Mathematical modelling

The development of a new process model of cement grinding in two-stage mills is discussed. The new model has been used to simulate cement grinding and predicting mill performance in open and closed circuit configuration. The new model considered the two-compartment mill as perfectly mixed slices in series. The breakage rate function uses the back calculation technique to determine offline using drop weight and abrasion tests.

A mathematical modelling technique for the analysis of the dynamics of a simple continuous EDA

This paper presents some initial attempts to mathematically model the dynamics of a continuous estimation of distribution algorithm (EDA) based on a Gaussian distribution and truncation selection. Case studies are conducted on both unimodal and multimodal problems to highlight the effectiveness of the proposed technique and explore some important properties of the EDA. With some general assumptions, we show that, for ID unimodal problems and with the (mu, lambda) scheme: (1). The behaviour of the EDA is dependent only on the general shape of the test function, rather than its specific form; (2). When initialized far from the global optimum, the EDA has a tendency to converge prematurely; (3). Given a certain selection pressure, there is a unique value for the proposed amplification parameter that could help the EDA achieve desirable performance; for ID multimodal problems: (1). The EDA could get stuck with the (mu, lambda) scheme; (2). The EDA will never get stuck with the (mu, lambda) scheme.

Classification and analysis of integrating frameworks in multiscale modelling

Chemical engineers are turning to multiscale modelling to extend traditional modelling approaches into new application areas and to achieve higher levels of detail and accuracy. There is, however, little advice available on the best strategy to use in constructing a multiscale model. This paper presents a starting point for the systematic analysis of multiscale models by defining several integrating frameworks for linking models at different scales. It briefly explores how the nature of the information flow between the models at the different scales is influenced by the choice of framework, and presents some restrictions on model-framework compatibility. The concepts are illustrated with reference to the modelling of a catalytic packed bed reactor. (C) 2004 Elsevier Ltd. All rights reserved.

Modelling of two-stage anaerobic digestion using the IWA Anaerobic Digestion Model No. 1 (ADM1)

The aim of the study presented was to implement a process model to simulate the dynamic behaviour of a pilot-scale process for anaerobic two-stage digestion of sewage sludge. The model implemented was initiated to support experimental investigations of the anaerobic two-stage digestion process. The model concept implemented in the simulation software package MATLAB(TM)/Simulink(R) is a derivative of the IWA Anaerobic Digestion Model No.1 (ADM1) that has been developed by the IWA task group for mathematical modelling of anaerobic processes. In the present study the original model concept has been adapted and applied to replicate a two-stage digestion process. Testing procedures, including balance checks and 'benchmarking' tests were carried out to verify the accuracy of the implementation. These combined measures ensured a faultless model implementation without numerical inconsistencies. Parameters for both, the thermophilic and the mesophilic process stage, have been estimated successfully using data from lab-scale experiments described in literature. Due to the high number of parameters in the structured model, it was necessary to develop a customised procedure that limited the range of parameters to be estimated. The accuracy of the optimised parameter sets has been assessed against experimental data from pilot-scale experiments. Under these conditions, the model predicted reasonably well the dynamic behaviour of a two-stage digestion process in pilot scale. (C) 2004 Elsevier Ltd. All rights reserved.

Using a non-invasive stable isotope tracer to measure the absorption of water in humans

The development of solutions that prevent dehydration or promote adequate re-hydration play a vital role in preventing fatigue during exercise, however, the methods commonly used to assess the hydration ability of such solutions are invasive and often assess the components of absorption separately. This paper describes using a non-invasive deuterium tracer technique that assesses gastric emptying and intestinal absorption simultaneously to evaluate the uptake of water during rest and exercise. The kinetics of absorption are further examined by mathematical modelling of the data generated. For the rest group, 0.05 g/kg of body weight of deuterium, contained in gelatine capsules, was ingested with ordinary tap water and saliva samples were collected every 5 min for one hour while the subject remained seated. The deuterium was administered as above for the exercise group but sample collection was during one hour of exercise on a treadmill at 55% of the subject's maximum heart rate. The enrichment data for each subject were mathematically modelled and the parameters obtained were compared across groups using an independent samples t-test. Compared with the rest condition, the exercise group showed delayed absorption of water as indicated by significant differences for the modelling parameters t(2), t(1/2), maximum absorption rate and solution absorption amount at t(1). Labelling with a deuterium tracer is a good measure of the relative rate ingested fluids are absorbed by the body. Mathematical modelling of the data generates rates of maximum absorption and allows calculation of the percentage of the solution that is absorbed at any given time during the testing period. Copyright (C) 2004 John Wiley Sons, Ltd.

