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The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1016/j.cej.2010.10.017.
The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1137/110821688.
Mathematical models have been extensively used in veterinary science to analyse data collected from experiments measuring the flow of digesta through the gastrointestinal tract (GIT) of ruminants. In this paper a classic two compartment digesta flow model is reformulated into a two compartment CSTR (continuous stir tank reactor) model. A segregated reactor model is then obtained by incorporating `non-mixing' stagnant regions into the ideal CSTR model. The ability to incorporate non-ideal mixing into the model allows a more accurate representation of the conditions within the GIT.
In analyzing this model our main focus is on the cumulative excretion curve, as this is used to estimate the mean residence time through the GIT. The mean residence time is an important indicator of animal nutrition, directly affecting the feeding strategy of an animal. The effects of stagnant regions in a `two stomach' GIT model are investigated by comparing the cumulative excretion curve with that obtained from an equivalent ideal `two stomach' GIT model. This comparison characterises a trend that non-ideal mixing delays the excretion of waste from the GIT.
The effect upon the cumulative excretion curve of small changes in parameter values is then investigated. Small changes in the size of the first stomach, and the division of the initial digesta ingested between the `well-mixed' and stagnant regions of the first stomach, are found to substantially effects the cumulative excretion of digesta from the GIT of a ruminant animal. This investigation is a good example of the applications of chemical engineering to a problem outside the traditional definition of the discipline.
Rodney Van Bentumu and Mark Ian Nelson. Modelling the Passage of Food Through an Animal Stomach: a Chemical Reactor Engineering Approach. Chemical Engineering Journal, 166(1), 315-323, 2011
The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1016/j.cej.2010.10.017.
R. Hudsonp, A. Porter and M. Nelson. Statistical Analysis Model Predicting Computer Use in Mathematics. In S. Barton et al. (Eds.), Proceedings of Global Learn Asia Pacific 2011, pages 712-720, Association for the Advancement of Computing in Education, Chesapeake, VA, USA, 2011.
An existing model for solvent penetration and drug release from a spherically shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of the polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as non-Fickian or Case~II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective.
M. Hsieh p, S.W. McCue, T.J. Moroney and M.I. Nelson. Drug diffusion from polymeric delivery devices: a problem with two moving boundaries. In W.~McLean and A.~J. Roberts, editors, Proceedings of the 15th Biennial Computational Techniques and Applications Conference, CTAC-2010, volume~52 of ANZIAM J., pages C549--C566, August 2011. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/3940 [August 3, 2011].
We analyse a model for the biological treatment of wastewater that is based upon Contois kinetics rather than the more commonly used Monod kinetics. The former growth rate law has increasingly been found to model the degradation of biodegradable organic materials. In particular, we investigate the steady state effluent concentration leaving a cascade of two reactors. Our particular concern is the improvement in performance that can be achieved through the use of one or two recycling units. With even one settling unit various configurations can be utilized. Combinations of reactors and recycle units are investigated. Surprisingly, we find that in general the performance of the reactor cascade with perfect recycle around each reactor does not produce the best performance. Also, contrary to what has been written in literature, the performance of a reactor cascade with recycle around the whole cascade does not always produce the best performance. Application of these results will lead to an improvement in the performance of reactor cascades for processes controlled by Contois kinetics.
R.T. Alqahtani p, M.I. Nelson and A.L. Worthy. A mathematical analysis of continuous flow bioreactor models governed by contois kinetics: A two reactor cascade. In Proceedings of the Australasian Chemical Engineering Conference, CHEMECA 2011, pages 1--11. Engineers Australia, 2011. On CDROM. ISBN 978 085 825 9225.
