This study aims to investigate opportunities to make commercial buildings in Pretoria, South Africa, more energy efficient, which is made by examining prerequisites in South Africa. To achieve this objective, barriers and measures to decrease cooling demand are investigated by a qualitative approach and a roof heat transfer model is developed to get a deeper understanding of the ceiling temperature distribution. The heat transfer model is simulated in MATLAB and is further validated by conducting a two-case scenario sensitivity analysis and by comparing the results to previous research. The results show that there is a great correlation between the Global Horizontal Irradiance [GHI] and the interior ceiling temperature and a higher GHI contributes to a higher ceiling temperature. The hot climate and the long summer period in South Africa indicate that there is a great demand for cooling during a year. Regarding barriers, the socioeconomic aspects in the country and the low electricity prices may contribute to less willingness to adapt to an environmentally friendly behaviour. As some technologies are still perceived as expensive, this may also provide a lower willingness to make changes regarding choices that contribute to a lower cooling demand and thus, energy consumption. Finally, it is concluded that there are several measures that can be applied to decrease the cooling demand, such as constructional changes or enhancement of the heating, ventilation and air-conditioning [HVAC] operation.

This licentiate thesis describes development of modellingtools, experimental physical modelling and numerical modellingto simulate real combustion processes for advanced industrialutility boiler before and after retrofit. The work presents extended study about formation,destruction and control of pollutants, especially NOx, whichoccur during combustion process. The main aim of this work is to improve mixing process incombustion chamber. To do this, the optimization of placementand direction of additional air and fuel nozzles, the physicalmodelling technique is used. By using that method, it ispossible to obtain qualitative information about processes,which occur in the real boiler. The numerical simulationsverify the results from physical modelling, because duringmathematical modelling quantitative informations about flow andmixing patterns, temperature field, species concentration areobtained. Two 3D cases, before and after retrofit, of pulverized fuelfired boiler at 125 MW output thermal power are simulated. Theunstructured mesh technique is also used to discretize theboiler. The number of grid was 427 656 before retrofit and 513362 after retrofit. The comparisons of results of numericalsimulation before and after retrofit are presented. The resultsfrom physical modelling and numerical simulation are alsoshown. Results present that nozzles of additional air and fuel givea considerably better mixing process, uniform temperature fieldand CO2 mass fraction. The whole combustion chamber worksalmost as a "well stirred reactor", while upper part of boilerworks as a "plug flow reactor". Differences between from measured of temperatures andpredicted temperatures are not too big, the maximum differenceis about 100 K. It seems, that calculated temperatures showgood agreement with measurement data. The results illuminate the potential of physical andnumerical modelling methods as promising tools to deal with thecomplicated combustion processes, even for practicalapplication in the industry. <b>Keywords:</b>air staging, fuel staging, boiler, furnace,computational fluid dynamics, numerical simulation, pollutants,physical modeling, pulverized fuel combustion. / NR 20140805

