In the following:
We analyze the steady-state operation of a generalized reactor model that encompasses a continuous flow bioreactor and an idealized continuous flow membrane reactor as limiting cases. The biochemical reaction kinetics is governed by a Contois growth model subject to noncompetitive substrate inhibition with a variable substrate yield coefficient. The steady-state performance of the reactor is predicted and stability of the steady-state solutions as a function of dimensionless residence time reported. Our results identified two cases of practical interest. The first feature corresponds to the case where solutions to both no-washout and washout conditions are bistable. The second feature identifies the parameter region in which periodic solutions can occur when the yield coefficient is not constant. Both these features are often undesirable in practical applications and must be avoided. Scaling of the model equations reveals that both the second-bifurcation parameters are functions of the influent concentration. Our results predict how the reactor behavior varies as a function of influent concentration and identify the range of influent concentrations where the reactor displays neither periodic nor bistable behavior.
R.T. Alqahtanip, M.I. Nelson and A.L. Worthy. Analysis of a Chemostat Model with Variable Yield Coefficient and Substrate Inhibition: Contois Growth Kinetics. Chemical Engineering Communications, 202(3), 332-344, 2015. http://dx.doi.org/10.1080/00986445.2013.836630. Trackable link: https://goo.gl/8b69FR.
We analyse the steady-state operation of two types of reactor cascade without recycle. The first is a standard reactor cascade in which the feed stream enters into the first reactor. The second is a step-feed reactor cascade in which an equal proportion of the feed stream enters each reactor in the cascade. The reaction is assumed to be a biological process governed by Monod growth kinetics with a decay coefficient for the microor- ganisms. The steady-states of both models are found for an arbitrary number of reactors and their stability deter- mined as a function of the residence time. We show that in a step-feed reactor cascade the substrate and biomass concentrations leaving the reactor of the cascade are identical to those leaving the first reactor of the cascade. We further show that this result is true for a general specific growth rate of the form μ(S,X). Thus for such processes the non-standard cascade offers no advantage over that of a single reactor. This is surprising because the use of a non-standard cascade has been proposed as a mechanism to improve the biological treatment of wastewater.
Harvinder S. Sidhu, Mark Ian Nelson and Easwaran Balakrishnan. An analysis of a Standard Reactor Cascade and a Step-Feed Reactor Cascade for Biological Processes Described by Monod Kinetics, Chemical Product and Process Modelling, 10(1), 27-37, 2015. http://dx.doi.org/10.1515/cppm-2014-0022. Trackable link: https://goo.gl/bVRvTi.
This paper analyses the steady-state operation of a generalized bioreactor model that encompasses a continuous-flow bioreactor and an idealized continuous-flow membrane bioreactor as limiting cases. A biodegradation of organic materials is modelled using Contois growth kinetics. The bioreactor performance is analysed by finding the steady-state solutions of the model and determining their stability as a function of the dimensionless residence time. We show that an effective recycle parameter improves the performance of the bioreactor at moderate values of the dimensionless residence time. However, at sufficiently large values of the dimensionless residence time, the performance of the bioreactor is independent of the recycle ratio.
A significant drawback of the activated sludge process is the production of excess `sludge'; the disposal of which can account for 50-60% of the running costs of a wastewater treatment plant. We investigate a model for the activated sludge process in which the influent contains a mixture of soluble and slowly biodegradable particulate substrate. Within the bioreactor, the particulate substrate is hydrolyzed to form soluble substrate. In turn, these are used for growth by the biomass. Biomass decay produces slowly biodegradable substrate and non-biodegradable particulates. Steady-state analysis is used to investigate how the amount of sludge formed depends upon the residence time and the use of a settling unit. We show that when the steady-state sludge content is plotted as a function of the residence time that there are three generic response diagrams. The value of the effective recycle parameter determines which type of response diagram is observed. If this parameter is greater than a critical value, then the sludge content is guaranteed to be greater than a target value. The dependence of this critical value upon the chemical oxygen demand in the feed and how the chemical oxygen demand is partitioned between its constitutive components is investigated.
A.O.M. Alharbip, M.I. Nelson, A.L. Worthy and H.S. Sidhu. Analysis of an activated sludge model in which dead biomass is recycled into slowly biodegradable particulate substrate. Asia-Pacific Journal of Chemical Engineering, 10(4), 580-597, 2015. http://dx.doi.org/10.1002/apj.1906.