Research in SFB 1313 aims to acquire the much-needed fundamental understanding of how interfaces affect flow, transport and deformation processes in porous-media systems. This will involve the challenging tasks of quantifying how the dynamics of fluid-fluid and fluid-solid interfaces in porous-media systems are affected by pore geometry, heterogeneity and fractures, and of developing mathematical and computational models that describe the effective behaviour of porous-media systems including the effects of interfaces that occur on much smaller spatial scales.
Project Area A: Free flow and porous-media flow
Most porous materials involve non-uniform solid surfaces. This project applies and further develops classical density functional theory (DFT) to study how chemical and structural heterogeneities of the porous material alter adsorption isotherms, wetting behaviour, surface tensions, and contact angles. Because water is the most important fluid for porous media, this project furthermore critically analyses the DFT formalism for water. Molecular simulations are conducted for assessing and improving the DFT model for water. With these developments, the project allows meaningful predictions of interfacial properties.
Exchange processes across a porous-medium free-flow interface occur in a wide range of environ-mental, technical and bio-mechanical systems. The primary objectives of this project are to (i) analyse and improve the theory, as well as (ii) offer solution methods for non-isothermal, multi-phase, multi-component flow and transport processes at a porous-medium free-flow interface and (iii) investigate the influence of these processes on both the porous medium and free-flow region for various application scales.
New, more general interface conditions are required to couple free-flow and porous-medium systems since traditional coupling concepts provide reliable results for simplified cases only. Averaging theory is a powerful mathematical tool that can be applied to derive such conditions. The objectives of this project are to (i) derive new interface concepts for single- and multi-phase flow systems using averaging techniques, (ii) validate the newly developed interface conditions, and (iii) develop robust and efficient numerical methods for coupled flow problems.
Drying and evaporation in porous media is relevant for many engineering processes and for soil cultivation. These processes occur over several scales, where the evolving liquid-gas interface is important to describe the evaporation at the pore scale, while its effect lies on the REV scale. Our goal is to provide a better mathematical description of REV-scale evaporation by starting with a pore-scale description of the relevant processes and using upscaling to derive an effective model at REV scale. The effect of the evolving interface is explicitly taken into account and different approaches to describe the evolving interface at the pore scale will be investigated.
Project Area B: Fracture propagation and fluid flow
Hydraulically induced fractures usually initiate at very small (microscopic) length scales and then merge to larger (macroscopic) crack discontinuities. The goal of the project is to resolve this inherent characteristic through the development of computational scale-bridging techniques for hydraulic fracturing of porous media. The project is divided in three steps: (i) Development of a general basis for the homogenization of porous media; (ii) Incorporation of a fracture phase-field at micro-scale; (iii) Incorporation of elastic-plastic effects at micro-level. The result will be a new quality in the modelling of hydraulic fracturing across length scales.
We describe fracturing porous solids with arbitrary pore content by two basic ingredients, the macroscopic Theory of Porous Media and the phase-field approach to fracturing. Initially, the solid is treated as a brittle elastic material that is permeable for arbitrary fluids in the sense of a Darcian pore-fluid flow. Under hydraulic fracturing conditions, cracks will open depending on fluid pressure and solid strength, and the fluid flow in the cracked zones changes from purely Darcian to Stokean type. Interfaces between the solid and the pore fluid are contributing to hydraulic-conductivity and fracturing conditions.
The propagation and bifurcation of fractures in fluid-filled porous media depends on the likewise inter-related flow in the pore space and on the mechanical displacement field in the solid matrix. Assuming that fractures cannot be homogenised but persist on a continuum-mechanical scale as sharp time-dependent interfaces, a discrete fracture-network approach is developed. The final task of the project is the construction of a multi-scale model that serves as the basis for numerical simu-lations by a moving mesh ansatz. In particular, the new approach accounts for the dynamical evolution of fractures and allows to integrate arbitrary flow processes within the fractures.
Fractured porous media are geometrically very complex. There are many competing model concepts to represent their structure in flow simulations; these models differ drastically in their level of geo¬metric detail and in their level of simplification and abstraction. Systematically choosing between these vastly different models, calibrating chosen models and specifying their predictive uncertainty is far from trivial. The goal of this project is to tackle the interlocked model-selection-and-calibration problem. Achieving this goal requires a list of algorithmic developments in the field of simulation-based Bayesian statistics.
