Gravity Segregation in Two-Phase Displacement Processes
Authors: Spivak Allan 
Published: December 2007

Spivak, Allan,* Member SPE-AIME, Chevron Oil Field Research Co., La Habra, Calif.

Abstract
This paper describes a study of gravity segregation (underrun or override of injected fluids) in two-phase, secondary recovery displacement processes. Reservoir simulation was used to investigate the factors that influence gravity segregation and the magnitude of gravity effects for both water floods and gas floods. The degree of segregation for a given set of conditions was determined bycomparing the results of two-dimensional cross-sectional with one-dimensional horizontal calculations, andcomparing the results of three-dimensional vs two-dimensional a real calculations.
The degree of segregation is quantitatively described by the dimensionless number E defined as
(Rbt)no gravity -(Rbt)gravity E =, (Rbt)no gravity
where Rbt is recovery at breakthrough. Gravity segregation effects in two-phase displacement processes were found to increase withincreasing processes were found to increase withincreasing permeability (either horizontal or vertical),permeability (either horizontal or vertical),increasing density difference,increasing mobility ratio,decreasing production rates. anddecreasing level of viscosity for a fixed viscosity ratio.
A series of calculations was made in which the parameters that affect gravity segregation were varied. The effect of each parameter on the degree of gravity segregation was observed. The effect of both stratified and random heterogeneity was also studied. A correlation between the degree of gravity segregation and the dimensionless groups
G = 0.00633
and
M = mobility ratio
was established. This correlation is based on the results of the simulator calculations and a detailed analysis of the equations for three-dimensional, two-phase. immiscible, incompressible flow. The correlation can be used to determine qualitatively whether gravity segregation will be a significant factor in a given flooding process. It can also be used to determine whether the assumption of vertical equilibrium is valid in the simulation by a two-dimensional a real simulation model of reservoirs where fluid saturations vary significantly in the vertical direction.

Introduction
For many years, gravity segregation in reservoir processes was not accounted for because it could processes was not accounted for because it could not be adequately handled in reservoir engineering calculations. The advent of reservoir simulation provided the capability to handle gravity, and it provided the capability to handle gravity, and it became apparent that gravity effects could significantly affect reservoir performance. This paper describes a study in which a three-dimensional paper describes a study in which a three-dimensional (3-D), two-phase, incompressible simulator was used to look at gravity effects in displacement processes. The objectives of this study wereto processes. The objectives of this study wereto determine what factors influence gravity segregation and in what way;to look at the magnitude of gravity segregation effects;to compare reservoir performance calculations with and without gravity performance calculations with and without gravity effects.

PREVIOUS WORK ON GRAVITY PREVIOUS WORK ON GRAVITY SEGREGATION IN DISPLACEMENT PROCESSES
Craig et al. did experimental work to study the effects of gravity segregation during water, gas, and solvent flooding. As a result of their studies, they concluded that segregation of fluids due to gravity effects could result in oil recoveries at breakthrough as low as 20 percent of those otherwise expected. They also concluded that performance may in some cases be influenced to a greater degree by heterogeneity than by gravity effects. They were not able to directly compare performance under a given set of conditions with and without gravity.
SPEJ
p. 619