Mathematical modelling using differential equations is an important tool to predict the behaviorof vanadium redox batteries, since it may contribute to improve the device performance and leadto a better understanding of the principles of its operation. Modelling can be complementedby asymptotic analysis as a mean to promote reductions or simplifications that make modelsless complex. Such simplifications are useful in this context, whereas these models usuallyaddresses one cell only – the smallest operating unit – while real applications demand tensor hundreds cells implying on larger computational requirements. In this research, severaloptions for asymptotic reductions were investigated and, applied to different models, were ableto speed up the processing time in 2.46× or reduce the memory requirements up to 11.39%. Thecomputational simulations were executed by COMSOL Multiphysics v.4.4, also by in-housecode developed in MATLAB. The validation of results was done by comparing it to experimentalresults available in literature. Additionally, correlating the results provided by COMSOL withthe ones arising from the implemented sub-routines allowed to validate the developed algorithm.Key-words: / A modelagem matemática por meio de equações diferenciais é uma importante ferramenta paraprever o comportamento de baterias redox de vanádio, pois ela pode contribuir para o aperfeiçoamentodo produto e melhor entendimento dos princípios da sua operação. Os estudos demodelagem podem ser aliados à análise assintótica no intuito de promover reduções ou simplificaçõesque tornem os modelos menos complexos, isso é feito a partir da observação da importânciaque cada termo exerce sobre as equações. Tais simplificações são úteis neste contexto, visto queos modelos geralmente abordam uma célula apenas - a menor unidade operacional da bateria- enquanto aplicações reais exigem o uso de dezenas ou centenas delas implicando em umamaximização do uso de recursos computacionais. Neste trabalho, foram investigadas múltiplasformas de reduções assintóticas que empregadas na construção dos modelos puderam acelerar otempo de processamento em até 2,46 vezes ou reduzir os requisitos de memória principal em até11,39%. As simulações computacionais foram executadas pelo software COMSOL Multiphysicsv. 4.4, e também por scripts desenvolvidos em ambiente de programação MATLAB. A validaçãodos resultados foi feita comparando-os a dados experimentais presentes na literatura. Talabordagem permitiu também validar as rotinas implementadas para a simulação dos modeloscomparando suas soluções com aquelas providas pelo COMSOL.

This study focused on the dynamic behaviour of the freeze lining and slag bath, and the interactions between these components in an ilmenite-smelting furnace process. The purpose of the work was to gain a better understanding of these issues and to ultimately contribute to an improved understanding of the ilmenite-smelting process in its entirety, and to future improvements in the design, operation and control of these processes. A mathematical model of the freeze lining and furnace sidewall was developed. This model was used in isolation for focused characterisation of the dynamic behaviour and interactions of the freeze lining and slag bath. The influences of net power input and slag composition were studied and various aspects of the freeze lining and slag bath were considered. These aspects included freeze lining thickness, temperature distribution through the freeze lining and furnace sidewall, composition distribution through the freeze lining, slag bath temperature and slag bath composition. The thermal response of thermocouples installed in the furnace sidewall to changing conditions on the inside of the furnace was also investigated. A mathematical model of the crust that forms on the slag bath surface was developed. This model was not used in isolation, and was only incorporated into a complete model of the process. A mathematical model of the entire ilmenite-smelting furnace process was constructed. This model incorporated the two models mentioned above and was able to describe the metal bath, slag bath, furnace atmosphere, freeze lining, furnace sidewall and the crust that is sometimes present on top of the slag bath. The model was used to study the influence of changes in operational parameters on the slag bath and freeze lining. The operational parameters that were studied included electrical power and reductant feed rate, both relative to ilmenite feed rate. The influence of severe operational errors and furnace down time were also investigated. Operational errors included loss of all feed while maintain electrical power input, and loss of reductant feed while maintaining power input and ilmenite feed. The above-mentioned studies were conducted by executing numerous experiments with two of the mathematical models. The experimental results were processed into sets of graphs displaying variations in the aspects that were considered. Many valuable insights resulted from the interpretation of these results. One specific aspect that formed part of the scope of this work was the origin of the compositional invariance of the slag close to the stoichiometric M3O5composition. This invariance was studied and a mechanism was proposed that explains the observed behaviour. The proposed mechanism created some questions about other mechanisms in the process. These mechanisms were also considered and elaborated on. The models and results produced in this study provide valuable insights into the behaviour of the ilmenite-smelting process. It also represents a useful foundation for future modelling work, and finally, it presents numerous opportunities for organisations operating ilmenite-smelting furnaces to improve their understanding and even the performance of their processes. / Thesis (PhD (Metallurgical Engineering))--University of Pretoria, 2004. / Materials Science and Metallurgical Engineering / unrestricted

