Stability of Displacement Fronts in WAG Operations
- G.A. Virnovsky (Rogaland Research) | H.M. Helset (Rogaland U. Center)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 1996
- Document Type
- Journal Paper
- 383 - 394
- 1996. Society of Petroleum Engineers
- 5.7.2 Recovery Factors, 5.4 Enhanced Recovery, 4.3.4 Scale, 5.5 Reservoir Simulation, 5.3.1 Flow in Porous Media, 5.4.2 Gas Injection Methods, 2.2.2 Perforating, 5.3.2 Multiphase Flow, 5.4.9 Miscible Methods
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This paper presents an analytical and numerical study of the stability of gas-oil-water displacement fronts in two and three spatial dimensions. The flow equations are simplified by averaging in the dip-normal direction assuming vertical equilibrium to give analytical expressions for three-phase pseudo relative permeabilities and capillary pressures for a stratified reservoir.
A similarity transform results in a set of two coupled, ordinary differential equations and a simple technique is presented to identify the traveling-wave solution when certain conditions are met, and the shape of the front is calculated. The technique is based on an analysis of initial and boundary conditions and is verified by numerical simulation.
Dietz's classical stability theory for two-phase displacement fronts has recently been extended to layered reservoirs. To our knowledge, the present paper is the first to treat three-phase flow. It is shown that stable water-oil-gas fronts occur only for a limited number of the injection gas-water ratio, if at all.
Gravity-segregated multiphase flow takes place in reservoirs with high vertical permeability and large distances between wells, a situation relevant for many North Sea reservoirs. Two-phase, gravity-segregated flow theory has been discussed in books and several papers and may be looked upon as fairly matured. The extension to three-phase flow is, however, still not developed even though there are important practical applications, e.g., water-alternate-gas injection.
There exist two approaches to two-phase gravity-segregated flow in the literature. Dietz and Ekrann considered the stability of the boundary between the two phases. Others have used averaging of the flow equations in the dip-normal direction and have introduced pseudo-functions.
In this paper we follow the the second approach and apply pseudo relative permeabilities and pseudo capillary pressures to allow two-dimensional flow in a cross-section to be modeled by a set of equations in one dimension. The solutions of the traveling-wave type entail conditions for stability of displacement fronts and the possibility of high vertical sweep efficiency.
The traveling-wave solution for gravity-segregated flow was introduced by Martin and expanded upon by Ingsoy et al. First, the problem is reduced from two to one dimension by pseudofunctions and then solved by the method of Rijhik et at. The works of Martin and Ingsoy et al. bridge the pseudofunction approach of Coats et al. with the front-shape calculation of Dietz and Ekrann.
Gravity Segregated Three-Phase Flow
In this section we derive pseudofunctions to model 2D reservoir flow by iD equations. The results may also be directly applied to describe 3D reservoir flow by 2D equations.
With capillary effects neglected, three-phase flow of immiscible, incompressible fluids in two dimensions is in general described by the following set of equations for each phase i,
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