To mathematically describe the long wall generator process of underground coal gasification the coalbed is considered as solid carbon with a system of vertical micro-fissures along which combustion reactions occur. Mass and energy balances for the solid and gas phases and a mass balance for each hydrocarbon component are derived. Two overall reactions are considered resulting in seven coupled, nonlinear partial differential equations. partial differential equations. The primary mechanisms of heat transfer are conduction in the solid phase and convection in the gas phase. Also, convective transfer-between the two phases along the fissure walls, phases along the fissure walls, expansion of the fissure system and effective Darcy permeability as a function of distance and time, and temperature-dependent reaction rates are considered.
The equations are written in implicit finite-difference form and solved stepwise in one dimension by direct methods with systematic updating of coefficients. Solutions are obtained for the solid and gas temperature, total gas density, and mole fractions of oxygen, carbon dioxide, and carbon monoxide as functions of distance and time. Boundary conditions include input and output pressures, inlet gas and/or solid temperatures, and inlet oxygen concentration.
Typical sets of temperature and gas component concentrations along the generator length are shown. Curves are shown indicating the effect of the dimensions of the seam and the applied pressure gradient on the energy content pressure gradient on the energy content of the output gas. Also the subsurface energy conversion efficiency is discussed.