Comparison of derivative algorithms used in pressure transient analysis

This work presents a detailed comparison of numerical methods that can be u sed to construct pressure derivative data for pressure transient analysis. Numerical methods compared include the algorithms based on interpolating po lynomials, least-squares (LS) polynomial fitting, smoothing splines, and La place transform method. Statistical measures are used to quantify the effec ts of noise (random measurement errors) and the sampling rate of measured p ressure data on the performance of algorithms. Noise amplification equation s associated with some of the derivative algorithms are derived. The effect of smoothing on the accuracy of well/reservoir parameters estimated from n onlinear LS regression analysis for pressure derivative data is also invest igated. It was found that the algorithms based on high-degree LS polynomial , spline, and Laplace transform methods are superior to the algorithms base d on interpolating polynomials (e.g., Bourdet et al. [4]), and low-degree L S polynomials in eliminating the unwanted effects of noise. It is also show n that parameters estimated from LS regression on derivative data become le ss accurate if derivative data are overly smoothed by the algorithm used. S everal theoretical examples and one published field example are used to ill ustrate the performance of the algorithms.