Global Approach for Simulated Moving Bed Model Identification: Design of Experiments, Uncertainty Evaluation, and Optimization Strategy Assessment

Santos, Rodrigo Souza; Prudente, Anderson; Ribeiro, Ana M.; Rodrigues, Alı́rio E.; Loureiro, José M.; Martins, Márcio A. F.; Pontes, Karen Valverde; Nogueira, Idelfonso B. R.

doi:10.1021/acs.iecr.1c01276

Cited by 9 publications

(14 citation statements)

References 35 publications

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“…As mentioned, previous studies considered a pseudo-homogeneous reaction that simplifies the model. In addition, SMBR modeling bears a high computational burden that can be prevented by substituting it by the TMBR model, which is simpler to be carried out and it is equivalent to SMBR by keeping constant the liquid velocity relative to the solid velocity in the model [13][14][15][16].…”

Section: Methodsmentioning

confidence: 99%

A Complete Heterogeneous Model for the Production of n-Propyl Propionate Using a Simulated Moving Bed Reactor

et al. 2022

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n-Propyl Propionate (ProPro) is a harmless biodegradable product employed in several fields for the production of drugs, inks, coating, food, and perfume. ProPro is synthesized in an equilibrium reaction for which its yield can be enhanced by constant withdraw of the products as the reaction takes place. Simulated Moving Bed Reactor (SMBR) is a candidate for the production of ProPro with high efficiency as it is a multifunction unit able to simultaneously run reaction and separation, hence shifting the equilibrium reaction toward products. This paper proposes a complete phenomenological model for the ProPro synthesis in a Simulated Moving Bed Reactor (SMBR) packed with the heterogeneous catalyst Amberlyst 46 resin. The operating conditions are defined by the Triangle Theory to design an SMBR unit to produce ProPro efficiently and a comprehensive parameter estimation procedure is employed to obtain more representative parameters. The validated phenomenological model was applied to design an SMBR unit to produce high purity (99.28%) ProPro.

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Section: Methodsmentioning

confidence: 99%

A Complete Heterogeneous Model for the Production of n-Propyl Propionate Using a Simulated Moving Bed Reactor

et al. 2022

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“…In this case, two routes can be taken, experimental estimation or calculation through correlations. The referred work took the second route, making use of the Wilson and Geankoplis equation, [ 14,18,19 ] depicted as:

{Sh}_{p} = \{\frac{1.09}{normalε} {((), {Re}_{p} Sc)}^{0.33} for 0.0015 < {Re}_{p} < 55

where

{Sh}_{p}

{Re}_{p},

and

Sc

are, respectively, the Sherwood, Reynolds, and Schmidt numbers, which, in their turn, are computed by:

{Sh}_{p} = \frac{k_{L, i} d_{normalp}}{D_{i, mix}}

{Re}_{p} = \frac{ρu d_{normalp}}{η}

Sc = \frac{η}{ρ D_{i, mix}}

where

ρ

is the fluid density,

η

is the fluid viscosity,

d_{normalp}

is the particle diameter, and

D_{i, mix}

is the diffusivity coefficient of the compound

i

in the mixture. The diffusivity coefficient can be calculated by the correlation of Perkins and Geankoplis.…”

Section: Methodsmentioning

confidence: 99%

Section: Fully Mechanistic Modelmentioning

confidence: 99%

Using scientific machine learning to develop universal differential equation for multicomponent adsorption separation systems

et al. 2022

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Universal differential equations are a concept in scientific machine learning that leverages the potential of the universal approximator theorem and the physical knowledge of a given system. Creating this level of hybridization within a stiff partial differential equation system is a challenge. On the other hand, adsorption phenomenological models have sink/source terms that describe the adsorption equilibrium through a well‐known simplified model (e.g., Langmuir; Sips; and Brunauer, Emmet, Teller [BET]). These suitable mechanistic assumptions are identified through experiments, providing the parameters of the sink/source model. However, these mechanistic assumptions are a simplification of the system phenomenology. Therefore, the resulting model is limited by its premises. In this scenario, the universal ordinary differential equations (UODE) is presented as an approach that conciliates the potential of artificial neural networks to learn given phenomena without conceptual simplifications. On the other hand, keeping into consideration the system physics. This work proposes a UODE system to solve the multicomponent separation by adsorption in a fixed bed column. Experimental data is used to identify the hybrid model. The required amount of data used in the model identification demonstrates that hybrid models can use a few data points to precisely describe the system. Furthermore, the obtained model can describe competitive adsorption with higher precision than the Langmuir model.

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“…The vacancies are filled with the region shape information by employing a method based on the Multivariate Law of Propagation of Probability Density Functions (MLPP), using Monte Carlo (MC) simulations, which requires less computational effort than re-evaluating the objective function. 21 To fill the coverage region in M1, a normal Gaussian with zero mean (μ = 0) and standard deviation equal to one (s = 1) is considered with points within the limits of the ellipse (coverage probability octave equals 99.9%, equivalent to x within −3.291 and 3.291). New points are created as given by (…”

Section: Uncertainty Evaluationmentioning

confidence: 99%

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

Santos,

Rebello,

Prudente

et al. 2023

Ind. Eng. Chem. Res.

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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.

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Global Approach for Simulated Moving Bed Model Identification: Design of Experiments, Uncertainty Evaluation, and Optimization Strategy Assessment

Cited by 9 publications

References 35 publications

A Complete Heterogeneous Model for the Production of n-Propyl Propionate Using a Simulated Moving Bed Reactor

A Complete Heterogeneous Model for the Production of n-Propyl Propionate Using a Simulated Moving Bed Reactor

Using scientific machine learning to develop universal differential equation for multicomponent adsorption separation systems

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

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