Mathematical models in physiology are useful to formulate and verify hypotheses, to make predictions, to estimate hidden parameters and in education. This thesis deals with modelling in physiology using the ​Modelica language. New methods for model implementation and simulator production were developed. Modelica is an ​open standard equation-based object-oriented language for modelling complex systems. It is highly convenient in physiology modelling due to its ability to describe extensive models in a lucid hierarchical way. The models are described by algebraic, ordinary differential and discrete equations. Partial differential equations are not supported by the Modelica standard yet. The thesis focuses on two main topics: 1) modelling of systems described by partial differential equations in Modelica 2) production of web-based e-learning simulators driven by models implemented in Modelica. A Modelica language extension called PDEModelica1 for 1-dimensional partial differential equations was designed (based on a previous extension). The OpenModelica modelling tool was extended to support PDEModelica1 using the method of lines. A model of countercurrent heat exchange between the artery and vein in a leg of a bird standing in water was implemented using PDEModelica1 to prove its usability. The...

The field of mathematical modelling for pedestrian dynamics has attracted significant scientific attention, with various models proposed from perspectives such as kinetic theory, statistical mechanics, game theory and partial differential equations. Often such investigations are seen as being a part of a new branch of study in the domain of applied physics, called sociophysics. Our study proposes three models that are tailored to specific scenarios of crowd dynamics. Our research focuses on two primary issues. The first issue is centred around pedestrians navigating through a partially dark corridor that impedes visibility, requiring the calculation of the time taken for evacuation using a Markov chain model. The second issue is posed to analyse how pedestrians move through a T-shaped junction. Such a scenario is motivated by the 2022 crowd-crush disaster took place in the Itaewon district of Seoul, Korea. We propose a lattice-gas-type model that simulates pedestrians’ movement through the grid by obeying a set of rules as well as a parabolic equation with special boundary conditions. By the means of numerical simulations, we investigate a couple of evacuation scenarios by evaluating the mean velocity of pedestrians through the dark corridor, varying both the length of the obscure region and the amount of uncertainty induced by the darkness. Additionally, we propose an agent-based-modelling and cellular automata inspired model that simulates the movement of pedestrians through a T-shaped grid, varying the initial number of pedestrians. We measure the final density and time taken to reach a steady pedestrian traffic state. Finally, we propose a parabolic equation with special boundary conditions that mimic the dynamic of the pedestrian populations in a T-junction. We solve the parabolic equation using a random walk numerical scheme and compare it with a finite difference approximation. Furthermore, we prove rigorously the convergence of the random walk scheme to a corresponding finite difference scheme approximation of the solution.

A major problem in the quantitative analysis of AC voltammetric data has been the variance in results between laboratories, often resulting from a reliance on "heuristic" methods of parameter estimation that are strongly dependent on the choices of the operator. In this thesis, an automatic method for parameter estimation will be tested in the context of experiments involving electron-transfer processes in solution-phase. It will be shown that this automatic method produces parameter estimates consistent with those from other methods and the literature in the case of the ferri-/ferrocyanide couple, and is able to explain inconsistency in published values of the rate parameter for the ferrocene/ferrocenium couple. When a coupled homogeneous reaction is considered in a theoretical study, parameter recovery is achieved with a higher degree of accuracy when simulated data resulting from a high frequency AC voltammetry waveform are used. When surface-confined reactions are considered, heterogeneity in the rate constant and formal potential make parameter estimation more challenging. In the final study, a method for incorporating these "dispersion" effects into voltammetric simulations is presented, and for the first time, a quantitive theoretical study of the impact of dispersion on measured current is undertaken.

