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

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Open Access
Analysis of the influence of structures and boundaries on flow and transport processes in fractured porous media
(2005) Süß, Mia; Helmig, Rainer (Prof. Dr.-Ing.)
This thesis is focused on the evaluation of tracer-breakthrough curves for the purpose of identifying domain structures and material properties. Examples of such structures are single fractures, fracture systems, layers or lenses. The investigations are based on the analysis of numerically modelled as well as measured data of domains on laboratory-scale. The numerical simulations are conducted using a flexible model set-up allowing variations of domain characteristics as well as of boundary conditions. First, the influence of impervious domain boundaries on flow and transport measurements is investigated. Initially, the general influence of boundaries on selected flow and transport variables is discussed. Subsequently, the significance of the influence of, on the one hand, impervious boundaries, and on the other hand, structures on the variation of selected variables of flow and transport is compared. The analysis is based on simulated tracer-breakthrough curves of one homogeneous system with exclusively boundary influence and of ensembles of heterogeneous systems with structure influence only. It is concluded that the influence of the boundaries is of the same magnitude as the influence of the structures. Finally, the sensitivity of tracer-breakthrough curves to structure variations depending on the existence of boundaries is investigated. For this purpose, simulation results from heterogeneous systems with and without impervious boundaries are compared. It is concluded that, in general, the sensitivity of flow and transport results is increased if the domain is limited by impervious boundaries. The investigations show that general predictions of the influence of boundaries on the flow and transport behaviour can only be made in exceptional cases for domains with very simple structure distributions. For more complex domains, boundary effects must be investigated individually in order to exclude unfavourable experimental or numerical set-ups and in order to interpret measured or simulated data correctly. The work presented demonstrates new ways of analysing different aspects of the boundary influence. Second, possibilities and limitations of structure identification are investigated. Based on three groups of test cases of varying characteristics, typical shapes of tracer-breakthrough curves are discussed and the fundamental mechanisms that lead to a certain curve shape are identified. Using the experience gained, an approach which is based on the shape of tracer-breakthrough curves and the initial arrival times, is developed for locating structures and approximating their permeabilities. The identification result is first assessed by applying the approach to the known test cases. Subsequently, the applicability to unknown artificial as well as real cases is tested. For domains containing block-shaped structures the new approach yields satisfying results for both artificial and real domains. For domains containing a few significant fractures, it is a useful support for approximating the structure distribution. Despite deviations, the fundamental characteristics are approximated correctly. The newly developed approach should be considered as one possible method to be used in combination with all other available data in order to obtain accurate identification results.
Open Access
Beyond local equilibrium : relaxing local equilibrium assumptions in multiphase flow in porous media
(2014) Nuske, Philipp; Helmig, Rainer (Prof. Dr.-Ing.)
One of the most basic assumptions in the field of multiphase flow in porous media is that of local equilibrium. This work is a contribution to the study and understanding of this assumption. Assuming local equilibrium basically means that heat and mass transfer processes between phases take place instantaneously. For a number of applications, this assumption is questionable for various reasons. In the following, two of these reasons are illustrated by examples. *Supply of Non-Equilibrium* If there are sources present in the porous medium which unbalance the system, assuming local equilibrium for all phases is a very strong assumption in need of justification. Practically, this source can be the supply of non-equilibrated, i.e. not fully water saturated, air bypassing soil. The assumption that the air immediately becomes fully vapor-saturated might be a serious oversimplification. Heat sources in porous media are another reason to doubt the applicability of local equilibrium assumptions. An evident example is the cooling of severely damaged nuclear reactor cores. In this case, the solid phase continuously provides energy and complex phase-change processes occur. *Insufficient Equilibration Time* If the considered porous medium is thin, for example paper during drying processes, the short residence time of air makes the idea of immediate equilibration far-fetched. Another case of questionable applicability of local equilibrium assumptions comes from the field of steam-assisted subsurface remediation. In order to predict remediation