A formal representation of assumptions in process modelling

In this work, we present a systematic approach to the representation of modelling assumptions. Modelling assumptions form the fundamental basis for the mathematical description of a process system. These assumptions can be translated into either additional mathematical relationships or constraints between model variables, equations, balance volumes or parameters. In order to analyse the effect of modelling assumptions in a formal, rigorous way, a syntax of modelling assumptions has been defined. The smallest indivisible syntactical element, the so called assumption atom has been identified as a triplet. With this syntax a modelling assumption can be described as an elementary assumption, i.e. an assumption consisting of only an assumption atom or a composite assumption consisting of a conjunction of elementary assumptions. The above syntax of modelling assumptions enables us to represent modelling assumptions as transformations acting on the set of model equations. The notion of syntactical correctness and semantical consistency of sets of modelling assumptions is defined and necessary conditions for checking them are given. These transformations can be used in several ways and their implications can be analysed by formal methods. The modelling assumptions define model hierarchies. That is, a series of model families each belonging to a particular equivalence class. These model equivalence classes can be related to primal assumptions regarding the definition of mass, energy and momentum balance volumes and to secondary and tiertinary assumptions regarding the presence or absence and the form of mechanisms within the system. Within equivalence classes, there are many model members, these being related to algebraic model transformations for the particular model. We show how these model hierarchies are driven by the underlying assumption structure and indicate some implications on system dynamics and complexity issues. (C) 2001 Elsevier Science Ltd. All rights reserved.

A dynamic model with on-line identification for rotary sugar drying processes

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to reidentified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.place the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.

Model based procedure for scale-up of wet overflow ball mills Part 1: Outline of the methodology

Bond's method for ball mill scale-up only gives the mill power draw for a given duty. This method is incompatible with computer modelling and simulation techniques. It might not be applicable for the design of fine grinding ball mills and ball mills preceded by autogenous and semi-autogenous grinding mills. Model-based ball mill scale-up methods have not been validated using a wide range of full-scale circuit data. Their accuracy is therefore questionable. Some of these methods also need expensive pilot testing. A new ball mill scale-up procedure is developed which does not have these limitations. This procedure uses data from two laboratory tests to determine the parameters of a ball mill model. A set of scale-up criteria then scales-up these parameters. The procedure uses the scaled-up parameters to simulate the steady state performance of full-scale mill circuits. At the end of the simulation, the scale-up procedure gives the size distribution, the volumetric flowrate and the mass flowrate of all the streams in the circuit, and the mill power draw.

Model-based procedure for scale-up of wet, overflow ball mills - Part II: Worked example

A new ball mill scale-up procedure is developed which uses laboratory data to predict the performance of MI-scale ball mill circuits. This procedure contains two laboratory tests. These laboratory tests give the data for the determination of the parameters of a ball mill model. A set of scale-up criteria then scales-up these parameters. The procedure uses the scaled-up parameters to simulate the steady state performance of the full-scale mill circuit. At the end of the simulation, the scale-up procedure gives the size distribution, the volumetric flowrate and the mass flowrate of all the streams in the circuit, and the mill power draw. A worked example shows how the new ball mill scale-up procedure is executed. This worked example uses laboratory data to predict the performance of a full-scale re-grind mill circuit. This circuit consists of a ball mill in closed circuit with hydrocyclones. The MI-scale ball mill has a diameter (inside liners) of 1.85m. The scale-up procedure shows that the full-scale circuit produces a product (hydrocyclone overflow) that has an 80% passing size of 80 mum. The circuit has a recirculating load of 173%. The calculated power draw of the full-scale mill is 92kW (C) 2001 Elsevier Science Ltd. All rights reserved.

Model-based procedure for scale-up of wet, overflow ball mills - Part III: Validation and discussion

A new ball mill scale-up procedure is developed. This procedure has been validated using seven sets of Ml-scale ball mil data. The largest ball mills in these data have diameters (inside liners) of 6.58m. The procedure can predict the 80% passing size of the circuit product to within +/-6% of the measured value, with a precision of +/-11% (one standard deviation); the re-circulating load to within +/-33% of the mass-balanced value (this error margin is within the uncertainty associated with the determination of the re-circulating load); and the mill power to within +/-5% of the measured value. This procedure is applicable for the design of ball mills which are preceded by autogenous (AG) mills, semi-autogenous (SAG) mills, crushers and flotation circuits. The new procedure is more precise and more accurate than Bond's method for ball mill scale-up. This procedure contains no efficiency correction which relates to the mill diameter. This suggests that, within the range of mill diameter studied, milling efficiency does not vary with mill diameter. This is in contrast with Bond's equation-Bond claimed that milling efficiency increases with mill diameter. (C) 2001 Elsevier Science Ltd. All rights reserved.

