Towards a Nonlinear Transfer Function in Dual Porosity Models

Traditional matrix-fractures transfer functions in dual porosity models are linear function of the pressure difference between averaged matrix and fractures pressures, which can lead to inaccuracies in resolution of intermediate-time behaviour. We address this issue by constructing nonlinear transfer functions which match the late-time asymptotics of the linear transfer functions, but provide a better match to fine-scale results for large values of the difference between averaged matrix and fractures pressures.
The proposed transfer functions are obtained by a nonlinear fit to dimensionless single-phase fine-scale matrix-fracture fluxes as a function of the matrix-fracture pressure difference. We demonstrate that the the coarse scale dual porosity/dual permeability results using the nonlinear transfer function lie closer to the reference fine scale solution as compared to the linear model.