Large volumes of oil are left behind in matrix system of naturally fractured reservoirs (NFR) with expanding gas cap and/or encroaching water influx upon years of oil production. Such systems are subjected to natural gravity drainage or induced gravity drainage/imbibitions by injection of external gas or chemical EOR treatments. Proper modeling of gravity drainage is a very challenging task for such situations in naturally fractured reservoirs. This is because the gravity term is not explicitly included in the exchange function between matrix and fracture in dual continuum formulation of most commercial numerical simulators. Classical discrete fracture models are generally impractical for being computationally expensive.

Much work has been done in the past on alternate ways of capturing gravity effects in numerical simulations of fractured systems. Often, pseudo capillary pressure terms have been proposed that combine gravity and rock capillary pressures and mimic proper transfer of fluids between matrix and fractures. Several methods have been published in the literature for the computation of pseudo capillary pressure for single and multiple matrix cases with varying results. However, their applicability and conditions for their applicability have remained uncertain.

In this paper we introduce a new method to derive pseudo capillary pressures that preserve gravity effects for both water/oil and gas/oil systems under various conditions. The method is applied to single block and multiple block cases, and is benchmarked against the corresponding single-porosity fine-grid simulations with explicit fractures. The paper also investigates other available pseudo capillary pressure methods on the same matrix/fracture configurations to evaluate their performance and to compare with the new method of this paper. Our simulation results show that proper pseudo capillary pressures effectively incorporate the gravity effects in simulations of oil/water and gas/oil systems; and as such they significantly improve modeling of oil recovery in dual porosity models. This capability is highly crucial in full-field simulations of naturally fractured reservoirs with continuum models.

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