Performance assessment of graph theory towards predicting fluid flow in rocks across multiple spatial scales

Fluids tend to migrate along preferential flow paths in rocks which depend on several factors including pore size distribution at sub-Darcy scales and heterogeneity in flow and petrophysical properties in Darcy scale domains. Typically, fluid migration in rocks across scales is determined using numerical simulations which can be computationally expensive. This study presents a graph theory based reduced physics approach to determine potential fluid flow pathways in pore and continuum scale domains. This is an improvement over the existing methods based on graph theory which have largely been focussed on the analysis of the minimum resistance faced by fluid when flowing in rocks. The presented method utilises rock properties as edge weights which are then used to calculate the probability of fluid invading a particular node in the domain. Predictions from the algorithm were validated against results from full physics numerical simulations at pore scale as well as experimentally measured data at pore, core and sand-tank scales. Some of the datasets used for this exercise include Ketton and Estaillades Limestones, and Berea and Bentheimer Sandstones. Further, the algorithm was applied on a suite of reservoir models of the Parasequence-2 of the Paaratte Formation, Otway Basin, Australia. This application was aimed at assessing the influence of grid size resolution and rock property distribution on the uncertainty in CO₂ migration. The algorithm showed computational advantages as it was possible to achieve model runs on some scenarios which are typically not possible using conventional numerical simulations.