success, the correct description of the high flow velocities as well as large temperature gradients that occur are crucial. What the systems described above have in common is that studying them experimentally is hard and/or expensive. Therefore, simulation technologies can be an important tool in this context. This work is a contribution to the study and understanding of such (non-) equilibrium situations in multiphase flow in porous media. In a first application of the non-equilibrium model developed here, a parameter study, motivated by evaporation from a porous medium, is conducted. In order to obtain the necessary input parameters (volume-averaged interfacial areas) a pore-network model is adapted and constitutive relations derived. Varying an unknown model parameter (scaling factor) within a range of values results in the physically expected behavior of the system. In order to put the study of non-equilibrium effects in multiphase flow in porous media on an experimental basis, a new platform is developed in collaboration with colleagues from the University of Utrecht. The experimental setup allows us to study thermal equilibration and immiscible displacement processes simultaneously in a transparent micro-model. This is accomplished by a setup which includes both an optical as well as an infrared camera, recording the same invasion process. Both the versatility and feasibility of the platform are demonstrated in qualitative findings and observations. Building on this, two different experimental runs are simulated by means of the model developed previously. In order to be able to use the non-equilibrium model, a new image-analysis procedure had to be developedfor the determination of constitutive relations. As the proposed scaling factor of heat transfer is still unknown, it had to be calibrated to the experimental observations. Remarkably, both simulations find that the same scaling factor results in the best reproduction of the experimental observations. In another effort to increase confidence in the model, a code intercomparison study is conducted. In this regard, the same technical application, a metallic evaporator, is simulated by two simulators developed independently. These are the model developed in this work and a model describing multiphase flow in porous media based on a mixture description. Although both models are different in terms of mathematics, numerics and the simulation environments employed, they produced very similar results. This was taken as a validation of the developed model. In summary, three things are accomplished in this thesis: a toolbox of models and methods allowing the study of local non-equilibrium effects in multiphase flow in porous media in a volume-averaged sense is developed and successfully applied to a number of different applications. Secondly, new procedures for sustainable software development and source code accessibility are developed. Thirdly, different ways to determine constitutive relations are developed and successfully applied.
Open Access
Capturing local details in fluid-flow simulations : options, challenges and applications using marker-and-cell schemes
(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2024) Lipp, Melanie Gloria; Helmig, Rainer (Prof. Dr.-Ing.)
Complex local flow structures appear in a wide range of free-flow systems, e.g. vortices build after obstacles. For understanding and predicting numerous processes, it is important to capture local details in free fluid flow, which is the focus of this work. Particularly, we are interested in local flow structures in free flow coupled to porous-medium flow. A better resolution of local structures in free flow can be achieved by refining computational grids, which is studied in this thesis. Particularly, we focus on finite-volume/finite-difference methods for the two-dimensional Navier-Stokes equations with constant density and constant viscosity, using the marker-and-cell method (pressures in cell centers, velocities on cell faces) and rectangular control volumes. There exists a variety of methods, with a range of characteristics, which can be used to refine computational grids. The first objective of this work was to develop for many different available approaches one common way of description of a class of methods within our focus and to display their similarities and differences. The second objective was to gain insight and in-detail understanding of the local-refinement-methods' behavior by examining one chosen method before numerical solution, i.e. by examining local truncation errors. The third objective was to gain further understanding of the local-refinement-methods' behavior as well as display examples, in which the chosen method is beneficial when neglecting computational-efficiency issues, by examining our chosen method after numerical solution, i.e. by examining actual numerical solutions.
Open Access
Coupled free and porous-medium flow processes affected by turbulence and roughness : models, concepts and analysis
(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2018) Fetzer, Thomas; Helmig, Rainer (Prof. Dr.-Ing.)
Open Access
Coupled free-flow-porous media flow processes including drop formation
(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2023) Veyskarami, Maziar; Helmig, Rainer (Prof. Dr.-Ing.)