A systematic approach to error isolation in computerized wastewater simulation models

Activated sludge models are used extensively in the study of wastewater treatment processes. While various commercial implementations of these models are available, there are many people who need to code models themselves using the simulation packages available to them, Quality assurance of such models is difficult. While benchmarking problems have been developed and are available, the comparison of simulation data with that of commercial models leads only to the detection, not the isolation of errors. To identify the errors in the code is time-consuming. In this paper, we address the problem by developing a systematic and largely automated approach to the isolation of coding errors. There are three steps: firstly, possible errors are classified according to their place in the model structure and a feature matrix is established for each class of errors. Secondly, an observer is designed to generate residuals, such that each class of errors imposes a subspace, spanned by its feature matrix, on the residuals. Finally. localising the residuals in a subspace isolates coding errors. The algorithm proved capable of rapidly and reliably isolating a variety of single and simultaneous errors in a case study using the ASM 1 activated sludge model. In this paper a newly coded model was verified against a known implementation. The method is also applicable to simultaneous verification of any two independent implementations, hence is useful in commercial model development.

Using clusters of computers for large QU-GENE simulation experiments

The QU-GENE Computing Cluster (QCC) is a hardware and software solution to the automation and speedup of large QU-GENE (QUantitative GENEtics) simulation experiments that are designed to examine the properties of genetic models, particularly those that involve factorial combinations of treatment levels. QCC automates the management of the distribution of components of the simulation experiments among the networked single-processor computers to achieve the speedup.

Application of heterogeneous vacancy solution theory to characterization of microporous solids

The vacancy solution theory of adsorption is re-formulated here through the mass-action law, and placed in a convenient framework permitting the development of thermodynamic ally consistent isotherms. It is shown that both the multisite Langmuir model and the classical vacancy solution theory expression are special cases of the more general approach when the Flory-Huggins activity coefficient model is used, with the former being the thermodynamically consistent result. The improved vacancy solution theory approach is further extended here to heterogeneous adsorbents by considering the pore-width dependent potential along with a pore size distribution. However, application of the model to numerous hydrocarbons as well as other adsorptives on microporous activated carbons shows that the multisite model has difficulty in the presence of a pore size distribution, because pores of different sizes can have different numbers of adsorbed layers and therefore different site occupancies. On the other hand, use of the classical vacancy solution theory expression for the local isotherm leads to good simultaneous fit of the data, while yielding a site diameter of about 0.257 nm, consistent with that expected for the potential well in aromatic rings on carbon pore surfaces. It is argued that the classical approach is successful because the Flory-Huggins term effectively represents adsorbate interactions in disguise. When used together with the ideal adsorbed solution theory the heterogeneous vacancy solution theory successfully predicts binary adsorption equilibria, and is found to perform better than the multisite Langmuir as well as the heterogeneous Langmuir model. (C) 2001 Elsevier Science Ltd. All rights reserved.

A generalised dynamic model for char particle gasification with structure evolution and peripheral fragmentation

A generalised model for the prediction of single char particle gasification dynamics, accounting for multi-component mass transfer with chemical reaction, heat transfer, as well as structure evolution and peripheral fragmentation is developed in this paper. Maxwell-Stefan analysis is uniquely applied to both micro and macropores within the framework of the dusty-gas model to account for the bidisperse nature of the char, which differs significantly from the conventional models that are based on a single pore type. The peripheral fragmentation and random-pore correlation incorporated into the model enable prediction of structure/reactivity relationships. The occurrence of chemical reaction within the boundary layer reported by Biggs and Agarwal (Chem. Eng. Sci. 52 (1997) 941) has been confirmed through an analysis of CO/CO2 product ratio obtained from model simulations. However, it is also quantitatively observed that the significance of boundary layer reaction reduces notably with the reduction of oxygen concentration in the flue gas, operational pressure and film thickness. Computations have also shown that in the presence of diffusional gradients peripheral fragmentation occurs in the early stages on the surface, after which conversion quickens significantly due to small particle size. Results of the early commencement of peripheral fragmentation at relatively low overall conversion obtained from a large number of simulations agree well with experimental observations reported by Feng and Bhatia (Energy & Fuels 14 (2000) 297). Comprehensive analysis of simulation results is carried out based on well accepted physical principles to rationalise model prediction. (C) 2001 Elsevier Science Ltd. AH rights reserved.

