Overcoming the Model-to-Experimental Data Fit Problem in Porous Media: a New Quantitative Method to Evaluate and Compare Models

Abstract:

Numerical modelling tools are extensively used for better understanding of processes related to multiphase flow in porous media. Actual experimental data helps to calibrate these models, and to test assumptions and hypotheses within models via model-to-experimental comparisons.

For highly spatially and temporally resolved data sets (like experimental movies), such comparisons are often problematic: a model will never stand a pixel-by-pixel comparison; instead, weaker methods like perceptual similarity or analysis of spatial moments are traditionally used. While perception is neither quantitative nor objective, but tediously manual and time-consuming, spatial moments analysis suffers from a large loss of information and lacks a meaningful way to combine several moments into a single goodness-of-fit metric.

To overcome the model-to-experimental data fit problem, we propose a comparison method based on a diffused version of the so-called Jaccard index (adapted from image analysis and object recognition) as an objective and quantitative goodness-of-fit metric.

As a case study, we compare many equiprobable realizations of an Invasion Percolation (IP) model against laboratory-scale experimental videos of gas injection in homogeneous, saturated sand. The model realizations vary in their initial entry pressure field to capture the inherent pore-scale heterogeneity of the sand. Comparing IP models to highly resolved data is especially challenging because of their lack of an explicit notion of time. To still enable an evaluation of the model-to-data fit, we perform a time matching before applying our proposed Jaccard metric.

This combined approach proves more objective and reliable than traditional comparison approaches. The diffused nature of the metric allows comparing models to data at different scales of interest, from pore-scale to field-scale. Overall, our proposed metric will be valuable for model calibration, model validation and inter-comparison of models.