# Thomas Zauner

**Thomas Zauner**

PhD student

Office: | 202 |
---|---|

Phone: | +49 711 685-67652 |

Fax: | +49 711 685-63658 |

Email: | Thomas.Zauner _at_ icp.uni-stuttgart.de |

Address: | Thomas Zauner Institute for Computational Physics Universität Stuttgart Allmandring 3 70569 Stuttgart Germany |

## Research Overview

The general field of my research is the **computational investigations of natural porous media**. A typical example of such a natural porous medium is sandstone.
It consists of very small consolidated grains that form a solid backbone but,
due to the space between individual grains, is permeable for many fluids.
Insight into physical transport phenomena of natural porous media,
such as flow rates, trapping behavior and prediction
of effective transport coefficients, has always been of great practical
interest for the oil and gas industry and has currently drawn public
attention in the context of CO_{2} sequestration.
Porous materials are also used for many industrial
applications, for example in filtration processes, as
catalyst in chemical reactions or building materials with specially
physical properties.

The scientific problems that I address in my work are:

**Developing algorithms that can generate realistic and macroscopic computer models for granular porous media**. These models will be made of many hundred millions of individual grains whose positions, orientations and sizes must fulfill certain correlations and restrictions. The associated large computational demand requires highly efficient parallelized computer algorithms.

**Identifying and evaluating numerical methods that allow accurate and predictive calculations of physical properties of porous media**. These calculations typically require numerically solving partial differential equations within a chosen discretization scheme and at a specific resolution or order of accuracy.

## Realistic computer models for granular porous media

In the reconstruction procedure we use a dense packing of spheres is created. The packing must fulfill given restrictions such as density, overlap, size distribution and others. The spheres are later substituted by more complex geometrical objects determined by the shapes of the grains used in the specific model. One option is to use polyhedrons as grain shapes. The resulting model then is a continuum model in the sense that the geometry is defined by a points in the continuum and polyhedrons with analytical defined shapes, sizes and orientations. An example of such a model for Fountainebleau sandstone is shown in image 1. Such a continuous computer model can then be discretized at any desired resolution, see image 2, for further analysis and computer simulations.

## Flow Simulations

A porous mediums **permeability** is an example of a
physical transport parameter. It describes the mediums ability to
transmit fluid flow through it. Using **Darcy's law** the permeability
of a porous medium can be calculated from the velocity and
corresponding pressure field on the porescale. These fields
are solutions of hydrodynamic partial differential
equations describing fluid flow on the porescale. Many different
numerical methods that solve different hydrodynamic equations
can be used to obtain the velocity and pressure field.
Possibilities are **Navier-Stokes simulations** and **Lattice-Boltzmann simulations**. Our Lattice-Boltzmann implementation, for example, numerically solves the Boltzmann equation using a **transient explicit finite-difference scheme**. The simulation is ran until a stationary solution has been reached. From this stationary solution the hydrodynamic fields can be calculated.
Simulations in stochastic geometries often require very large system sizes to obtain representative solutions. In our investigations, typical sizes of the discretized system are in the range 1024³-4096³ voxel.

## Publications

[1] A. Narvaez, T. Zauner, F. Raischel, R. Hilfer, J. Harting, “Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations”, Journal of Statistical Mechanics, P11026, 2010, Preprint

[2] S. Grottel, G. Reina, T. Zauner, R. Hilfer, T. Ertl, "Particle-based Rendering for Porous Media", SIGRAD, 2010, Preprint

[3] J. Harting, T. Zauner, R. Weeber, and R. Hilfer Numerical modeling of fluid flow in porous media and in driven colloidal suspensions in High Performance Computing in Science and Engineering '08, edited by W. Nagel, D. Kröner, M. Resch, Springer ,2008. Preprint