Behavior of a coupled free-flow-porous medium system is determined by the interface between the two domains. Formation of droplets at the interface governs transport processes in the whole system by enormously affecting the exchange of mass, momentum, and energy between the free flow and the porous medium. A droplet that forms at the interface might grow or shrink due to the flow from the porous medium and evaporation from its surface into the free flow. It also might be detached from the interface by the free flow. An example of such phenomena in nature is formation of sweat droplets on the skin by perspiration and the resulted cooling effect through their evaporation into the surrounding air. Water management in fuel cells, cooling systems, and inkjet printing are just a few technical applications in which droplet formation at the interface between a free flow and a porous medium appears. In this work, we developed a novel model to describe the formation, growth and detachment as well as evaporation of droplets at the interface between a coupled free-flow-porous medium system. Pore-network modeling is used as a tool to capture pore-scale phenomena occurring in porous media. New coupling concepts between the free flow and the porous medium are developed, which include storing mass, momentum and energy in the droplet. The formation and growth of a droplet is described and a new approach is developed to include the impact of the growing droplet on the free-flow field. Description of the forces acting in the system is given and accordingly the droplet detachment is predicted. A clear description of the droplet evaporation is provided and the impact of free-flow and porous medium properties on the droplet evaporation have been analyzed.
Open Access
Coupling free flow and flow in porous media in biological and technical applications : from a simple to a complex interface description
(2014) Baber, Katherina; Helmig, Rainer (Prof. Dr.-Ing.)
The objective of this work is the development of model concepts and methods for the coupling of free flow and flow in porous media. Coupling concepts of varying complexity ranging from a simple to a pore-scale to a complex interface approach are derived. The main focus is the development and testing of an REV-scale coupling concept that accounts for drop dynamics at the interface. The developed coupling concepts are based on the assumption of thermodynamic equilibrium and on flux balances. The formulation of mechanical equilibrium in the pore-scale and complex interface concept is challenging due to the scale-dependent definition of pressure. The combination of microscopic and macroscopic pressure formulations causes pressure jumps at the interface and non-physical pressure gradients. Hence, an extensive discussion of the pressure conditions is given. The coupled model is implemented in the C++ simulator DuMux (Flemisch et al., 2011) using the mortar method. The applicability of the developed concepts is assessed on the basis of two applications: transvascular exchange and drop dynamics in PEM fuel cells. In Mosthaf et al. (2011) and Baber et al. (2012), we develop a simple interface concept for coupling non-isothermal compositional two-phase flow in the porous-medium with a non-isothermal compositional single-phase system in the free-flow region. The concept is based on the two-domain approach with a simple interface devoid of thermodynamic properties. In this work, the simple interface concept is applied to model transvascular exchange. The simulations reproduce filtration and reabsorption and reveal the influence of wall and tissue parameters on the final distribution of therapeutic agents. However, the complex structure of the micro-vascular wall and the influence of the different pathways cannot be resolved by the presented approach. In some applications, the complex structure of the interface and the processes happening therein cannot be described by a simple interface devoid of thermodynamic properties. In such cases, it might be beneficial to resolve the interface layer or interface region on the pore-scale. We present a first step towards a resulting coupled pore-/REV-scale model where the interface is described by a bundle-of-tubes approach. The coupling concept between the one-phase free-flow, the pore-scale and the two-phase porous-medium model is based on flux continuity and the assumption that pore-and REV-scale pressure are equal. We develop an REV-scale interface concept - the complex interface concept - that describes drop formation, growth and detachment on hydrophobic interface between free and porous-medium flow. The interface stores the mass and energy of the drops without resolving them. The direct exchange between free-flow and porous-medium region next to the drop is also part of the coupling concept since it preserves the exchange processes described by the simple interface concept. The fraction of the interface which is covered by drops is used to obtain an area-weighted average of the coupling conditions with and without drop so that coupling conditions for the whole interface are obtained. The complex interface concept captures drop formation, growth and detachment. These processes are influenced by the conditions of both the free-flow and porous-medium region. The temporal evolution of the drop volume is an outcome of the model. The number of drops that can form on the interface is defined a priori by choosing the size of a drop REV. Neither the influence of the drops on the free-flow conditions nor film flow or sliding and merging of drops is included since the focus is on the interface description. The model is applied to simulate drop formation in the cathode of PEM fuel cells. In fuel cells, water is generated by the electro-chemical reaction in the catalyst layer and flows through the hydrophobic porous fibre structure of the GDL. Reaching the GC, water forms drops on the hydrophobic interface between GC and GDL. The drops significantly influence the water management in fuel cells which must be optimised to achieve good performance and durability. The numerical results show that it is possible to include drop dynamics in the REV-scale coupling conditions between free and porous-medium flow. Drop formation, growth and detachment are represented correctly, if the evaporation from the drop surface is neglected. The interface-coverage ratio, which is an indicator for the quality of the water management, can be predicted. The simulations for a higher number of drops suggest that the interface conditions dominate the system. A parameter study shows that interface wettability and free-flow velocity have a significant influence on the drop growth and detachment. In summary, this work reveals the potential of the developed coupling concepts to deal with realistic problems and exposes the need for further improvement and development.
