Difference between revisions of "Multiphase Flow in Porous Media"
| (3 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
__NOTOC__ | __NOTOC__ | ||
== Introduction == | == Introduction == | ||
| − | Many natural and technical processes involve multiphase flow | + | <onlyinclude>Many natural and technical processes involve multiphase flow |
processes in porous media. Despite that fact fundamental | processes in porous media. Despite that fact fundamental | ||
concepts of twophase flow on macroscopic scales still remain unclear. The | concepts of twophase flow on macroscopic scales still remain unclear. The | ||
| Line 7: | Line 7: | ||
theory is at best limited to simple problems where neither hysteresis nor | theory is at best limited to simple problems where neither hysteresis nor | ||
dynamic effects like trapping nor varying residual saturations have a | dynamic effects like trapping nor varying residual saturations have a | ||
| − | substantial impact on the solutions. | + | substantial impact on the solutions.</onlyinclude> |
== Our Project == | == Our Project == | ||
| Line 17: | Line 17: | ||
== Recent results == | == Recent results == | ||
| − | * Initial and boundary conditions have been formulated to model experiments with a homogeneous porous column in the gravity field. The resulting 9 PDE have been solved with an adaptive moving grid PDE solver. | + | * Initial and boundary conditions have been formulated to model experiments with a homogeneous porous column in the gravity field. The resulting 9 PDE have been solved with an adaptive moving grid PDE solver. |
| + | * A limiting case of immobile nonpercolating fluid phases has been formulated. Hyperbolic and parabolic limits of this case have been treated (quasi) analytically. | ||
== Current Coworkers == | == Current Coworkers == | ||
| Line 29: | Line 30: | ||
== Publications == | == Publications == | ||
| + | <bibentry> hilfer06c</bibentry> | ||
| + | <bibentry> hilfer06b</bibentry> | ||
| + | <bibentry> hilfer06a</bibentry> | ||
| + | <bibentry> hilfer00h</bibentry> | ||
| + | <bibentry> hilfer00g</bibentry> | ||
<bibentry> hilfer98a</bibentry> | <bibentry> hilfer98a</bibentry> | ||
| + | [[Category:Research]] | ||
Latest revision as of 16:42, 20 September 2011
Introduction
Many natural and technical processes involve multiphase flow processes in porous media. Despite that fact fundamental concepts of twophase flow on macroscopic scales still remain unclear. The predictive power of the most commonly used extended multiphase Darcy theory is at best limited to simple problems where neither hysteresis nor dynamic effects like trapping nor varying residual saturations have a substantial impact on the solutions.
Our Project
It is known that percolating and nonpercolating fluid parts show fundamental different behavior (e.g. Abrams (1975), Avraam et al. (1995), Taber (1969), Wyckoff (1936)). This insight is incorporated into a macroscopic theory which treats percolating(=connected) and nonpercolating (=nonconnected) fluid parts as separate phases. Thereby a two phase system is described by four phases.
The resulting set of partial differential equations is strongly coupled, highly nonlinear and of mixed type. We study these equations analytically and numerically .
Recent results
- Initial and boundary conditions have been formulated to model experiments with a homogeneous porous column in the gravity field. The resulting 9 PDE have been solved with an adaptive moving grid PDE solver.
- A limiting case of immobile nonpercolating fluid phases has been formulated. Hyperbolic and parabolic limits of this case have been treated (quasi) analytically.
Current Coworkers
- Prof. Dr. Rudolf Hilfer, Project supervisor
- Florian Doster, PhD Student
Collaborations
- The project is part of Nupus (International Research Training Group 'Non-linearities and Upscaling in PoroUS media').
- Prof. Dr. Paul Zegeling, Department of Mathematics, Faculty of Sciences, Utrecht University
- Prof. Dr. Majid Hassanizadeh, Department of Earth Sciences, Faculty of Geosciences, Utrecht University
Publications
-
R. Hilfer.
Macroscopic capillarity without a constitutive capillary pressure function.
Physica A 371:209–225, 2006.
[PDF] (297 KB)
-
R. Hilfer.
Macroscopic Capillarity and Hysteresis for Flow in Porous Media.
Physical Review E 73:016307, 2006.
[PDF] (135 KB)
-
R. Hilfer.
Capillary Pressure, Hysteresis and Residual Saturation in Porous Media.
Physica A 359:119–128, 2006.
[PDF] (167 KB)
-
R. Hilfer, H. Besserer.
Old Problems and New Solutions for Multiphase Flow in Porous Media.
In Porous Media: Physics, Models, Simulation, pages 133. Edited by A. Dmitrievsky, M. Panfilov.
World Scientific Publ. Co., Singapore, 2000.
[PDF] (135 KB)
-
R. Hilfer, H. Besserer.
Macroscopic Two Phase Flow in Porous Media.
Physica B 279:125, 2000.
[PDF] (95 KB)
-
R. Hilfer.
Macroscopic Equations of Motion for Two Phase Flow in Porous Media.
Physical Review E 58:002090, 1998.
[PDF] (147 KB)