Difference between revisions of "Transport in Porous Media"

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[[Image:Porousflow.png|300px|right|thumb| LB simulation of flow (top to bottom) in a discretized porous media model (sandstone). In  blue the volume with  V>0. Brow isosurfaces  visualize regions with a high velocity.]]
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== Introduction ==
 
== Introduction ==
Many natural and technical processes involve multiphase flow
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<onlyinclude>Understanding fluid transport in natural porous media is important for many
processes in porous media. Despite that fact fundamental
+
industrial and scientific applications.  Computer simulations require accurate
concepts of twophase flow on macroscopic scales still remain unclear. The
+
three-dimensional microscopic structure data as input and efficient numerical
predictive power of the most commonly used extended multiphase Darcy
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algorithms for fluid flow simulations.  Natural porous media such as carbonates
theory is at best limited to simple problems where neither hysteresis nor
+
and clay filled sandstones exhibit heterogeneities on many scales and cannot be
dynamic effects like trapping nor varying residual saturations have a
+
modeled by existing modeling techniques.
substantial impact on the solutions.
+
</onlyinclude>
  
 
== Our Project ==
 
== Our Project ==
It is known that percolating and nonpercolating fluid parts show fundamental different
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A continuum model is developed for generating synthetic microcomputer-tomography data of multiscale porous media at arbitrary resolution. Large scale parallelized lattice-Boltzmann simulations are performed to calculate transport parameters, such as permeabilities using Darcy's Law, and other material parameters.
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 ==
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== Lattice Boltzmann Method ==
* 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.
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The Lattice Boltzmann (LB) method numerically solves the discretized Boltzmann equation
* A limiting case of immobile nonpercolating fluid phases has been formulated. Hyperbolic and parabolic limits of this case have been treated (quasi) analytically.
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using a linearized collision operator to simulate the flow of a Newtonian fluid. We use the  D3Q19 lattice model together with a single relaxation time (BGK) or two relaxation time (MRT/TRT) collision operator. Extensive calibrations for our LB-implementations were performed by simulating Poiseuille Flow in pipes of varying shapes and sizes.
  
 
== Current Coworkers ==
 
== Current Coworkers ==
 
* Prof. Dr. [[Rudolf Hilfer]], Project supervisor
 
* Prof. Dr. [[Rudolf Hilfer]], Project supervisor
* [[Florian Doster]], PhD Student
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* [[Thomas Zauner]], PhD Student
 
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[[Category:Research]]
== Collaborations ==
 
* The project is part of [http://www.nupus.uni-stuttgart.de Nupus] (International Research Training Group 'Non-linearities and Upscaling in PoroUS media').
 
* Prof. Dr. [http://www.math.uu.nl/people/zegeling/ Paul Zegeling], Department of Mathematics, Faculty of Sciences, Utrecht University
 
* Prof. Dr. [http://www.geo.uu.nl/~wwwhydro/majid.html Majid Hassanizadeh], Department of Earth Sciences, Faculty of Geosciences, Utrecht University
 
 
 
== Publications ==
 
<bibentry> hilfer06c</bibentry>
 
<bibentry> hilfer06b</bibentry>
 
<bibentry> hilfer06a</bibentry>
 
<bibentry> hilfer00h</bibentry>
 
<bibentry> hilfer00g</bibentry>
 
<bibentry> hilfer98a</bibentry>
 

Latest revision as of 16:38, 20 September 2011

LB simulation of flow (top to bottom) in a discretized porous media model (sandstone). In blue the volume with V>0. Brow isosurfaces visualize regions with a high velocity.

Introduction

Understanding fluid transport in natural porous media is important for many industrial and scientific applications. Computer simulations require accurate three-dimensional microscopic structure data as input and efficient numerical algorithms for fluid flow simulations. Natural porous media such as carbonates and clay filled sandstones exhibit heterogeneities on many scales and cannot be modeled by existing modeling techniques.


Our Project

A continuum model is developed for generating synthetic microcomputer-tomography data of multiscale porous media at arbitrary resolution. Large scale parallelized lattice-Boltzmann simulations are performed to calculate transport parameters, such as permeabilities using Darcy's Law, and other material parameters.

Lattice Boltzmann Method

The Lattice Boltzmann (LB) method numerically solves the discretized Boltzmann equation using a linearized collision operator to simulate the flow of a Newtonian fluid. We use the D3Q19 lattice model together with a single relaxation time (BGK) or two relaxation time (MRT/TRT) collision operator. Extensive calibrations for our LB-implementations were performed by simulating Poiseuille Flow in pipes of varying shapes and sizes.

Current Coworkers