In the southern coast of the Gulf of Mexico some deep geothermal aquifers are associated to hydrocarbon reservoirs. Some of their wells are invaded by geothermal brine, producing a variable mixture of hot water and oil. This water, at temperatures of 150?C and having a density of 1150 kg/m3; flows vertically through a fault from the aquifer located 6000 m depth. The non isothermal conditions affect the effective saturations and the relative permeabilities of the immiscible phases. The relative permeability of oil is increased by the increase of temperature produced by the geothermal water. This effect reduces the residual saturation of heavy oils. At the same time the dynamic viscosities of water and oil are diminished, affecting the displacement of both fluids. Although the oil is extracted in wells finished upper the aquifer, the total volume of produced water, in some cases, equals or exceeds the oil production. The handling of this extra hot water becomes a practical serious problem. We introduce a numerical original model able to predict the critical oil rate for which the wells can be totally invaded by geothermal brine.

For the construction of the model we apply classic laws and equations. We use standard published formulas for both relative permeabilities and capillary pressure. We obtain a single non - linear partial differential equation (PDE) which depends only on water saturation, space and time. This PDE is a 3D generalization of the classical 1D Buckley-Leverett model. To solve the new PDE we use non linear finite elements. The numeric simulation could reproduce the effect of water invasion: After some time elapsed, the original oil volume diminishes abruptly, displacing the boundary of the water-oil contact and the transition zone in the vertical direction. Our objective is to estimate the optimum mass rate for producing wells in order to minimize the production of water or to achieve a mixture oil-water extraction where oil always prevails.

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