Heterogeneity in Sedimentary Deposits: A Review of Structure‐Imitating, Process‐Imitating, and Descriptive Approaches

Abstract

Numerical models that solve governing equations for subsurface fluid flow and transport are commonly applied to analyze quantitatively the effects of heterogeneity. These models require maps of spatially variable hydraulic properties. Because complete three‐dimensional information about hydraulic properties is never obtainable, numerous methods have been developed to interpolate between data values and use geologic, hydrogeologic, and geophysical information to create images of aquifer properties. Image creation approaches fall into three general categories: structure‐imitating, process‐imitating, and descriptive. Structure‐imitating methods rely on one or more of the following to constrain the geometry of spatial patterns in geologic media: correlated random fields, probabilistic rules, and deterministic constraints developed from facies relations. Structure‐imitating methods include spatial statistical algorithms and geologically based sedimentation pattern‐matching approaches. Process‐imitating models include aquifer model calibration methods and geologic process models. Aquifer model calibration methods use governing equations for subsurface fluid flow and transport to relate hydraulic properties to heads and solute information through history and steady state data matching. Geologic process models combine fundamental laws of conservation of mass and momentum with sediment transport equations to simulate spatial patterns in grain size distributions. At the sedimentary basin scale, multiprocess models include thermomechanical mechanisms of basin subsidence. Descriptive methods couple geologic observations with facies relations to divide an aquifer into zones of characteristic hydraulic properties. All approaches are capable of reproducing heterogeneity over a range of scales and considering some types of geologic information. Some approaches are strictly spatial while some are linked to the time evolution of sedimentation. Some approaches can be conditioned on measurements. Recent advances aimed at infusing geologic information into images of the subsurface include extracting more information from sedimentological facies models, incorporating qualitative geologic information into random field generators and simulating depositional processes. Classes of research missing from the literature include multiprocess models that incorporate diagenesis and three‐dimensional surface water flow, hybrid methods that combine features of existing approaches, and approaches that can make use of all available geologic, geophysical, and hydrologic data.

Nonideal transport of reactive solutes in heterogeneous porous media: 5. Simulating regional‐scale behavior of a trichloroethene plume during pump‐and‐treat remediation

“…Geologic borehole-log data and core-scale permeability data were used to produce a core-scale threedimensional hydraulic conductivity distribution [Zhang and Brusseau, 1998]. This distribution, however, cannot be entered [Koltermann and Gorelick, 1996]. First, an areal distribution of field-scale hydraulic conductivities is developed using the values determined from pumping tests.…”

Application of Multiple-Point Geostatistics on Modelling Groundwater Flow and Transport in a Cross-Bedded Aquifer

“…Such complex sedimentological heterogeneity may induce a highly heterogeneous spatial distribution of hydrogeological parameter values in porous media at different scales (Klingbeil et al, 1999) and may consequently greatly influence subsurface fluid flow and solute migration (Koltermann and Gorelick, 1996). Because of the limited access to the relevant hydraulic properties, deterministic models often fall short in characterizing the subsurface heterogeneity and its inherent uncertainty.…”

“…Complex geological patterns including sedimentary structures, multi-facies deposits, structures with large connectivity, curvi-linear structures, etc. cannot be characterized using only two-point statistics (Koltermann and Gorelick, 1996;Fogg et al, 1998). Moreover, variograms, as a limited and parsimonious mathematical tool, cannot take full advantage of the possibly rich amount of geological information from outcrops (Caers and Zhang, 2004).…”

Inverse hydrologic modeling using stochastic growth algorithms

“…Others have used geologic process models and related ideas to generate reservoir structure [Koltermann and Gorelick, 1996;Wang, 1996;Bogdan and Lerche, 1985]. Among these approaches are stochastic models that duplicate structure but , that are not explicitly related to formation processes, such as the "structure-imitating" processes described by Koltermann and Gorelick [1996].…”