title: Fluid flow in porous media : A combined numerical and experimental approach
Creators: name: Eichheimer, Philipp
Publisher: name: University of Bayreuth
Year: 2020
Subjects: subject: Fluid flow
subject: Porous Media
subject: 500

description: Earth’s plate tectonics provides the basis for different material cycles, which exchange chemical compounds, like water, between Earth’s surface and mantle. At subduction zones, the oceanic lithosphere sinks into the mantle, transporting both chemically bound water within minerals and free water within its pore space into Earth’s interior. At shallow depth the free water is expelled from the pore space through compaction. However, a significant amount of water remains chemically bound in hydrous mineral phases. With increasing pressure and temperatures those hydrous minerals break down, releasing water, which percolates into the mantle wedge. Those dehydration reactions provide the main source of water in subduction zones, causing partial melt in the mantle wedge and trigger volcanism at the Earth’s surface. As already small amounts of water have significant effects on chemical and physical properties of the mantle, it is therefore of crucial importance to constrain the amount of water entering the Earth’s mantle. Until now the distribution and total amount of water in Earth’s mantle is under debate and estimates for water storage in the deeper mantle range from 0.25 - 4 ocean masses. For this reason it is of major importance for several geoscience disciplines, including Hydrogeology, Petrophysics and Volcanology to investigate fluid flow and its related processes on various scales. A key parameter controlling fluid flow is the permeability of rocks. Thus, as permeability is a function of the rock microstructure, an accurate determination and prediction of this parameter is necessary. Numerical predictions, where laboratory measurements struggle, has become an important method to complement laboratory approaches. Employing high grid resolutions, this prediction becomes computationally very expensive, which makes it necessary to develop methods that maximize accuracy and efficiency. For this reason the method of stencil rescaling is implemented into the Finite Difference code LaMEM (Lithosphere and Mantle Evolution Model) by Anton Popov. The stencil rescaling method improves the description of the solid-fluid interface and therefore allows for a more accurate computation of permeability in porous media using Darcy’s law at low Reynolds numbers. The accuracy of this method is successfully verified by comparing numerical to analytical solutions for a set of simplified model setups. Results show that stencil rescaling significantly increases the accuracy at no additional computational costs. Additionally, the modeling framework is used to predict the permeability of a Fontainebleau sandstone and to demonstrate numerical convergence. Results show very good agreement with experimental measurements as well as with previous studies. As the flow of non-Newtonian fluids through porous media has gained importance in recent years due to, e.g. the use of nanofluids for enhanced oil recovery, additionally the ability of the code to simulate the flow of power-law fluids through porous media is also demonstrated. As in case of a Newtonian fluid, results show good agreement with analytical solutions. However, as most of Earth’s dynamics like magma migration and ground water flow occur on a larger scale, it is necessary to parameterize permeability, which can be used as input parameter to investigate fluid flow in large-scale numerical simulations. For this reason several soda-lime glass bead samples with various porosities are sintered. Microstructural parameters like effective porosity and effective specific surface are determined using image processing. Furthermore, flow properties like hydraulic tortuosity and permeability are computed using LaMEM. By fitting an analytical equation for the microstructural and flow properties to porosity, a modified Kozeny-Carman equation for isotropic low-porosity media is obtained. This permeability parameterization can be used to simulate fluid flow on the large-scale. In comparison to numerically computed and experimentally measured permeability values this parameterization shows good agreement. To investigate also the fluid flow on the macroscale results on modelling fluid flow in subduction zones are presented. In a first step a corner flow benchmark is performed successfully and a water migration scheme is implemented into the Finite Element code MVEP2. Water migration is modelled with the following three steps: 1) Determination of the amount of free water and bound water as well as the maximum storage capacity of each marker. 2) Extraction of the pressure gradients of the solid phase flow to compute Darcy velocities. 3) Advection of the free water along the computed Darcy velocities. Markers containing more chemically bound water than the storage capacity are oversaturated and dehydrate, whereas markers are undersaturated if the chemically bound water is below the water storage capacity, leading to hydration in case water is present. First simulations using this routine with different grid resolutions show that the total amount of water is conserved. Future studies are required to include temperature profiles and several normal faults, enriched with water, to finally investigate the effect on the resulting fluid flow within subduction zones.