Print Email Facebook Twitter Three-Phase Fractional-Flow Theory of Foam-Oil Displacement in Porous Media with Multiple Steady States Title Three-Phase Fractional-Flow Theory of Foam-Oil Displacement in Porous Media with Multiple Steady States Author Tang, J. (TU Delft Reservoir Engineering) Castañeda, Pablo (Instituto Tecnológico Autónomo de México (ITAM)) Marchesin, Dan (Instituto Nacional de Matemática Pura e Aplicada - IMPA) Rossen, W.R. (TU Delft Reservoir Engineering) Date 2019 Abstract Understanding the interplay of foam and non-aqueous phases in porous media is key to improving the design of foam for enhanced oil recovery and remediation of aquifers and soils. A widely used implicit-texture foam model predicts phenomena analogous to cusp catastrophe theory: the surface describing foam apparent viscosity as a function of fractional flows folds backwards on itself. Thus there are multiple steady states fitting the same injection condition J defined by the injected fractional flows. Numerical simulations suggest the stable injection state among multiple possible states but do not explain the reason.We address the issue of multiple steady states from the perspective of wave propagation, using three-phase fractional-flow theory. The wave-curve method is applied to solve the two conservation equations for composition paths and wave speeds in 1D foam-oil flow. There is a composition path from each possible injection state J to the initial state I satisfying the conservation equations. The stable displacement is the one with wave speeds (characteristic velocities) all positive along the path from J to I. In all cases presented, two of the paths feature negative wave velocity at J; such a solution does not correspond to the physical injection conditions. A stable displacement is achieved by either the upper, strong-foam state or lower, collapsed-foam state, but never the intermediate, unstable state. Which state makes the displacement depends on the initial state of a reservoir. The dependence of the choice of the displacing state on initial state is captured by a boundary curve. Subject foam flow with oilfractional-flow theorymultiple steady statesporous mediawave-curve method To reference this document use: http://resolver.tudelft.nl/uuid:fb67538e-e311-49f5-9d5d-83e542913198 DOI https://doi.org/10.1029/2019WR025264 ISSN 0043-1397 Source Water Resources Research, 55 (12), 10319-10339 Part of collection Institutional Repository Document type journal article Rights © 2019 J. Tang, Pablo Castañeda, Dan Marchesin, W.R. Rossen Files PDF 2019WR025264.pdf 11.69 MB Close viewer /islandora/object/uuid:fb67538e-e311-49f5-9d5d-83e542913198/datastream/OBJ/view