Open Access
A decoupled model for compositional non-isothermal multiphase flow in porous media and multiphysics approaches for two-phase flow
(2010) Fritz, Jochen; Helmig, Rainer (Prof. Dr.-Ing.)
The demands of computational resources of a simulator and the necessary efforts in defining boundary and initial conditions increase with the physical complexity of a model. Thus, a trade-off between physical accuracy and computational demands of a model are made. In many practical applications of porous media flow simulators, the most complex processes are confined to a small part of the model domain. In such a case, either high complexities are neglected in favor of a slim model or all processes are captured with a complex model which is superfluous in large parts of the domain. As a compromise between both options, an interface coupling method is introduced. It couples simple and complex models and adapts the resulting multiscale model to the actually occurring physical processes. As a basis for this, a decoupled formulation for non-isothermal compositional multiphase flow is introduced. It provides the advantage that the size of the linear system of equations does not grow with the number of phases or components involved. This work reviews the common concepts for the description of multiphase flow in porous media and provides a consistent derivation of the conservation equations of non-isothermal compositional flow and transport processes. Based on these equations, decoupled formulations for isothermal and non-isothermal compositional flow are derived using the concept of local conservation of total fluid volume. The implementation of the derived formulations into a finite volume method with an implicit pressure explicit concentration time discretization is presented. The resulting simulation tool is tested and verified with results from different experimental and computational investigations and its range of applicability is considered. Based on the decoupled formulations derived before, an isothermal and a non-isothermal multiphysics concepts for the transition of complexity within a porous media domain is presented. Furthermore, a simple and robust subdomain control scheme is developed which assures optimal adaption of the model complexity to the occurring processes at any time. Both models are implemented and tested towards their accordance with the globally complex decoupled models. It is shown that computational demands of a simulator can be lowered by incorporation of the multiphysics schemes. Finally, further ideas for the extension of the multiphysics towards more complex systems and possible interfaces with multiscale methods are considered.
Open Access
Development of efficient multiscale multiphysics models accounting for reversible flow at various subsurface energy storage sites
(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2021) Becker, Beatrix; Helmig, Rainer (Prof. Dr.-Ing.)
Energy storage is an essential component of future energy systems with a large share of renewable energy. Apart from pumped hydro storage, large scale energy storage is mainly provided by underground energy storage systems. In this thesis we focus on chemical subsurface storage, i.e., the storage of synthetic hydrogen or synthetic natural gas in porous formations. To improve understanding of the complex and coupled processes in the underground and enable planning and risk assessment of subsurface energy storage, efficient, consistent and adequate numerical models for multiphase flow and transport are required. Simulating underground energy storage requires large domains, including local features such as fault zones and a representation of the transient saline front, and simulation times spanning the whole time of plant operation and beyond. In addition, often a large number of simulation runs need to be conducted to quantify parameter uncertainty, and efficient models are needed for data assimilation as well. Therefore, a reduction of model complexity and thus computing effort is required. Numerous simplified models that require less computational resources have been developed. In this thesis we focus on a group of multiscale models which use vertically integrated equations and implicitly include fine-scale information along the vertical direction that is reconstructed assuming vertical equilibrium (VE). Classical VE models are restricted to situations where vertical equilibrium is valid in the whole domain during most of the simulated time. This may not be the case for underground energy storage, where simulated times may be too short and locally a high degree of accuracy and complexity may be required, e.g., around the area where gas is extracted for the purpose of energy production. The three core chapters of this thesis present solutions to adapt VE models for the simulation of underground energy storage, with increasing complexity.
