Statistical integro-differential fracture model (Sid-FM) for homogenised scalar transport

This work presents an efficient statistical model to simulate expected scalar transport in fractured porous media below the representative elementary volume scale. We focus on embedded, highly conductive, isolated fractures. The statistical integro-differential fracture model (Sid-FM) solves for ensemble-averaged solutions directly, avoiding computationally expensive Monte Carlo simulation. The expected fluid exchange between isolated fractures and the porous matrix is modelled via a non-local kernel function, leading to a set of integro-differential equations. The model is validated against reference data from Monte Carlo simulations for statistically one-dimensional test cases and shows good agreement.