Galerkin Finite Element Based Modeling of One Dimensional Packed Bed Reactor for Underground Coal Gasification (UCG) Process

Mathematical models of a complex physicochemical underground coal gasification process involve multidimensional non-linear partial differential equations (PDEs). Therefore, researchers always seek a suitable numerical scheme that would give a good balance between accuracy of the solution and computational complexity. In this paper, the non-linear PDEs describing energy and mass balances of both coal and char are solved by Galerkin finite element method (GFEM). The infinite-dimensional spatial domain is transformed into a finite number of elements, whose dynamics are governed by a system of 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 find a solution of the UCG process. The resultant syngas compositions and the calibrated heating value are influenced by the operation parameters and the type of oxidant used. The results are compared with the experimental data obtained from the Thar coal UCG site, and with existing work, based on the finite difference method (FDM) for the one dimensional (1D) model. The simulated results along with the quantitative analysis show the superiority of the GFEM model over the FDM model.