Pressure Buildup Analysis for a Well Produced at Constant Bottomhole Pressure

Abstract

This paper presents procedures to analyze the pressure buildup behavior at a well produced at a constant pressure. Introduction Pressure buildup analyses generally assume that the well produces either at a constant surface rate or at a series of discrete constant rates prior to shut-in. To our knowledge, only Clegg1 has attempted to analyze by conventional semilog techniques2 the buildup behavior of a well produced at a constant wellbore pressure. The lack of research efforts in this area of pressure analysis is not due to the lack of the importance of the problem or the lack of application to petroleum engineering; it is mainly due to the difficulty of obtaining a simple analytical expression to describe the bottomhole pressure buildup behavior at a well, subsequent to production at a constant pressure. The mathematical problem stems from the difficulty of handling the change in the inner boundary condition when the flowing well is shutin - i.e., changing the Dirichlet condition to a Neumann condition. This problem does not occur in the constant-flow-rate case, since the pressure buildup equations can be obtained directly by using the principle of superposition. In fact, the requirement that a well be produced at a constant rate prior to shut-in is imposed by theoretical considerations. Our objective is to suggest simple procedures to analyze the pressure buildup behavior at a well producing at a constant flowing pressure similar to those used for the constant-flow-rate case. To date, this type of problem usually is solved by treating the continuous change in rate as a sequence of discrete (step-function) rate changes and then applying the principle of superposition.4,5 This is a tedious and cumbersome procedure, and data often are not available for this type of analysis. The approach taken here is to follow a generalized procedure similar to the one suggested by Ramey and Cobb6 for the constant-flow-rate case. We obtain pressure buildup data, graph data along conventional lines, and seek simple interpretive rules to analyze these data. We avoid restrictions on producing time which commonly are employed in the classic developments2,3 and do not require that the well be produced at a constant rate prior to shut-in. This work is a study of pressure behavior during the buildup period. It includes the examination of the effects of producing time prior to buildup, the nature of the outer boundary condition (closed and constant-pressure drive), damage (or stimulation) around the well, and well bore storage. It also includes the analysis of interference data due to the closing in of the producing well. All the results in this study were obtained by a numerical (finite difference) model. p. 1813–1824