Dissertations / Theses on the topic 'Coal liquefaction Mathematical models'

Traditionally, void ratio, e has been used as a state variable for predicting the liquefaction behaviour of soils under the Critical State (Steady State) framework. Recent publications show that void ratio, e may not be a good parameter for characterizing sand with fines as the steady state, SS data points move downward in e-log(p) space up to certain fines content termed as threshold fines content, TFC. Thus, it was difficult to apply SS concept on sand with fines as a small variation of fines content may lead to different SS line. Many researchers proposed to used equivalent granular void ratio, e* as an alternative state variable (i.e. in lieu of void ratio, e) in attempt to obtain a narrow trend line for SS data points irrespective of fc provided fc  TFC. The e* is obtained from e. For the conversion from e to e*, one need a parameter b which presents the active fraction of fines in overall force structure of sand. However, predicting the b is problematic. Most, if not all, of the b reported were determined by case-specific back-analysis, that is, the b-value was selected so that the test results for a given sand-fines type could be correlated with the equivalent granular void ratio, e* irrespective of fines content. This thesis examines the factors that affecting the b value by examining published work on binary packing. This leads to a simple semi-empirical equation for predicting the value of b based onparticle size ratio,  and fines content, fc. Published data and experimental results on Sydney sand appears to be in support of the proposed equation. The single relation of SS data points in e*-log(p) space for sand with fines is referred as Equivalent Granular Steady State Line, EG-SSL. The EG-SSL is then used to define the equivalent granular state parameter,*. A good correlation observed between * and q-p, q- q responses in undrained shearing. The e* and * are also used to modified a state dependent constitutive model. Seven model input parameters are needed in addition four to critical state input parameters. These parameters are obtained from drained test. The model is used to predict q-pand q- q responses for flow, non-flow and limited flow behaviour for 0% to 30% fines contents. The model predictions are in good agreement with experimental results. The effect of fines types (in terms of plasticity and angularity) on the prediction equation of b are also examined with four different types of fines. A negligible effect of fines type on the prediction equation of b is observed. The link between monotonic and cyclic loading behaviour for sand with fines are also examined with emphasis on cyclic instability and strain hardening behaviour after quasi steady state, QSS for a range of fines contents (provided that fc < TFC). It is found that a single set of rules could be used to correlate monotonic and cyclic behaviour for a range of fines contents at same *.

Pulverized coal injection (PCI) technology is widely practised in blast furnace ironmaking due to economic, operational and environmental benefits. High burnout of pulverized coal in the tuyere and raceway is required for high PCI rate operation. A comprehensive review reveals that although there have been a variety of PCI models, there is still an evident need for a more realistic model for PCI operation in blast furnace. Aiming to build a comprehensive PCI model of a full-scale blast furnace, this thesis presents a series of three-dimensional mathematical models, in terms of model development, validation and application, in a sequence from a pilot-scale to a full-scale, from a simple to complicated geometry, from a coal only system to a coupled coal/coke system. Firstly a three-dimensional model of pulverized coal combustion is developed and applied to a pilot-scale PCI test rig. This model is validated against the measurements from two pilot-scale test rigs in terms of gas species composition and coal burnout. The gas-solid flow and coal combustion are simulated and analysed. The results indicate that the model is able to describe the evolutions of coal particles and provide detailed gas species distributions. It is also sensitive to various parameters and hence robust in examining various blast furnace operations. This model is then extended to examine the combustion of coal blends. The coal blend model is also validated against the experimental results for a range of coal blends conditions. The overall performance of a coal blend and the individual behaviours of its component coals are analysed. More importantly, the synergistic effect of coal blending on overall burnout is examined and the underlying mechanisms are explored. It is indicated that such synergistic effect can be optimized by adjusting the blending fraction, so as to compensate for the decreased burnout under high coal rate operation. The model provides an effective tool for the optimum design of coal blends. As a scale-up phase, the coal combustion model is applied to the blowpipe-tuyereraceway region of a full-scale blast furnace, where the raceway is simplified as a tube with a slight expansion. The in-furnace phenomena are simulated and analysed, focusing on the main coal plume. The effect of cooling gas conditions on combustion behaviours is investigated. Among the three types of cooling gas (methane, air, and oxygen), oxygen gives the highest coal burnout. Finally, a three-dimensional integrated mathematical model of pulverized coaVcoke combustion is developed. The model is applied to the blowpipe-tuyere-raceway-coke bed region of a full-scale blast furnace, which features a complicated raceway geometry and coke bed properties. The model is validated against the measurements in terms of coal burnout from a test rig and gas composition from a blast furnace, respectively. The model gives a comprehensive full-scale picture of the flow and thermo-chemical characteristics of PCI process. The typical operational parameters are then examined in terms of coal burnout and gas composition. It is indicated that the final burnout along the tuyere axis is insensitive to some operational parameters. The average burnout over the raceway surface can better represent the amount of unburnt coal particles entering the surrounding coke bed and it is also found to be more sensitive to the changes of most parameters. In addition, the underlying mechanisms of coal combustion are obtained. The coal burnout strongly depends on both oxygen availability and residence time. The existence of recirculation region gives a more realistic coal particle residence time and burnout. Compared with the fore-mentioned two models, this model is considered as a more comprehensive model of PCI operation for understanding the infurnace behaviours and provides more reliable information for the design of operational parameters.

