Analytical solution for chemical fluid injection into linear heterogeneous porous media based on the method of characteristics

Abstract

Injection of Newtonian fluids in porous media to displace linearly another Newtonian fluid is described by the Buckley-Leverett (BL) fractional flow theory derived for incompressible, constant viscosity fluids at constant injection rate in a homogeneous and isotropic reservoir. Injection of non-Newtonian fluids can be addressed by modifying the fractional flow equation by considering the dependence of injected fluid viscosity with velocity, changes of residual oil saturation and chemical adsorption on rock. In this work, the BL fractional flow model is extended to describe injection of non-Newtonian fluids into a 1D linear heterogeneous formation accounting for fluid adsorption, permeability reduction, inaccessible pore volume, and presence of a denuded water bank developed over time ahead of non-Newtonian zone. Results from derived analytical solutions demonstrate fluids saturation and pressure drop across the formation, fluids production rate and cumulative volumes to be in close agreement with the ones from a commercial reservoir simulator.