Pressure transient formation & well testing: convolution, deconvolution & nonlinear estimation (Developments in petroleum science, Vol. 57): convolution, deconvolution & nonlinear estimation ((Developments in petroleum science, Vol. 57) Series)

This reference presents a comprehensive description of flow through porous media and solutions to pressure diffusion problems in homogenous, layered, and heterogeneous reservoirs. It covers the fundamentals of interpretation techniques for formation tester pressure gradients, and pretests, multiprobe and packer pressure transient tests, including derivative, convolution, and pressure-rate and pressure-pressure deconvolution. Emphasis is placed on the maximum likelihood method that enables one to estimate error variances in pressure data along with the unknown formation parameters.

1.1 Introduction. 1.2 Convolution Integral. 1.3 Discrete Convolution. 1.4 Duhamels (Superposition) Theorem and Pressure-Rate Convolution. 1.5 Wellbore Pressure for Certain Variable Sandface Flow Rate Schedules. 1.5.1 Polynomial Rate Functions. 1.5.2 Exponential Flow Rate. 1.6 Logarithmic Convolution (Multirate Well Testing). 1.7 Rate-Pressure Convolution. 1.8 Pressure-Pressure Convolution. 2 Deconvolution. 2.1 Introduction. 2.2 Analytical Methods. 2.3 Direct Numerical Deconvolution. 2.4 Deconvolution with Constraints. 2.5 Nonlinear Least-Squares Pressure-Rate Deconvolution. 2.5.1 Deconvolution, Gauge Resolution, and Radius of Investigation. 2.5.2 Practicalities of Deconvolution Implementation.

Reservoir engineers, geologists, petrophysicists