Imbibition-Dominated Matrix-Fracture Fluid Transfer in Dual Porosity Simulators

Abstract

ABSTRACT Published imbibition experiments of an advancing fracture water level surrounding a single matrix block are simulated using a fine grid single porosity model and various double porosity models. The fine grid simulations show that a stationary water saturation profile quickly develops and advances in the matrix at the same rate as the fracture water level. A new double porosity transfer function for imbibition dominated matrix/fracture fluid exchange is presented based on stationary profile solutions of the fractional flow equation. This transfer function models the imbibition recovery for these advancing water level experiments better than the conventional double porosity imbibition formulations. It is shown that the stationary profile transfer function is best suited to systems where the time to develop the stationary profile is short relative to the length of the waterflood. The experimental data was also simulated using a diffusion equation with a nonlinear diffusion coefficient in combination with a moving boundary condition as the imbibition model. A constant diffusion coefficient based upon water relative permeability and capillary pressure gradient values at 1 − Sor matched the experimental results as well as the nonlinear diffusion coefficient, but required much less computer time. From analyzing two different diffusion type equations as imbibition models, we show that countercurrent imbibition is not a likely recovery mechanism for this type of advancing water level imbibition experiment.