Comparisons Between Mixture Theory and Darcy law for two-phase Flow in Porous Media using Gitt and Fluent Simulations

Between Mixture Theory and Darcy law

Methodologies in reservoir simulations for recovery of oil by water displacement are investigated in a joint work with PETROBRAS, Fluminense Federal University and ESSS. The saturation differential equation and the mixture theory were used to solve the recovery of oil by water displacement using Fluent CFD code.

Water injection into oil formations has a very wide application in the oil industry. The injection of water has as main objective: to maintain formation pressure and provide the recovery of oil by water displacement. This work compares two different theoretical formulations used in reservoir simulations. One is the saturation differential equation and the other is the mixture theory equation applied to fluid flow in porous media. The saturation differential equation is widely used in reservoir simulations. This equation is found when Darcy’s Law for each phase is applied in the continuity equation for each phase. However, there is another theoretical approach for multiphase flows in porous media.

Between Mixture Theory and Darcy law

Mixture theory allows a local description of the flow in a porous medium, supported by a thermodynamically consistent theory which generalizes the classical continuum mechanics. This article compares the results obtained by the equation based on the mixture theory with the saturation differential equation. To solve the saturation equation the Generalized Integral Transform Technique (GITT) was employed. The GITT has been successfully employed in various petroleum reservoir simulation problems. The numerical method for the solution of mixture theory was obtained using advanced, commercial, general-purpose CFD code: FLUENT.

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