Various EOR methods lead to the appearance of various zones with different number of phases and different thermodynamic state. They are separated by specific surfaces called the interfaces of phase transition. Consecutively, the flow equations are also different in various zones and cannot be deduced from each other by continuous degeneration, which imposes serious difficulties in numerical modelling. We suggest a new conceptual mathematical method based on the replacement of real single-phase fluid by an imaginary multiphase muticomponent continuum having fictitious properties. As the result, the fluid over all zones becomes three-phase and can be described by uniform three-phase hydro- and thermodynamic equations, which allows applying the direct numerical simulation. The equivalence principle determines the physical properties of the fictitious multiphase fluid, as well as the structure of the uniform multiphase equations. It also proves that the saturation of each phase may become negative in non-equilibrium zones, which becomes the efficient method of tracking the interface and the number of phases at any point. The method was developed by the authors for two-phase case. In the present paper the new version is developed for three-phase case. Several examples of simulation are presented.


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