Analysis and interpretation of well test and production data for bounded reservoir systems

Abstract

The overall goal of analyzing reservoir performance (rate and pressure behavior as a function of time) is to characterize or describe the reservoir in terms of average or "bulk" properties. This work focuses specifically on the analysis of well performance data to determine the influence of reservoir boundaries. We provide new, closed form solutions for bounded circular reservoirs with and without vertical fractures, and we provide methodologies for the analysis and interpretation of test data influenced by closed reservoir boundaries. The general goals for analysis and interpretation of production and well test data from homogeneous reservoir systems are to estimate the following: Reservoir drainage volume; Effective permeability of the reservoir; Near-well "skin" damage or stimulation; and average reservoir pressure in the vicinity of a particular well. These parameters are used for reservoir evaluation (comparison and combination with petrophysical data), prediction of future reservoir performance, and to plan reservoir development activities (e.g., additional wells, stimulation, and additional recovery efforts). While there are a variety of methods we can use to estimate these parameters, our focus in this work is to use pressure buildup test data to estimate reservoir drainage volume and effective permeability, using the pressure derivative and pressure integral derivative functions. This is a new approach and one that we show to be very effective at isolating and interpreting data trends that can be used to make such determinations.Methods to estimate reservoir volume have been used in petroleum engineering for quite some time, but the current analysis methods do not cover all possible physical constraints. Our efforts focus on the pressure derivative and pressure integral derivative functions for the following reasons. First, these functions do not require prior knowledge of initial reservoir pressure or the correct initial shut-in pressure, but these methods do require accurate pressure measurements. Second, these functions provide a unique resolution of reservoir and well features that cannot be determined from pressure data alone. Type curves for pressure drawdown solutions for a bounded circular reservoir have been introduced in the literature, but the procedures for the analysis and the general applicability of the type curves are not described. During boundary-dominated flow these type curves can be used for any reservoir shape, although the type curves are developed from circular reservoir solutions. Our major result is our development of new type curves for analyzing pressure buildup data in a bounded circular reservoir. The problem in using the pressure derivative method is that there is no simple means to account for the effect of producing time. Although these new type curves can be used for the analysis of non-circular reservoirs, only boundary-dominated flow data can be readily analyzed. This is especially the case for non-symmetrical reservoirs, which have large transitions from transient to boundary-dominated flow behavior. These new type curves can be used as a diagnostic tool for analysis and interpretation of bounded reservoirs since the pressure derivative and integral derivative functions have been appropriately correlated in terms of the reservoir volume.