in (29). We solve the system in (29) at all the parameters in the training set P RB train := {µ j | µ j ∈ P, j = 1, .…”

“…Nevertheless, it is time-consuming to solve such high-fidelity models, especially in manyquery contexts, e.g., in optimization, uncertainty quantification (UQ), and real-time control settings. To overcome this obstacle, surrogate models via reduced-order modeling have gained increasing attention in the past decades [14,15,27,29,53].…”

“…A balanced truncation MOR method was applied to a linear SMB model in [14]. Recently, a Krylov-subspace MOR method was successfully applied, also to linear SMB chromatography in [29]. For nonlinear SMB chromatography, the application of proper orthogonal decomposition (POD) can be found in [27,53].…”

“…In the next section, we introduce an error estimation for the ROM, which is used as the error indicator ψ in the POD-greedy algorithm during the construction of the ROM. Once the ROM is constructed, it needs not be updated during the optimization process, unlike the POD based MOR method in [29].…”

Model Predictive Control Method of Simulated Moving Bed Chromatographic Separation Process Based on Subspace System Identification

“…en, the feasibility of the model was verified by experiments [7]. Aiming at the existing problems of the discretization model by utilizing the finite-dimensional partial differential equations, two Krylov-type reduced-order models were proposed to optimize the computational accuracy and computational efficiency of the model [8]. e main control objective of the SMB chromatographic separation process is to increase the target yield of the SMB separation process.…”