Recognizing the complexity of coal mining management, e.g., the scarcity of financial resources and the high level of uncertainty, a mixed binary programming model has been developed as an aid for generating production schedules which maximize the associated net present value. Defining the mine layout as a precedence network, with the nodes representing mining blocks, a solution procedure is developed, based on Benders' partitioning scheme. That is, the procedure iterates between two problems, namely, the master (primal) problem, solved by a combination of heuristic and exact methods, and the subproblem (dual problem), solved partly by inspection and partly as a minimal cost network flow problem. The heuristic methods are based on improvements of existing algorithms for scheduling precedence-related jobs on m processors. Computational experiences are presented and the procedure is demonstrated on a mining case.
Ph. D.

In the increasingly competitive coal market, it is becoming more important for coal operators to develop mathematical models for surface mining which can estimate mining costs before the actual mining begins. The problem becomes even more acute with the new reclamation laws, as they affect surface coal mining methods, productivity, and costs. This study presents a computer simulator for a mountaintop removal type of surface mining operation. It will permit users to compare the costs associated with different overburden handling and reclamation plans. It may be used to minimize productivity losses, and, perhaps, to increase productivity and consequently to reduce operating costs through design and implementation of modified mountain top removal methods.
M.S.

In Victoria, Australia, brown coal is utilised as a major source of energy for the power generation industry. Victorian and South Australian brown coals have a very high moisture content and therefore, the efficiencies of power generation in traditional pulverised fuel fired furnaces are low. Fluidised beds offer a number of advantages over conventional furnaces, leading to improvements in efficiency and environmental impact. A disadvantage with implementing fluidised bed technology is the issue of scale-up. Fluidised bed behaviour can alter significantly with changes in scale, because of their strong dependence on the bed hydrodynamics. Hence, there is a need to accurately model bed behaviour to ensure that the effect of changes in scale are well understood and will not become costly and time consuming. Computational Fluid Dynamics (CFD) techniques can be applied to fluidised bed systems to gain a better understanding of the hydrodynamic behaviour involved. In the past, numerical models have considered only single particle sizes due to the added complexity of interaction between particles of differing sizes and densities. Industrial fluidised beds typically contain more than one particle size and density, therefore there is a need to develop a numerical model which takes this into account. The aim of this thesis is to develop and validate CFD techniques for modelling the behavior of a gas-solid fluidised bed containing more than one particle size and density. To provide validation data for the numerical model, physical experiments are undertaken on a small two-dimensional bubbling gas-solid fluidised bed. Mixing and segregation behaviour of different materials are investigated. The experiments demonstrate that whilst only a small proportion of the bed consists of different size/density particles, significant changes in bed behaviour are apparent. Changes in bubble rise velocity, bubble size and bubble shape are observed. A number of constitutive equations must be included in the numerical model, including relationships for the momentum transfer between various phases and solids pressure. Different combinations of these constitutive equations are investigated. A new equation for particle-particle interactions is derived and included in a CFD model. The CFD model is validated against both data in the literature and physical experiments. From the validation studies, an optimum equation set is identified. This optimum equation set produces numerical results that closely resemble experimental bed behaviour, thus bringing the goal of solving scale-up problems one step closer. The use of this type of CFD model will ultimately result in timely and cost effective solutions for both the power generation and chemical processing industries.

