Towards predictive models for organic solvent nanofiltration

Abstract

Organic solvent nanofiltration (OSN) is a promising technology for an energy-efficient separation of organic mixtures. However, due to the lack of suitable models that allow for a quantitative prediction of the separation performance in different chemical systems OSN is rarely considered during conceptual process design. The feasibility of OSN is usually determined by means of an experimental screening of different membranes. Further experiments are conducted for a selected membrane in order to determine membrane specific parameters for a model-based description of the separation performance for a specific mixture. Obviously, this classical approach is experimentally demanding. The effort in identifying a suitable membrane in the first step could be significantly reduced if a theoretical evaluation of the separation performance was possible. The current article proposes an automatic method for the determination of a suitable predictive model for a given membrane, taking into account a limited set of experimental data. Specially, the rejection of different solutes in a specific solvent is modeled based on a set of physical and chemical descriptors. The proposed approach is based on a combination of genetic programming and global deterministic optimization, allowing for the identification of innovative models, including nonlinear parameter regression. The predictive capability of the generated models is validated on a separate data set. The identified models were able to predict the rejection of different components in the considered case studies with a deviation from the experimental values below 5%.

Introduction

Separation processes in the chemical industry are commonly dominated by energy-intensive thermal separations like distillation (Sholl and Lively (2016)). Especially pressure-driven membrane processes, such as organic solvent nanofiltration (OSN), offer a high potential for significantly improving the energy efficiency, since phase transitions and high operating temperatures are avoided (Marchetti et al. (2014)). Recent developments in solvent stable polymeric membranes allow for the application of OSN in a variety of industrial sectors, ranging from pharmaceuticals to petrochemicals and food industry (Lutze and Górak (2016)). However, despite the large prospect of OSN, it is rarely considered during conceptual process design as reliable predictions of the separation performance in different chemical systems are not available yet. In order to facilitate an effective consideration during conceptual design, a model-based description of the separation characteristics of the membrane is indispensable. Common models for OSN separation are solution-diffusion or pore-flow models (Marchetti et al. (2014)). However, these models require experimentally determined model parameters for each component in the system. Hence, the implementation of OSN is often linked to expensive and time-consuming screening experiments. Moreover, some experimental results comply best with the pore-flow model, whereas others can be described better by solution-diffusion models or a combination of both (Marchetti et al. (2014)). Thus, it is not possible to determine which model type is more suitable for OSN in general. Obviously, a general mechanistic model would be desirable for the prediction of the separation performance. However, such an approach is yet a long-range target that is extremely challenging, due to the strong interactions between the solute(s), the solvent(s) and the membrane material.

In order to allow for a predictive description of the membrane performance, Bhanushali et al. (2001), Geens et al. (2006) and Darvishmanesh et al. (2009) developed different models to describe the permeation of a pure solvent, each based on a number of molecular descriptors, such as the viscosity or the surface tension. These models allow for the evaluation of the solvent flux. A prediction of the separation performance, especially the rejection of different solutes, was not reported so far. Furthermore, the proposed models are based on a fixed structure and membrane-specific parameters, resulting in strong variations in the quality of the prediction for different membranes. Since the number of available polymeric membranes for OSN is yet limited, tailored model structures for each membrane type are a feasible option. However, the complexity of determining an optimal model structure and parametrization represents a much more complicated problem than a mere parameter identification for a fixed model. In order to solve this problem, an optimization-based data-driven approach is proposed. The method utilizes a combination of genetic programming (GP) and deterministic global optimization for the identification of optimal parameters, in order to automatically identify models with linear as well as nonlinear parameters. While the capability of the method to identify predictive models for pure solvent flux was demonstrated in a previous work (van den Bongard et al. (2017)), the current work illustrates that also models for the separation performance can be derived by such an approach.