In the following:
In this research we analyze the steady-state operation of a continuous flow bioreactor, with or without recycle, and an idealized or non-idealized 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 idealized recycle has the same performance as an idealized membrane reactor and that the performance of a non-idealized membrane reactor is identical to that of an appropriately defined continuous flow bioreactor with non-idealized 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 Chemical Engineering Communications, 199(3), 417-433, 2012. http://dx.doi.org/10.1080/00986445.2010.525155.
The steady-state treatment of industrial wastewaters in a cascade reactor with recycle is analyzed. A number of cascades with alternative arrangements of the settling units are considered. Specifically, we consider the case when the recycle stream leaving a settling unit which is placed around a reactor goes back into the feed stream for that reactor. The Contois kinetic model is used to study the degradation of biodegradable organic materials.
The steady-states for the model are found and their stability determined as a function of the total residence time in the cascade. Asymptotic solutions in the limit of large total residence time are obtained for the effluent concentration leaving a cascade. This analysis is used to determine the reactor configuration that minimizes the effluent concentration leaving the final reactor.
It is found that, when settling units are deployed, the optimised reactor cascade is obtained by using perfect recycle around the final reactor and imperfect recycle around the preceding reactors. When only one settling unit is used we find the performance of the reactor cascade is optimized at short residence times by placing it around the first reactor whilst at large total residence times the performance is optimized by placing it around the final reactor. However, at sufficiently large total residence times there is a little benefit gained by using any settling units.
R.T. Alqahtani^{p}. M.I. Nelson and A.L. Worthy. A fundamental analysis of continuous flow bioreactor models with recycle around each reactor governed by Contois kinetics. III. Two and three reactor cascades. A fundamental analysis of continuous flow bioreactor models with recycle around each reactor governed by Contois kinetics. III. Two and three reactor cascades. Chemical Engineering Journal, 183, 422-432, 2012. http://dx.doi.org/10.1016/j.cej.2011.12.061.
The steady-state production of a product produced through the growth of microorganisms in a continuous flow bioreactor is presented. A generalised reactor model is used in which both the classic well-stirred bioreactor and the idealised membrane bioreactor are considered as special cases. The reaction is assumed to be governed by Monod growth kinetics subject to non-competitive product inhibition. Inhibition is modelled as a decaying exponential function of the product concentration. This reaction scheme is well documented in the literature, although a stability analysis of the governing equations has not previously been presented. The performance of a well-stirred bioreactor with microorganisms death is also not currently available in the literature. The steady-state solutions for the models have been obtained, and the stability has been determined as a function of the residence time. The key dimensionless parameter (γ) that controls the degree of non-competitive product inhibition is obtained by scaling of the equations, and its effect on the reactor performance is quantified in the limit when product inhibition is `small'. The parameter γ is a scaled inhibition constant (K_{p}) that depends upon the substrate and product yield factors and the Monod constant [γ = (α_{s}/α_{p}) * (K_{s}/K_{p})].
Mark Ian Nelson and Wei Xian Lim ^{u}. A fundamental analysis of continuous flow bioreactor and membrane reactor models with non-competitive product inhibition. II. Exponential inhibition. Asia-Pacific Journal of Chemical Engineering, 7(1), 24-32, 2012. http://dx.doi.org/10.1002/apj.485.
Food processing wastewaters and slurries typically contain high concentrations of biodegradable organic matter. Before the wastewater can be discharged, the pollutant concentration must be reduced. One way to achieve this is by using a biological species (biomass) that consumes the organic matter (substrate). We investigate an unstructured kinetic model for a bioreactor with a variable yield coefficient, taking into account the death rate of the microorganisms. The growth rate is given by a Contois expression, which is often used to model the growth of biomass in wastewaters containing biodegradable organic materials. The analysis shows that the system has natural oscillations for some ranges of the parameters. We also investigate the effects of the death rate parameter on the region of periodic behaviour.
R.T. Alqahtani ^{p}, M.I. Nelson and A.L. Worthy. Analysis of a chemostat model with variable yield coefficient: Contois kinetics. In M. Nelson, M. Coupland, H. Sidhu, T. Hamilton and A.J. Roberts, editors, Proceedings of the 10th Biennial Engineering Mathematics and Applications Conference, EMAC 2011, ANZIAM J, 53, pages C155-C171, 2012. Download the paper from http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/5093 .
We consider the self heating process in a two dimensional spatially dependent model of a compost pile which incorporates terms that account for self heating due to both biological and oxidation mechanisms. As moisture is a crucial factor in both the degradation process and spontaneous ignition within a compost pile, this model consists of four mass-balance equations, namely, energy, oxygen, vapour and liquid water concentrations. Analyses are undertaken for different initial water contents within the compost pile. We show that when the water content is too low, the reaction is almost negligible; whereas when it is too high, the reaction commences only when the water content evaporates and the water ratio drops to within an appropriate range. However, for an intermediate water content range, the biological reaction is at its optimum and there is a possibility of spontaneous ignition within the compost pile.