Thesis (MBA)--Stellenbosch University, 2000.
ENGLISH ABSTRACT: It was found that the hot metal cost of ISCOR Newcastle's single blast furnace can significantly be reduced by the correct use of an integrated model to predict reductant cost based mainly on coal blend. The model uses coal ash chemistry, fluiidity, vitrinite rank and volatile matter to predict coke strength after reaction (CSR), coke ash and coking yield. CSR is used to predict maximum allowable coke nut- and pea consumption in the furnace as well as hot blast temperature. Pitch injection levels are predicted using CSR and blast furnace production rates. Coke ash, pitch injection and hot blast temperature is used to predict the coke rate. The above is used with imported Chinese coke cost to accurately predict reductant cost. It was found that the current optimum blends should include Australian en Nieu Zeeland coals because of price and quality conciderations. Because of its low cost of production and low quality the optimum percentage of Grootegeluk in the blend is determined largely by its transfer price.
AFRIKAANSE OPSOMMING: Die vloeiyster koste van ISCOR Newcastle se enigste hoogoond kan drasties verlaag word deur die korrekte gebruik van 'n geïntegreerde model wat reduktant koste voorspel op grond van steenkoolmengsel. Die model gebruik die chemiese samestelling van steenkool-as, fluiiditeit, vitriniet rang en vlugstof om kooks warmsterkte (SNR), kooks-as en verkooksingsopbrengs te voorspel. SNR is gebruik om die maksimum kooksneute- en -erteverbruik in die hoogoond sowel as blaastemperatuur te voorspel. Pikinspuiting is bereken met SNR en hoogoond produksietempo's. Pikinspuiting en blaastemperatuur word saam met kooks-as gebruik om kookskoers te voorspel. Bogenoemde is saam met die koste van ingevoerde Chinese kooks gebruik om reduktant koste akkuraat te voorspel. Daar was bevind dat die huidige optimum mengsels Australiese en Nieu Zeelandse steenkool moet bevat as gevolg van huidige prys- en kwaliteitsoorwegings. As gevolg van sy lae produksiekoste en lae kwaliteit word die optimum hoeveelheid Grootegeluk bepaal deur sy oordragprys.

