Pressure/Pressure Convolution Analysis of Multiprobe and Packer-Probe Wireline Formation Tester Data

Abstract

Summary In cases in which flow-rate data are not reliable, the need for flow rate in estimating permeability from wireline formation tester multiprobe and packer-probe pressure-data sets can be eliminated by the use of the so-called pressure/pressure (p/p) convolution. The p/p convolution is based on the use of different pressure-data sets recorded at two different spatial locations and thus enables one to perform parameter estimation without flow rate. In this work, we present a detailed analysis of multiprobe and packer-probe pressure-transient tests by considering various p/p convolution options for both single-layer and multilayer systems. Approximate equations that apply during spherical and radial flow for a vertical well in a single-layer system for various p/p convolution options are derived. These equations indicate which parameters can be determined uniquely from p/p convolution. It is shown that p/p convolution analysis sometimes may not provide unique parameter estimates. Also, we provide a flow-rate-estimation method that proves useful to check the validity of parameter estimates obtained from p/p convolution analysis. Two example tests, a synthetic multiprobe test and a field packer-probe test, are given to illustrate the methodology and procedures developed in this work.