In the following:
This paper is available at http://www.bepress.com/cppm/vol4/iss3/14.
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.
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. http://dx.doi.org/10.1016/j.aml.2008.05.003.
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.
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. http://dx.doi.org/10.1007/s10910-008-9463-7.
We investigate a model for the treatment of wastewater in the activated sludge process. The process is based on the aeration of waste water with flocculating biological growth, followed by the separation of treated waste water from biological growth. The biochemical model consists of two types of bacteria: sludge bacteria and sewage bacteria; and two types of ciliated protozoa: free-swimming ciliates and ciliates attached to sludge flocs. A combination of steady-state analysis, path following techniques and numerical integration of the governing equations are used to compare the performance for a single tank system with that of a two-reactor cascade.
H.S. Sidhu, S.D. Watt, and M.I. Nelson. Performance comparison between a two-reactor cascade and a single tank in an Activated Sludge Wastewater Treatment Process. International Journal of Environment and Waste Management, 3(3/4), 214-225 2009. http://dx.doi.org/10.1504/IJEWM.2009.026338.
This paper reports the lipase-catalyzed esterification of oleic acid (with ethanol) in a batch reactor at temperatures between 298 to 338 K using a wide range of the reactant ratio, β (0<β<2). All kinetics runs were performed under conditions of negligible transport limitations. The sigmoidal behaviour evidenced from the initial rate - substrate concentration curve suggests the allosteric nature of the acrylic-supported Aspergillus lipase and hence the data were described by a non-Michaelis Menten kinetic model. The associated oleic acid binding coefficient and ethanol inhibition constant were obtained as 2.382 mmol/L and 1.643 mmol/L respectively. The allosteric effect was attributed to conformational change in the enzyme site occasioned by the presence of trace amounts of water formed within the first few minutes of the reaction. Indeed, the transient water concentration profile at different β values revealed an initial overshoot in water concentration before the relaxation to final equilibrium value after about 6 hours. The appearance of the initial overshoot increased with decreasing β. The water concentration history is symptomatic of two 1st order interacting processes containing a linear generative term for water (input) consistent with the two-enzyme state concerted symmetry proposition for feedback autoregulatory behaviour. The rate-temperature envelope showed a maximum at about 318 K suggesting protein denaturation above this temperature. Even so, a fit of the raw data obtained between 298 to 318 K gave an activation energy of 22.4 kJ/mol typical of many enzymatic reactions. FTIR spectra of the catalysts were displayed peaks at wave-numbers 1723.23 /cm and 1666.12 /cm assigned to COO- and NH2+ groups respectively for both fresh and used specimens. BET measurements, however, revealed a significant drop in surface area between fresh (165 m2/g) and used (5-20 m2/g) catalysts. This was attributed to pore blockage of the immobilised enzyme by the relatively large oleic-acyl-lipase complex left after the reaction.
M.S. Mahmudp, T. Safinski, M. Nelson, H.S. Sidhu and A.A. Adesina. Kinetic Analysis of Oleic Acid Esterification Using Lipase as Catalyst in a Microaqueous Environment, Proceedings 8th World Congress of Chemical Engineering, paper DNC3ZU (on USB key). 2009. ISBN 0-920804-44-6.
We investigate the behavior of a reaction described by Michaelis-Menten kinetics in an immobilized enzyme reactor (IER). The IER is treated as a well stirred flow reactor, in which the immobilized bounded and unbounded enzyme species are constrained to remain within the reaction vessel. The product species leaves the IER in the reactor outflow. Before the substrate can react with the enzyme, the enzyme must first be activated by absorption of an activator. We use steady state analysis to identify the best operating conditions or the reactor. To this end, we show that the concentration of product is maximized at low residence time whereas the productivity of the reactor is maximized at high residence times.
M.I. Nelson, H.S. Sidhu and A.A. Adesina.
Analysis of an Immobilised Enzyme Reactor with Catalyst Activation.
Chemical Product and Process Modeling
4, Issue 3, Article 14, 2009.
We formulate and investigate a one-dimensional model for self-heating in compost piles. The self-heating occurs through a combination of biological and chemical mechanisms. Biological heat generation is known to be present in most industrial processes handling large volumes of bulk organic materials. The heat release rate due to biological activity is modelled by a function which at sufficiently low temperatures is a monotonic increasing function of temperature. At higher temperatures it is a monotonic decreasing function of temperature. This functionality represents the fact that micro-organisms die or become domant at higher temperature. The heat release due to oxidation reaction is modelled by Arrhenius kinetics. The model consists of mass balance equations for oxygen and energy. Steady-state temperature diagrams are determined as a function of the size of the compost pile and the flow rate of air through the pile. We show that there is a range of flow rates for which elevated temperatures, including the possibility of spontaneous ignition, occur within the pile.
T. Luangwilaip, H.S. Sidhu, M.I. Nelson and X.D. Chen. Biological self-heating of compost piles with air flow. In Proceedings of the 37th Australasian Chemical Engineering Conference, CHEMECA 2009, (on CDROM), Engineers Australia, 2009. ISBN 978-0858259225.