As the coal reserves at shallow depths become exhausted companies have to develop deeper deposits and increase percentage extraction to maintain production levels. Total extraction for room and pillar mines can only be achieved by pillar extraction. The unsupported roof increases during pillar extraction and hence the cost of ground control also increases. Nevertheless, pillar extraction where possible has many potential advantages such as decreased operating cost, increased utilization of reserves, and extended life of the mine. There are several variables such as depth, mining height, rock strength, mining geometry, roof and floor conditions, and retreat mining methods, which affect pillar extraction cost. Cost components of pillar extraction are classified as direct, indirect, fixed, and subsidence compensation costs. A discounted cash flow pillar extraction cost simulator has been developed and used to compute total pillar extraction cost for a variety of conditions and to explore the possibilities of optimizing ground control and retreat mining techniques to maximize extraction ratio. The computer program computes the safe and optimum pillar dimensions and determines the suitable pillar extraction method for the computed pillar width. Pillar extraction cost components are generated and totalled using the net present value method by the simulator. The total extraction cost simulator evaluates the potential advantages of pillar extraction and tests individual variables for sensitivity to changes in other variables attributable to ground control and pillar extraction techniques. Cost of pillar extraction per ton of coal versus depth is presented in the form of a simple nomogram by the simulator. The simulator can be used to determine the economic feasibility of pillar extraction at a particular depth, geologic and mining environment when the market price of mined coal is known.
Ph. D.
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[Truncated abstract] Mine lakes are a water body created after an open-cut mine ceases operating. The lakes develop in the former mine-pit due to the combination of groundwater inflow, surface run-off and, in some cases, due to rapid filling from river diversion. While potentially valuable water resources, these lakes often have poor water quality and managing the water body is an important part of the overall process of mine site rehabilitation. As mine lakes form in man-made pits, they have a bathymetry that is typically quite distinct from natural lakes and this can, in turn, strongly influence the hydrodynamics and hence the water quality of the water body. Despite the potential importance of these water bodies, there have been very few studies on the hydrodynamics of mine lakes. This study describes a field investigation of the hydrodynamics of a former coal mine lake, Lake Kepwari, in south-western Western Australia. In particular, this study examines the hydrodynamic processes in both the surface mixing layers and the internal mixing in the density stratified lake. Wind sheltering in the surface mixing layer occurs due to the presence of the steep walls and lake embankments. A week long field experiment was conducted in December 2003 using a combination of moored thermistor chains with meteorological stations and the deployment of rapid vertical profiling turbulent microstructure instruments and CTD drops from two boats operating on the lake. ... Simulations indicated that inclusion of a site specific sheltering effect, based on the results of the field campaign, significantly improved the models‘ performance in capturing the surface mixed layer deepening associated with episodic strong wind events that occur on the lake. Considerable internal mixing was indicated by the high dissipation rates observed, particularly near the boundaries. Large basin-wide diffusivities were also calculated from the heat budget method over long periods, showed a consistency with time, and were slightly higher in summer than during the Autumn Winter period. Although light, there are persistent winds over the lake and yet little basin-scale internal wave activity or seiching. It is hypothesized that any seiching motion was rapidly damped by strong mixing over the hydraulically rough bathymetry bathymetry created by the remnant benches from the open cut mining operation itself. This boundary mixing, in turn, drives secondary relaxation currents that transport mixed fluid from the boundaries to the interior, resulting in high effective basin-wide diffusivities. A simple boundary mixing model is proposed to describe this process.

Coal continues to be burned by direct combustion in packed or moving bed in small size domestic furnaces, medium size industrial furnaces, as well as small power stations. Recent stringent restrictions on exhaust emissions call for a better understanding of the process of combustion of coal in beds. The present study is a prelude to developing methods of analysis to obtain this improved understanding. A one-dimensional steady-state computational model for combustion of a bed of solid fuel particles with a counterflowing oxidant gas has been developed. Air, with or without preheating, is supplied at the bottom of the bed. Spherical solid fuel particles (composed of carbon and ash) are supplied at the top of the bed. Upon sufficient heating in their downward descent, the carbon in particles reacts with oxygen of the flowing gas. The governing equations of conservation of mass, energy, and species are integrated numerically to obtain the solid supply rate whose carbon content can be completely consumed by a given gas supply rate. The distributions of solid and gas temperatures, of concentrations of various gas species, of carbon content in solid, and of velocity and density of gas mixture are also calculated along the bed length. The dependence of these distributions on the solid and gas supply rates, the air supply temperature, the size of solid fuel particle, and the initial carbon content in solid is also investigated. The calculated distributions are compared with the available measurements from literature to find reasonable agreement. More gas supply is needed for complete combustion at higher solid supply rate. At a given gas supply rate, more solid fuel particles can be consumed at higher gas supply temperature, for larger particle size, and for lower initial carbon content in solid. The temperature of the bed becomes higher for higher solid supply rate, higher gas supply temperature, larger solid particle diameter, or lower initial carbon content in solid. These reasonable results lead one to encourage extension of the model presented here to more complex problems involving combustion of coals in beds including the effects of drying and pyrolysis.
Graduation date: 1994

