engleski

A multi-resolution approach for modeling flow and solute transport in heterogeneous porous media

Subsurface processes are usually characterized by rare field experiments, sparse measurements, multi-resolution interpretations, stochastic description, related uncertainties and computational complexity. Over the last few decades, different computational techniques and strategies have become indispensable tools for flow and solute transport prediction in heterogeneous porous media. This thesis develops a multi-resolution approach based on Fup basis functions with com-pact support, enabling the use of an efficient and adaptive procedure, closely related to current understood physical interpretation. All flow and transport variables, as well as intrinsic heteroge-neity, are described in a multi-resolution representation, in the form of a linear combination of Fup basis functions. Each variable is represented on a particular adaptive grid with a prescribed accuracy. The methodology is applied to solving problems with sharp fronts, and to solving flow and advective transport in highly heterogeneous porous media, under mean uniform flow condi-tions. The adaptive Fup collocation method, through the well known method of lines, efficiently tracks solutions with sharp fronts, resolving locations and frequencies at all spatial and/or tem-poral scales. The methodology yields continuous velocity fields and fluxes, enabling accurate and reliable transport analysis. Analysis of the advective transport proves the robustness of the first-order theory for low and mild heterogeneity. Moreover, due to the accuracy of the improved Monte-Carlo methodology, this thesis presents the effects of high heterogeneity on ensemble flow and travel time statistics. The difference between Eulerian and Lagrangian velocity statistics and the importance of higher travel time moments are indicative of high heterogeneity. The third travel time moment mostly describes a peak and late arrivals, while higher moments are required for early arrivals which are linked with the largest uncertainty. A particular finding is the linearity of all travel time moments, which implies that in the limit an advective transport in multi-Gaussian field becomes Fickian. By comparison, the transverse displacement pdf converges to a Gaussian distribution around 20 integral scales after injection, even for high heterogeneity. The capabilities of the presented multi-resolution approach, and the quality of the obtained results, open new areas for further research.

Multi-resolution adaptive approach ; Atomic and Fup basis functions ; Monte-Carlo method ; Heterogeneous porous media ; Flow ; Transport ; Travel time

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