Upscaling of transport through discrete fracture networks via random walk: A comparison of models

Many models have been created for upscaled transport modeling in discrete fracture networks (DFNs). Random walk examples of these are the Markov directed random walk (MDRW), Monte Carlo solution of the Boltzmann transport equation (BTE), and the spatial Markov model (SMM). Each model handles the correlation between the random walk steps using different techniques and has successfully reproduced the results of full-resolution transport simulations in DFNs. However, their predictive capabilities under different modeling scenarios have not been compared. We construct a set of random 2D DFNs for three different fracture transmissivity distributions to comparatively evaluate model performance. We focus specifically on random walk models to determine what aspects of the space and time step distributions (e.g., correlation and coupling) must be accounted for to get the most accurate predictions. For DFNs with low heterogeneity in fracture transmissivity, accounting for correlation generally leads to less accurate predictions of transport behavior, but as the fracture transmissivity distribution widens, preferential pathways form and correlation between modeling steps becomes important, particularly for early breakthrough predictions.