NUMERICAL SIMULATION OF THE INJECTION-PRODUCTION HISTORY OF A MULTIPLE-WELL SYSTEM USING THE METHOD OF LINES (ADDENDUM TO THE FINAL REPORT)

A three-dimensional model which simulates the injection-production air flow rate in a tar sand bed was developed by the author in fulfillment of ERDA Contract (E(29-2)). The model consisted of a non-linear partial differential equation derived from the continuity equation, Darcy's Law and the ideal gas equation of state. A finite difference scheme based on the work developed by Bruce et al. was incorporated in a computer code which determines both the injection-production-air flow rates and the pressure distribution in the tar sand bed. The major drawback of the finite difference scheme is the question of stability, which imposes a severe restriction on the size of the time step required for convergence. Such a restriction increased the computation time considerably and necessitated a major revision of the previous computer code. Thus, the finite difference scheme was abandoned in favor of a more stable computer code based on the method of lines. Furthermore, a two-dimensional formulation replaced the more cumbersome three-dimensional code used on the previous stages. This was possible because the flow pattern obtained from the three-dimensional model exhibited negligible transverse flow normal to the bedding plane.