Upscaling models of solute transport in porous media through genetic programming

David J. Hill (corresponding author) Barbara S. Minsker Albert J. Valocchi Department of Civil and Environmental Engineering, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA Tel: +1 (217) 714 3490 Fax: +1 (217) 333 6968 E-mail: [email protected] Vladan Babovic Department of Civil Engineering, National University Singapore, 1 Engineering Drive 2, E1A 07-03, Singapore 117576 Maarten Keijzer Free University Amsterdam, Amsterdam, The Netherlands Due to the considerable computational demands of modeling solute transport in heterogeneous porous media, there is a need for upscaled models that do not require explicit resolution of the small-scale heterogeneity. This study investigates the development of upscaled solute transport models using genetic programming (GP), a domain-independent modeling tool that searches the space of mathematical equations for one or more equations that describe a set of training data. An upscaling methodology is developed that facilitates both the GP search and the implementation of the resulting models. A case study is performed that demonstrates this methodology by developing vertically averaged equations of solute transport in perfectly stratified aquifers. The solute flux models developed for the case study were analyzed for parsimony and physical meaning, resulting in an upscaled model of the enhanced spreading of the solute plume, due to aquifer heterogeneity, as a process that changes from predominantly advective to Fickian. This case study not only demonstrates the use and efficacy of GP as a tool for developing upscaled solute transport models, but it also provides insight into how to approach more realistic multi-dimensional problems with this methodology.