Conventional numerical simulation of hydrocarbon reservoirs is inadequate for the prediction of bottom-hole pressures at production wells. This problem can be overcome by using a special mathematical model which combines individual well simulation with reservoir simulation. Severe computational instability is commonly encountered in the radial models due to the relatively small grid-blocks and high fluid velocities in the vicinity of the well bore. This instability is found to be more pronounced during depletion of the reservoir when the pressure near the well bore is below bubble-point pressure. A new technique is introduced here for saturation calculations in the critical region near the well. This technique is found to be stable for computing saturations in the small inner elements of the radial grid. Stability is maintained even for the simulation of reservoir behavior within a few inches of the producing sand face.
The mathematical model developed in this study was used to predict performance of a hypothetical oil field, and these predictions were com- , pared to the performance predicted by an areal model. It is suggested that this type of model be used for reservoirs where pressure drawdown at producing wells is large, and bottom-hole pressure is less than bubble-point pressure --Abstract, pages ii-iii
