A new effective flow model for formations with spatially varying fracture statistics

 

Fractures serve as highly conductive flow conduits in subsurface formations and thus have a significant impact on flow and transport. The length of fractures can vary over several orders of magnitude, with the largest fractures potentially being comparable in size to the domain of interest. This makes it impossible to define a representative elementary volume for the extraction of effective flow parameters. Furthermore, due to the high uncertainty in fracture locations and parameters, a Monte Carlo (MC) study is typically needed to accurately estimate expected flow rates.

 

Alternatively, a new kernel-based model \cite{jenny2020sub} has recently been proposed, which allows for the direct computation of mean flow rates from a conservation law in integro-differential form. This model uses a dual-continuum formulation which incorporates the non-local effect of fractures through fracture kernels. To fully determine these kernels, transfer coefficients describing the expected matrix/fracture flow exchange are required.

 

In this work, a new scaling analysis is presented, which provides transfer coefficients as functions of fracture lengths and fracture densities. Furthermore, the resulting coefficients are used in flow simulations with spatially varying fracture statistics and good agreement against high-fidelity MC simulations has been found.