(348d) Holistic solvent screening: Modeling of multicomponent mass transfer in liquid-liquid extraction columns

Liquid-liquid extraction processes are a commonly used separation technique whose performance strongly depends on the selected solvent. To identify economically beneficial solvents, model-based solvent screening is a helpful tool.

Kampwerth et al. (2020) propose a holistic framework for model-based solvent screening, taking the investment cost as well as the operational cost of the entire separation process into account [1]. Using a rate-based modeling approach strikes a compromise between accuracy and computational effort. Additionally, this approach does not need any preliminary experiments. Instead, the model uses tabulated pure component physical properties and several physical-empirical correlations from literature to describe the fluid dynamics and mass transfer in the extraction process. Thus, the model-based approach is fully predictive and allows a wide range of solvents to be compared [2]. However, the model by Kampwerth et al. (2020) and Polte et al. (2022) only considers one transfer component and the carrier and solvent phases' mutual solubility is neglected. Thus, coupling products or the influence of auxiliary substances, such as catalysts, can not be described.

To overcome this drawback, we implement a multicomponent mass transfer model for an arbitrary number of components. Furthermore, the improved mass transfer model does not depend on additional experimental data, preserving the predictivity of the model. The overall design framework is presented in this contribution, focusing on the extraction column model extension.

Method

To consider additional components in the separation task, we developed two multicomponent mass transfer models, 1) solving the Maxwell-Stefan equations and 2) calculating effective Fick’s diffusivites and implemented both into the rate-based extraction model. The Maxwell-Stefan equations are solved using the approach outlined by Taylor et al. (1993), a highly iterative method that poses significant numerical challenges [3]. For calculating effective Fick’s diffusivities, we predict the carrier base self-diffusion coefficients using a machine learning algorithm following Zeng et al. (2022), significantly reducing computational time [4]. The mass transfer models are based on tabulated pure component physical data and interaction parameters and consider the strong coupling of the flux of all components in multicomponent liquid mixtures.

A comprehensive, variance-based sensitivity analysis was employed to investigate the impact of all input parameters and the precision of the model. The sensitivity study involved varying all input parameters using a uniform distribution. Subsequently, , experimental operating points were simulated to discriminate between the implemented mass transfer models, selecting raffinate concentrations as discriminative variables.

Experimental validation is vital for evaluating the accuracy of the improved extraction model. The final validation study additionally utilized experimental concentration profiles of all components alongside the column to compare the accuracy of boths modeling approaches. For this purpose, the quaternary system levulinic acid - formic acid - MIBK - water is investigated experimentally. First, the liquid-liquid equilibrium at 293.15K is examined, and NRTL parameters are regressed from the equilibrium data. Additionally, experiments are conducted using the substance system in a pilot plant pulsed sieve tray extraction column. Finally, the concentration profiles alongside the column are measured to evaluate the proposed models embedding the regressed NRTL parameters.

Results & Conclusion

The sensitivity analysis highlighted key substance properties as critical input parameters, notably the partition coefficient, surface tension, and density. Moreover, the 95% confidence interval is maintained within a relative deviation of less than 10% in the raffinate concentrations, defining the model's precision.

We show that the average deviation between measured and predicted concentration profiles for all pilot plant experiments is less than 2% for both models. Thus, the extended models simulate the mass transfer of all components with high accuracy.

We found that the physical-empirical correlation used in the column model can accurately predict the fluid dynamics. The regressed NRTL parameters describe the liquid-liquid equilibrium data within a deviation of 1.5%. They are found to be crucial in estimating the correct concentration profiles in the extraction column.

References

[1] Kampwerth, J.; Weber, B.; Rußkamp, J.; Kaminski, S.; Jupke, A., 2020 Towards a holistic solvent screening: On the importance of fluid dynamics in a rate-based extraction model, Chemical engineering science 227, 115905

[2] Polte, L., Raßpe-Lange, L., Latz, F., Jupke, A. and Leonhard, K. (2023), COSMO-CAMPED – Solvent Design for an Extraction Distillation Considering Molecular, Process, Equipment, and Economic Optimization. Chemie Ingenieur Technik, 95: 416-426. https://doi.org/10.1002/cite.202200144

[3] Taylor, Ross, and Krishna, Rajamani. 1993. Multicomponent mass transfer. Wiley series in chemical engineering. New York: Wiley.

[4] Predicting the Self-Diffusion Coefficient of Liquids Based on Backpropagation Artificial Neural Network: A Quantitative Structure–Property Relationship Study

Fazhan Zeng, Ren Wan, Yongjun Xiao, Fan Song, Changjun Peng, and Honglai Liu

Industrial & Engineering Chemistry Research 2022 61 (48), 17697-17706,

DOI: 10.1021/acs.iecr.2c03342