Splitting between thermodynamics and hydrodynamics in compositional modelling

Abstract

Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. Displacement of oil by any of these fluids involves complex physicochemical processes of interphase mass transfer, phase transitions and transport properties changes. These processes can be divided into two main categories: thermodynamical and hydrodynamical ones. They occur simultaneously during the displacement, and are coupled in the modern mathematical models of EOR. The model for one-dimensional displacement of oil by gas is analyzed in this paper. The main result is the splitting of thermodynamical and hydrodynamical parts in the EOR mathematical model. The introduction of a potential associated with one of the conservation laws and its use as an independent variable reduces the number of equations. The algorithm to solve the problem includes the solution of the derived lifting hyperbolic equation and inversion of the coordinate transformation. The reduced auxiliary system contains just thermodynamical (equilibrium fractions of each phase) variables and the lifting equation contains just hydrodynamical (phases relative permeabilities and viscosities) parameters while the initial EOR model contains both thermodynamical and hydrodynamical functions. So, the problem of EOR displacement was divided into two independent problems: one thermodynamical and one hydrodynamical. Therefore, phase transitions occurring during displacement are determined by the auxiliary system, i.e., they are independent of hydrodynamic properties of fluids and rock. For example, the minimum miscibility pressure (MMP) is independent of relative permeabilities and phases viscosities. In this paper, the splitting technique is used for the development of an analytical model for the non-self-similar problem of displacement of oil by rich gas solvent slug with lean gas drive.