Modeling Spatial and Structural Uncertainty in the Subsurface

Abstract

Whether subsurface modeling is performed on a laboratory or reservoir scale, uncertainty is inherently present due to lack of data and lack of understanding of the underlying phenomena and processes taking place. We highlight several issues, techniques, and practical modeling tools available for modeling spatial and structural uncertainty of complex subsurface models. We pay particular attention to the method of training images, since this is a recent and novel approach that we think can make significant advances in uncertainty modeling in the subsurface and other application areas. The subsurface is a difficult area of modeling uncertainty: porosity and permeability of subsurface rock can vary orders of magnitude on a variety of scales, fractures or faults may exist, and the available data can be sparse. Modeling of uncertainty in the subsurface is of much interest to society, because of, for example, the exploration and extraction of natural resources including groundwater, fossil fuels, and geothermal energy; the storage of nuclear material; and sequestration of carbon dioxide. Although we focus on the subsurface, many of the techniques discussed are applicable to other areas of uncertainty modeling in engineering and the sciences.