| Popis: |
Membrane processes reportedly provide a tremendous potential for improving separation performance and energy efficiency compared to thermal separation processes (Sholl and Lively, 2016). However, the benefits of membrane processes, as e.g. the ability to overcome limitations of other separation techniques introduced by azeotropes or eutectic points, are exploited best when integrated in hybrid processes (Skiborowski et al., 2013). Nevertheless, industrial applications are still limited due to a lack of reliable models that allow for an accurate description of the separation performance of the membrane. Process design approaches oftentimes neglect limiting effects, such as pressure drop, or concentration and temperature polarization. However, the impact of ignoring these limitations was recently demonstrated by Micovic et al. (Micovic et al., 2014) for modeling organic solvent nanofiltration. Additionally, the correct consideration of the flow pattern, such as co- and counter-current as well as cross flow, can have an equally significant impact on the accuracy of the model. However, the consideration of cross flow requires a two dimensional discretization resulting in a more complicated model compared to co- or counter-current flow. In order to consider all these complex effects in a simultaneous process optimization an efficient model reduction without sacrificing model accuracy has to be performed. In this respect, Skiborowski et al. (Skiborowski, 2014) proposed to model a pervaporation-assisted distillation process, using an orthogonal collocation on finite elements (OCFE) for accurately modeling a co-currently operated membrane module, while applying external functions for computing thermodynamic properties. However, only temperature polarization was considered. The current work extends this approach by implementing concentration polarization and pressure drop computations. Furthermore, modifications of the OCFE approach towards the alternative flow patterns are investigated and comparisons with simple discretization schemes are presented. The results indicate the benefits of the efficient model reduction by OCFE in order to allow for the consideration of more accurate modeling of the membrane process. |
