Pressure Behavior in a Linear Porous Media for Partially Miscible Displacement of Oil by Gas

Miscible gas flooding improves oil displacement through mass exchange between oil and gas phases. It is one of the most efficient enhanced oil recovery methods for intermediate density oil reservoirs. In this work, analytical solutions for saturation, concentration and pressure are derived for oil displacement by a partially miscible gas injection at a constant rate. The mathematical model considers two-phase, three-component fluid flow in a one-dimensional homogeneous reservoir initially saturated by a single oil phase. Phase saturations and component concentrations are described by a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></semantics></math></inline-formula> hyperbolic system of partial differential equations, which is solved by the method of characteristics. Once this Goursat–Riemann problem is solved, the pressure drop between two points in the porous media is obtained by the integration of Darcy’s law. The solution of this problem may present three different fluid regions depending on the rock–fluid parameters: a single-phase gas region near the injection point, followed by a two-phase region where mass transfer takes place and a single-phase oil region. We considered the single-phase gas and the two-phase gas/oil regions as incompressible, while the single-phase oil region may be incompressible or slightly compressible. The solutions derived in this work are applied for a specific set of rock and fluid properties. For this data set, the two-phase region displays rarefaction waves, shock waves and constant states. The pressure behavior depends on the physical model (incompressible, compressible and finite or infinite porous media). In all cases, the injection pressure is the result of the sum of two terms: one represents the effect of the mobility contrast between phases and the other represents the single-phase oil solution. The solutions obtained in this work are compared to an equivalent immiscible solution, which shows that the miscible displacement is more efficient.