A computer model for characterizing reacting flows through packed beds is presented. These flows are related to the underground coal gasification conditions in terms of combustion and multi-component chemical reactions that take place inside beds of coal char. Time-dependent, two-dimensional (including axisymmetrical) partial differential equations (PDE's) describing conservation of mass, species, momentum, and the thermal energy are formulated. These PDE's are then recast into a set of ordinary differential equations (ODE's) with time as independent variable. The resulting ODE's are solved by applying a method-of-lines (MOL) technique to multi-component flows through packed char beds. The present formulation considers: the transport phenomena at the wall; various transient flow cases; multiple reactions and species; a wide range of options on the boundary conditions: temperature-dependent physical parameters; and rezoning capabilities. A numerical code called GSF has been developed, and computer runs have been performed to verify various aspects of the physical models as well as the numerical approach taken in the present analysis. These include favorable agreements with available analytical solutions for simple, one-dimensional flows and two-dimensional non-isotropic heat transfer to a wall. For more complicated flow situations for which there are no analytical solutions, good agreements have also been obtained between the results of the present method and those of alternative numerical methods. The code has been applied to several physical situations bearing on the underground coal gasification processes, i.e., wall drying, wall regression during gasification, and water injection into a gasifying bed. Preliminary results demonstrate that the present numerical modeling approach shows promise as a first step in describing the transient thermophysical phenomena taking place inside packed beds. 35 refs., 19 figs.