1Finite volume schemes for two phase incompressible Darcy flows

Massonr

Description

1Finite volume schemes for two phase incompressible Darcy flows • Two phase Darcy flow models • Saturations • Relative permeabilities: two phase Darcy velocities • Scalar hyperbolic conservation laws • Two points monotone fluxes • Explicit scheme and CFL condition • IMPES discretization of two phase flows • Pressure computation: elliptic equation • Saturation computation: scalar hyperbolic equation

• mass conservation


• finite volume schemes


• phase volume


• pore volume


• pressure computation


• relative permeabilities


• volume fraction


• conservation laws


• darcy flow

Sujets

• Conservation of mass
• Volume fraction
• Conservation law

Informations

• Publié par: pefav
• Nombre de lectures: 20
• Langue: English

Extrait

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Finite volume schemes for two phase incompressible Darcy flows

Two phase Darcy flow models

•Saturations •Relative permeabilities: two phase Darcy velocities

Scalar hyperbolic conservation laws •Two points monotone fluxes •Explicit scheme and CFL condition

IMPES discretization of two phase flows •Pressure computation: elliptic equation •Saturation computation: scalar hyperbolic equation

1

OIL AND WATER SATURATIONS

In a given pore volume V p , let V w be the water phase volume and V o the oil phase volume with V p = V w + V o .

The oil and water satur fractions of the oil S w = V w V p

with

ations are the volume and water phases S= V o o V p

S w +S o

=1

2

Oil residual Saturation and Irreducible Water Saturation

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3

RELATIVE PERMEABILITIES AND TWO PHASE DARCY VELOCITIES

V w = −

V o = −

kr w (S w ) K∇P µ w

kr o (S o ) K∇P µ o

4

TWO PHASE DARCY FLOW

Mass conservation forα=o,w

∂ ( α S α ) +di ρ V=0 v ∂t α α Darcy velocities forα=o,w V α − k K r ∇P = α µ α

Pore volume conservation S α =1 α =w,o

5