A Method for Pressure Buildup Analysis of Drillstem Tests

Abstract

ABSTRACT Analysis of the pressure response obtained from a drill stem test (DST) provides important additional information for deciding whether it is economical to complete a well. Interpretation of DST pressure buildup data has been based on the Horner method. The basic assumption of the Horner method is that the well is produced at a constant rate before the shut-in. When rate changes with time, a cumbersome application of the superposition principle is required to analyze the pressure buildup data. Furthermore, the solution of the diffusivity equation for a constant production rate gives a declining flowing pressure with time, but most DST's show an increasing flowing pressure during production. Therefore, the application of the Horner method may lead to inconsistent results in the interpretation of DST pressure buildup data. An original approach was used to model the DST problem. A DST can be characterized as a changing wellbore storage problem following an instantaneous pressure drop at the well. During production the wellbore storage coefficient is given by the rate of fluid accumulation inside the wellbore. After the shut-in of the well the wellbore storage mechanics change due to the compressibility of the fluid below the bottom hole valve. Therefore, using this concept, the flowing and the pressure buildup phases are modeled with a single inner boundary condition. In this paper an analytical solution correct for both the flowing and shut-in periods was obtained by solving the diffusivity equation with a single inner boundary condition which included the mixed conditions for flow and buildup. Both a skin effect and wellbore storage were considered. Solution was obtained by Laplace transformation. The solution was used to develop methods of interpretation for the pressure buildup period of drill stem tests. Application of these new methods of interpretation to DST field data may provide the initial reservoir pressure, the formation permeability and the skin effect. The interpretation methods are based on graphical analysis of the data and are easily applied in the field. The interpretation methods are generalized to include multiple production-shut-in cycles, including step changes in the wellbore storage coefficient due to changes in the drill pipe diameter and/or due to variations in fluid properties. Unlike the results obtained from the application of the Horner method, interpretation of field data using these new methods show excellent agreement between the parameters obtained from the analysis of the first and second shut-in periods of short term double-cycled DST's. Field examples are presented.