Probabilistic modelling of CO2 corrosion laboratory data using neural networks

The present paper addresses two major concerns that were identified when developing neural network based prediction models and which can limit their wider applicability in the industry. The first problem is that it appears neural network models are not readily available to a corrosion engineer. Therefore the first part of this paper describes a neural network model of CO2 corrosion which was created using a standard commercial software package and simple modelling strategies. It was found that such a model was able to capture practically all of the trends noticed in the experimental data with acceptable accuracy. This exercise has proven that a corrosion engineer could readily develop a neural network model such as the one described below for any problem at hand, given that sufficient experimental data exist. This applies even in the cases when the understanding of the underlying processes is poor. The second problem arises from cases when all the required inputs for a model are not known or can be estimated with a limited degree of accuracy. It seems advantageous to have models that can take as input a range rather than a single value. One such model, based on the so-called Monte Carlo approach, is presented. A number of comparisons are shown which have illustrated how a corrosion engineer might use this approach to rapidly test the sensitivity of a model to the uncertainities associated with the input parameters. (C) 2001 Elsevier Science Ltd. All rights reserved.

A simulation model for analysing patient activity in dermatology

We developed a general model to assess patient activity within the primary and secondary health-care sectors following a dermatology outpatient consultation. Based on observed variables from the UK teledermatology trial, the model showed that up to 11 doctor-patient interactions occurred before a patient was ultimately discharged from care. In a cohort of 1000 patients, the average number of health-care visits was 2.4 (range 1-11). Simulation analysis suggested that the most important parameter affecting the total number of doctor-patient Interactions is patient discharge from care following the initial consultation. This implies that resources should be concentrated in this area. The introduction of teledermatology (either realtime or store and forward) changes the values of the model parameters. The model provides a quantitative tool for planning the future provision of dermatology health-care.

Advances in application of climate prediction in agriculture

Agricultural ecosystems and their associated business and government systems are diverse and varied. They range from farms, to input supply businesses, to marketing and government policy systems, among others. These systems are dynamic and responsive to fluctuations in climate. Skill in climate prediction offers considerable opportunities to managers via its potential to realise system improvements (i.e. increased food production and profit and/or reduced risks). Realising these opportunities, however, is not straightforward as the forecasting skill is imperfect and approaches to applying the existing skill to management issues have not been developed and tested extensively. While there has been much written about impacts of climate variability, there has been relatively little done in relation to applying knowledge of climate predictions to modify actions ahead of likely impacts. However, a considerable body of effort in various parts of the world is now being focused on this issue of applying climate predictions to improve agricultural systems. In this paper, we outline the basis for climate prediction, with emphasis on the El Nino-Southern Oscillation phenomenon, and catalogue experiences at field, national and global scales in applying climate predictions to agriculture. These diverse experiences are synthesised to derive general lessons about approaches to applying climate prediction in agriculture. The case studies have been selected to represent a diversity of agricultural systems and scales of operation. They also represent the on-going activities of some of the key research and development groups in this field around the world. The case studies include applications at field/farm scale to dryland cropping systems in Australia, Zimbabwe, and Argentina. This spectrum covers resource-rich and resource-poor farming with motivations ranging from profit to food security. At national and global scale we consider possible applications of climate prediction in commodity forecasting (wheat in Australia) and examine implications on global wheat trade and price associated with global consequences of climate prediction. In cataloguing these experiences we note some general lessons. Foremost is the value of an interdisciplinary systems approach in connecting disciplinary Knowledge in a manner most suited to decision-makers. This approach often includes scenario analysis based oil simulation with credible models as a key aspect of the learning process. Interaction among researchers, analysts and decision-makers is vital in the development of effective applications all of the players learn. Issues associated with balance between information demand and supply as well as appreciation of awareness limitations of decision-makers, analysts, and scientists are highlighted. It is argued that understanding and communicating decision risks is one of the keys to successful applications of climate prediction. We consider that advances of the future will be made by better connecting agricultural scientists and practitioners with the science of climate prediction. Professions involved in decision making must take a proactive role in the development of climate forecasts if the design and use of climate predictions are to reach their full potential. (C) 2001 Elsevier Science Ltd. All rights reserved.