Page 63 - Principles of Applied Reservoir Simulation 2E
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Chapter 6
Frontal Stability
The stability of a flood front can influence the efficiency of fluid
displacement. A front is stable if it retains the shape of the interface between
displaced and displacing fluids as the front moves through the medium. An
analysis of frontal stability is presented in this chapter in terms of a specific
example - the advance of a water-oil displacement front in the absence of gravity
and in the presence of gravity. The stability of the front is then studied using
linear stability analysis.
6.1 Frontal Advance Neglecting Gravity
The displacement of one phase by another may be analytically studied
if a linear, homogenous porous medium is assumed. Let us first consider the
displacement of oil by water in a horizontal porous medium of length L. We
assume piston-like displacement of a front located atx f. Application of Darcy's
law and the continuity equation leads to a pressure distribution described by
Poisson's equation. The absence of sources or sinks in the medium reduces
Poisson's equation to the Laplace equation for the water phase pressure:
£3 D
= 0, 0<x<x r (6.1)
dx
The corresponding equation for oil phase pressure is
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