Pressure Transient Formation and Well Testing: Convolution, Deconvolution and Nonlinear Estimation: Volume 57 (Developments in Petroleum Science)

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