Miscible EOR Processes: Existence of Elliptic Regions in Gasflood Modeling

Abstract

Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. Analytical models for 1-D displacement of oil by gas have been developed during the last 15 years. It was observed from semi-analytical and numerical experiments that several thermodynamic features of the process are not dependent on transport properties. The model for one-dimensional displacement of oil by miscible fluids 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 reduced auxiliary system contains just thermodynamical (equilibrium fractions of each phase, sorption isotherms) 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. The new technique developed permits splitting for both self-similar continuous injection problems and for non-self-similar slug injection problems. Splitting significantly reduces amount of calculations for sensitivity study with respect to transport properties: auxiliary thermodynamic problem may be solved once for given reservoir and injected compositions; variation of relative permeabilities and viscosities should be performed just in the solution of one transport equation. In this paper, different analytical solutions for 4-component gas injection problems are analysed. It was considered the injection of nitrogen and hydrocarbon gases into a three-component liquid reservoir fluid. The eigenvalues of the system are related to the propagation velocity of each component in porous media. The existence of elliptic regions (complex eigenvalues) is well known in three-phase flow, but for the first time it is shown that this feature may also occur in two-phase flow. The independence of compositional dynamics on transport properties can be used for testing numerical compositional simulators. If the mobility ratio is close to one, this model may be applied in the development of streamlines simulators. Copyright 2007, Society of Petroleum Engineers.