Effectiveness Factors and Conversion in a Biocatalytic Membrane Reactor

Abstract

Analytical expressions of the effectiveness factor of a biocatalytic membrane reactor, and its asymptote as the Thiele modulus becomes large, are presented. The evaluation of the effectiveness factor is based on the solution of the governing equations for solute transport in the two regions of the reactor, i.e. the lumen and the matrix (with the biofilm immobilized in the matrix). The lumen solution accounts for both axial diffusion and radial convective flow, while the matrix solution is based on Robin-type boundary conditions. The effectiveness factor is shown to be a function of the Thiele modulus, the partition coefficient, the Sherwood number, the Peclet number, and membrane thickness. Three regions of Thiele moduli are defined in the effectiveness factor graphs. These correspond with reaction rate limited, internal-diffusion limited, and external mass transfer limited solute transport. Radial convective flows were shown to only improve the effectiveness factor in the region of internal diffusion limitation. The assumption of first order kinetics is shown to be applicable only in the Thiele modulus regions of internal and external mass transfer limitation. An iteration scheme is also presented for estimating the effectiveness factor when the solute fractional conversion is known. The model is validated with experimental data from a membrane gradostat reactor immobilised with Phanerochaete chrysosporium for the production of lignin and manganese peroxidases. The developed model and experimental data allow for the determination of the Thiele modulus at which the effectiveness factor and fractional conversion are optimal.

Protein‐inorganic calcium‐phosphate supraparticles as a robust platform for enzyme co‐immobilization

“…The increase of these values is not considered detrimental for future applications. It should also be noted that, based on the apparent pore diameters from the internal structure of supraparticles in Scanning Electron Microscopy in previous studies, supraparticles are unlikely to limit diffusion in a way that makes the Weisz‐Prater criterion a subject of concern (Godongwana, 2016; Park & Champion, 2016; Zhao & Sun, 2014). This is corroborated by Figure S5, which shows rapid loading of eGFPZ E into supraparticles during a diffusion experiment.…”

“…Given the moderate enzymatic reaction rates and large pore volumes, mass transfer limitations are unlikely to be a serious problem. However, these phenomena can be investigated in the future using continuous flow reactors (Bommarius, 2015; Godongwana, 2016; Sheldon, 2012).…”

Application of finite difference method in the study of diffusion with chemical kinetics of first order

“…Following we proceed to determine the effectiveness factor (η), which indicates the ratio between the reaction rate and the reaction rate without resistance to diffusion [7], [8] as described in (15)…”

Analysis of Mass Transport through Anisotropic, Catalytic/Bio-Catalytic Membrane Reactors

“…The value of the superficial convective velocity can vary across the membrane, depending on its structure, porosity change, and/or the change of the volumetric flow rate due to a reaction, etc. The effect of the chemical reactions with different reaction kinetics was relatively intensively studied in the literature for simple diffusive transport [12,13], but perhaps less intensively for the diffusive plus convective transport process [25][26][27][28][29][30][31][32].This study focuses on the reactant(s) transport's description with variable transport parameters (diffusion coefficient, convective velocity) without chemical/biochemical reactions and those accompanied by chemical/biochemical reactions, assuming constant and variable diffusion coefficients and/or reaction rate constant [6], as well as with constant and variable solvent/solute convective velocities. The effect of the variable convective velocity is of emphasized importance in this discussion.…”

“…The value of the superficial convective velocity can vary across the membrane, depending on its structure, porosity change, and/or the change of the volumetric flow rate due to a reaction, etc. The effect of the chemical reactions with different reaction kinetics was relatively intensively studied in the literature for simple diffusive transport [12,13], but perhaps less intensively for the diffusive plus convective transport process [25][26][27][28][29][30][31][32].…”