Solution of hollow fibre bioreactor design equations for zero-order limit of Michaelis-Menten kinetics
TL;DR: In this article, the mass balance equations for hollow fiber bioreactors have been solved for the zero-order limit of the Michaelis-Menten kinetics, and the membrane and spongy matrix equations can be decoupled from the overall set of equations.
About: This article is published in Chemical Engineering Journal.The article was published on 1993-06-01. It has received 2 citations till now. The article focuses on the topics: Mass balance & Numerical analysis.
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TL;DR: Gottifredi et al. as discussed by the authors used a non-linear algebraic equation to calculate the effectiveness factor for a reaction-diffusion process in an immobilized biocatalyst pellet.
8 citations
TL;DR: In this paper, the original set of differential mass balance equations is cast into an equivalent system of integral equations by generating the appropriate Green's functions, and the derived integral equations are numerically solved on an appropriately transformed coordinate system.
7 citations
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TL;DR: The advantages and limitations of using membrane bioreactors for entrapping whole cells and enzymes, including single, laminated and microporous, for the conversion of optically active enantiomers are reviewed.
Abstract: Integrating the properties of synthetic membranes with biological catalysts such as cells and enzymes forms the basis of an exciting new technology called membrane bioreactors. The impetus behind this marriage comes from the recent spectacular advances in recombinant DMA and cell fusion technologies and the need to develop competitive bioprocessing schemes to produce complex and active biological molecules. The advantages and limitations of using membrane bioreactors for entrapping whole cells and enzymes are reviewed. Various membrane configurations such as microcapsules, hollow fibers, and flat sheets are compared. Several different entrapped membrane bioreactors, including single, laminated and microporous, for the conversion of optically active enantiomers are described. As with new and exciting technologies, the future of membrane bioreactors in biotechnology will depend on their ability to produce desired molecules at competitive costs.
114 citations
TL;DR: A numerical finite difference solution for nonlinear Michaelis-Menten reaction kinetics is shown to agree with the analytic solution, as Km/C0, the ratio of the Michaelis constant to the initial substrate concentration, becomes large (> 100).
Abstract: The behavior of an immobilized enzyme reactor utilizing asymmetric hollow fibers is simulated using a theoretical model. In this reactor, an enzyme solution contained within the annular open-cell porous support structure of the fiber is separated from a substrate flowing through the fiber lumen by an ultrathin dense membrane impermeable to enzyme but permeable to substrate and product. The coupled set of model equations describing the behavior of this reactor represents an extended Graetz problem in the fiber lumen, with diffusion through the ultrathin fiber skin and reaction in the microporous sponge region. Exact analytic expressions for substrate concentration profiles throughout an idealized fiber which incorporate the membrane and hydrodynamic mass transfer resistances are obtained for a first-order enzyme reaction, and numerical techniques for their evaluation are given. This analysis is extended to yield a numerical finite difference solution for nonlinear Michaelis-Menten reaction kinetics, which is shown to agree with the analytic solution, as Km/C0, the ratio of the Michaelis constant to the initial substrate concentration, becomes large (> 100).
107 citations
TL;DR: Analysis of analytical expressions for the radial and axial velocities and pressure profiles in the hollow-fiber bioreactor, operated in either the closed-shell (recycle) or open- shell (ultrafiltration) mode, by solving the coupled momentum and continuity equations in the fiber lumen, matrix, and surrounding shell demonstrate the complex dependence of the flow on membrane properties, hollow- fiber module geometry, and operating conditions.
79 citations
TL;DR: In this article, the first and zero-order limits of the Michaelis-Menten rate law are used in generating effectiveness factor expressions for a reactor system employing immobilized whole cells a biocatalyst.
Abstract: Analytical expressions, which allow the generation of effectiveness factor graphs for a reactor system employing immobilized whole cells a biocatalyst, are presented. In particular hollow-fiber devices (such as dialysis or ultrafiltration units) are considered. Such devices are analogs to a shell-and-tube heat exchanger. Whole cells are entrapped on the shell side: a nutrient solution is circulated through the tubes, substrate diffuses from the tube side, across the fiber, and into the cell mass on the shell side, where it irreversibly reacts to form product. The product back-diffuses into the circulating nutrient solution. The overall substrate mass-transfer process is hypothesized to be either diffusion limited in the hollow-fiber tube wall and/or the shell-side cell suspension and/or reaction limited at the enzyme sites within the whole cells. The first- and zero-order limits of the Michaelis-Menten rate law are used in generating effectiveness factor expressions. The effectiveness factor is a function of reaction order, Thiele modulus, diffusion coefficient ratio (defined as the effective substrate diffusivity in the hollow-fiber membrane wall divided by the effective substrate diffusivity in the cell suspension), partition coefficient, volume of the cell suspension, and hollow-fiber width. Equations for the effectiveness factor are also detailed when the hollow-fiber mass-transfer resistance is far greater than the cell suspension mass-transfer resistance. An effectiveness factor chart is presented specifically for the commercially available C-DAK 4 dialyzer (Cordis Dow Co., Miami, Florida). In general terms the effectiveness factor expressions are applicable for characterizing diffusion and reaction within a catalytically active cylindrical annulus, Whose inner surface offers a diffusional resistance and whose outer surface is impermeable to reactants. Some generalization of the Thiele modulus is undertaken which serves to draw the asymptotes on the effectiveness factor charts together. Comment is made on the variation of the slope of the effectiveness factor graph and its relation to the change in the observed reaction activation energy. Possible application of the model to the catalytic tube wall reactor is discussed.
54 citations
TL;DR: In this article, a series solution to the governing equation is presented assuming Darcy flow, first order kinetics, steady state transport, and irreversible reaction, for large axial Peclet number, Pe−1/3 < 1, it is permissible to ignore the mass transfer resistance in the lumen.
Abstract: Entrapped cells (or enzyme) in hollow fiber perfusion reactors is an attractive method for producing concentrated biologicals. Inherent in densely packed-cell masses are possible mass transfer limitations due to rate limiting transport processes resulting in loss of cell viability. To overcome this limitation, convective fluxes superimposed on diffusion have recently been proposed for entrapped animal cell perfusion bioreactors. We assessed whether radial fluid convection would enhance performance. In an asymptotic analysis using singular perturbation, we show that for large axial Peclet number, Pe−1/3 «« 1, it is permissible to ignore the mass transfer resistance in the lumen. Data from the literature appear to support this assumption. Radial convection of the feed in a shell and tube hollow fiber perfusion reactor is shown to be useful in increasing catalyst efficiency and production rates per unit volume. A series solution to the governing equation is presented assuming Darcy flow, first order kinetics, steady state transport, and irreversible reaction. The effect of convection is studied for many Thiele moduli, for each of two cases; catalyst activity being spatially uniform in one case and distributed in the second. Performance is essentially the same in each case.
51 citations