Uncertainty quantification in porous media fluid flow.

摘要

Reservoir fractures, deformation bands, and multiscale heterogeneities are capable of affecting porous media fluid flow in a variety of ways. In terms of fracture effects, we typically encounter an unchanged or increased permeability when considering flow parallel to a fracture, whereas we expect a reduced permeability when considering flow across a deformation band. In considering multiscale heterogeneities, it is important to capture both the fine scale behavior and general trends of related flow scenarios. For the first portion of this dissertation, we assess the effects that deformation bands have on multi-component fluid flow. Under the assumption that the width of a band is a random variable, Monte Carlo simulations can then be performed to obtain statistical representations of the transport quantity in relation to the nature of uncertainty. We introduce a stochastic perturbation model as an alternative to Monte Carlo simulations and compare the results with analytical solutions. For the next topic, we propose a method for efficient solution of pressure equations with multiscale features and randomly perturbed permeability coefficients. We use the multiscale finite element method (MsFEM) as a starting point and mention that the method is intended to be used within a Monte Carlo framework where solutions corresponding to samples of the randomly perturbed data need to be computed. We show that the proposed method converges to the MsFEM solution in the limit for each individual sample of the data. The method is then applied to a standard multi-phase flow problem where a number of permeability samples are constructed for Monte Carlo simulations. We focus our quantities of interest on the Darcy velocity and breakthrough time and quantify their uncertainty by constructing corresponding cumulative distribution functions. In the final portion of the dissertation, we introduce a dual porosity, dual permeability model which accounts for differences in matrix and fracture parameters. Fine scale benchmark solutions are obtained and we perform a comparison between corresponding dual porosity, dual permeability model solutions. In the context of subsurface characterization of fractured reservoirs, we apply the Markov chain Monte Carlo method to the dual porosity, dual permeability model. In doing so, we obtain matrix and fracture permeability fields resulting from a distribution conditioned to dynamic tracer cut data. In all chapters, a number of numerical examples are presented to illustrate the performance of the each approach.