In the following:
Abstract
In this research we analyze the steady-state operation of a continuous flow bioreactor, with or without recycle, and an idealized or nonidealized continuous flow membrane reactor. The model extends to include a fixed bed reactor where a fraction of the biomass is detached by the flow. The reaction is assumed to be governed by Tessier growth kinetics. We show that a flow reactor with idealized recycle has the same performance as an idealized membrane reactor and that the performance of a nonidealized membrane reactor is identical to that of an appropriately defined continuous flow bioreactor with nonidealized recycle. The performance of all three reactor types can therefore be obtained by analyzing a flow reactor with recycle. The steady states of the recycle 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.
M.I. Nelson, E. Balakrishnan and and H.S. Sidhu. A fundamental analysis of continuous flow bioreactor and membrane reactor models with Tessier kinetics Chemical Engineering Communications, 199(3), 417-433, 2012. http://dx.doi.org/10.1080/00986445.2010.525155.
Abstract
The steady-state treatment of industrial wastewaters in a cascade reactor with
recycle is analyzed. A number of cascades with alternative arrangements of the
settling units are considered. Specifically, we consider the case when the
recycle stream leaving a settling unit which is placed around a reactor goes
back into the feed stream for that reactor. The Contois kinetic model is used
to study the degradation of biodegradable organic materials.
The steady-states for the model are found and their stability determined as a function of the total residence time in the cascade. Asymptotic solutions in the limit of large total residence time are obtained for the effluent concentration leaving a cascade. This analysis is used to determine the reactor configuration that minimizes the effluent concentration leaving the final reactor.
It is found that, when settling units are deployed, the optimised reactor cascade is obtained by using perfect recycle around the final reactor and imperfect recycle around the preceding reactors. When only one settling unit is used we find the performance of the reactor cascade is optimized at short residence times by placing it around the first reactor whilst at large total residence times the performance is optimized by placing it around the final reactor. However, at sufficiently large total residence times there is a little benefit gained by using any settling units.
R.T. Alqahtanip. M.I. Nelson and A.L. Worthy. A fundamental analysis of continuous flow bioreactor models with recycle around each reactor governed by Contois kinetics. III. Two and three reactor cascades. A fundamental analysis of continuous flow bioreactor models with recycle around each reactor governed by Contois kinetics. III. Two and three reactor cascades. Chemical Engineering Journal, 183, 422-432, 2012. http://dx.doi.org/10.1016/j.cej.2011.12.061.
Abstract
The steady-state production of a product produced through the growth of
microorganisms in a continuous flow bioreactor is presented. A generalised
reactor model is used in which both the classic well-stirred bioreactor and
the idealised membrane bioreactor are considered as special cases. The
reaction is assumed to be governed by Monod growth kinetics subject to
non-competitive product inhibition. Inhibition is modelled as a decaying
exponential function of the product concentration. This reaction scheme is
well documented in the literature, although a stability analysis of the
governing equations has not previously been presented. The performance of a
well-stirred bioreactor with microorganisms death is also not currently
available in the literature. The steady-state solutions for the models have
been obtained, and the stability has been determined as a function of the
residence time. The key dimensionless parameter (γ) that controls the
degree of non-competitive product inhibition is obtained by scaling of the
equations, and its effect on the reactor performance is quantified in the
limit when product inhibition is `small'. The parameter γ is a scaled
inhibition constant (Kp) that depends upon the substrate and
product yield factors and the Monod constant
[γ = (αs/αp)
* (Ks/Kp)].
Mark Ian Nelson and Wei Xian Lim u. A fundamental analysis of continuous flow bioreactor and membrane reactor models with non-competitive product inhibition. II. Exponential inhibition. Asia-Pacific Journal of Chemical Engineering, 7(1), 24-32, 2012. http://dx.doi.org/10.1002/apj.485.