Scale-up of two-phase flow in heterogeneous porous media

The objective of this work is to study the scale-up of multiphase flow properties obtained from core-scale experiments to the grid-scale required for typical field simulations of oil recovery. Typical naturally-occurring porous media represented by field simulation grid-blocks are internally heterogeneous. Heterogeneity is modeled here as a correlated random field parameterized in terms of its variance and two-point variogram. Variogram models of both finite (spherical) and infinite (fractal) correlation length are included as special cases. Local core-scale porosity, permeability, capillary pressure function, relative permeability functions, and initial water saturation are assumed to be correlated. Capillary pressure and relative permeability hysteresis are modeled at the core-scale. Water injection is simulated and effective flow properties (not pseudo-functions) and flow equations are calculated. Conditions under which the traditional relative permeability formulation is valid are identified. For strongly water-wet media and small variance in permeability, flow can be described by an effective relative permeability. In water-wet grid-blocks of large permeability variance and finite correlation length, effective relative permeabilities can describe the average front movements, but a stochastic term is needed to describe the detailed fluctuations. In fractal media, effective relative permeabilities cannot describe even the average front movements.