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. Introduction When a flowing well is shut in, the pressure in the wellbore increases with time as the pressures throughout the reservoir approach a static value. Analysis of the pressure increase, or pressure buildup, often provides useful information about the reservoir and the wellbore itself. Techniques exist for determination of wellbore storage, skin effect, reservoir permeability and porosity, and either the initial reservoir pressure or the volumetric average reservoir pressure at the time the well was shut in. Effects of fractures penetrated by or near the wellbore also can be detected, as well as nearby faults or reservoir drainage boundaries.Most of the techniques for pressure buildup analysis were developed for wells which, prior to shut-in, were produced at a constant rate. When the production rate before shut-in changes rapidly, conventional analysis is often suspect. If the exact rate history is known, the theory of superposition in time of constant-rate solution leads to the method derived by Horner which compensates for changing production rates. This method results in long calculations. However, in the same paper Horner proposed a simplified procedure in which the last established rate was assumed constant and the flow time was set equal to the cumulative production divided by the last established rate. Other methods for analysis of pressure buildup after a variable-rate production history were proposed by Odeh et al.A special case of variable-rate production results when a well is produced at constant pressure. The first published application of pressure buildup analysis for a well produced at constant pressure prior to shut-in was by Jacob and Lohman. Their graph of residual drawdown vs. total time divided by shut-in time results in a semilog straight line. SPEJ P. 105^