Open Access
Diskretisierungsansätze zur Modellierung von Strömungs- und Transportprozessen in geklüftet-porösen Medien
(2003) Neunhäuserer, Lina; Helmig, Rainer (Prof. Dr.-Ing.)
Im Zusammenhang mit z.B. der Trinkwassergewinnung aus Kluftaquiferen oder der Beurteilung von Deponiestandorten kommt der Simulation von Strömungs- und Transportprozessen in geklüfteten Systemen eine große Bedeutung zu. Die oft sehr unterschiedlichen hydraulischen Eigenschaften von Kluft und umgebender Gesteinsmatrix prägen das Strömungs- und Transportverhalten stark. Unter gesättigten Bedingungen können Klüfte bevorzugte Fließwege darstellen, während die umgebende Gesteinsmatrix dagegen häufig wie ein Speicher wirkt. Diese gegensätzlichen physikalischen Prozesse müssen bei der numerischen Simulation von dem zur Anwendung kommenden Modellkonzept mit den dazugehörigen Diskretisierungsverfahren in Abhängigkeit von der Fragestellung hinreichend erfasst werden.Vor diesem Hintergrund werden in der vorliegenden Arbeit Diskretisierungsansätze für die Simulation von Strömungs- und Transportprozessen in geklüftet-porösen Medien entwickelt und untersucht. Als Grundlage wird der kombinierte Modellansatz verwendet. Die Klüfte werden dabei üblicherweise mit Elementen niedrigerer Dimension diskretisiert als die Matrix. Dieses Vorgehen wird als niederdimensional bezeichnet. Dabei ist allerdings die lokale Flusserhaltung am Kluft-Matrix-Übergang nicht gewährleistet und der zugrunde liegende physikalische Prozess gegebenenfalls nicht richtig erfasst. Um hier eine bessere Prozessdarstellung zu erreichen, wird als neuer Ansatz eine äquidimensionale Formulierung vorgestellt, der Kluft und Matrix mit Elementen gleicher Dimension beschreibt. Es werden eine Reihe etablierter numerischer Diskretisierungsansätze aus dem Bereich der Finite-Elemente-und Finite-Volumen-Verfahren hinsichtlich ihrer Eignung sowohl für die nieder- als auch für die äquidimensionale Approximation der Strömungs- und Transportprozesse in beliebig geklüfteten Systemen analysiert. Als Resultat dieser Untersuchung wird für die Strömung ein Boxverfahren und ein gemischt-hybrides Finite-Elemente-Verfahren, für den Transport ein Boxverfahren mit unterschiedlichen Upwinding-Strategien ausgewählt. Die im Rahmen der Modellbildung implementierte und verwendete Software für Kluft- und Netzgenerierung und für die numerische Diskretisierung wird vorgestellt. Die Anwendbarkeit und die Eigenschaften sowohl der äquidimensionalen im Vergleich mit der niederdimensionalen Formulierung als auch der gewählten numerischen Diskretisierungsverfahren im Hinblick auf diese beiden Ansätze wird anhand von Modellbeispielen von ansteigend geometrischer Komplexität diskutiert. Die Ergebnisse zeigen, dass die Verwendung eines äquidimensionalen Ansatzes bei langsameren Systemen mit Klüften quer zur Hauptströmung deutliche Auswirkungen auf die approximierte Lösung zeigt, während bei schnelleren Systemen eher lokale Effekte auftreten. Der Einsatz gemischt-hybrider Finiter Elemente ist bei äquidimensionaler Formulierung sinnvoll. Das für den Transport verwendete Boxverfahren mit Streamline Orientation in der Matrix erzeugt deutlich steilere Konzentrationsfronten im Matrixbereich als mit reinem Fully Upwinding.
Open Access
Efficient modeling of environmental systems in the face of complexity and uncertainty
(2014) Oladyshkin, Sergey; Helmig, Rainer (Prof. Dr.-Ing.)
