Computational Experiments Quantifying the Scale-up of Geometric Facies Structure on Conductivity and Transport through Composite Porous Media

Abstract

We develop reduced-order, phenomenological models for effective conductivity, and for mass transport, in highly heterogeneous, composite porous media. Composite porous media consist of two or more distinct materials that occur in irregularly shaped, coherent blocks, called facies. Due to sparse sampling of the subsurface, uncertainty of facies structure is epistemic, and we conduct computational experiments that use thresholded random fields to generate realistic realizations of composite porous media. Darcy’s law is assumed to hold at local (mesoscopic) and large (macroscopic) scales, and flow is simulated through the facies structure to quantify the effects of the random, irregular configuration of the facies. Scale-up is addressed by Monte Carlo simulation. In the first chapter, simulations verify the importance of the percolation threshold, vc , which determines three regimes in effective conductivity that coincide with three corresponding regimes in the spatial variability of the flow fields. In the second chapter, further simulations motivate a continuous time Markov chain model that is able to explain anomalous dispersion in highly heterogeneous media. The model is parameterized directly from the statistics of the trajectories of synthetic particles that flow through the medium. In the third chapter, a stochastic optimization algorithm generates composite media characterized by the curvature along the facies interface, thereby controlling the connectedness of the facies structure to quantify its effects on conductivity and mechanical dispersivity in composite porous media.