Mathematical Modeling of the Stream Method of Underground Coal Gasification
Authors: Magnani C.F. , Ali S.M. Farouq 
Published: December 2007

Abstract
This investigation focuses on mathematical modeling of the process of underground gasification of coal by the stream method. A one-dimensional, steady-state model consisting of five coupled differential equations was formulated, and the solution, extracted analytically, was used to develop closed-form expressions for the parameters influencing coal gasification.
The model then was used for interpreting field performance curves, predicting the results of The performance curves, predicting the results of The field tests, and ascertaining the over-all process sensitivity to the input variables. The usefulness of the model was shown by establishing the parameters influencing the success or failure of parameters influencing the success or failure of an underground gasification project.

Introduction
One method of eliminating many of the technological and environmental difficulties encountered during the production of synthetic gas through aboveground coal gasification involves gasifying cod in situ. This process, known as underground coal gasification, was first proposed in 1868 by Sir William Siemens and is based on the controlled combustion of coal in situ. This in-situ combustion results in the production of an artificial or synthetic gas that is rich in carbon dioxide, carbon monoxide, hydrogen, and hydrocarbon gases. Despite the fact that reaction stoichiometry is a moot element of underground coal gasification, it is nonetheless believed thatcarbon dioxide is formed by the partial oxidation of coal,carbon monoxide is generated by the subsequent reduction of carbon dioxide, andthe hydrogen and hydrocarbon gases result from the water-gas reaction and carbonization of coal, respectively.
To effect the controlled combustion of coal in situ, the coal seam first must be ignited and a means must be provided for supporting combustion (through injection of a suitable gasification agent) and producing the gases generated underground. Fig. 1 presents a schematic diagram of an underground gasification system that complies with these requirements. This approach to gasifying coal is known as the stream or channel method and necessitates drilling two parallel galleries, one serving as an injection gas inlet and the other as a producer gas outlet. These wells are then linked by a borehole drilled horizontally through the coal seam. Ignition occurs in the coal seam at the gas inlet and proceeds in the direction of flow. The combustion front thus generated moves essentially perpendicular to the direction of gas flow. perpendicular to the direction of gas flow.Since the technological inception of underground gasification, over 1,500 publications have appeared in the literature that bear testimony to the absence of a complete, legitimate, theoretical analysis of the underground gasification process. Given this observation, it is the basis of this paper that progress in underground coal-gasification research progress in underground coal-gasification research has suffered from the absence of "interpretative theory"; that is, it has suffered from a lack of logical, physical, and mathematical analysis of the governing and underlying aerothermochemical principles. The difficulties in formulating a principles. The difficulties in formulating a mathematical model adequately describing the numerous phenomena involved during coal gasification are indeed formidable.
SPEJ
P. 425