In search of preferential flow paths in structured porous media using a simple genetic algorithm

Fracture network and preferential flow path images from exposed outcrops of geological formations, exposed soil pedon faces, and extracted soil columns and rock cores are often used to conceptualize and construct models to predict the fate and transport of subsurface contaminants. Both the scale resolutions inherent in these observations and the upscaling methods used to obtain macroscopic flow and transport parameters may result in uncertainties in the prediction. We present a mechanistic‐based approach that utilizes a discrete fracture flow and transport model, a distributed and high performance computational architecture, and a genetic‐based search algorithm to invert scale‐ representative, equivalent fracture networks or the preferential flow paths. Synthetic breakthrough curves (BTCs) and exposed structural information from known fracture networks in hypothetical soil columns are presented to the search algorithm. Using three genetic operators, a simple genetic algorithm (SGA) is able to invert the correct pictures of simple but not complex fracture networks. Solute transport experiments using soil columns often assume that the structure of soil columns is laterally uniform with respect to the macroscopic transport direction and the transport process is longitudinally one‐ dimensional. This assumption and the one BTC thus collected for each injection of solutes, even with flow interruptions, are not sufficient to guide the search algorithm toward the global optimum. Additional information (e.g., multiple solute BTCs along a cross section of the soil column) is necessary for the SGA to invert the correct fracture network. Three SGA population statistics, fracture network uncertainty, informatic entropy, and matrix‐fracture contact area, are proposed to measure the uncertainty of SGA near optima. A positive correlation between the reduction of these statistics and the level of relevant information to better confine the SGA search space was found. The SGA search algorithm is then applied to a laboratory solute transport problem. Multiple scenarios of search constraints, derived from visually traced surface features, are examined. The hypothesis that variation in fracture aperture may reduce the uncertainty of SGA near optima is also tested. The results from these applications suggest that there is a certain degree of uncertainty regarding the flowing nature of the exposed fracture segments that are visually traced. The uncertainty of SGA near optima is not improved by incorporating fracture aperture information into the fracture networks. Breakthrough curves thus calculated have marginal improvement, relative to the uniform aperture SGA near optima, in fitting the observations. The lack of improvement may be caused by the relative uniform structure of the soil and the scale of the problem. It is further suggested that in applying the search algorithm to laboratory and field problems, one explores only the search scenarios that relevant information and search constraints may warrant.