Improvement of Buckley–Leverett and Fractional Flow Models for Heterogeneous Porous Media

Abstract

Most of the reservoirs in Iran and also around the world are in the middle of their production life and have passed their natural production period. Therefore, they should be a candidate for immiscible injection, e.g., water injection for secondary recovery, and/or miscible injection, like solvent injection for tertiary recovery. Also, it should be pointed out that most of the Iranian reservoirs are carbonate reservoirs. This type of reservoir is fractured and heterogenic. Heterogeneity causes an earlier breakthrough and immiscible injection causes an unstable front, which leads to a lower recovery. This article presents the modified equation of Buckley–Leverett and fractional flow equations. Heterogeneity and pore size distribution can be investigated by applying a heterogeneity factor to these equations. Experimental data from core samples of homogeneous sandstone and heterogeneous carbonated reservoir are used to validate the modified model. The goal of this project is to determine the heterogeneity factor of the reservoirs, which is an indicator of the effect of the heterogeneity of a porous medium on flow of fluids.

Keywords:

• breakthrough
• fracture reservoir
• front
• heterogeneous
• immiscible displacement

NOMENCLATURE

	=	fractional flow of displaced fluid
	=	relative permeability of displaced fluid
	=	relative permeability of oil
	=	exponent in relative permeability correlation for oil, dimensionless
	=	exponent in relative permeability correlation for displaced fluid, dimensionless
	=	pore volume injected
	=	displaced fluid saturation
	=	initial displaced fluid saturation
	=	residual oil saturation
	=	dimensionless distance
	=	viscosity of displaced fluid
	=	viscosity of oil
	=	coefficient for oil relative permeability correlation, relative permeability to oil at
	=	coefficient for displaced fluid relative permeability correlation, relative permeability to displaced fluid at