A dissertation submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master in Science in Engineering, Johannesburg September 1998
Combustion modelling of utility furnace chambers provides a cost efficient means to extrapolate the combustion behaviour of pulverised fuel (pf) as determined from drop tube furnace (DTF) experiments to full scale plant by making use of computational fluid dynamics (CFD). The combustion model will be used to assimilate essential information for the evaluation and prediction of the effect of • changing coal feedstocks • proposed operational changes • boiler modifications. TRI comrnlssloned a DTF in 1989 which has to date been primarily used for the comparative characterisation of coals in terms of combustion behaviour. An analysis of the DTF results allows the determination of certain combustion parameters used to define a mathematical model describing the rate at which the combustion reaction takes place. This model has been incorporated into a reactor model which can simulate the processes occurring in the furnace region of a boiler, thereby allowing the extrapolation of the DTF determined combustion assessment to the full scale. This provides information about combustion conditions in the boiler which in turn are used in the evaluation of the furnace performance. Extensive furnace testwork of one of Eskom's wall fired plant (Hendrina Unit 9) during 1996, intended to validate the model for the ar plications outlined above, included the measurement {If : • gas temperatures • O2, C02, CO, NOx and S02 concentrations • residence time distributions • combustible matter in combustion residues extracted from the furnace • furnace heat fluxes. The coal used during the tests was sampled and subjected to a series of chemical and other lab-scale analyses to determine the following: • physical properties • composition • devolatilisation properties " combustion properties The same furnace was modelled using the University of Stuttgart's AIOLOS combustion code, the results of Which are compared with the measured data. A DTF derived combustion assessment of a coal sampled from the same site but from a different part of the beneficiation plant, which was found to burn differently, was subsequently used in a further simulation to assess the sensitivity of the model to char combustion rate data. The results of these predictions are compared to the predictions of the validation simulation. It was found that the model produces results that compare well with the measured data. Furthermore. the model was found to be sufficiently sensitive to reactivity parameters of the coal. The model has thereby demonstrated that it can be used in the envisaged application of extrapolating DTF reactivity assessments to full scale plant. In using the model, it has become apparent that the evaluations of furnace modifications and assessments of boiler operation lie well within the capabilities of the model.
MT2017

We investigate several aspects of the numerical solution of the radiative transfer equation in the context of coal combustion: the parallel efficiency of two commonly used opacity models, the sensitivity of turbulent radiation interaction (TRI) effects to the presence of coal particulate, and an improvement of the order of temporal convergence using the coarse mesh finite difference (CMFD) method. There are four opacity models commonly employed to evaluate the radiative transfer equation in combustion applications; line-by-line (LBL), multigroup, band, and global. Most of these models have been rigorously evaluated for serial computations of a spectrum of problem types [1]. Studies of these models for parallel computations [2] are limited. We assessed the performance of the Spectral-Line- Based weighted sum of gray gasses (SLW) model, a global method related to K-distribution methods [1], and the LBL model. The LBL model directly interpolates opacity information from large data tables. The LBL model outperforms the SLW model in almost all cases, as suggested by Wang et al. [3]. The SLW model, however, shows superior parallel scaling performance and a decreased sensitivity to load imbalancing, suggesting that for some problems, global methods such as the SLW model, could outperform the LBL model. Turbulent radiation interaction (TRI) effects are associated with the differences in the time scales of the fluid dynamic equations and the radiative transfer equations. Solving on the fluid dynamic time step size produces large changes in the radiation field over the time step. We have modifed the statistically homogeneous, non-premixed flame problem of Deshmukh et al. [4] to include coal-type particulate. The addition of low mass loadings of particulate minimally impacts the TRI effects. Observed differences in the TRI effects from variations in the packing fractions and Stokes numbers are difficult to analyze because of the significant effect of variations in problem initialization. The TRI effects are very sensitive to the initialization of the turbulence in the system. The TRI parameters are somewhat sensitive to the treatment of particulate temperature and the particulate optical thickness, and this effect are amplified by increased particulate loading. Monte Carlo radiative heat transfer simulations of time-dependent combustion processes generally involve an explicit evaluation of emission source because of the expense of the transport solver. Recently, Park et al. [5] have applied quasidiffusion with Monte Carlo in high energy density radiative transfer applications. We employ a Crank-Nicholson temporal integration scheme in conjunction with the coarse mesh finite difference (CMFD) method, in an effort to improve the temporal accuracy of the Monte Carlo solver. Our results show that this CMFD-CN method is an improvement over Monte Carlo with CMFD time-differenced via Backward Euler, and Implicit Monte Carlo [6] (IMC). The increase in accuracy involves very little increase in computational cost, and the figure of merit for the CMFD-CN scheme is greater than IMC.
Graduation date: 2012

