Reservoir Parameter Estimation Using Wavelet Analysis


Pengbo Lu







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This work focuses on several important issues of reservoir characterization and data integration using wavelet analysis. The goal of reservoir characterization is to estimate the spatial distribution of the reservoir properties, e.g., permeability and porosity, 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, to gain advantage from the multiresolution properties of wavelets. Wavelet analysis can compress the model parameter space, stabilize the algorithm, and avoid local minima. This new approach also significantly improves the computational efficiency by varying the resolution of 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 this newly developed procedure to some multiphase reservoir examples that demonstrate the reliability and .exibility of the approach. We also gained very good convergence rates and excellent computational efficiency compared to conventional methods. The most important conclusion of this work 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 with wavelet analysis has substantial advantages over the conventional algorithms.

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