Modeling the flux of volatile fatty acid in a membrane distillation with the effect of pH

Abstract

This study aims to develop a mathematical model to estimate the initial flux of volatile fatty acids (VFAs) in the direct contact membrane distillation (DCMD) process. VFAs are toxic and emit odors. However, they have recently been recognized as valuable raw materials. Water and VFAs can be separated together using membrane distillation (MD). Water vapor and volatile compounds can pass through the membrane pores. They move toward the permeate side. Flux occurs not only for water but also for VFAs in DCMD process due to the volatility of VFAs. Parameters affecting the flux of VFAs were identified. Their relationship was confirmed experimentally. Acetic acid, butyric acid, and valeric acid were selected as target compounds because they have different Henry's constants and hydrophobicity. The ionization of acid solution varies depending on pH. MD tests were performed under various pH conditions. The flux of VFAs was observed to vary depending on the pH. The flux of VFAs was found to be proportional to the ionization fraction (α0) of the feed solution. Therefore, the model was developed to reflect the ionization fraction. An empirical formula was derived to predict the flux of VFAs using experimental data. A statistical analysis supported that the flux predicted by the model fitted very well with the observed flux. Additionally, experiments were performed with acid solutions of various concentrations. The concentration range applicable to the derived empirical formula was validated. The developed model can provide further insight into the relationship between flux and pH.