Overcoming the Model‐Data‐Fit Problem in Porous Media: A Quantitative Method to Compare Invasion‐Percolation Models to High‐Resolution Data
Creators: name: Banerjee, I.
name: Guthke, A.
name: Van De Ven, C. J. C.
name: Mumford, K. G.
name: Nowak, W.
Publisher: name: FID GEO
Year: 2021

description: 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.
description: Plain Language Summary: Computer models are becoming popular tools to gain a better understanding of processes happening in soils. Gas flow in the subsurface is relevant for many engineering problems. Models need to be compared to experimental or field data to test how well they represent the truth. For very large datasets such as time‐series of images, this experiment‐to‐model comparison is often problematic. On the one hand, manually identifying similarities between the model and experimental images is a tedious method that can lead to errors (e.g., two researchers might arrive at two different conclusions). On the other hand, using automated “summary metrics” can lead to loss of information from the images, and again may trigger wrong conclusions. In this work, we present an experiment‐to‐model comparison method for raster‐image type datasets that overcome these limitations. We demonstrate our method using simple, fast, and computationally cheap invasion percolation models for gas flow in soil. In our method, we use a metric to quantify perceptual similarity along with a “switch” that allows the user to control the application‐specific strictness of the match. We find that our automated method is reliable and intuitive and can be used for gaining insights for model development in many research areas.
description: Key Points: We present a quantitative method for model‐to‐experiment comparison of gas migration in porous media. We use an Invasion Percolation model and light‐transmission‐based experiments for demonstration. Comparison method is automated, objective and allows scale‐dependent conclusions.
description: German Research Foundation (DFG) http://dx.doi.org/10.13039/501100001659