Abstract
The effect of a waxy crude oil's yield stress is numerically investigated on the "water coning phenomenon" using the Bingham rheological model. After modifying Darcy's law for purely viscous non-Newtonian fluids, it was used to relate the flow rate to the pressure gradient. Having derived the governing equations for the axisymmetric case, the implicit pressure explicit saturation (IMPES) method was used to numerically solve the governing equations. To verify the code, a comparison was made with published data for the water coning of Newtonian/Newtonian pair. The effect of yield stress and plastic viscosity on the critical rate, the breakthrough time, and the cone shape was obtained numerically. It is shown that by an increase in the yield stress of the displaced oil, the time needed by the water to cone upward and break into the wellbore is decreased. That is to say, the yield stress of the displaced fluid has a negative effect on the water coning phenomenon. On the other hand, the yield stress induced in the displacing fluid by polymeric additives is predicted to delay the coning phenomenon.
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