Abstract
Inference of spatially distributed reservoir properties from production data in scattered wells poses an under-constrained inverse problem that has nonunique solutions. One major contributor to problem ill-posedness is over-parameterization of spatially distributed reservoir properties. We recently introduced sparse representations of unknown reservoir properties for history matching by exploiting the correlation in their spatial distribution. In this approach, during history matching, instead of estimating reservoir properties for each model grid cell, the sparse representation of the reservoir properties are estimated from production data. The resulting history-matching problem can be solved using recent developments in sparse signal processing, widely known as compressed sensing. This novel sparse formulation of history matching effectively searches for relevant geologic patterns in a diverse collection of geologic elements, known as a sparse geologic dictionary, to explain the production data. We demonstrate the effectiveness of sparse history matching and illustrate its suitability for field-scale application. We discuss efficient reduced-order methods to speed up the computational aspect of constructing sparse geologic dictionaries for large-scale applications. We present history matching results with an adapted version of the Brugge benchmark model in which sparse geologic dictionaries are learned from a collection of uncertain prior model realizations. The proposed framework has several important properties that make it desirable for history matching application, including reconciling the disparity in data and model resolutions, respecting the expected geologic continuity, and accounting for uncertainty in geologic scenario.
