Pressure Buildup for Wells Produced at a Constant Pressure

Abstract

Abstract Conventional well test analysis has been developed primarily for production at a constant flow rate. However, there are several common reservoir production conditions which result in flow at a constant pressure instead of a constant rate. In the field, wells are produced at constant pressure when fluids flow into a constant-pressure separator and during the rate decline period of reservoir depletion. In geothermal reservoirs, produced fluids may drive a backpressured turbine. Open wells, including artesian water wells, flow at constant atmospheric pressure. Most of the existing methods for pressure buildup analysis of wells with a constant-pressure flow history are empirical. Few are based on sound theory. Hence, there is a need for a thorough treatment of pressure buildup behavior following constant-pressure production. In this work, the method of superposition of continuously changing rates was used to generate an exact solution for pressure buildup following constant-pressure flow. The method is general. Storage and skin effects were incorporated into the theory, and both bounded and unbounded reservoirs were considered. Buildup solutions were graphed using conventional techniques for analysis. Horner's method for plotting buildup data after a variable-rate flow was found to be accurate in a majority of cases. Also, the method by Matthews et al. for determining the average reservoir pressure in a closed system was determined to be correct for buildup following constant-pressure flow.