Mathematical models have been used to capture the behaviour of biological systems, from low-level biochemical reactions to multi-scale whole-organ models. Models are typically based on experimentally-derived data, attempting to reproduce the observed behaviour through mathematical constructs, e.g. using Ordinary Differential Equations (ODEs) for spatially-homogeneous systems. These models are developed and published as mathematical equations, yet are of such complexity that they necessitate computational simulation. This computational model development is often performed in an ad hoc fashion by modellers who lack extensive software engineering experience, resulting in brittle, inefficient model code that is hard to extend and reuse. Several Domain Specific Languages (DSLs) exist to aid capturing such biological models, including CellML and SBML; however these DSLs are designed to facilitate model curation rather than simplify model development. We present research into the application of techniques from software engineering to this domain; starting with the design, development and implementation of a DSL, termed Ode, to aid the creation of ODE-based biological models. This introduces features beneficial to model development, such as model verification and reproducible results. We compare and contrast model development to large-scale software development, focussing on extensibility and reuse. This work results in a module system that enables the independent construction and combination of model components. We further investigate the use of software engineering processes and patterns to develop complex modular cardiac models. Model simulation is increasingly computationally demanding, thus models are often created in complex low-level languages such as C/C++. We introduce a highly-efficient, optimising native-code compiler for Ode that generates custom, model-specific simulation code and allows use of our structured modelling features without degrading performance. Finally, in certain contexts the stochastic nature of biological systems becomes relevant. We introduce stochastic constructs to the Ode DSL that enable models to use Stochastic Differential Equations (SDEs), the Stochastic Simulation Algorithm (SSA), and hybrid methods. These use our native-code implementation and demonstrate highly-efficient stochastic simulation, beneficial as stochastic simulation is highly computationally intensive. We introduce a further DSL to model ion channels declaratively, demonstrating the benefits of DSLs in the biological domain. This thesis demonstrates the application of software engineering methodologies, and in particular DSLs, to facilitate the development of both deterministic and stochastic biological models. We demonstrate their benefits with several features that enable the construction of large-scale, reusable and extensible models. This is accomplished whilst providing efficient simulation, creating new opportunities for biological model development, investigation and experimentation.

This thesis considers the development of a Hammerstein-bilinear approach to non-linear systems modelling, analysis and control systems design, which builds on and extends the applicability of an existing bilinear approach. The underlying idea of the Hammerstein-bilinear approach is to use the Hammerstein-bilinear system models to capture various physical phenomena of interest and subsequently use these for model based control system designs with the premise being that of achieving enhanced control performance. The advantage of the Hammerstein-bilinear approach is that the well-structured system models allow techniques that have been originally developed for linear systems to be extended and applied, while retaining moderate complexity of the corresponding system identification schemes and nonlinear model based control designs. In recognition of the need to be able to identify the Hammerstein-bilinear models a unified suite of algorithms, being the extensions to the simplified refined instrumental variable method for parameter estimation of linear transfer function models is proposed. These algorithms are able to operate in both the continuous-time and discrete-time domains to reflect the requirements of the intended purposes of the identified models with the emphasis being placed on straightforward applicability of the developed algorithms and recognising the need to be able to operate under realistic practical system identification scenarios. Moreover, the proposed algorithms are also applicable to parameter estimation of Hammerstein and bilinear models, which are special cases of the wider Hammerstein-bilinear model class. The Hammerstein-bilinear approach has been applied to an industrial heating, ventilation and air conditioning (HVAC) system, which has also been the underlying application addressed in this thesis. A unique set of dynamic control design purpose oriented air temperature and humidity Hammerstein-bilinear models of an environmentally controlled clear room manufacturing zone has been identified. The greater insights afforded by the knowledge of the system nonlinearities then allow for enhanced control tuning of the associated commercial HVAC control system leading to an improved overall control performance.