T. Luangwilai ^{p}, H.S. Sidhu and M.I. Nelson. A two dimensional, reaction-diffusion model of compost piles. In M. Nelson, M. Coupland, H. Sidhu, T. Hamilton and A.J. Roberts, editors, Proceedings of the 10th Biennial Engineering Mathematics and Applications Conference, EMAC 2011, ANZIAM J, 53, pages C34-C53, 2012. Download the paper from http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/5083 .
The steady-state production of a product produced through the growth of microorganisms in a continuous flow bioreactor is presented. A generalised reactor model is used in which both the classic well-stirred bioreactor and the idealised membrane bioreactor are considered as special cases. The reaction is assumed to be governed by Monod growth kinetics subject to non-competitive product inhibition. Inhibition is modelled as a decreasing linear function of the product concentration with a finite cut-off. This reaction scheme is well documented in the literature, although a stability analysis of the governing equations has not previously been presented.
The steady-state solutions for the models have been obtained, and the stability has been determined as a function of the residence time. The key dimensionless parameter (γ) that controls the degree of non-competitive product inhibition is obtained by scaling of the equations, and its effect on the reactor performance is quantified in the limit when product inhibition is ``small'' and ``large''. The parameter γ is the reciprocal of a scaled inhibition constant (P_{m}) that depends upon the substrate and product yield factors and the Monod constant [γ = α_{s}K_{s}/( α_{p}P_{m}) ].
Mark Ian Nelson and Wei Xian Lim ^{u}. A fundamental analysis of continuous flow bioreactor and membrane reactor models with non-competitive product inhibition. III. Linear inhibition. Asia-Pacific Journal of Chemical Engineering, 7(3), 343-352, 2012. http://dx.doi.org/10.1002/apj.545.
This paper considers semi-analytical solutions for a class of generalised logistic partial differential equations with both point and distributed delays. Both one and two-dimensional geometries are considered. The Galerkin method is used to approximate the governing equations by a system of ordinary differential delay equations. This method involves assuming a spatial structure for the solution and averaging to obtain the ordinary differential delay equation models. Semi-analytical results for the stability of the system are derived with the critical parameter value, at which a Hopf bifurcation occurs, found. The results show that diffusion acts to stabilise the system, compared to equivalent non-diffusive systems and that large delays, which represent feedback from the distant past, act to destabilize the system. Comparisons between semi-analytical and numerical solutions show excellent agreement for steady state and transient solutions, and for the parameter values at which the Hopf bifurcations occur.
H.Y. Alfifi ^{p}, T.R. Marchant and M.I. Nelson. Generalised Diffusive Delay Logistic Equations: Semi-analytical solutions. Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms, 19, 579--586, 2012.
We analyse a model for a continuously stirred tank reactor with imperfect mixing in which the reactor is represented by two well mixed compartments with material transfer between them. These reactors represent `highly agitated' and `less agitated' regions. The chemical model used is a quadratic autocatalytic scheme with linear decay of the autocatalyst. We investigate how the reactor performance depends upon the degree of mixing in the reactor and the size of the less agitated region. Surprisingly, the performance of the reactor with sufficiently small values of mixing is inferior to that with no mixing between the compartments.
A.H. Msmali ^{p}, M.I. Nelson and M. Edwards. The effect of incomplete mixing upon quadratic autocatalysis. In M. Nelson, M. Coupland, H. Sidhu, T. Hamilton and A.J. Roberts, editors, Proceedings of the 10th Biennial Engineering Mathematics and Applications Conference, EMAC 2011, ANZIAM J, 53, pages C266-C279, 2012. Download the paper from http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/5105 .
Semi-analytical solutions for a cubic autocatalytic reaction, with linear decay and a precursor chemical, are considered. The model is coupled with diffusion and considered in a one-dimensional reactor. In this model the reactant is supplied by two mechanisms, diffusion via the cell boundaries and decay of an abundant precursor chemical present in the reactor. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations in the reactor. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations and analyzed to obtain semi-analytical results for the reaction-diffusion cell. Singularity theory and a local stability analysis are used to determine the regions of parameter space in which the different types of bifurcation diagrams and Hopf bifurcations occur. The effect of the precursor chemical concentration is examined in detail and some novel behaviours are identified.
M.R. Alharthi ^{p}, T.R. Marchant and M.I. Nelson. Semi-analytical solutions for cubic autocatalytic reaction-diffusion equations; the effect of a precursor chemical. In M. Nelson, M. Coupland, H. Sidhu, T. Hamilton and A.J. Roberts, editors, Proceedings of the 10th Biennial Engineering Mathematics and Applications Conference, EMAC 2011, ANZIAM J, 53, pages C511-C524, 2012. Download the paper from http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/5340 .
