In the following:
This paper is available at http://www.bepress.com/cppm/vol4/iss3/14.
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. 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. http://dx.doi.org/10.1007/s10910-008-9463-7.
Abstract
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.
Abstract
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.
Abstract
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.
http://www.bepress.com/cppm/vol4/iss3/14.
Abstract
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 dormant 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.