Digital pressure derivative method and program storage device

Abstract

In a Digital Pressure Derivative Technique (DPDT) which uses convolution, an input signal including noise is convolved with a wavelet to produce an output signal which is a derivative of the input signal and which is substantially devoid of the noise. The DPDT can be used in many applications; however, in one such application, a pressure signal from a wellbore including noise is convolved with a special wavelet to produce an output signal which is the derivative of the input pressure signal, the output signal being substantially devoid of the noise. The wavelet is made from the unit sample response of a bandlimited, optimum linear phase Finite Impulse Response digital differentiator. The DPDT technique enables analysts to customize the differentiation based on the quality of the measured data without having to use traditional, subjective smoothing algorithms. The results presented here, in connection with the one such application mentioned above, bring significant improvements to the diagnosis and interpretation of pressure transient data, and interpretation techniques that utilize higher-order derivatives are now practical.