1 Convolution


1.1 Introduction


1.2 Convolution In tegral


1.3 Discrete Convolution


1.4 Duhamels (Superp osition) Theorem and Pressure-Rate Convolution


1.5 Wellbore Pr essure 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 Ra te-Pressure Convolution


1.8 Pressure-Pressure Convolution

< br>2 Deconvolution


2.1 Introduction


2.2 Analytica l Methods


2.3 Direct Numerical Deconvolution


2.4 Dec onvolution with Constraints


2.5 Nonlinear Least-Squares Pressu re-Rate Deconvolution


2.5.1 Deconvolution, Gauge Resolution, a nd Radius of Investigation


2.5.2 Practicalities of Deconvoluti on Implementation


2.5.3 Deconvolution Parameters Selection


2.6 Pressure-Rate Deconvolution Examples


2.6.1 Simulate d Well Test Example


2.6.2 Horizontal Field Test Example


2.6.3 Wirelin Formation Tester Example


2.7 Pressure-Pressu