Using Resampling Residuals for Estimating Confidence Intervals of the Effective Viscosity and Forchheimer Coefficient

Abstract

Determination of parameters characterizing flows in porous media is a complex inverse problem. It is especially difficult to determine confidence intervals of such parameters. In this note, we develop a method based on utilization of bootstrapping in order to find confidence intervals of model parameters, which are determined by minimizing the discrepancy between model predictions and published experimental results. The discrepancy is characterized by the objective function defined as the sum of squared residuals in the points where experimental measurements are taken. A residual is defined as the difference between the experimentally measured value and the model prediction of this value. We utilized bootstrapping to generate surrogate experimental data by randomly resampling residuals and then adding them back to model predictions. The model parameters that give the best fit with a large number of surrogate data were then determined. By analyzing the histograms of best-fit parameter values, we were able to find confidence intervals for these parameters. We utilized the developed method to determine confidence intervals for the effective viscosity and Forchheimer coefficient.

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