Numerical Simulation of Drillstem Tests as an Interpretation Technique

Abstract

A numerical solution of the diffusivity equation with appropriate boundary conditions allows a more rigorous analysis of drillstem test data than previously has been possible. When combined with a systematic history matching technique, the combined program can predict interwell permeability and damaged zone permeability and predict interwell permeability and damaged zone permeability and radius with less severe limitations on shut-in times. Introduction A drillstem test (DST) is a temporary completion of a well to determine the contents of a formation and its ability to produce. Information obtained is invaluable in determining the economic feasibility of permanently completing a well. Even in a well known to permanently completing a well. Even in a well known to be productive, a DST may be run to determine the best location for a casing seat or perforations, or to locate a gas or water contact. The pressure and production data obtained yield estimates of formation capacity, static reservoir pressure, skin effect, damage ratio, productivity index, pressure, skin effect, damage ratio, productivity index, and drainage radius or radius of investigation. Under ideal conditions faults may be detected. DST's can be used to detect low-volume reservoirs and to determine the possibility of well clean-up once a well is placed on permanent production. Thus, "a properly run and interpreted drill-stem test probably yields more valuable information per dollar invested than any other evalusion tool." With conventional interpretation methods, pressure data obtained during the drawdown periods and initial stages of buildup are subjected only periods and initial stages of buildup are subjected only to qualitative analysis. Only those pressure data that are used to determine a straight line on a Homer-type plot are analyzed. Because of high rig-time cost or plot are analyzed. Because of high rig-time cost or down-hole conditions that limit the length of the test period, this range of data is never obtained in many period, this range of data is never obtained in many tight wells or in wells damaged an appreciable distance into the reservoir. Descriptions of DST equipment, operational procedures, and conventional interpretation techniques are not included in this paper. This information can be found in the appropriate references. The method presented here of using all the pressure data obtained in a DST is based on a numerical pressure data obtained in a DST is based on a numerical solution of the diffusivity equation. The well is assumed to be located at the center of a region bounded by two concentric cylindrical discontinuities (Fig. 1). The inner region represents the damaged zone around the well. Properties of both the formation and the fluid are considered to be constant in each region; however, certain formation properties in the damaged zone may be different from those in the undamaged zone. This representation has previously been called the composite reservoir. A no-flow outer boundary is imposed at all times. During the drawdown period, measured pressures are used for the inner boundary condition, and cumulative production or production rate is calculated. During production or production rate is calculated. During the buildup portion of the test, a no-flow boundary is imposed at the wellbore and wellbore pressures are calculated. Since after-flow is negligible in DST'S, it is not necessary to consider wellbore effects. A function is defined that compares calculated and measured cumulative production and buildup pressures. Formation properties are varied systematically until the function is minimized, resulting in a history match. JPT P. 1413