In the following:
Abstract:
The standard Semenov model is extended to incorporate flammability experiments
in which oxygen-fuel-inert mixtures are assembled in a closed vessel
at a specified initial pressure and temperature.
The model contains three generic steady-state diagrams: unique; isola; and, mushroom. Of these the mushroom response represents the most severe hazard. The three types of response arise as the system is unfolded from a winged cusp singularity by varying the nitrogen fraction and/or the ambient temperature. A complete unfolding of this singularity is not possible as it is degenerate.
The isola steady-state structure contains two extinction limit points which define the lower and upper flammability limits. Unfolding these points with secondary bifurcation parameters mimics certain experimental procedures revealing qualitatively agreement between theory and experiment.
Keywords: boundary bifurcation, flammability limits, isola, singularity theory, winged-cusp.
M.I. Nelson. Flammability limits in closed vessel experiments: A Semenov model. Submitted, 2000.
Abstract
In this paper we investigate autothermal
behaviour in a catalytic reactor as a function of the coolant temperature.
Under specified conditions it is shown that fixing the coolant temperature
and heating the catalyst is
equivalent to fixing the power and varying the coolant temperature.
As the inflow concentration of the reactant is increased from zero there is a critical value at which a cusp singularity occurs. Below criticality there is a unique stable steady-state. Above criticality the steady-state diagram exhibits the classic S-shaped response curve. Above criticality three types of catalytic behaviour are distinguished, depending upon the values of the coolant temperature at the extinction and ignition points. These are: non-autothermal behaviour, autothermal behaviour, and self-ignition. The crossover points from non-autothermal to autothermal behaviour and from autothermal to self-ignition are defined by boundary bifurcations.
M.I. Nelson and X.D. Chen. Heterogeneously catalysed combustion in a continuously stirred tank reactor. II Autothermal behaviour in low temperature reactions Submitted, 2000.
Abstract
We model the extraction of polyphenolic compounds from grape skins during
the fermentation of grape juice. Our first model is based upon current
experimental practice and consists of a porous layer of grape skins
sitting on top of the fermenting juice. To maintain wetness of the grape
skins, which is required for extraction of polyphenolic compounds which
give red wine its character and quality, fermenting juice is
poured over the grape skins. We assume that the current process of
wetting the grapes for half an hour in a six hour period over seven
days is equivalent to a continuous operation of fourteen hours.
In the second model we consider
a new reactor configuration in which the cap is placed in a separate
reactor to the fermenting juice and recirculation is not used. For both
models we investigate how the performance of the system, as measured by
the fractional extraction, depends upon the flowrate and total run-time.
We find that the the system without recirculation
has the potential to significantly decrease the total processing time.
M.I. Nelson, R.O. Weber and A.G. Tate. Modelling of Open Vat Red Wine Fermenters. Submitted 2002.
Abstract
Previously coal drying has been modelled using a moving boundary analysis
with two approaches: one assuming that heat transfer is limiting and
one considering the diffusion of water vapor in a dry shell but still
having a moving sharp evaporation interface. In this paper, a new
Biot number and Lewis number analysis is presented
showing that there is a likelihood for a mass transfer limiting process
to occur depending on the parameter ranges such as particle size and
drying air temperature etc. Under certain circumstances, it may be more
fundamentally correct to assume a uniform temperature distribution and
to solve a PDE for effective water transfer. Alternatively, the
simultaneous heat and mass transfer PDEs can be solved in order
to account for the physics properly.
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. Part of this
growth is then wasted, and the remainder is returned to the system.
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 study the
dynamics of this system in a network of two coupled reactors arranged
in a series. We compare the treatment efficiency for a single tank
system with that of a two-reactor cascade. In the latter scenario
the total residence time is fixed and the residence time in the first
reactor is taken to be a design parameter. Process parameters that
ensure optimal performance are discussed.
S.D. Watt, H.S. Sidhu and M.I. Nelson. Wastewater Treatment by Activated Sludge Process: comparing the performance of a two-reactor cascade with a single tank. Accepted for publication in the International Journal of Environment and Waste Management, 11th April 2007.
Abstract
We investigate an experimentally verified model for the production of
ethanol through continuous fermentation. Previous studies have
investigated this model using direct integration. This approach is time
consuming as parameter regions of interest can only be determined
through laborious and repetitive calculations. Using techniques from
nonlinear dynamical systems theory, in particular a combination of
steady-state analysis and path following methods, practical insights
into operating strategies can be found. The optimisation of ethanol
productivity is considered here.
S.D. Watt, H.S. Sidhu, M.I. Nelson, A.K. Ray. Analysis of a model for ethanol production through continuous fermentation in multiple tanks. Submitted, 2008.
Abstract
In many circumstances it is useful to know the mean residence time of
food substrates within the body following digestion. For instance,
such information is crucial to estimate the extent to which dietary
components are fermented inside animal stomaches. The mean residence time
can be estimated by measuring the rate at which non-absorbable
markers, mixed as a supplement into an animals food, are deposited in the
animals faces. The experimental data are analysed with the use of an
appropriate mathematical model.
We analyse multicompartmental models for the flow of digesta along the gastrointestinal tract of animals. The problem can be treated as a sequence of `tanks' in series. Of interest is the fact that the volume of the tanks is not necessarily constant. For example, following digestion of food, secretion of pancreatic juices may occur; diluting the tracer. Thus the problem can be treated as a series of semi-batch reactors in series.
