Towards predictive models for organic solvent nanofiltration
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.
Section snippets
Optimization-based approach for model identification
The optimization-based approach for model identification utilizes a combination of GP and global deterministic optimization in order to derive a model structure and the corresponding parametrization, which reproduces a set of experimental data in the best way. For modeling OSN rejection, different descriptors that account for physical and chemical properties of the solutes and the solvent are correlated, taking into account experimentally measured rejection data of different components solved
Case Study
The proposed optimization-based method was used to identify predictive models for the rejection of different solutes in either toluene or isopropanol (IPA) for a PuraMem® S600 membrane manufactured by Evonik Resource Efficiency GmbH. A data set with 18 solutes for toluene as well as 16 solutes for IPA were considered, including a homologous series of even numbered alkanes, a branched isomer and different aromatic components. Besides the solubility of the solutes in the specific solvent a
Conclusion
The current article proposed an optimization-based approach for a systematic model identification and its application to organic solvent nanofiltration. For the first time rejection models are generated and the results are very promising, showing a high degree of accuracy when compared to the experimental data for two investigated solvents with a broad range of different solutes. These models can further be used to evaluate the applicability of the given membrane for the rejection of specific
Acknowledgement
Financial support by the Federal Ministry for Economic Affairs and Energy under project number 03ET1279F is gratefully acknowledged.
References (14)
- et al.
Performance of solvent-resistant membranes for nonaqueous systems: solvent permeation results and modeling
Journal of Membrane Science
(2001) - et al.
Coupled series–parallel resistance model for transport of solvent through inorganic nanofiltration membranes
Separation and Purification Technology
(2009) - et al.
Transport model for solvent permeation through nanofiltration membranes
Separation and Purification Technology
(2006) - et al.
Systematic investigation on the influence of solutes on the separation behavior of a pdms membrane in organic solvent nanofiltration
Journal of Membrane Science
(2013) - et al.
Genetic algorithms and genetic programming: modern concepts and practical applications
(2009) - et al.
Multimodel inference
Sociological Methods and Research
(2004) - et al.
AIChE J.
(2014)
Cited by (1)
Organic Solvent Nanofiltration
2021, Nanofiltration: Principles, Applications, and New Materials: Volume 1 and 2