Abstract
This study theoretically analyzes the mass transport through capillary, asymmetric, biocatalytic membrane reactor, where the diffusive plus convective mass transport is accompanied by biochemical reaction with Michaelis-Menten kinetics. An approach mathematical model was developed that provides the mass transfer properties in closed, explicit mathematical forms. The inlet and outlet mass transfer rates can then put into the differential mass transport expressions of the lumen and the shell fluid phases as boundary values. The approach solution was obtained by dividing the membrane layer into very thin sub-layers with constant transport and reaction kinetic parameters and the obtained second-order differential equation with constant parameters, given for every sublayer, could be solved analytically. Two operating modes are analyzed in this paper, namely, with and without a sweeping phase on the permeating side. These models deviate by the boundary conditions, only, defined them for the outlet membrane surface. The main purpose of this study is to show how the cylindrical space affects the transport process, concentration distribution, mass transfer rates and conversion in presence of a biochemical reaction. It is shown that the capillary transport can significantly be affected by the lumen radius, by the biocatalytic reactor thickness and the convective flow. Decreasing values of the lumen radius reduce the effect of the biochemical/chemical reaction; the increasing reactor thickness also decreases the physical mass transfer rate and, with it, increases the effect of reaction rate. The model can also be applied to reactions with more general kinetic equations with variable parameters.
Highlights
Biocatalytic/catalytic membrane reactors, as a promising novel technology, are widely recommended in the chemical and the biochemical, food, pharmaceutical, etc. industries [1,2,3,4,5,6] or environmental applications [7]
We have looked for such an approach solution, which can be used in case of variable mass transfer coefficients as well as the results are expressed in closed, explicit mathematical form
This study elaborates and discusses theoretical results which is obtained by predicted mass transport process, using the developed mathematical models
Summary
Biocatalytic/catalytic membrane reactors, as a promising novel technology, are widely recommended in the chemical and the biochemical, food, pharmaceutical, etc. industries [1,2,3,4,5,6] or environmental applications [7]. Biocatalytic/catalytic membrane reactors, as a promising novel technology, are widely recommended in the chemical and the biochemical, food, pharmaceutical, etc. Different biochemical/chemical reactions have been studied by this process, e.g., dehydrogenation of alkanes to alkenes, partial oxidation reactions using inorganic or organic peroxides, as well as partial hydrogenations, hydration, etc. Catalano et al [12] measured the hydrogen transfer rate through a Pd-Ag selective membrane layer and examined the role of the polarization layer. They calculated the overall mass transfer coefficient as a function of Reynolds number
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