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.
Highlights
Membrane bioreactors (MBR’s) offer a number of advantages over traditional bioreactors and their use for various bioconversions have been extensively reported [1,2,3]
In the first region (F < 0.01) the effectiveness factor is unity, and the rate of solute transport in the MBR is controlled by the rate of reaction
In the third region (F > 0.1) external mass transfer limitations control the rate of solute transport through the MBR, and the effectiveness factor is greatly influenced by the Sherwood number
Summary
Membrane bioreactors (MBR’s) offer a number of advantages over traditional bioreactors and their use for various bioconversions have been extensively reported [1,2,3]. In both equations the parameters with the greatest influence on the effectiveness factor are: the Thiele modulus, partition coefficient, Sherwood number, and membrane thickness.
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