Overcoming the Model-Data-Fit Problem in Porous Media: A Quantitative Method to Compare Invasion-Percolation Models to High-Resolution Data

Abstract

Invasion percolation (IP) models offer a computationally inexpensive way to simulate multiphase flow in porous media, but only very few studies have compared their results to actual laboratory experimental image data. One reason might be the difficulty in quantitative assessment: IP models do not have a notion of experimental time but only have an integer counter for simulation steps that imply a time order. Previous experiments-to-model comparison studies have either used perceptual similarity or spatial moments as measures of comparison. In this work, we present an objective and quantitative comparison method that overcomes the limitations of the traditional approaches. First, we perform a volume-based time matching between real-time experiments and IP model results. Then, we evaluate the quality of fit using a diffused version of the so-called Jaccard coefficient, which is known from image recognition. We demonstrate our method's applicability on a laboratory-scale experimental video of gas injection in homogeneous, saturated sand, comparing it to a Macro-IP model's simulation results. We consider random realizations of the initial entry pressure field to capture the sand's inherent pore-scale heterogeneity. We find that our proposed method is reliable and intuitive in identifying realistic model realizations. The “strictness”of the method can be adjusted to relevant scales of interest via the blurring (diffusion) radius of the compared images. Beyond the application presented here, our comparison method can be used to compare any high-resolution space-time model output to experimental data given as raster images, thus providing valuable insights for model development in many research areas.