This problem is a good illustration of the application of the methods of chemical reactor engineering to a situation that, at first sight, does not appear to be a chemical engineering problem.
M.I. Nelson, H.S. Sidhu and X.D. Chen. The passage of food through animal stomachs: A chemical reactor engineering approach. Submitted, 2008.
Abstract
We investigate the behaviour of a reaction described by Michaelis-Menten
kinetics in an immobilised enzyme reactor (IER). The IER is treated
by a well-stirred flow reactor, in which the bound and unbounded enzyme
species are immobilised and therefore constrained to remain within the
reaction vessel. The product species leaves the bioreactor either in
the reactor outflow or by permeating through the semi-permeable reactor
wall. We explore how the concentration of recovered product and the
reactor productivity vary with process parameters, particularly those
associated with the separation of the product from the substrate through
the semi-permeable reactor wall.
We show that at low residence times membrane extraction through the reactor walls increases the total product concentration recovered whereas at high residence times membrane extraction decreases the total product concentration. We also show that the reactor productivity is maximised at high residence times. For reactor productivity the key control variable is the ratio of the reactor volume to the jacket volume (V*). If this ratio is greater than one, then membrane extraction increases the productivity. If this ratio is less than one, then membrane extraction decreases the productivity.
M.I. Nelson, H.S. Sidhu and A.A. Adesina. An operational model for a well-stirred membrane bioreactor: reactor performance analysis. Submitted, 2008.
Abstract
In this research we analyze the steady-state operation of a continuous
flow bioreactor, with or without
recycle, and an idealised, or non-idealised, 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 idealised recycle has the same
performance as an idealised membrane reactor and that the performance
of a non-idealised membrane reactor is identical to
an appropriately defined continuous flow bioreactor with
non-idealised 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 Submitted, 2008.
Abstract
When reactant consumption is ignored the flammability limits of a fuel-oxygen
mixture may be identified as bifurcation points on a steady-state
diagram. When reactant consumption is included there is no longer
a clear-cut definition of criticality.
We investigate the flammability of a simple global mechanism for
oxidation in a batch reactor. Regions of super- and sub-criticality are
distinguished using sensitivity analysis.
It is numerically convenient to reduce problems in two-dimensions to one-dimension. This can be done formally through the use of centre manifold techniques, or informally using physical reasoning. We investigate the extent to which diabatic two-dimensional problems may be accurately represented by a one-dimensional model.
M.I. Nelson and H.S. Sidhu. Flammability limits of an oxidation reaction in a batch reactor. Submitted 2008.
Abstract
We analyze the steady-state operation of a membrane
bioreactor system (MR) incorporating a sludge disintegration unit (SD).
The latter is used to prevent excess sludge production.
The relationship between process control parameters
and the performance of the MR-SD is determined by
finding the steady-states of the model and determining their
stability as a function of the residence time.
Asymptotic solutions for the steady-state solutions in the
limit of high residence times are obtained. These show that
at sufficiently high residence times
the mixed liquor suspended solids (MLSS) content of the bioreactor
is independent of the operation of the sludge disintegration unit.
Thus the main role played by the sludge disintegration unit is to
improve the performance at `low' residence times.
For a specified MLSS concentration
the values of the dimensionless
residence time and the sludge disintegration factor are determined
that ensure zero excess sludge production. If the
sludge disintegration factor is sufficiently high then
the MLSS content is guaranteed to be below the target value
(`negative' excess sludge production) provided
that the residence time is higher than the washout value.
It is shown that zero excess
sludge production can be achieved with a slight decrease in effluent
quality.
M.I. Nelson and T.C.L. Yuem. A fundamental analysis of a membrane bioreactor containing a sludge disintegration system Submitted, 2008.
Abstract
We investigate the behaviour of a reaction described by Michaelis-Menten
kinetics in an immobilised enzyme reactor (IER).
The IER is treated as a well-stirred flow reactor,
in which the immobilised 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 for the reactor.
To this end we show that the concentration of product is maximised at low
residence times whereas the productivity of the reactor is maximised at
high residence times.
M.I. Nelson, H.S. Sidhu and A.A. Adesina. Analysis of an immobilised enzyme reactor model. Submitted, 2008.
Abstract
We investigate a model for the production of ethanol through continuous
fermentation using Saccharomyces cerevisiae in a single reactor
and cascades of upto five reactors. Using path-following methods
we investigate how the ethanol productivity varies with the residence time in
each reactor of the cascade. With a substrate feed concentration
of 160 g/l we find the optimal productivity is
3.80 g/l/h,
5.08 g/l/h,
and
5.18 g/l/h in a single reactor,
a double reactor cascade and a triple reactor cascade respectively.
For the case of a cascade containing reactors of equal size we
investigate reactor configurations of up to five reactors and find
that the maximum productivity is obtained in a cascade containing three
reactors.
S.D. Watt, H.S. Sidhu, M.I. Nelson and A.K. Ray. Analysis of a model for ethanol production through continuous fermentation: ethanol productivity. Submitted, 2008.
Abstract
We investigate the behaviour of a reaction described by Michaelis-Menten
kinetics in an immobilised enzyme reactor (IER).
The IER is treated as a well-stirred flow reactor,
in which the immobilised 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
M
We use steady-state analysis to identify the best operating conditions for the reactor. To this end we show that the concentration of product is maximised at low residence times whereas the productivity of the reactor is maximised at high residence times.
M.I. Nelson, H.S. Sidhu and A.A. Adesina. Analysis of an immobilised enzyme reactor model with catalyst activation. Submitted, 2008.