Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. These processes can be divided into two main categories: thermodynamical and hydrodynamical ones. 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 (MMP, key tie lines, etc) are not dependent of 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 splitting technique may be used for the solution of Riemann problems and for non-self-similar displacement of oil by rich gas solvent slug with lean gas drive considering ideal behavior of the fluids, i.e. constant distribution coefficients. For 3-D displacements, the splitting is valid if and only if the total mobility is constant. It allows the application of the obtained 1-D analytical solutions in streamline simulators. The technique reduces significantly the amount of calculations for sensitivity study of gasflooding processes 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.


The injection of different gases (methane, rich hydrocarbon gases, carbon dioxide, nitrogen and various combinations) in order to improve displacement by mass exchange between oleic and gas phases is the basis of the solvent methods of enhanced oil recovery[1].

One dimensional displacement of oil by gas in large scale approximation is described by (n-1)x(n-1) hyperbolic system of conservation laws, where n is the number of components[2–5]. Continuous gas injection results in a Riemann problem for this hyperbolic system. Displacement of oil by a gas slug with another gas drive is described by the initial and boundary value problem with piece-wise initial data[6].

The elementary hyperbolic waves in the 2x2 system for two-phase three-component displacement can be described both analytically and graphically[7]. It may be used to find several exact solutions for Riemann problems of continuous gas injection. Analytical 1D models for different types of ternary phase diagrams and boundary conditions related to injection of different fluids were developed using the same technique[1,8–10].

The semi-analytical solutions for n-component gas flooding obtained by numerical combination of shocks and rarefactions waves allow thermodynamic analysis, minimum miscibility pressure (MMP) calculations and recovery estimates[2–5]. The technique was developed for any number of components.

A hyperbolic system for gas flooding is similar to the one of polymer flooding. The observation that concentration waves in 2-phase environment can be obtained from one phase multi component flow was used for the development of a semi-analytical Riemann problem solver for two-phase n components polymer flooding[11]. The exact solutions for this problem with adsorption governed by Langmuir isotherm were obtained using 1 phase solution[11,12]. This technique cannot be extended for non-self-similar problems of oil displacement by polymer slugs.

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