Concept of Gravity Drainage in Layered Porous Media
- F. Correa Antonio Claudio (Petrobras) | Abbas Firoozabadi (Reservoir Engineering Research Institute)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 1996
- Document Type
- Journal Paper
- 101 - 111
- 1996. Society of Petroleum Engineers
- 5.2.1 Phase Behavior and PVT Measurements, 5.3.2 Multiphase Flow, 2.4.3 Sand/Solids Control, 5.6.4 Drillstem/Well Testing
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Gas-oil gravity drainage in layered porous media is, under certain conditions, an unstable process. Even for two layers, gas could finger through a less permeable top layer to reach a more permeable bottom layer.
This paper provides a criterion for instantaneous gas fingering towards the more permeable layer. A non-linear form of the diffusivity equation is used to study gas-oil drainage in layered systems. Numerical examples show that recovery performance of layered systems, unlike homogeneous media, is sensitive to capillary pressure.
Oil drainage in gas-oil gravity drainage process in homogeneous porous media has two important characteristics: 1) the gas-oil front is stable, and 2) the recovery performance is nearly independent of capillary pressure where residual oil to gas, Sorg, is not affected. Due to both low values of Sorg and these characteristics, gravity drainage is a known efficient recovery process for homogeneous reservoirs. However, gas-oil gravity drainage may not be an efficient process for some layered reservoirs.
To our knowledge, there is no published work on gas-oil immiscible drainage in layered heterogeneous porous media. Our research work in gas-oil flow in fractured porous media indicates erroneous results due to averaging permeability in the study of gas-oil gravity drainage flow in layered porous media. An important practical question is the difference in characteristics of gravity drainage in homogeneous and layered reservoirs.
In this paper, we first formulate the gas-oil gravity drainage process in a homogeneous porous medium by means of a nonlinear form of the diffusivity equation. Then the concept of gas-oil gravity drainage in layered porous media is presented. Features of gravity drainage in layered media are shown in three numerical examples. Verification by experiments is also briefly discussed. The paper concludes with a discussion.
Modeling of Gravity Drainage in Homogeneous Media
Modeling of the gravity drainage process may be accomplished by combining the continuity equation and Darcy's law. For isothermal immiscible flow with constant porosity and incompressible oil phase, one may derive:
In Eq. 1, z is the vertical upward direction and it is assumed that gas has an infinite mobility.
Pressure and saturation of the oil phase are related by the capillary pressure curve. Assuming that the gas phase density is constant, such that pg(z)=pg(z=0)-?ggz, and assigning a zero value to pg(z=0), then the capillary pressure is related to the oil pressure by:
(Note that pg(z = 0) = 0 is a matter of convenience and that constant values will not change the derivations.)
Drainage capillary pressure may be represented by1:
where Pc0 is the threshold capillary pressure. are defined in the nomenclature.
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