TY - JOUR
T1 - A locally conservative Eulerian-Lagrangian numerical method and its application to nonlinear transport in porous media
AU - Douglas, Jim
AU - Pereira, Felipe
AU - Yeh, Li-Ming
PY - 2000/5
Y1 - 2000/5
N2 - Eulerian-Lagrangian and Modified Method of Characteristics (MMOC) procedures provide computationally efficient techniques for approximating the solutions of transport-dominated diffusive systems. The original MMOC fails to preserve certain integral identities satisfied by the solution of the differential system; the recently introduced variant, called the MMOCAA, preserves the global form of the identity associated with conservation of mass in petroleum reservoir simulations, but it does not preserve a localized form of this identity. Here, we introduce an Eulerian-Lagrangian method related to these MMOC procedures that guarantees conservation of mass locally for the problem of two-phase, immiscible, incompressible flow in porous media. The computational efficiencies of the older procedures are maintained. Both the original MMOC and the MMOCAA procedures for this problem are derived from a nondivergence form of the saturation equation; the new method is based on the divergence form of the equation. A reasonably extensive set of computational experiments are presented to validate the new method and to show that it produces a more detailed picture of the local behavior in waterflooding a fractally heterogeneous medium. A brief discussion of the application of the new method to miscible flow in porous media is included.
AB - Eulerian-Lagrangian and Modified Method of Characteristics (MMOC) procedures provide computationally efficient techniques for approximating the solutions of transport-dominated diffusive systems. The original MMOC fails to preserve certain integral identities satisfied by the solution of the differential system; the recently introduced variant, called the MMOCAA, preserves the global form of the identity associated with conservation of mass in petroleum reservoir simulations, but it does not preserve a localized form of this identity. Here, we introduce an Eulerian-Lagrangian method related to these MMOC procedures that guarantees conservation of mass locally for the problem of two-phase, immiscible, incompressible flow in porous media. The computational efficiencies of the older procedures are maintained. Both the original MMOC and the MMOCAA procedures for this problem are derived from a nondivergence form of the saturation equation; the new method is based on the divergence form of the equation. A reasonably extensive set of computational experiments are presented to validate the new method and to show that it produces a more detailed picture of the local behavior in waterflooding a fractally heterogeneous medium. A brief discussion of the application of the new method to miscible flow in porous media is included.
KW - Miscible flow
KW - Modified method of characteristics
KW - Transport-dominated diffusion processes
KW - Two-phase flow
KW - Waterflooding
UR - http://www.scopus.com/inward/record.url?scp=0034048046&partnerID=8YFLogxK
U2 - 10.1023/A:1011551614492
DO - 10.1023/A:1011551614492
M3 - Article
AN - SCOPUS:0034048046
VL - 4
SP - 1
EP - 40
JO - Computational Geosciences
JF - Computational Geosciences
SN - 1420-0597
IS - 1
ER -