Model Development

The quantity of methane emitted into the mine atmosphere and the movement of gas through solid coal and the adjoining country rock are dependent on the physical properties of the medium, boundary con¬ditions, the initial gas pressure distribution, and the combination of natural and mining factors. Functional relationships between these factors are not yet known. Consequently, the development of rigorous mathematical models to predict methane flow into the mine air is difficult and to date no model has been reported which is capable of such a function. Thus far, empirical formulas available for the calculation of gas quantity released from underground sources require too much his¬torical data, not currently available. Again, these estimations are at best only crudely approximate. The numerical methods available have not been made practical enough for industry wide application. Therefore, the development of a relationship amenable to numerical analysis and practical enough for use in the industry would provide the flexibility lacking in analytical approaches. The mathematical models given in equations (7) and (8) are further attempts in presenting practical models for predicting the quantity of methane emission into the mine environment. Equation (7) is the steady state model and equation (8) is the unsteady state model.