Finite Dimensional Modelling of Underground Coal Gasification
Abstract
Underground coal gasification (UCG) is an industrial process for exploring coal reserves, particularly at great depths where conventional mining, extraction, transportation or handling of the coal is not economically feasible. By means of controlled combustion and gasification, deep coal deposits can be converted to gaseous products. In its final state, the predominant component gas of syngas is mainly made up of hydrogen, methane, carbon monoxide, carbon dioxide, nitrogen with traces of ethane and other components. In the oil, gas, and coal industries, UCG claims numerous applications. In Pakistan, 185 billion tons of coal are found, including 175 billion tonnes of Lignite-B in Thar. UCG is the preferred technology for gasifying coal in Thar due to factors such as type of coal, depth and thickness of coal seam, and location of water aquifers under the earth's surface.
A computational model represents a system using variables to characterize it, and it is used to simulate and study the behavior of complex physical processes. It is a well consensus that the mathematical models of a complex physicochemical underground coal gasification process contain multidimensional non-linear partial differential equations (PDEs). These equations are very difficult to solve both analytically and computationally. Therefore, the researchers always seek a suitable numerical scheme, which gives a good balance between the convergence of the solution and computational complexity.
In this thesis, the non-linear PDEs narrating energy and mass balances of both coal and char are solved by Galerkin finite element method (GFEM), based on seeking an approximate solution in a finite-dimensional space The infinite-dimensional spatial domain is transformed into a finite number of elements, whose dynamics are governed by the time based, vector ordinary differential equations (ODEs). Owing to the execution of GFEM, the time domain and space dependent first-order ODEs for solids (coal and char) and gases are solved numerically to report the solution of the UCG process. A numerical discretization scheme transforms an infinite-dimensional model into a finite-dimensional model, which can be briefly represented as a model reduction. The results are compared to experimental data obtained from the Thar coal UCG site, and to existing work based on the finite difference method (FDM) for the one-dimensional (1D) model of the Thar coal UCG process. Both the simulated results and the quantitative analysis support the superiority of the GFEM model over the FDM model.
Model solution is also subjected to a detailed parametric analysis that improves the effectiveness of the model. The findings show that compositions of product gas depends on coal properties and operations conditions, based on coal type, flow rate of injected gas, and thickness of coal, along with temperatures through the UCG reactor during mass and heat transport. The gasification model is more stable, improves the heating values for syngas prediction and the compositions of combustible gas based on experiments. As UCG is site-specific, there is limited scope to adjust parameters. Variations in feed rate, steam-oxygen ratio, operating pressure, and particle size are examined to observe their effects on the composition of the product gas and flow rate, and the temperature at the gas outlet.
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