Catalytic hydrotreating (HDT) is a mature process technology practiced in the petroleum refining industries to treat oil fractions for the removal of impurities (such as sulfur, nitrogen, metals, asphaltene). Hydrotreating of whole crude oil is a new technology and is regarded as one of the more difficult tasks that have not been reported widely in the literature. In order to obtain useful models for the HDT process that can be confidently applied to reactor design, operation and control, the accurate estimation of kinetic parameters of the relevant reaction scheme are required. This thesis aims to develop a crude oil hydrotreating process (based on hydrotreating of whole crude oil followed by distillation) with high efficiency, selectivity and minimum energy consumption via pilot plant experiments, mathematical modelling and optimization. To estimate the kinetic parameters and to validate the kinetic models under different operating conditions, a set of experiments were carried out in a continuous flow isothermal trickle bed reactor using crude oil as a feedstock and commercial cobaltmolybdenum on alumina (Co-Mo/γ-Al2O3) as a catalyst. The reactor temperature was varied from 335°C to 400°C, the hydrogen pressure from 4 to10 MPa and the liquid hourly space velocity (LHSV) from 0.5 to 1.5 hr-1, keeping constant hydrogen to oil ratio (H2/Oil) at 250 L/L. The main hydrotreating reactions were hydrodesulfurization (HDS), hydrodenitrogenation (HDN), hydrodeasphaltenization (HDAs) and hydrodemetallization (HDM) that includes hydrodevanadization (HDV) and hydrodenickelation (HDNi). An optimization technique is used to evaluate the best kinetic models of a trickle-bed reactor (TBR) process utilized for HDS, HDAs, HDN, HDV and HDNi of crude oil based on pilot plant experiments. The minimization of the sum of the squared errors (SSE) between the experimental and estimated concentrations of sulfur (S), nitrogen (N), asphaltene (Asph), vanadium (V) and nickel (Ni) compounds in the products, is used as an objective function in the optimization problem using two approaches (linear (LN) and non-linear (NLN) regression). The growing demand for high-quality middle distillates is increasing worldwide whereas the demand for low-value oil products, such as heavy oils and residues, is decreasing. Thus, maximizing the production of more liquid distillates of very high quality is of immediate interest to refiners. At the same time, environmental legislation has led to more strict specifications of petroleum derivatives. Crude oil hydrotreatment enhances the productivity of distillate fractions due to chemical reactions. The hydrotreated crude oil was distilled into the following fractions (using distillation pilot plant unit): light naphtha (L.N), heavy naphtha (H.N), heavy kerosene (H.K), light gas oil (L.G.O) and reduced crude residue (R.C.R) in order to compare the yield of these fractions produced by distillation after the HDT process with those produced by conventional methods (i.e. HDT of each fraction separately after the distillation). The yield of middle distillate showed greater yield compared to the middle distillate produced by conventional methods in addition to improve the properties of R.C.R. Kinetic models that enhance oil distillates productivity are also proposed based on the experimental data obtained in a pilot plant at different operation conditions using the discrete kinetic lumping approach. The kinetic models of crude oil hydrotreating are assumed to include five lumps: gases (G), naphtha (N), heavy kerosene (H.K), light gas oil (L.G.O) and reduced crude residue (R.C.R). For all experiments, the sum of the squared errors (SSE) between the experimental product compositions and predicted values of compositions is minimized using optimization technique. The kinetic models developed are then used to describe and analyse the behaviour of an industrial trickle bed reactor (TBR) used for crude oil hydrotreating with the optimal quench system based on experiments in order to evaluate the viability of large-scale processing of crude oil hydrotreating. The optimal distribution of the catalyst bed (in terms of optimal reactor length to diameter) with the best quench position and quench rate are investigated, based upon the total annual cost. The energy consumption is very important for reducing environmental impact and maximizing the profitability of operation. Since high temperatures are employed in hydrotreating (HDT) processes, hot effluents can be used to heat other cold process streams. It is noticed that the energy consumption and recovery issues may be ignored for pilot plant experiments while these energies could not be ignored for large scale operations. Here, the heat integration of the HDT process during hydrotreating of crude oil in trickle bed reactor is addressed in order to recover most of the external energy. Experimental information obtained from a pilot scale, kinetics and reactor modelling tools, and commercial process data, are employed for the heat integration process model. The optimization problem is formulated to optimize some of the design and operating parameters of integrated process, and minimizing the overall annual cost is used as an objective function. The economic analysis of the continuous whole industrial refining process that involves the developed hydrotreating (integrated hydrotreating process) unit with the other complementary units (until the units that used to produce middle distillate fractions) is also presented. In all cases considered in this study, the gPROMS (general PROcess Modelling System) package has been used for modelling, simulation and parameter estimation via optimization process.