Browsing by Author "Helmig, Rainer (Prof. Dr.-Ing. habil.)"

Now showing 1 - 2 of 2

Open Access
Multi-scale modeling of multi-phase-multi-component processes in heterogeneous porous media
(2006) Niessner, Jennifer; Helmig, Rainer (Prof. Dr.-Ing. habil.)
Flow and transport phenomena in porous media are the governing processes in many natural and industrial systems. Considering the flow and transport processes on the one hand, they occur on different spatial and temporal scales and may also differ locally. Highly complex processes may take place in one part of the system necessitating an examination of the processes on a fine spatial and temporal scale, while in other parts of the system, physically simpler processes may take place allowing an examination on a coarser scale. Considering the porous medium on the other hand, its heterogeneous structure shows a high dependence on the spatial scale. The porous medium is generally heterogeneous on every spatial scale, but different kinds of heterogeneities predominate on different scales. To study these issues, a domain with randomly distributed heterogeneities is considered where complex multi-phase--multi-component processes are relevant only in a small (local) subdomain. This situation might well be an LNAPL contamination in the unsaturated zone of the groundwater, where complex three-phase--three-component processes take place in a subdomain in and around the contaminated zone. This subdomain needs fine resolution as the complex processes are governed by small-scale effects. For a comprehensive fine-scale model taking into account multi-phase--multi-component processes as well as heterogeneities in the whole (global) model domain, the data collection is often far too expensive and the computational effort is high. Therefore, a general multi-scale concept is developed where on the one hand, the global flow field influences the local multi-phase--multi-component processes on the fine-scale. On the other hand, the coarse-scale effects of the fine-scale multi-phase--multi-component processes in the subdomain are captured by source / sink terms and the coarse-scale effects of fine-scale heterogeneities by a macrodispersion term. Specifically, a fine-scale pressure equation is solved globally to obtain a fine-scale velocity field. Equations accounting for the total concentrations of components are solved in a local domain on a fine scale. An averaged velocity as well as a source / sink term resulting from the concentration solution are passed to an upscaled coarse-scale saturation equation. The overall algorithm is presented and tested for locally occurring two-phase--two-component as well as for locally occurring three-phase--three-component processes in homogeneous and different heterogeneous domains, for both linear and nonlinear model equations. Various test examples are used to investigate the quality of the algorithm by studying the error introduced due to the coarse-scale form of the saturation model. Furthermore, the computing times of the model in which the total concentration equations are solved only locally are compared to the computing times of the model in which the concentration equations are solved globally in the whole domain. It is shown, that the algorithm developed in this work provides a convenient, general and expandable tool for modeling processes of different complexity occurring at different locations and on different scales.
Open Access
The role of interfacial areas in two-phase flow in porous media : bridging scales and coupling models
(2010) Niessner, Jennifer; Helmig, Rainer (Prof. Dr.-Ing. habil.)
This habilitation deals with a thermodynamically consistent modeling of two-phase flow in porous media which is extremely relevant for the understanding, the prediction, and optimization of the processes in many environmental, technical, and biological systems. Among these are the storage of carbon dioxide in the subsurface, methane migration from abandoned coal mines, the migration of radioactive gases from nuclear waste disposal sites (environmental systems), the processes in fuel cells and heat exchangers (technical systems) or the interaction between blood vessels and interstitial space (biological systems) which is very important for cancer therapy. The presented thermodynamically consistent model of two-phase flow in porous media is the first to numerically account for the extremely important role of phase-interfacial areas. This is put into practice through use of a rational thermodynamics approach by Hassanizadeh and Gray [1990] which not only includes interfaces as parameter in the equations, but additionally as entities allowing the formulation of conservation equations for interfaces. To be exact, conservation equations of mass, momentum, energy, and entropy are formulated on the pore scale for phases and interfaces and volume-averaged to the macro scale. The entropy productions of the entropy conservation equations are used to formulate the second law of thermodynamics. A speciality of the approach is the fact that thus, constitutive relationships do not need to be empirically formulated, but can be obtained by exploiting the residual entropy inequality. The aim of this work is to make the thermodynamically consistent and physically-based model accessible to numerical modeling allowing to represent effects which could otherwise not (or only using completely empirical approaches) be described. Among these are capillary hysteresis as well as the kinetics of mass and energy transfer between phases as these transfer processes take place across interfaces and thus, are highly dependent on them. Based on indicators and dimensionless quantities, the integration of the interfacial-area-based model into a multi-scale multi-physics framework is shown. This allows for the solution of the physically-based and thermodynamically consistent model whenever this is necessary and the solution of the empirical, but less costly, classical model wherever and whenever the physical situation allows. With such an approach, computing times and the amount of data needed can be drastically reduced.