Strategies for Simulated Moving Bed Model Parameter Estimation Based on Minimal System Minimal Knowledge: Adsorption Isotherm Equation Screening and Estimability Analysis

The simulated moving bed (SMB) is a widely recognized technique for the resolution of several high-value-added compounds, and its mathematical modeling plays a crucial role in predicting its behavior. However, modeling can be challenging as it needs parameter estimation and topology definition, especially for such complex systems. SMB modeling might incorporate different adsorption isotherm equations (AIEs), which might better represent the behavior of a certain mixture to be separated. This work proposes two methodologies for SMB modeling and AIE selection relying on minimal system knowledge that can provide a representative model by a global parameter estimation instead of the traditional "Step by Step" approach. The first methodology proposes an architecture for global parameter estimation that encompasses the screening of the most suitable AIE in the lower level and the definition of the minimum number of experiments necessary for model identification in the upper level. In the second methodology, an extended generic isotherm, a combination of AIE, is formulated; and an estimability analysis is carried out to determine the estimable parameters. Both methodologies apply Latin Hypercube Sampling (LHS) for the design of experiments and emulation of a real unit by incorporating noise in the experimental data under a Gaussian error distribution. Moreover, uncertainty evaluation and data reconciliation are performed to enhance the robustness, reliability, and precision of the proposed approaches. The methodologies are validated by considering experimental data from the literature, apart from the LHS-generated samples, and are subject to cross-validations. Finally, the two methodologies are compared, with the first methodology demonstrating a superior performance for the case study. This work contributes to the advancement of SMB modeling, providing valuable tools for parameter estimation and AIE selection.