Tzold

Tzold
PhD student

Office:	202
Phone:	+49 711 685-67652
Fax:	+49 711 685-63658
Email:	Thomas.Zauner _at_ icp.uni-stuttgart.de
Address:	Tzold Institute for Computational Physics Universität Stuttgart Allmandring 3 70569 Stuttgart Germany

Research Overview

Sandstone is a very common natural porous medium. ©wikipedia

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<\sub> 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 (insulating material).}

Two scientific problems that I address in my work are:

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

• Evaluating numerical methods to allow accurate and predictive calculations of physical transport properties. These calculations usually 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 a dense packing of possibly polydisperse spheres is created. The packing must fulfill some given restrictions such as density, overlap and size distribution and more. The spheres are subsequentially 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 shape. The resulting model then is a continuum model in the sense that the microgeometry is defined by a points in the continuum and polyhedrons with analytical defined shapes and orientations. An example of such a model for Fountainebleau sandstone is shown in image 1. This continuous computer model can then be discretized at any desired resolution for further analysis and computer simulations, see image 2.

Picture 1: Three dimensional rendering of a model for Fontainebleau sandstone. The model contains over 1.2 million quartz grains. Each grain is modeled as a polyhedron. A crosssection is shown in orange.

Picture 2: Two dimensional crosssections of the discretized model.The sidelength of the crossection is L and the resolution a. The porespace is black and the grains are gray. A the highest resolution narrow channel are solved by more than 20 nodes.

Flow Simulations

A porous mediums permeability is an example of a effective 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 solution 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 or Lattice-Boltzmann simulations. Our Lattice-Boltzmann implementation, for example, numerically solves the Boltzmann equation using a transient explicit finite-difference scheme. The simulation is then carried out long enough to obtain a stationary solution. From this stationary solution the hydrodynamic fields can be calculated.

Very small subvolume (128³ voxel) of a sandstone. The porespace-matrix interface is shown as a mesh. The velocity magnitude, as calculated by a Lattice-Boltzmann simulation, is shown within the porespace. Areas of slow flow are blue, fast flow is shown in red. An empty porespace indicates areas where the fluid is at rest. It can be seen that only a small portion of the porespace contributes to the mass transport. Media:poreflow.avi Media:poremovie.avi

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