A mathematical model to describe the heat transfer process in an oil field composed of a three-phase system is presented. The system consists of a porous medium saturated with a two-phase flow, oil and gas. Using the volume-averaging method a heat transfer one-equation model is derived. The principle of local thermal equilibrium was imposed in order to develop a one-equation model for heat transfer process in the three-phase system. The average one-equation model derived contains terms representing the convection, conduction, compressibility, and source term in addition to a term representing the exchange with the surrounding region for transient process.

In this article an equation of continuity of multiphase flow in naturally fractured reservoirs was derived. The scaling analysis is presented in order to identify the characteristic scales where the fractured porous media can be studied. The system under consideration consists of two regions and an inter-region. One region is porous medium saturated with multiphase flow (η -region) and the other region is multiphase flow in the fracture (ω-region). The multiphase flow analyzed in both regions is water-oil-gas. The oneequation model (single velocity) was obtained for predicted energy transfer in naturally fractured reservoirs using the non-local averaging approximation.

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