Abstract
Calibrating reservoir models against production history, also known as history matching, is commonly performed to improve reservoir prediction quality. Data scarcity and over-parameterization typically lead to an ill-posed formulation of history matching inverse problems where too many unknown parameters have to be estimated from limited measurements. As a consequence, many non-unique solutions can be found to match the observed data. Parameterization of reservoir models is often used to improve problem ill-posedness and solution plausibility (i.e., geologic realism). The existing parameterization techniques can be classified as prior-dependent (specialized) and prior-independent (generic) methods. Prior dependent methods such as the principle component analysis (PCA) utilize prior knowledge about the unknown reservoir property distributions (e.g., covariance model) and construct effective parametric descriptions for history matching. These methods immediately lose their effectiveness when the prior model becomes inaccurate. Alternatively, prior-independent methods such as Wavelet or Fourier image compression techniques are more generic (robust) in that they do not assume any prior knowledge in parameterizing reservoir properties. However, because they do not use prior knowledge, these methods are less effective when a reliable prior model is available. What complicates realistic reservoir parameterization is the uncertainty in prior knowledge. Here, we propose a hybrid parameterization approach that, by combining generic and specialized parameterization methods, offers the advantages of two techniques. By combining a set of significant prior-independent generic compression basis elements with a subset of prior-dependent learned basis components we construct a robust hybrid parameterization basis is less sensitive to errors in the prior model and more effective in reproducing more specialized geologic features in the prior. Using the proposed hybrid parameterization in several history matching examples, we show that under (in)correct prior knowledge the generic portion of the hybrid basis becomes (less) more relevant. We conclude that for realistic history matching problems where accounting for geologic uncertainty is imperative, a hybrid parameterization is more appropriate.
