FourComponent Gas/Oil Displacements in One Dimension: Part I: Global Triangular Structure
 Thormod Johansen,
 Yun Wang,
 Franklin M. Orr Jr.,
 Birol Dindoruk
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This paper presents an analysis of the mathematical structure of threecomponent and fourcomponent gas displacements. The structure of onedimensional flows in which components partition between two phases is governed by the geometry of a set of equilibrium tie lines. We demonstrate that for systems of four components, the governing mass conservation laws for the displacement can be represented by an eigenvalue system whose coefficient matrix has a global triangular structure, which is defined in the paper, for only specific types of phase behavior. We show that fourcomponent systems exhibit global triangular structure if and only if (1) tie lines meet at one edge of the quaternary phase diagram or (2) if tie lines lie in planes. For such systems, shock and rarefaction surfaces coincide and are planes. We prove that systems are of category (2) if equilibrium ratios (Kvalues) are independent of mixture composition. In particular, for such systems shock and rarefaction curves will coincide. We also show that for systems with variable Kvalues, the rarefaction surfaces are almost planar in a precise sense, which is described in the paper. Therefore, systems with variable Kvalues may be well approximated by assuming shock and rarefaction surfaces do coincide. For these special systems the construction of solutions for onedimensional, twophase flow with phase behavior simplifies considerably. In Part II, we describe an application of these ideas to systems in which Kvalues are constant.
 Title
 FourComponent Gas/Oil Displacements in One Dimension: Part I: Global Triangular Structure
 Journal

Transport in Porous Media
Volume 61, Issue 1 , pp 5976
 Cover Date
 200510
 DOI
 10.1007/s1124200467486
 Print ISSN
 01693913
 Online ISSN
 15731634
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 global triangular structure
 tie line geometry
 constant Kvalue
 developable surface
 Industry Sectors
 Authors

 Thormod Johansen ^{(1)}
 Yun Wang ^{(2)}
 Franklin M. Orr Jr. ^{(3)}
 Birol Dindoruk ^{(4)}
 Author Affiliations

 1. Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. Johns, NF, A1C 5S7, Canada
 2. BP America Production Company, 200 WestLake Park Boulevard, Houston, TX, 77079, U.S.A
 3. Department of Petroleum Engineering, Stanford University, Stanford, CA, 94305, U.S.A
 4. Shell International Exploration and Production Inc., 200 North Dairy Ashford, Houston, TX, 77079, U.S.A