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.

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.

Improved slope adjustment functions for soil erosion prediction

Numerous studies in the last 60 years have investigated the relationship between land slope and soil erosion rates. However, relatively few of these have investigated slope gradient responses: ( a) for steep slopes, (b) for specific erosion processes, and ( c) as a function of soil properties. Simulated rainfall was applied in the laboratory on 16 soils and 16 overburdens at 100 mm/h to 3 replicates of unconsolidated flume plots 3 m long by 0.8 m wide and 0.15 m deep at slopes of 20, 5, 10, 15, and 30% slope in that order. Sediment delivery at each slope was measured to determine the relationship between slope steepness and erosion rate. Data from this study were evaluated alongside data and existing slope adjustment functions from more than 55 other studies from the literature. Data and the literature strongly support a logistic slope adjustment function of the form S = A + B/[1 + exp (C - D sin theta)] where S is the slope adjustment factor and A, B, C, and D are coefficients that depend on the dominant detachment and transport processes. Average coefficient values when interill-only processes are active are A - 1.50, B 6.51, C 0.94, and D 5.30 (r(2) = 0.99). When rill erosion is also potentially active, the average slope response is greater and coefficient values are A - 1.12, B 16.05, C 2.61, and D 8.32 (r(2) = 0.93). The interill-only function predicts increases in sediment delivery rates from 5 to 30% slope that are approximately double the predictions based on existing published interill functions. The rill + interill function is similar to a previously reported value. The above relationships represent a mean slope response for all soils, yet the response of individual soils varied substantially from a 2.5-fold to a 50-fold increase over the range of slopes studied. The magnitude of the slope response was found to be inversely related ( log - log linear) to the dispersed silt and clay content of the soil, and 3 slope adjustment equations are proposed that provide a better estimate of slope response when this soil property is known. Evaluation of the slope adjustment equations proposed in this paper using independent datasets showed that the new equations can improve soil erosion predictions.

Modelling of froth transportation in industrial flotation cells: Part I. Development of froth transportation models for attached particles

Modelling of froth transportation, as part of modelling of froth recovery, provides a scale-up procedure for flotation cell design. It can also assist in improving control of flotation operation. Mathematical models of froth velocity on the surface and froth residence time distribution in a cylindrical tank flotation cell are proposed, based on mass balance principle of the air entering the froth. The models take into account factors such as cell size, concentrate launder configuration, use of a froth crowder, cell operating conditions including froth height and air rate, and bubble bursting on the surface. (C) 2004 Elsevier Ltd. All rights reserved.

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.

Numerical modelling of radiating superorbital flows

Experimental aerodynamic studies of the flows around new aerocapture spacecraft configurations are presently being done in the superorbital expansion tubes at The University of Queensland. Short duration flows at speeds of 10--13 km/s are produced in the expansion tube facility and are then applied to the model spacecraft. Although high-temperature effects, such as molecular dissociation, have long been a part of the computational modelling of the expansion tube flows for speeds below 10 km/s, radiation may now be a significant mechanism of energy transfer within the shock layer on the model. This paper will study the coupling of radiation energy transport for an optically thin gas to the flow dynamics in order to obtain accurate predictions of thermal loads on the spacecraft. The results show that the effect of radiation on the flowfields of subscale models for expansion tube experiments can be assessed by measurements of total heat transfer and radiative heat transfer.

Quantifying effects of soil heterogeneity on groundwater pollution in four sites in the USA

Four sites located in the north-eastern region of the United States of America have been chosen to investigate the impacts of soil heterogeneity in the transport of solutes (bromide and chloride) through the vadose zone (the zone in the soil that lies below the root zone and above the permanent saturated groundwater). A recently proposed mathematical model based on the cumulative beta distribution has been deployed to compare and contrast the regions' heterogeneity from multiple sample percolation experiments. Significant differences in patterns of solute leaching were observed even over a small spatial scale, indicating that traditional sampling methods for solute transport, for example the gravity pan or suction lysimeters, or more recent inventions such as the multiple sample percolation systems may not be effective in estimating solute fluxes in soils when a significant degree of soil heterogeneity is present. Consequently, ignoring soil heterogeneity in solute transport studies will likely result in under- or overprediction of leached fluxes and potentially lead to serious pollution of soils and/or groundwater. The cumulative beta distribution technique is found to be a versatile and simple technique of gaining valuable information regarding soil heterogeneity effects on solute transport. It is also an excellent tool for guiding future decisions of experimental designs particularly in regard to the number of samples within one site and the number of sampling locations between sites required to obtain a representative estimate of field solute or drainage flux.

Modelling of entrainment in industrial flotation cells: the effect of solids suspension

Solids concentration and particle size distribution gradually change in the vertical dimension of industrial flotation cells, subject primarily to the flotation cell size and design and the cell operating conditions. As entrainment is a two-step process and involves only the suspended solids in the top pulp region near the pulp-froth interface, the solids suspension characteristics have a significant impact on the overall entrainment. In this paper, a classification function is proposed to describe the state of solids suspension in flotation cells, similar to the definition of degree of entrainment for classification in the froth phase found in the literature. A mathematical model for solids suspension is also developed, in which the classification function is expressed as an exponential function of the particle size. Experimental data collected from three different Outokumpu tank flotation cells in three different concentrators are well fitted by the proposed exponential model. Under the prevailing experimental conditions, it was found that the solids content in the top region was relatively independent of cell operating conditions such as froth height and air rate but dependent on the cell size. Moreover, the results obtained from the total solids tend to be similar to those from a particular gangue mineral and hence may be applied to all minerals in entrainment calculation. (C) 2004 Elsevier Ltd. All rights reserved.

Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.