Transmission dynamics of the Echinococcus granulosus sheep-dog strain (G1 genotype) in camels in Tunisia

Cystic echinococcosis, caused by Echinococcus grantilosus, is highly endemic in North Africa and the Middle East. This paper examines the abundance and prevalence of infection of E. granulosus in camels in Tunisia. No cysts were found in 103 camels from Kebili, whilst 19 of 188 camels from Benguerden (10.1%) were infected. Of the cysts found 95% were considered fertile with the presence of protoscolices and 80% of protoscolices were considered viable by their ability to exclude aqueous eosin. Molecular techniques were used on cyst material from camels and this demonstrated that the study animals were infected with the G1 sheep strain of E. granulosus. Observed data were fitted to a mathematical model by maximum likelihood techniques to define the parameters and their confidence limits and the negative binomial distribution was used to define the error variance in the observed data. The infection pressure to camels was somewhat lower in comparison to sheep reported in an earlier study. However, because camels are much longer-lived animals, the results of the model fit suggested that older camels have a relatively high prevalence rate, reaching a most likely value of 32% at age 15 years. This could represent an important source of transmission to dogs and hence indirectly to man of this zonotic strain. In common with similar studies on other species, there was no evidence of parasite-induced immunity in camels. (C) 2004 Elsevier B.V. All rights reserved.

Passive air sampling theory for semivolatile organic compounds

The mathematical modelling underlying passive air sampling theory can be based on mass transfer coefficients or rate constants. Generally, these models have not been inter-related. Starting with basic models, the exchange of chemicals between the gaseous phase and the sampler is developed using mass transfer coefficients and rate constants. Importantly, the inter-relationships between the approaches are demonstrated by relating uptake rate constants and loss rate constants to mass transfer coefficients when either sampler-side or air-side resistance is dominating chemical exchange. The influence of sampler area and sampler volume on chemical exchange is discussed in general terms and as they relate to frequently used parameters such as sampling rates and time to equilibrium. Where air-side or sampler-side resistance dominates, an increase in the surface area of the sampler will increase sampling rates. Sampling rates are not related to the sampler/air partition coefficient (K-SV) when air-side resistance dominates and increase with K-SV when sampler-side resistance dominates.

A dynamic mathematical model for sequential leach bed anaerobic digestion of organic fraction of municipal solid waste

A mathematical model that describes the operation of a sequential leach bed process for anaerobic digestion of organic fraction of municipal solid waste (MSW) is developed and validated. This model assumes that ultimate mineralisation of the organic component of the waste occurs in three steps, namely solubilisation of particulate matter, fermentation to volatile organic acids (modelled as acetic acid) along with liberation of carbon dioxide and hydrogen, and methanogenesis from acetate and hydrogen. The model incorporates the ionic equilibrium equations arising due to dissolution of carbon dioxide, generation of alkalinity from breakdown of solids and dissociation of acetic acid. Rather than a charge balance, a mass balance on the hydronium and hydroxide ions is used to calculate pH. The flow of liquid through the bed is modelled as occurring through two zones-a permeable zone with high flushing rates and the other more stagnant. Some of the kinetic parameters for the biological processes were obtained from batch MSW digestion experiments. The parameters for flow model were obtained from residence time distribution studies conducted using tritium as a tracer. The model was validated using data from leach bed digestion experiments in which a leachate volume equal to 10% of the fresh waste bed volume was sequenced. The model was then tested, without altering any kinetic or flow parameters, by varying volume of leachate that is sequenced between the beds. Simulations for sequencing/recirculating 5 and 30% of the bed volume are presented and compared with experimental results. (C) 2002 Elsevier Science B.V. All rights reserved.