Comparison of derivative algorithms used in pressure transient analysis

Abstract EN

This work presents a detailed comparison of numerical methods that can be used to construct pressure derivative data for pressure transient analysis.

Numerical methods compared include the algorithms based on interpolating polynomials, least-squares (LS) polynomial fitting, smoothing splines, and Laplace transform method.

Statistical measures are used to quantify the effects of noise (random measurement errors) and the sampling rate of measured pressure data on the performance of algorithms.

Noise amplification equations associated with some of the derivative algorithms are derived.

The effect of smoothing on the accuracy of well/reservoir parameters estimated from nonlinear LS regression analysis for pressure derivative data is also investigated.

It was found that the algorithms based on high-degree LS polynomial, spline, and Laplace transform methods are superior to the algorithms based on interpolating polynomials {e.g., Bourdet et al.

[4]), and low-degree LS polynomials in eliminating the unwanted effects of noise.

It is also shown that parameters estimated from LS regression on derivative data become less accurate if derivative data are overly smoothed by the algorithm used.

Several theoretical examples and one published field example are used to illustrate the performance of the algorithms.