Model Application

Mathematical modeling is a scientific exercise with the objective of developing simplified mathematical statements that relate to one another the same way as the processes that are being modeled. The utility value of the model is dependent on the ability of the model to closely approximate prototype behavior. Development of a perfect model, therefore, is an unrealistic objective because of the simpli¬fying assumptions made in building it. However, for a model to be acceptable for application, its operating characteristics or data generated from it should, within reasonable accuracy, duplicate proto¬performance. The validity and accuracy of a model depends on the mathematical constraints presupposed in model formulation. The final model must be tested for mathematical validity and for closeness of representation of the prototype. Mathematical validity, does not, however, imply that the model is accurate and correct but is prerequisite. Model testing and verification for the steady state model are given in Owili-Eger et al (1973). The unsteady state model has been tested for mathematical validity and found to be correct but has not yet been applied to a field condition for lack of data. However, in the application discussed below, the unsteady state model results are compared with pressure curves reported in literature and also with results from the steady state model. Coal seam characteristics and gas reservoir pressure used in this application are extracted from Kissell (1972). These characteristics are for the Pittsburgh seam, Federal No. 2 Mine, Fairview, West Virginia.