This paper considers the self-heating process occurring in a compost pile using one- and two-dimensional spatially-dependent models and incorporating terms that account for self-heating due to both biological and oxidative 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 is, at sufficiently low temperatures, a monotonically increasing function of temperature and, at higher temperatures, a monotonically decreasing function of temperature. This functionality represents the fact that micro-organisms die or become dormant at high temperatures. The heat release rate due to oxidation reactions is modelled by Arrhenius kinetics. As moisture is another crucial factor in the degradation process of compost, 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, for the case when the water content is too high, the reaction only commences when the water content evaporates and the water ratio drops into an appropriate range. However, for an intermediate water content range, biological reaction is at its optimum and there is a possibility of spontaneous combustion of the compost pile.
T. Luangwilai p, H.S. Sidhu, M.I. Nelson, and X.D. Chen. Modelling the effects of moisture content in compost piles. In Proceedings of the Australasian Chemical Engineering Conference, CHEMECA 2011, pages 1--12. Engineers Australia, 2011. On CDROM. ISBN 978 085 825 9225.
We consider a model to describe the performance of a membrane-coupled anaerobic fermentor which was developed and calibrated using experimental data by Kim and Chung (2010). The model consists of six differential equations, modelling the concentration of five biochemical species and the rate of gasification. In the original work it was assumed that reactor is well-mixed. We use a two parameter mixing model to investigate the effect of incomplete mixing upon the performance of this process. The parameters in the mixing mode are the size of the stagnant region (ε) and a parameter controlling the degree of mixing between the regions (δ ). Perfect mixing corresponds to the limit in which delta approaches infinity. There are six differential equations in each region.
We investigate how the concentration of volatile fatty acids in the agitated region depends upon the degree of mixing in the reactor and the size of the stagnant region.
A.H. Msmali p, M.I. Nelson and J. Kavanagh. The effect of incomplete mixing upon the performance of a membrane-coupled anaerobic fermentor. In Proceedings of the Australasian Chemical Engineering Conference, CHEMECA 2011, pages 1--12. Engineers Australia, 2011. On CDROM. ISBN 978 085 825 9225.
We analyze the steady-state operation of an activated sludge process incorporating a sludge disintegration unit (SDU) to prevent excess sludge production. We obtain an understanding of the effect of the SDU by finding the steady-state solutions of the model and determining their stability. For a specified mixed liquor suspended solids (MLSS) content the values of the residence time and the sludge disintegration factor are determined that ensure zero excess sludge production. We show that if the sludge disintegration factor is sufficiently high then the MLSS content is guaranteed to be below the target value for all values of the residence time.
M.I. Nelson and E. Balakrishnan. An analysis of an activated sludge process containing a sludge disintegration system. In Proceedings of the Australasian Chemical Engineering Conference, CHEMECA 2011, pages 1--11. Engineers Australia, 2011. On CDROM. ISBN 978 085 825 9225.
A continuous flow bioreactor is a well-stirred vessel containing microorganisms (X) through which a substrate (S) flows at a continuous rate. The microorganisms grow through the consumption of the substrate, producing more microorganisms and products. The products will typically contain carbon dioxide, nitrogen, water and other species, including biological compounds, specific to the process under consideration. The nature of these products is unimportant in this study. Unused substrate, microorganisms, and products flow out of the reactor. The use of a continuous flow bioreactor to treat sewage or industrial wastewaters is known as the activated sludge process.
One drawback associated with the activated sludge process is the production of `sludge'. Traditional methods for disposing of excess sludge, which include incineration, the use of landfill sites and dumping at sea, are becoming increasingly regulated in many countries due to environmental concerns about the presence of potentially toxic elements in the sewage sludge. Furthermore, a combination of the limited amount of land available for landfill, particularly in urban areas, with stringent legislation has seen the economic costs of using landfill sites to increase sharply. It should be noted that incineration does not eliminate the need for landfill sites as a product of incineration is an ash containing high heavy materials content and general toxicity. Thus there is a pressing need, and growing interest, in methods that reduce the volume and mass of excess sludge produced as part of biological wastewater treatment processes.
