FIrst Principle Based MOdelling of Transport in Unsaturated Media

The goal of our group is to compute appropriate material functions for porous media based on the pore space geometry and the physical properties of the two-phase system. To reach this goal, direct numerical simulations of the twophase system based on artifiially generated as well as reconstructed porous media are performed. The artificial geometries are constructed in such a way, that the parameter space describing the pore space geometry is appropriately covered. The main work is to enhance the lattice Boltzmann method (Multi-time relaxation, Semiimplicit time stepping schemes) to cover a wider parameter range and a rigorous analysis of the parameters describing the pore space geometry and their impact on the material functions.

In order to achieve the targeted goals we are working close to our work schedule which contains:

Dimensional analysis together with SP III for the pore- and macroscale:

- Simulating a reference problem numerically either on the meso- or the microscale should yield the same result for a homogenous porous medium. Due to the fact, that the differential equations on the meso- and microscale are qualitatively different and that there is no direct mapping between their variables and parameters, a direct comparison of both systems is difficult. Therefore a detailed dimensional analysis for both systems is carried out to understand differences and similarities and how to connect the different parameters, time and length scales.

Characterisation of the pore space geometry together with SP I:

The material functions of the porous medium strongly depend on the pore space geometry. There are different parameters describing the pore space geometry such as the porosity, the pore size distribution and the Euler-Poincare characteristic (indicating the connectivity of the pores). There is a strong indication, that these parameters are not suffcient to describe the pore space geometry appropriately.

Determination of the material functions for artifcially generated and reconstructed porous media:

These relationships (called material functions or constitutive relationships) are needed for the simulations of SPIII on the macroscale.

- Static capillary pressure - saturation relationship:

This relationship is obtained by two methods for porous media: First by performing the drainage and imbibition using a pressure difference. The second method imposes a uniform volume force to drive the flow. This relationship shows important phenomena like microscale hysteresis and the residual saturation, which affect the flow on the macroscale.

- Relative permeability - saturation relationship:

This relationship is obtained from the following procedure: For a fixed saturation a pressure gradient is imposed and the mass flow is determined yielding one point of this material function. The determination of this relationship is very costly, since many different runs are required to construct the function and it is also very sensitive to the capillary number, which is in general very low yielding very long computation times.

- Dynamic capillary pressure - saturation relationship:

There is a strong indication, that the static capillary pressure - saturation relationship is not sufficient to describe multiphase flows on the macroscale correctly in some cases. Therefore a dynamic capillary pressure - saturation relationship is incorporated by SPIII as a new material function, which depends not only on the saturation, but also on the rate of change of the saturation. In contrast to the static case this requires different runs for one geometry to determine this function.

Sensitivity analysis with respect to different dimensionless parameters:

The most important material functions of the soil depend on the pore space geometry, but also on dimensionless parameters like capillary number or the ratio of the viscosities. The sensitivity of the material functions with respect to these parameters has to be examined. Even for a coarse discretisation of the appropriate parameter space a very large number of different runs are needed.

Investigation of a new boundary condition for the macroscale between two different materials:

For a reconstructed porous media (SPI), which is composed of two different materials (grain size differs one order of magnitude) and separated by a more or less sharp interface, we investigate the macroscopic interface conditions proposed by SPIII.

Incorporation of a dynamic contact angle model into the LB simulation kernel followed by extensive validation:

Design and Implementation of Multi-Time-Relaxation Multiphase model and of an implicit LBM Evolution equation:

Applicants

Prof. Dr.-Ing. habil. Manfred Krafczyk Institute of Computerapplications in Civil Engineering Technical University of Brunswick Pockelsstr. 3 38106 Braunschweig Germany Phone: +49 (0) 531 391 7590 Fax: +49 (0) 531 391 7599 kraft@cab.bau.tu-bs.de

Dr. Ing. Jonas Tölke Institute of Computerapplications in Civil Engineering Technical University of Brunswick Pockelsstr. 3 38106 Braunschweig Germany Phone: +49 (0) 531 391 7592 Fax: +49 (0) 531 391 7599 toelke@cab.bau.tu-bs.de

Staff

Dipl.-Ing. Benjamin Ahrenholz Institute of Computerapplications in Civil Engineering Technical University of Brunswick Pockelsstr. 3 38106 Braunschweig Germany Phone: +49 (0) 531 391 7584 Fax: +49 (0) 531 391 7599 ahrenholz@cab.bau.tu-bs.de

Last update:  13:49 30/03 2005

Institutions

Institute for Computerapplications in Civil Engineering, Braunschweig Technical University

Dept. of Hydromechanics and Modeling of Hydrosystems,
Institute of Hydraulic Engineering,
University of Stuttgart

Paul Scherrer Institut,
ETH Zürich

Department of Soil Science and Soil Physics,
Institute of GeoEcology,
Braunschweig Technical University