Strong industrial development of the last century has led to a significant increase in public demand for different types of energy and, as a consequence, to an enormous increase in demand for natural resources. Naturally, all types of nature resources form a part of our surrounding environment. In order to extract natural resources a wide variety of technologies has been developed. This has led to a strong rise in interventions in the environment continuing up to the present days. At the same time, environmental systems form one of the largest and most important classes of complex dynamic systems. For this reason, society needs a better understanding of the environment in order to have an efficient and safe interaction for the sake of maximized welfare and sustainability in resources management. In particular, the ability to predict how the environment changes over time or how it will react to planned interventions is indispensable. However our surroundings behave non-trivially in various time and spatial scales. Moreover, many environmental systems are heterogeneous, non-linear and dominated by real-time influences of external driving forces. Unfortunately, a complete picture of environmental systems is not available, because many of these systems cannot be observed directly and only can be derived using sparse measurements. Moreover, environmental data is hardly available and expensive to acquire. Overall, this leads to limited observability, and an inherent uncertainty in all modeling endeavors. Still, research over several decades has showed that modeling plays a very important role in reconstructing (as far as possible) the complete and complex picture of the environment systems and offers a unique way to predict behavior of such multifaceted systems. The current thesis contains research in the field of environmental modeling in the face of complexity and uncertainty. The presented thesis is divided into three parts and refers to diverse applications such as underground petroleum reservoirs, groundwater flow, radioactive waste deposits and storage of energy relevant gases. Part 1 focuses on physical concepts and offers several possibilities to accelerate the modeling process. Part 2 deals with efficient model reduction methodologies for uncertainty quantification. Part 3 demonstrates application to the storage of energy relevant gases in geological formations and discusses related challenges.
Open Access
Evaluation of CO2 injection processes in geological formations for site screening
(2009) Kopp, Andreas; Helmig, Rainer (Prof. Dr.-Ing.)
The concentration of greenhouse gases in the atmosphere has increased due to tremendous human fossil fuel consumption since the Industrial Revolution. This is most likely the cause for an observed global increase in the average temperature and for the changing climate. It is expected that further global warming will have drastic ecological and economic impacts. No single technology will be sufficient to achieve the necessary emission reductions. Carbon dioxide capture and storage (CCS) is a promising technology which could make a substantial contribution. It is a process which captures CO2 from large local sources and then stores it away from the atmosphere. Storage capacity estimates for deep saline aquifers are most promising. The initial procedure for selecting a few aquifers for a CCS project is called site screening. Aquifers identified in site screening then have to prove their suitability in further investigations. Site screening is a challenging task, since usually few data are available and the prognosis of the complex processes occurring in a reservoir after CO2 injection is difficult. This study aims at improving the insight into CO2 injection processes in geological formations to assist site screening. The criteria in site screening include the estimation of the storage capacity, which should be sufficient to store the long-term production of the CO2 source, and the long-term ability to store CO2 ,which is related to the efficiency of the project and risk arising due to possible CO2 leakages. At first, the statistical characteristics of storage sites in potential geological formations are calculated by analysis of a large database. The parameter ranges and distributions are used to define typical reservoirs and serve as a basis for generating random reservoir setups respecting statistical characteristics. The relation of forces occurring in reservoirs after CO2 injection is analysed by dimensional analysis. By the identification of dominant forces and processes, reservoirs with different parameter setups are compared with respect to their potential CO2 storage capacity and risk. A sophisticated concept for estimating the CO2 storage capacity of geological formations is developed. Detailed, time-dependent storage-capacity estimates are calculated in numerical experiments. The results are interpreted using the simultaneously calculated ratios of forces. The influence of individual reservoir parameters on storage capacity and risk is investigated in a sensitivity analysis. Finally, a risk analysis on potential CO2 leakage through pre-existing wells is performed. In numerous numerical experiments, individual parameters are randomly sampled from the statistical parameter distributions and leakage is calculated. A risk surface is derived which represents the average risk for CO2 leakage through pre-existing wells for any site with unknown reservoir properties.