A promising method to reduce excess sludge production is to increase the biodegradability of the sludge by disintegrating it within the reactor. This approach works primarily by causing the disintegration of bacterial cell walls. Among the many techniques that have been reported for application to the activated sludge process, chemical treatments and ozone treatments have been the most widely adopted commercially [Oh et al, 2007]. In processes involving ozonation a part of the sludge is removed from the reactor and treated with ozone in a sludge disintegrator. This ozonation stage converts the live sludge into a mixture of soluble substrate and particulates. The liquidized sludge is then returned to the bioreactor as a feed solution where the soluble substrate is biodegraded by live sludge. These techniques have shown to lead to much lower levels of MLSS (mixed liquor suspended solids).
A simple model is considered for a reactor cascade in which each reactor may be connected to both a settling unit and a sludge disintegration unit (SDU). The sludge disintegration unit is not modelled per se. Instead sludge disintegration terms are added to a conventional activated sludge model. These terms assume that the disintegrator unit destroys the biochemical activity of the sludge, converting a fraction, α, directly into usable substrate and the remainder, (1-α), into organic particulates. We obtain a qualitative understanding of the performance of the process by finding the steady-state solutions of the model and determining their stability.
For a specified mixed liquor suspended solids (MLSS) content the values of the dimensionless residence time and the sludge disintegration factor are determined that ensure zero excess sludge production. We show that if the sludge disintegration factor is sufficiently high then the MLSS content is guaranteed to be below the target value provided that the residence time is higher than the washout value.
M.I. Nelson and E. Balakrishnan. An analysis of an activated sludge process containing a sludge disintegration system. In F. Chan, D. Marinova, and R.S. Anderssen, editors, 19th International Congress on Modelling and Simulation, MODSIM 2011, pages 331-337. Modelling and Simulation Society of Australia and New Zealand, 2011. On CDROM. ISBN 978-0-9872143-1-7. Download the paper from http://www.mssanz.org.au/modsim2011/A3/nelson.pdf.
Many industrial processes, particularly in the food industry, produce slurries or wastewaters containing high concentrations of biodegradable organic materials. Before these contaminated wastewaters can be discharged the concentration of these pollutants must be reduced. A method which has been extensively employed to remove biodegradable organic matter is biological treatment. In this process the wastewater (or slurry) is passed through a bioreactor containing biomass which grows through consumption of the pollutants.
The industrial treatment of wastewaters typically employs a reactor cascade. In a reactor cascade of n reactors the effluent stream from the ith reactor in the cascade acts as the feed stream for the (i+1)th reactor, i.e. the next reactor. The efficiency of the reactor cascade may be improved by using a settling unit. The settling unit `captures' and concentrates the microorganisms in the effluent stream of reactor (i) and recycles it into the influent stream of reactor (j, j≤i). The benefit of using the settling unit is that it increases the concentration of microorganisms in reactor j, hopefully leading to an improvement in the performance of the cascade. When i=j the operation of the settling unit is characterised by a single parameter, the dimensionless recycle parameter, which can take values between zero (no recycle) and one (perfect recycle). When i<j the operation of the settling unit is characterised by two parameters: a concentrating factor (C) and a recycle parameter (R). The maximum value of the concentrating factor that be achieved in a specific settling unit is related to the value of the recycle parameter.
We investigate how recycle affects the performance of a reactor cascade with four reactors. We consider the use of one settling unit. Steady state analysis is used to study and compare the performance for the various reactor configurations.
In the first configuration we consider the scenario in which the effluent stream leaving a settling unit placed around the ith reactor enters the feed stream for the ith reactor. With even one settling unit various configurations can be utilized. For instance, the settling unit can be placed after the first, second, third or fourth reactor. We find that if the settling unit is placed around the final reactor the performance of the cascade is optimised when the settling unit operates with perfect recycle. If the settling unit is placed around one of the other reactors the performance is optimised with a value of the dimensionless recycle parameter less than one.