The aim of the study is to describe the work pattern of personal care workers (PCWs) in nursing homes. This knowledge is important for staff performance appraisal, task allocation and scheduling. It will also support funding allocation based on activities.
A time-motion study was conducted in 2010 at two Australian nursing homes. The observation at Site 1 was between the hours of 7:00 and 14:00 or 15:00 for 14 days. One PCW was observed on each day. The observation at Site 2 was from 10:00 to 17:00 for 16 days. One PCW working on a morning shift and another one working on an afternoon shift were observed on each day. Fifty-eight work activities done by PCWs were grouped into eight categories. Activity time, frequency, duration and the switch between two consecutive activities were used as measurements to describe the work pattern.
Personal care workers spent about 70.0% of their time on four types of activities consistently at both sites: direct care (30.7%), indirect care (17.6%), infection control (6.4%) and staff break (15.2%). Oral communication was the most frequently observed activity. It could occur independently or concurrently with other activities. At Site 2, PCWs spent significantly more time than their counterparts at Site 1 on oral communication (Site 1: 47.3% vs. Site 2: 63.5%, P=0.003), transit (Site 1: 3.4% vs. Site 2: 5.5%, P<0.001) and others (Site 1: 0.5% vs. Site 2: 1.8%, P<0.001). They spent less time on documentation (Site 1: 4.1% vs. Site 2: 2.3%, P<0.001). More than two-thirds of the observed activities had a very short duration (1 minute or less). Personal care workers frequently switched within or between oral communication, direct and indirect care activities.
At both nursing homes, direct care, indirect care, infection control and staff break occupied the major part of a PCWs work, however oral communication was the most time consuming activity. Personal care workers frequently switched between activities, suggesting that looking after the elderly in nursing homes is a busy and demanding job.
S-Y Qian ^{p}, P. Yu, Z-Y Zhang, D.M. Hailey, P.J. Davy and M.I. Nelson. The work pattern of personal care workers in two Australian nursing homes: a time-motion study. BMC Health Services Work, 12, 305, 2012. http://dx.doi.org/10.1186/1472-6963-12-305.
The aim of this research is to investigate the effect of incomplete mixing upon the existence of periodic solutions. To this end we study the behaviour of the Belousov-Zhabotinskii (B-Z) reaction in a batch reactor. The B-Z reaction is a well studied chemical system that exhibits periodic behaviour. Furthermore, simplified mathematical models exist which have been validated both against experimental data and larger chemical mechanisms. Specifically, we study the `Oregonator' model for the B-Z reaction due to Fields and Noyes (1974). This consists of five chemical reactions involving three chemical intermediates. We extend this model by combining it with a two parameter incomplete mixing model to investigate the effect of incomplete mixing upon the existence of periodic solutions.
In the incomplete mixing model the batch reactor is split into two compartments: a larger and a smaller compartment; the latter representing a stagnant region. The incomplete mixing parameters are the size of the stagnant region (ε) and a parameter controlling the degree of mixing between the regions (δ). IN the limit that delta approaches zero epsilon becomes a dead volume in the reactor. Perfect mixing corresponds to the limit in which delta approaches infinity.
We investigate how the periodicity of the B-Z reaction depends upon the degree of mixing in the reactor and the size of the stagnant compartment.
A.H. Msmali ^{p}, M.I. Nelson and M. Edwards. The effect of incomplete mixing upon the Belousov-Zhabotinskii reaction. In Proceedings of the Australasian Chemical Engineering Conference, CHEMECA 2012, pages 1--10. Engineers Australia, 2012. On CDROM. ISBN 978 1 922107 59 6.
This paper considers the self-heating process which occurs in a compost pile using one-dimensional spatially-dependent models and incorporating terms that account for self-heating due to both biological and oxidation mechanisms. As the moisture content in a compost pile is a crucial factor in its degradation process, we utilise a model which incorporates four mass-balance equations, namely, energy, oxygen, vapour and liquid water concentrations, to investigate the behaviour of compost piles when moisture content is present.
Analyses of different initial water contents within a compost pile, different ambient relative humidities and different amounts of water added to the pile by rainstorms are undertaken. We show that the effects of the ambient relative humidity are not significant but that a rainstorm either accelerates or decelerates a compost pile's self-heating process significantly depending on the initial moisture content of the compost materials and the amount of water that is added.
T. Luangwilai ^{p}, H.S. Sidhu and M.I. Nelson. Understanding the role of moisture in the self-heating process of compost piles. In Proceedings of the Australasian Chemical Engineering Conference, CHEMECA 2012, pages 1--13. Engineers Australia, 2012. On CDROM. ISBN 978 1 922107 59 6.