Modeling density-driven flow and solute transport in heterogeneous reservoirs with micro/macro fractures

Abstract

In this paper, a numerical model is presented to simulate the density-driven flow in heterogeneous porous media with micro- and macro-fractures. The micro-fractures (like fissures) with relatively small fracture lengths compared to the reservoir are modeled using an equivalent continuum model. The macro-fractures (like faults) with large fracture lengths are modeled using the extended finite element method (XFEM). Governing equations are based on the mass conservation equation for both the matrix and fracture domains together with the proper constitutive laws for the fluid velocity, dispersive velocity of solute, and equation of state for density of fluid phase. Several parameter studies are performed to investigate the effects of fracture characteristics on the solute spread in the medium. It is demonstrated that in the absence of macro-fractures, the influence of micro-fractures’ aperture on the solute spread is fully substantial and predictable. However, in the presence of macro-fractures, there is a region where the macro-fracture performs like a vacuum diminishing the influence of nearby micro-fractures. Finally, a real hydrological problem of the Gödöllő Hills reservoir located in Hungary with five different layers and eight faults, which is full of saline water is numerically modeled to investigate the effect of pressure gradient, anisotropy, and density difference on the solute transport. It is illustrated that in the top layers of the Gödöllő Hills reservoir, the gravitational force and vertical permeability are mostly accountable for the solute flow across the faults, whereas in the bottom layers, the horizontal pressure gradient is primarily responsible for the solute transport.