We characterise static and evolving fluid-saturated fractures and fracture networks with high-resolution X-ray Computed Tomography. Besides the characterisation of the geometries of fractures, we aim for the quantification of the fractures’ apertures. This allows for the characterisation of hydro-mechanical coupling effects and the validation of combined numerical investigations. The experiments are performed in an X-ray-transparent triaxial cell under defined confining pressure and axial stresses. The experimental results are the basis for the adjacent quantification of coarse-grained effective material properties.
Project Area C: Fluid-solid phase change
We investigate the flow structure and the porosity-permeability relationship of porous media that undergo morphology modifications due to evaporation or microbially induced calcite precipitation, as well as wettability modifications of the solid-fluid interface due to fluid pH, composition, or salt con¬centration changes. We develop simulation methods based on coupled multi-phase and multi-component Lattice-Boltzmann and solute molecular dynamics simulations, capable of reproducing these processes in detail on the pore scale, yielding results to be used to improve existing continuum models.
Processes like multi-phase flow and reactive transport in porous media are encountered in many engineering applications. Such processes occur and interact on different scales and in complex domains. Particularly challenging is the case when evolving interfaces are encountered on the pore scale. These interfaces may separate two immiscible fluids flowing through the pores of a porous medium, or when the pore geometry is changing in time due to processes like dissolution or depo-sition. The focus of this project is on developing Darcy-scale mathematical models and suitable numerical schemes for such processes, taking explicitly into account the interfaces evolving at the pore scale.
The effectiveness of bone-cement injection during vertebroplasty is highly dependent on the cement-injection-distribution pattern, the interface effects between the porous bone structure and the initially liquid cement, as well as the curing process of the bone cement itself. Taking vertebroplasty as motivation, this project aims at taking into account interface and material deposition processes on the pore scale to describe material-injection processes in porous media on the REV (representative elementary volume) scale. The modelling process will be exemplified on vertebra-like structures.
Porosity and permeability are two major hydraulic properties that govern flow through porous media. Different kinds of processes can lead to alterations of the pore space which eventually change the hydraulic properties. This project focuses primarily on fluid-solid interfaces that are prone to change as a result of microbial activity. The alterations need to be measured experimentally and interpreted on the scales of interest by means of numerical simulations. It is also required to improve the efficiency of corresponding complex numerical simulation methods.
Fluid-solid reactions pose a challenge for modelling flow and transport in porous media due to the dynamic changes in the pore space and the associated alteration of the permeability. This project aims to use Magnetic Resonance Imaging and X-ray computer microtomography measurements on synthetic porous media made from glass beads and soil columns to experimentally elucidate differ¬ences in porosity-permeability relationships for three different fluid-solid reactions: salt precipitation during evaporation, microbially-induced calcite precipitation, and dissolution during chemical stimulation.
Project Area D: Benchmarks, computing, and visualization
The long-term goal of this project is to develop new visualization techniques to support the projects of the CRC in understanding flow, transport, and deformation phenomena occurring at interfaces in and around porous media. This requires the integrated visual analysis of processes captured across multiple fields to relate different quantities, analyse simulation ensembles, and compare simulations against experiments. The interactive exploration of large and heterogeneous volumes of data is achieved by efficiently using parallel architectures as well as in-situ data aggregation.
The aim of the project is to provide technical and numerical methods for the coupling of free flow and porous-media flow at the REV (representative elementary volume) scale. This involves the development of sophisticated methods in three basic coupling components: (i) iterative solvers ensuring a fast convergence towards the correct solution of the coupled system, (ii) data mapping between different discretisations used in the computational components of the simulation environ-ment, and (iii) point-to-point communication between several parallel codes.
The goal of this project is to formulate and conduct benchmarks which assist in the validation of several computational models developed within the proposed CRC. Here, the main challenge arises from the possibly large uncertainties that are present in the experimental data as well as in the simulation results. A so-called validation metric which compares system response quantities of an experiment with the ones from a computational model has to integrate these uncertainties in a rigorous way. In the proposed project, such validation metrics will be developed by means of a Bayesian validation framework that incorporates parameter and conceptual uncertainty.