ON THE CORRELATION OF NONLINEAR FLOW AND LINEAR TRANSPORT WITH APPLICATION TO DUAL-POROSITY MODELING

A novel relationship between nonlinear fluid flow and diffusion- convection transport is presented. This correlation indicates that neglecting the quadratic gradient term in the flow equation can be considered as equivalent to neglecting convective flow in the diffusion-convection transport mechanism. In addition, linearization of the nonlinear flow equations using logarithmic transformation and conversion of the diffusion-convection transport equation into a parabolic-like formulation using exponential transformation are complementary. As a result of this disclosure, a new dual-porosity theory based on the convective flow is developed. For convection-dominated flow, which tends to occur in a medium possessing significant permeability contrast such as in a fractured-porous formation, the presented convective dual-porosity formulation may provide more reasonable utilities than the present interporosity flow models with reduced computational efforts.