Sid-FM: A Statistical Integro-Differential Fracture Model for Efficient Flow Simulations in Fractured Sub-Surface Formation

Typically, the available information for the characterization of sub-surface formations is very limited, inducing significant uncertainties. This challenge is particularly pronounced in fractured formations and complicates predictive numerical simulations of flow and transport. For instance, isolated fractures can act as long-range highly conductive flow pathways, thus significantly influencing flow and transport. Since fractures may extend over lengths comparable to the domain of interest, homogenization approaches often yield unsatisfactory results. A common alternative is fracture-resolving Monte Carlo simulation (MCS), but there the high computational cost limits the inclusion of numerous fractures, which compromises the representation of realistic formations.

Alternatively, the Sid-FM approach offers a different methodology by bypassing fracture-resolving descriptions. Instead, it directly determines the ensemble-averaged flow field by incorporating non-local effects of extended fractures through fracture kernels. The present study demonstrates that suitably chosen kernel functions can effectively capture the influence of diverse fracture distributions, shapes, and connected fracture clusters. Numerical experiments compare Sid-FM results to fracture-resolving Monte Carlo simulations and demonstrate that Sid-FM provides accurate flow estimates at very low computational cost.