Open Access
Experimental investigations on longitudinal dispersive mixing in heterogeneous aquifers
(2005) Jose, Surabhin Chackiath; Helmig, Rainer (Prof. Dr.-Ing.)
Reactive mixing of compounds in porous media is a topic of current research interest because accurate estimation of reaction rates are crucial in planning aquifer remediation methods. It is suggested that relative parameters for dilution are better quantities to estimate reaction rates than the generally used classical macrodispersion coefficients. Most of the concepts developed in the field of reactive mixing are based on theoretical and numerical studies, and have not been experimentally tested. In this thesis, reactive mixing experiments are carried out in two different setups and the applicability of some of the existing numerical and theoretical studies to the observed data is tested. Two types of experimental setups - a homogeneously packed one-dimensional column setup and a heterogeneously packed two-dimensional sandbox setup - are used in the study. The column is 2m long with an inner diameter of 10cm, while the sandbox has dimensions 14m x 0.5m x 0.13m. Silica sand is used to fill both setups. The heterogeneity in the sandbox resembles the sedimentation pattern in nature. A conservative test and a reactive test each is conducted in both setups. Fluorescein is used as both the conservative and the reactive tracer. Dilution coefficients are estimated from the temporal moments of the conservative breakthrough curves obtained within in the porous media. Fiber optic fluorometry is used as the point measurement system. The measurement tip of the optic fiber probes has a diameter of 2.5mm. Reactive mixing in the porous media is predicted from the dilution coefficients estimated from the conservative tests, and is compared with the actual reactive mixing from the reactive tests. I conclude that point-like measurements provide reliable information of dilution and mixing in porous media, and therefore are effective enough in predicting product formation, provided sorption parameters are effectively quantified. I found that regions with large contrast in hydraulic conductivity give opportunity to enhanced mixing. Considering the typical length scales of the heterogeneities, the experimental findings are qualitatively in agreement with the linear stochastic theory.
Open Access
Experimental investigations on transverse dispersive mixing in heterogeneous porous media
(2005) Rahman, Md. Arifur; Helmig, Rainer (Prof. Dr.-Ing.)
Transverse mixing has been identified to be a controlling factor in natural attenuation of extended biodegradable plumes originating from continuously emitting sources in the subsurface. The heterogeneity of natural formations causes both spreading and mixing such plumes with oxidants from the ambient groundwater. Out of these two processes, it is only the transverse mixing with oxidants from the ambient groundwater that facilitates degradation. This thesis offers a promising approach to the characterization and quantification of transverse dispersion coefficients in heterogeneous porous media. The aim is to deepen the understanding of transverse dispersion and mixing in natural heterogeneous porous media. Particularly, I develop an experimental method to determine transverse dispersion coefficients. Then, I investigate to what extent the heterogeneity of natural porous media enhances transverse mixing. To this end, I conduct and evaluate conservative and reactive tracer tests in one-dimensional as well as quasi two-dimensional laboratory and technical scale sandboxes. The heterogeneous filling used in these experiments mimics natural sediments including a distribution of different hydro-facies and micro-structures within sand lenses. The effective dispersion coefficient which describes mixing and dilution excludes the spreading of plumes. Without knowledge of spreading and meandering, it is not possible to determine the transverse effective dispersion coefficient from concentration profiles in vertical cross-sections. In order to determine this coefficient from such profiles, I corrected for the effects of plume meandering. The vertical transverse dispersion coefficients I determined from the experiments are fairly small and depend on travel time. This is as expected from analytical expressions for the time-dependent effective dispersion coefficient based on stochastic linear theory. The values obtained are less than an order of magnitude larger than the effective molecular diffusion coefficient. For typical groundwater flow velocities, therefore, the velocity-independent contribution to transverse dispersion cannot be ignored. Analytical expressions for the transverse vertical macrodispersion coefficient, also based on stochastic linear theory, predict only a small increase towards the large-time limit. In my experiments, I found that there is no significant increase in the transverse dispersion coefficient with increasing travel distance. This indicates that the heterogeneity has hardly any impact on vertical transverse mixing. In general, my findings are in very good agreement with the results of stochastic linear theory.