For the second configuration we consider the scenario in which the settling unit is placed after the fourth reactor and the effluent stream from the settling unit is recycled back into the first reactor. We find that there is a critical value of the residence time. If the residence time is below the critical value then the settling unit improves the performance of the reactor cascade whereas if the residence time is above the critical value the performance of the cascade is reduced compared to that of a cascade without a settling unit.
We conclude by noting that the first configuration outperforms the second configuration at high residence time. This is noteworthy as the latter is often used in industry.
R.T. Alqahtani p, M.I. Nelson and A.L. Worthy. A mathematical model for the biological treatment of industrial wastewaters in a cascade of four reactors In F. Chan, D. Marinova, and R.S. Anderssen, editors, 19th International Congress on Modelling and Simulation, MODSIM 2011, pages 256-262. Modelling and Simulation Society of Australia and New Zealand, 2011. On CDROM. ISBN 978-0-9872143-1-7. Download the paper from http://www.mssanz.org.au/modsim2011/A3/alqahtani.pdf.
A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modeled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyze the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multilayered drug delivery device is suggested, which allows for more flexible control of drug release.
S.W. McCue, M. Hsieh p, T.J. Moroney and M.I. Nelson. Asymptotic and numerical results for a model of solvent-dependent drug-diffusion through polymeric spheres. SIAM Journal on Applied Mathematics, 71(6), 2287-2311, 2011. http://dx.doi.org/10.1137/110821688.
Spray drying is a primary process for the manufacture of powders, which satisfy a vast array of societal demands in the areas of nutrition, health and medicine. The functionality of a spray-dried product begins with its incorporation into water (wetting followed by dispersion). Therefore, as its surface chemical composition and structure determine its first contact with water (that is, its hydrophilic nature), these are of prime concern. Laboratory studies on this first layer, which is in the order of several nm in depth from the surface, have been extensive but there is still a lack of a fundamental quantitative explanation of it. This has hampered the development of any sort of approach, which would enable industries to predict what the product may be like before conducting costly trials. This current study is an attempt to describe the on-set of solid formation around the outermost layer of a single droplet during the drying process using an innovative `conventional' continuum approach, i.e. diffusion-convection equations, with a few innovative derivations. Though some complexities such as multi-component equations deduced from irreversible thermodynamics, are avoided for simplicity, some comparisons with experimental/industrial results are made. The main feature of this work is that the multi-component effect is combined with the viscosity (at the surface) effect upon the diffusivities of individual components in the solution droplets or suspension droplets. The derivations allow some extended analytical procedures to proceed in order to help make sense of the experimental observations. Comparisons are made against the data published on dairy fluids. This work provides a good basis for a fruitful area of study that will have a positive impact for spray drying industries. In particular, to help this kind of industry to forge ahead into high performing functional particle production, which are becoming increasingly popular.
X.D. Chen, H.S. Sidhu, and M.I. Nelson. Theoretical probing of the phenomenon of the formation of the outermost layer of a multi-component particle, and the surface chemical composition after the rapid removal of water in spray drying. Chemical Engineering Science, 66(24):6375--6384, 2011. http://dx.doi.org/10.1016/j.ces.2011.08.035.
A Change Evaluation was conducted in the School of Mathematics and Applied Statistics, at the University of Wollongong (UOW) with a view to identifying which resources to improve in order to facilitate better student learning outcomes. One hundred and thirty students took the subject MATH151 during the autumn term of the 2010 academic year with 101 students responding to the evaluation questionnaire. Data collection was used to discover which resources had the greatest potential for improvement or replacement and to examine if the structure of the subject could be improved for better student understanding and learning. The survey was also employed to evaluate the effectiveness of the e-learning page, and this led to an emphasis on finding an alternative learning design. Several possible approaches to learning designs are discussed.
B. Bukhatowa p, A.L. Porter and M.I. Nelson. Experience with change evaluations suggests the need for better learning designs: one possibility for mathematics. In S. Barton, J. Hedberg & K. Suzuki, editors, Proceedings of Global Learn Asia Pacific 2011, pages 875-884. EDiTLib, USA. 2011.