In the following:
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.
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.
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.
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.
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.
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.
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.
We investigate the behavior 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 bioreactor either in the reactor outflow or it permeates through the semi-permeable reactor wall and is removed through the jacket side. The aim of this work is to explore how important practical quantities, the concentration of recovered product and the reactor productivity, vary with process parameters, most notable those associate with separation of the product from the substrate through the semi-permeable reactor wall.
We show that at low residence times membrane extraction increases the total product concentration recovered, compared to a reactor without membrane extraction, whereas at high residence times membrane extraction decreases the total product concentration. For reactor productivity the key control variable is the reactor volume ratio (V*), which is the ratio of the volumes of the reactor to that of the jacket. 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. In either case 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.
In many agricultural and pharmaceutical case studies it is important to know the quantity of nutrients, or the specific amount of an oral drug absorbed, into the body of an animal. The rate of absorption is dependant upon the mean residence time of the substance through the gastrointestinal tract (GIT). Thereby it is important to know the mean residence time of food substrates within the GIT follo wing digestion. The mean residence time of digesta may be estimated by an in vivo experiment in which a non-absorbable marker, supplemented into a food source, is fed to an animal. An estimate of the mean residence time is obtained by measuring the rate at which the non-absorbable marker is deposited in the animal faeces. The experimental data are analysed with the use of an appropriate mathematical model.
This problem is a good illustration of the application of the mathematical techniques taught in first-year calculus courses including solving systems of linear differential equations, and the use of Taylor series expansions to approximate the behaviour of the solution at small and large values of time. This modelling task can also be used to provide first year university students with the experience of undertaking individual research, utilizing several literature sources to obtain parameter values, an essential skill in a higher education learning environment.
Rodney Van Bentumu and Mark Ian Nelson. The Passage of Food Through an Animal Stomach: A case Study for first-year calculus students. Submitted 2009.
R.T. Alqahtani p, M.I. Nelson and A. Worthy. The biological treatment of industrial wastewater: Contois kinetics. Submitted, 2011.
X.D. Chen, H.S. Sidhu and M.I. Nelson. Unique properties of dimensionless crossing-point-temperature (CPT) versus Frank-Kamenetskii Reactivity Parameter in Transient Self-Heating Test. Submitted, 2011.
M.I. Nelson and T.C.L. Yuem. A mathematical analysis of a membrane bioreactor containing a sludge disintegration system Submitted, 2012.
S. Qian, P. Yu, D. Hailey, P. Davy & M.I. Nelson. How personal carers spend their time on direct care activities in two Australian nursing homes: a time-motion study. Submitted, 2012.