A Multiresolution Approach to Reservoir Parameter Estimation Using Wavelet Analysis

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Abstract In this paper, a new multiresolution approach is proposed for reservoir parameter estimation, i.e., to estimate the spatial distribution of the reservoir properties by proper integration of all types of data available (either static or dynamic). We considered the integration of production history data, seismic data and well test data in this work. One of the key issues in parameter estimation is to develop an efficient and reliable nonlinear regression procedure. We adapted wavelet analysis to describe the distribution of sensitivity coefficients, since wavelet analysis is a powerful tool in multiresolution analysis and is widely used in signal and image processing. Wavelet analysis can compress the parameter space, stabilize the algorithm and avoid local minima. This new approach also improves the computational efficiency significantly by varying the resolution of the estimation at different regression stages. Wavelet analysis also has the capability to integrate different types of data efficiently, using different levels of wavelets to incorporate different data types. We can account explicitly for the resolving power of different data and estimate reservoir properties with nonuniform resolution. We have applied the procedure to multiphase reservoir examples that demonstrate the reliability and flexibility of the approach. We also gained very good convergence and excellent computational efficiency compared to conventional methods. The most important conclusion of this paper is that wavelet analysis is a very useful tool for reservoir parameter estimation and can speed up the computation and improve the performance. The nonlinear regression procedure integrating wavelet analysis has substantial advantages over the conventional …