Chapter 8 - Non-Darcy Flow of Immiscible Fluids

Abstract

This chapter discusses advances in studies of multiphase non-Darcy flow in reservoirs. This chapter presents the mathematical method for quantitative analysis of multiphase non-Darcy flow in porous and fractured rocks using both numerical and analytical approaches. The Forchheimer equation and the Barree and Conway model are incorporated into numerical formulation for modeling multiphase non-Darcy flow in porous and fractured media. Furthermore, it presents Buckley and Leverett type analytical solutions for non-Darcy displacement in a linear and radial composite system according to two non-Darcy flow models. For application, a practical procedure is presented for calculating saturation profiles for non-Darcy displacement. The analytical solutions and resulting procedure can be regarded as an extension of the Buckley–Leverett theory to non-Darcy displacement. Then, analytical solutions are used to obtain insight into non-Darcy displacement and to verify numerical simulation results.