Volume-averaged Mass Equations for Multiphase Flow in Porous Media for In Situ Combustion

Abstract

The multiphase flow of oil, water, and gas through porous media is presented when the in situ combustion technique is applied in oil reservoirs. This technique implies phenomena such as phase change, chemical reactions, and heat transfer, among others. The mathematical modeling of such a technique requires the deduction of mass, momentum, and energy equations, taking into account the phenomena mentioned. In this work the volume-averaged mass transport equations for gas (g), oil (o), and water (w) flowing simultaneously through a homogeneous, isotropic, rigid, and nonpermeable porous media (s) were obtained. The mass equation for the deposited coke in the porous media was also obtained. To obtain the equations, the local mass equations for phases as well as their corresponding jump conditions were used as starting point. We took the following into account: (a) the gas compressibility, (b) the mass generation of coke due to the chemical reaction of oil, (c) the mass generation of gas due to the combustion reaction between coke and oxygen, and (d) the mass transfer due to the phase change of oil and water. To obtain closed mass equations, phase change expressions for water and oil were proposed.

Keywords:

• averaging volume
• closure equations
• mass equation
• multiphase flow
• porous media