Robust Well Test Interpretation by Using Nonlinear Regression with Parameter and Data Transformations

Abstract

AbstractNonlinear regression is a well-established technique in well test interpretation. However, this widely-used technique is vulnerable to issues commonly observed in real data sets, namely sensitivity to noise, parameter uncertainty, and dependence on starting guess. In this paper, we show significant improvements in nonlinear regression by using transformations on the parameter space and the data space. In addition to providing more accurate results, faster convergence, and reduced sensitivity to starting guesses, our techniques can also provide noise reduction and data compression.The first part of the paper discusses the basis of parameter transformations and gives suitable transform pairs for common reservoir parameters. We analyzed the homogeneous probability distribution of transformed parameters using Monte Carlo analysis and verified that the transform pairs proposed generate Cartesian parameters. We found performance improvement in terms of faster convergence and increased probability of convergence for a random starting guess.The second part of the paper discusses nonlinear regression using the wavelet transformation of the data set. The wavelet transformation is a process that can compress and denoise data automatically. By using regression on a reduced wavelet basis rather than the original pressure data points we achieved improved performance in terms of likelihood of convergence and narrower confidence intervals. We investigated four different wavelet strategies, which differ in the method of choosing a reduced wavelet basis.Combinations of the techniques discussed in this paper were used to analyze 20 data sets to find the technique or combination of techniques that work best with a particular data set. Using the appropriate combination of our techniques will allow for more reliable estimation of reservoir parameters using nonlinear regression.