In the following:
The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1002/apj.234.
The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1016/j.aml.2008.05.003.
The DOI (Digital Object Identifier) link for this article is http://dx.doi.org//10.1016/j.cej.2009.01.028.
The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1007/s10910-008-9463-7.
Abstract
We analyze the steady-state production of a product produced through
the growth of microorganisms in both a continuous flow bioreactor
and in an idealized continuous flow membrane reactor. The
reaction is assumed to be governed by Monod growth kinetics
subject to noncompetitive product inhibition. Although this
reaction scheme is often mentioned in textbooks, a stability
analysis does not appear in the literature.
The steady-state solutions of the model are found and their stability determined as a function of the residence time. The performance of the reactor at large residence times is obtained. The key dimensionless parameter that controls the degree of non-competitive product inhibition is identified and we quantify the effect that this has on the reactor performance in the limit when product inhibition is `small' and `large'.
M.I. Nelson and J.L. Quigleyu and X.D. Chen. A fundamental analysis of continuous flow bioreactor and membrane reactor models with non-competitive product inhibition. Asia-Pacific Journal of Chemical Engineering, 4(1), 107-117, 2009. http://dx.doi.org/10.1002/apj.234.
Abstract
We analyse a model for the activated sludge process occurring in a
biological reactor without recycle. The biochemical processes
occurring within the reactor are represented by the activated sludge
model number 1 (ASM1). In the past the ASM1 model has been
investigated via direct integration of the governing equations. This
approach is time consuming as parameter regions of interest (in terms
of the effluent quality leaving the plant) can only be determined
through laborious and repetitive calculations. In this work we use
continuation methods to determine the steady-state behaviour of the
system. In particular, we determine bifurcation values of the
residence time, corresponding to branch points, that are crucial in
determining the performance of the plant.
M.I. Nelson and H.S. Sidhu. Analysis of the activated sludge model (number 1). Applied Mathematics Letters, 22, 629-635, 2009.
The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1016/j.aml.2008.05.003.
Abstract
The rate determining step of a number of biological processes is now
known to be described by Contois growth kinetics. In particular this
growth rate has been found to describe the treatment of contaminated
wastewaters containing biodegradable organic materials from a variety
of industrial processes. The efficient treatment of such waste
materials is of ever growing environmental concern. This contribution
is the first steady-state analysis for the treatment of
industrial wastewaters, obeying Contois kinetics,
in a cascade of continuous flow bioreactors without recycle.
The steady-states of the model are found and their
stability determined as a function of the residence time in each reactor
of the cascade.
Asymptotic solutions are obtained for the effluent concentration leaving a cascade of $n$ reactors for two scenarios, in which it is assumed that the reactors in the cascade have the same residence time In the first scenario the limiting case of large total residence time (&taut*) is considered. The effluent concentration leaving the reactor (Sn*) is found to be given by Sn* ≈ τ*-n, when n =1, 2, 3 and 4,. It is conjectured that this relationship holds for all n. Thus, for a fixed total residence time increasing the number of reactors in the the cascade has a dramatic effect on the quality of the wastewater leaving the cascade. In the second scenario, the limiting case when the total residence time is slightly larger than the washout point is considered. In this region, a small increase in the total residence time leads to a large decrease in the effluent concentration.
These results are illustrated by considering the anaerobic digestion of ice-cream wastewater.
M.I. Nelson and A. Holderu. A fundamental analysis of continuous flow bioreactor models governed by Contois kinetics. II. Reactor cascades. Chemical Engineering Journal, 149 (1-3), 406-416, 2009. http://dx.doi.org//10.1016/j.cej.2009.01.028.
Abstract
We investigate a chemostat model
in which the growth rate is given by
a Tessier expression with a variable yield coefficient. We combine analytical
results with path-following methods. The washout conditions are
found. When washout does not occur we establish the conditions under
which the reactor performance and reactor productivity
are maximised. We also determine the parameter region in which
oscillations may be generated in the reactor. We briefly discuss the
implications of our
results for comparing the performance of a single
bioreactor against a cascade of two bioreactors.
Keywords: Bioreactors; Bifurcation; Continuous Culture; Nonlinear Dynamics; Reaction Engineering; Stability; Variable yield.
M.I. Nelson and H.S. Sidhu. Analysis of a chemostat model with variable yield coefficient: Tessier kinetics The Journal of Mathematical Chemistry, 46(2), 303-321.
The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1007/s10910-008-9463-7.