A two-dimensional, numerical, mathematical model has been developed to predict methane influx into coal mines under a variety of mining conditions. A set of time-dependent, partial differential equations for two-phase darcy flow in a porous medium was developed. The equations comprehend various microscopic flow phenomena and time- and pressure-dependent adsorption and desorption of methane. One- dimensional models were expanded to two-dimensional models by appropriate geometric modification of the basic equation set. Numerical solutions were obtained with an implicit method-of-lines technique. Boundary conditions corresponding to the appropriate mining system can be selected. The model and solution procedure are coded in a structured dialect of Fortran, and a preprocessor is included for adaptation to popular computer systems. To obtain data for comparison with the model, methane measurements were made in three coal mines in the eastern United States to encompass a range of gas contents, porosities, permeabilities, coal rank, and mining methods. Results of the simulation of methane emission during advance of the mining face following idle periods were in general agreement with observed values. Volume 1 contains the final report and summary, methane measurement data, mathematical components, and simulation demonstrations.