Data-Driven Multiscale Model Identification and Scaling via Random Renormalization Group Operators for Subsurface Transport

Purdue University, West Lafayette IN

Investigators

Abstract

One of the major contributors to enhanced dispersion (mixing) of anthropogenic contaminants in hydrogeological formations is multiscale heterogeneity, which in many cases leads to anomalous dispersion (anomalous means non-Brownian, i.e., the process does not possess at least one of the following: stationary increments, Gaussian increments or independent increments.) Heterogeneity may be associated with spatial/temporal variations in hydraulic conductivity, porosity, sorbtivity, fractures, and differential swelling to name a few contributors. Natural and man-made (such as occurs during fracking) heterogeneity makes accurate modeling of contaminant movement in the subsurface an extremely challenging problem. A number of disparate models have been proposed to capture behavior associated with hydrologic transport. These include Brownian and Levy motion and fractional versions of these processes. Additionally, these models have been conditioned on other random processes (subordination) and non-linear clocks (time transformations) have been introduced. When two or more of these models are combined (summed), multiscale heterogeneity that drives anomalous dispersion can be accounted for. The proposed research will employ tools from statistical physics, identify optimal models and develop user friendly software which relies on available data for a given site. If a very rich model is used, it can be easy to over fit data. If a less rich model is used, it may not be fully capable of capturing the behavior under consideration. The proposed techniques circumvent this problem by considering a cascade of models that range from the very simple to the extremely complex and many models in between. The codes developed to identify data with models will be released under open source software licenses and tutorials will be written and made available to make the use of the codes as easy as possible. A large portion of the world?s fresh water resources reside in the upper portion of the Earth?s crust; approximately 30 times the volume of the world?s fresh surface water. Most importantly, half of the U.S. population relies on ground water for domestic use. Thus to protect this precious natural resource it is imperative that we understand and can predict how anthropogenic contaminants spread in the subsurface. The proposed research addresses this fundamental problem by creating an optimal model identification scheme based on available data for natural geologic formations and subsequently making the resulting software open source.