Difference between revisions of "Multiphase Flow in Porous Media"
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__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 ==  
−  It is known that  +  It is known that percolating and nonpercolating fluid parts show fundamental different 
−  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 
−  behavior (e.g. Abrams (1975), Avraam et al. (1995), Taber (1969), Wyckoff (1936)  +  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. 
−  macroscopic  +  
−  nonpercolating  +  The resulting set of partial differential equations is strongly coupled, highly nonlinear and of mixed type. We study these equations analytically and numerically . 
−  and  +  
+  == 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 ==  == Current Coworkers ==  
Line 30:  Line 30:  
== Publications ==  == Publications ==  
−  <bibentry>  +  <bibentry> hilfer06c</bibentry> 
−  </bibentry>  +  <bibentry> hilfer06b</bibentry> 
+  <bibentry> hilfer06a</bibentry>  
+  <bibentry> hilfer00h</bibentry>  
+  <bibentry> hilfer00g</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 'Nonlinearities 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 and H. Besserer.
"Old Problems and New Solutions for Multiphase Flow in Porous Media".
Porous Media: Physics, Models, Simulation , pages 133, Editors: A. Dmitrievsky and M. Panfilov, , Singapore, 2000.
World Scientific Publ. Co..
[PDF] (135 KB)

R. Hilfer and 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)