Transport in Porous Media

, Volume 72, Issue 1, pp 83–96

# Four-component gas/water/oil displacements in one dimension: part II, example solutions

• Tara LaForce
• Kristian Jessen
• Franklin M. OrrJr.
Article

## Abstract

In this article analytical solutions are constructed for a system of conservation laws modeling compositional flow of four components in three phases using the method of characteristics (MOC). Every component partitions between all phases present, and the equilibrium volume ratios of the components in each phase are fixed. Riemann problems modeling the injection of carbon dioxide and water in a depleted oil reservoir are studied, and the sensitivity of the solutions to changes in boundary conditions is analyzed. Finally the MOC solutions are compared to simulated displacements.

## Keywords

Three-phase flow Compositional model Four-component system Conservation laws Hyperbolic system Constant K-value

## Nomenclature

$$\overline{\overline D}(S_1,S_1)$$

The dispersion tensor

q

“Saturation” of phase one on the tie-triangle extension

r

“Saturation” of phase two on the tie-triangle extension

Λ

Shock velocity

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## Authors and Affiliations

• Tara LaForce
• 1
Email author
• Kristian Jessen
• 2
• Franklin M. OrrJr.
• 3
1. 1.Department of Chemical and Petroleum EngineeringUniversity of WyomingLaramieUSA
2. 2.Department of Chemical Engineering and Materials ScienceUniversity of Southern CaliforniaLos AngelesUSA
3. 3.Department of Energy Resources EngineeringStanford UniversityStanfordUSA