(350b) Towards Improved Performance Predictions in Organic Solvent Nanofiltration: A Hybrid Modelling Approach

Given the critical importance that separation processes have for a wide variety of industries and the fact that they represent around 15% of the global energy consumption [1], there is a growing environmental and economic interest in challenging the current status quo in this area. One promising technology with the potential of achieving this feat is Organic Solvent Nanofiltration (OSN), which can deliver energy-efficient separations with high selectivity, and under moderate temperatures. Nevertheless, the application of OSN on an industrial scale is still far from being widespread, even though large-scale technical feasibility has been achieved. Among others, one of the main reasons for this state of affairs is the relatively poor understanding of the process, which often leads to the requirement of expensive and time-consuming experimental screening campaigns prior to any industrial deployment. The development of improved models with adequate predictive power is thus vital to boost the industrial relevance of this technology and to open the door to process optimization.

Considering the above, two main approaches can be undertaken. On the one hand, mechanistic models can be formulated to describe the behaviour of the system of interest in terms of the physicochemical phenomena that are understood to act as driving forces. On the other hand, data-driven methodologies can be leveraged to learn the functional relationships between outputs of interest and selected input variables. The first method is the classic one. It has the important advantage of requiring comparatively small amounts of data, while potentially allowing for greater fundamental insights to be gained and even for extrapolations outside the original calibration space. In contrast, the second alternative is often viewed as a feasible way of avoiding the gaps in the fundamental knowledge that often limit the value of purely mechanistic models, which is the reason why they have been gaining proponents among OSN practitioners in recent years. While these methodologies have been shown to provide accurate predictions in many cases, these can be notoriously difficult to link with underlying physical phenomena. Moreover, large amounts of high-quality data are needed for training purposes, which are often not available for OSN applications.

Both alternatives thus have significant advantages and disadvantages when one is concerned with the prediction of species transport in organic solvent nanofiltration. Accordingly, in this contribution we propose a middle ground alternative: hybrid modelling. Under this paradigm, mechanistic and data-driven models are combined in order to magnify their strengths and minimize their shortcomings [2]. We have developed two complementary model architectures: parallel, and serial. In the former, the mechanistic component was calibrated with experimental data to predict flux and rejection information, which was then corrected by the predictions of a data-driven algorithm trained to estimate the residual error of the mechanistic model. Alternatively, in the serial architecture the same machine learning algorithm was re-tasked with learning the expected values of the parameters of the chosen mechanistic component, which was subsequently used to estimate the expected performance of the analysed systems [3]. The proposed methodologies were analysed in terms of their predictive power, interpretability, and potential engineering application.

Since their development is relatively recent and they offer a number of significant advantages in comparison to the more widely used polymeric supports, we focused here on ceramic membranes. For this, a large experimental database containing both native and functionalized membranes was generated. A wide range of industrially relevant solvents and solutes was used. Steady-state measurements under different transmembrane pressures were performed in-house or extracted from the published literature [3]. Taking into account the characteristics of the studied systems, a solution-diffusion model considering the non-ideal mixing of solvent and solute was selected as the mechanistic component of the proposed methodology. In turn, the XGBoost algorithm was used as the data-driven module given its robustness and predictive performance [4]. Appropriate physicochemical parameters were used as training features. The proposed models were observed to offer very accurate predictions and an improved performance in comparison with the baseline solution-diffusion model. Additionally, good out-of-sample predictive power was observed, and the models made extensive use of information related to the affinity interactions among membrane, solute, and solvent. As the usage of an underling mechanistic component gives hybrid models a physical foundation and less data is needed to train them, the approach proposed in this work is expected to contribute towards the development of a robust, generic, and accurate description of OSN.

References

[1] R.P. Lively, D.S. Sholl, From water to organics in membrane separations, Nat. Mater. 16 (2017) 276–279. https://doi.org/10.1038/nmat4860.

[2] M.Y. Schneider, W. Quaghebeur, S. Borzooei, A. Froemelt, F. Li, R. Saagi, M.J. Wade, J.-J. Zhu, E. Torfs, Hybrid modelling of water resource recovery facilities: status and opportunities, Water Sci. Technol. 85 (2022) 2503–2524. https://doi.org/10.2166/wst.2022.115.

[3] J.P. Gallo-Molina, B. Claessens, A. Buekenhoudt, A. Verliefde, I. Nopens, Capturing unmodelled phenomena: A hybrid approach for the prediction of the transport through ceramic membranes in organic solvent nanofiltration, J. Membr. Sci. 686 (2023) 122024. https://doi.org/10.1016/j.memsci.2023.122024.

[4] T. Chen, C. Guestrin, XGBoost: A Scalable Tree Boosting System, in: Proc. 22nd ACM SIGKDD Int. Conf. Knowl. Discov. Data Min., ACM, New York, NY, USA, 2016: pp. 785–794. https://doi.org/10.1145/2939672.2939785.