Characterization of Uncertainties of Parameters with F-Statistic for Flows through Porous Media

by Guo-Qiang Yang.

Abstract: The F-test (lack-of-fit) is applied to characterize the uncertainties in the estimation of parameters for flows through porous media. In the forward simulation, mixed finite element and second-order donor cell methods are used for the pressure-velocity equation and concentration equation respectively. The treatment of the wells are described. We show that $F$-test is flexible when handling the (ill-posed) inverse problem and gives the (exact) confidence regions for the unknown permeability field. Although the high dimensional confidence regions usually cannot be visualized, the simple evaluation of the $F$-statistic for each realization is desirable, as opposed to the usual Monte Carlo methods, which can only lead to approximate confidence levels with sufficient many samplings.

Key Words: Uncertainty, Forward and Inverse Problems, Mixed Finite Element, Donor Cell, $F$-Test and Lack-of-Fit, Confidence Regions and Confidence Intervals, Singular Value Decomposition

Guo-Qiang Yang,

Editor: Alexander Kolesnik,

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