Mutual interactions between penetrants have importance in the permeation behavior -Mutual slowing down of penetrants observed -Permeation behavior analyzed with a Maxwell-Stefan model -Ethanol-water separations both in pervaporation and vapor permeation conditions

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In this study, the modified bounded homotopies presented by Malinen and Tanskanen (Malinen, I.; Tanskanen, J. Modified bounded homotopies to enable a narrow bounding zone. Chem. Eng. Sci. 2008, 63, 3419) are investigated in order to solve phase stability analysis problems in liquidÀliquid equilibrium cases for phase-splitting calculations. The tangent-plane distance criterion is used to analyze the phase stability. The emphasis is on approaching the first root on the homotopy path. According to the observations, the bounding of the homotopy path with respect to the problem variables aids in the solving of a phase stability analysis problem. The main shortcomings of the modified bounded Newton, affine, and fixed-point homotopies are the starting point isolas, the existence of unfeasible solutions, and the convergence to only certain roots, respectively. The attraction domain of the global minimum was observed to be the largest with the fixed-point homotopy. Sequential usage of the fixed-point homotopy and starting points near pure components results in a robust algorithm for phase stability analysis and gives feasible initial estimates for the solving of phase splitting.

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In the enzymatic hydrolysis of cellulose, several phenomena have been proposed to cause a decrease in the reaction rate with increasing conversion. The importance of each phenomenon is difficult to distinguish from batch hydrolysis data. Thus, kinetic models for the enzymatic hydrolysis of cellulose often suffer from poor parameter identifiability. This work presents a model that is applicable to fed-batch hydrolysis by discretizing the substrate based on the feeding time. Different scenarios are tested to explain the observed decrease in reaction rate with increasing conversion, and comprehensive assessment of the parameter sensitivities is carried out. The proposed model performed well in the broad range of experimental conditions used in this study and when compared to literature data. Furthermore, the use of data from fed-batch experiments and discretization of the model substrate to populations was found to be very informative when assessing the importance of the rate-decreasing phenomena in the model.

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