A Genetic Programming–Based Model for Colloid Retention in Fractures

Understanding the behavior of colloids in groundwater is critical as some are pathogenic while others may facilitate or inhibit the transport of dissolved contaminants. Colloid behavior in saturated fractured aquifers is governed by the physical and chemical properties of the groundwater-particle-fracture system. The interaction between these properties is nonlinear, and there is a need for a mathematical model describing the relationship between them to advance the mechanistic understanding of colloid transport in fractures and facilitate modeling in fractured environments. This paper coupled genetic programming and linear regression within a multigene genetic programming framework to develop a robust mathematical model describing the relationship between colloid retention in fractures and the physical and chemical parameters that describe the system. The data employed for model development and validation were collected from a series of 75 laboratory-scale colloid tracer experiments conducted under a range of conditions in three laboratory-induced discrete dolomite fractures and their epoxy replicas. The model sufficiently reproduced the observed data with coefficients of determination (R² ) of 0.92 and 0.80 for model development and validation, respectively. A cross-validation demonstrated the model generality to 86% of the observed data. A variance-based global sensitivity analysis confirmed that attachment is the primary retention mechanism in the systems employed in this work. The model developed in this study provides a tool describing colloid retention in factures, which furthers the understanding of groundwater-particle-fracture system conditions contributing to the retention of colloids and can aid in the design of groundwater remediation strategies and development of groundwater management plans.