A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Doctor of Philosophy (Chemical Engineering), 25 May 2016
The Integrated Gasification Combined Cycle (IGCC) is a promising technology in the power generation industry to increase efficiency and reduce environmental emissions associated with fossil fuels. The performance of the gasifier and its economic feasibility largely depends on the gasifier island and many problems experienced during gasification are associated with extreme operating conditions. There is, however, no evidence that the extreme operating conditions in the gasifier yield the maximum possible fuel gas heating value. The main objective of this research was, therefore, to develop a mathematical model to simulate and optimize the performance of the IGCC, particularly focusing on maximizing the fuel gas heating value. The work carried out in this thesis was divided into three parts. The first part presented a 1-D simulation model for a dry-fed entrained flow gasifier with oxygen and steam used as oxidizing agents. The model was then validated against published models for a similar reactor configuration and then extended to an existing entrained flow gasifier of Elcogas IGCC power plant in Puertollano, Spain. The second part presented the optimization model in which the objective function was to maximize the fuel gas heating value. The last part combined gasifier and the gas turbine models and evaluated the overall performance of the gas path. The formulated mathematical model which consisted of mass and energy balances of the system was solved in gPROMS platform in order to determine the optimum conditions of the gasifier. Multiflash for Windows was used to obtain the thermodynamic properties of gas phase. The model was first used to replicate three published simulation models, particularly focusing on the carbon conversion, cold gas efficiency, gasification peak temperature and gasifier exit gas temperature. The results obtained during optimization of the Elcogas entrained flow gasifier showed a 14% increase in fuel gas heating value was realized with a decrease of 519K in operating temperature. The pressure did not have a significant impact on the fuel gas heating value, with only less than 2% increase in heating value being achieved by changing the pressure from 2MPa to 5MPa. Owing to a decrease in operating temperature, the conversion was reduced from 97% to about 63% and that led to a decrease of almost 60% in O2 and 50% in steam used in the gasifier. The results also indicate an almost 2% increase in the efficiency of the gas turbine when burning the gas of the higher heating value. This was mainly due to the increase in the expander inlet temperature. The gas turbine exhaust temperature and the exhaust gas heat capacity also iii increased, thereby, increasing the amount of heat available in the heat recovery steam generator. There was also a 7% notable increase of the overall gas path efficiency. A reduction in operating temperature and pressure of the gasifier, therefore, guarantee an extended operating cycle of the gasifier, thereby, improving commercial attractiveness and competitiveness of the technology compared to other available power generation technologies. These new proposed operating conditions, which are less severe, therefore, signify a possible improvement availability and reliability of the IGCC power plant.

M. Tech. Engineering Chemical.
Aims to investigate how the addition of impurities in a CO2 stream affects the adsorption capacity of CO2 on South African coals. To achieve this aim, the following objectives were carried out. 1. To measure the adsorption isotherms and adsorption capacities of pure CO2 and flue gas mixtures on various South African coals under in-seam conditions including pressures up to 88 bar and isothermal temperature of 35 º%x;C; 2. To evaluate the effects of coal rank on the adsorption isotherms and adsorption capacities of pure CO2 and flue gas mixtures; 3. To do a comparative study to evaluate the effects of CO2 impurities on the adsorption capacity of pure CO2 on coal; 4. To study the degree of preferential sorption of the individual flue gas mixtures components on coal; 5. To determine the suitability of the Langmuir, Freundlich, and Temkin adsorption isotherm models in representing pure CO2 adsorption onto coal; and 6. To determine the suitability of Extended Langmuir (EL) adsorption models in representing the flue gas mixture adsorption onto coal.