Open Access
Flow and transport modelling of fractured aquifers based on a geostatistical approach
(2008) Assteerawatt, Anongnart; Helmig, Rainer (Prof. Dr.-Ing.)
Aquifer-analogue studies established in the petroleum reservoir have been widely used for characterizing fractured aquifer systems because detailed analysis can be performed practically and characteristics of fractured systems obtained on this scale can be upscaled to fractured systems on field scales. A discrete model approach is an attractive alternative compared with a continuum model approach for aquifer analogue studies because there is no a priori assumption that a fractured system behaves as a continuum, and the effect of individual fractures can be explicitly investigated. However, a generation of a representative'' fracture network remains a challenging task when the discrete model is applied. In a case where a fracture network is embedded in a porous matrix, known as a fracture-matrix system, the numerical study of flow and transport processes requires a full two- or three-dimensional description of the fractures and the surrounding matrix. This causes a rise in computational demand for the numerical study of the flow and transport behavior of such a fractured system. The overall purpose of this work is to improve the study of flow and transport processes in a fracture-matrix system on an analogue scale by using a discrete fracture model. An important prerequisite for this is the generation of a representative'' fracture network. Subsequently, an alternative approach to advective-dispersive transport which requires high computational demand for simulating transport in a fracture-matrix system has to be considered. In the first part of this work, a geostatistical fracture generation (GFG) which integrates statistical geometries and spatial characteristics has been developed and the technique for evaluating spatial characteristics in terms of a standardized variogram, neighborhoods, a fracture-cell density and a variance has been presented. In the following part, streamline tracing (STR) in a fracture-matrix system has been introduced as an alternative to advective-dispersive transport (ADT). The comparative study of geostatistical fracture generation (GFG) and statistical fracture generation (SFG) shows that the spatial characteristics of a fracture network observed from the field as well as the flow and transport behavior of a fracture-matrix system (such as discharge, peak arrival time and mean effective time) are better represented by the results of GFG than those of SFG. Hence, integrating the spatial characteristics and the statistical geometries in GFG have improved the discrete fracture generation and the fractured system behavior can be better predicted. Furthermore, the transport behavior in terms of an accumulated breakthrough curve (AccBTC) and a breakthrough curve (BTC) of fracture-matrix systems are investigated by using streamline tracing (STR) and compared with the results obtained by using advective-dispersive transport (ADT). STR shows significant reduction in computation time and clearly less numerical diffusion in comparison with ADT. In the cases considering a single fracture and systematically distributed fractures in a porous matrix, the effect of fast flow in fractures and slow flow in matrix, which is obviously noticed in STR, is smeared out due to the numerical diffusion in ADT. In complex fracture-matrix systems, numerical diffusion in ADT delays plume migration, whereas purely advective transport in STR leads to fast solute transport. As a result, the difference between the AccBTCs and the BTCs from the two approaches are clearly distinguished. Further investigations involving comparisons with experimental or field studies have to be carried out in order to validate the results of the two approaches.
Open Access
Model concepts for coupling free flow with porous medium flow at the pore-network scale : from single-phase flow to compositional non-isothermal two-phase flow
(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2020) Weishaupt, Kilian; Helmig, Rainer (Prof. Dr.-Ing.)
Open Access
Modeling and analysis of coupled porous-medium and free flow with application to evaporation processes
(2014) Mosthaf, Klaus; Helmig, Rainer (Prof. Dr.-Ing.)
Exchange processes between fluid-filled porous media and an adjacent free flow occur in a wide range of natural and technical systems. In the course of these processes, the flow dynamics in the porous domain and in the free flow exhibit a strong interdependency, which is often controlled by mechanisms at the common interface. Understanding and modeling these interactions is decisive for divers technical, medical and environmental applications. Prominent technical examples are the drying of products such as food, concrete or clothes. Further technical examples comprise landmine detection, industrial filtration processes, and the flow and transport processes in proton exchange membrane fuel cells (PEM-FC). A possible medical application is the exchange and transport of substances like therapeutic agents between blood vessels and tissue in the human body. Evaporation from natural soils as an environmental example is an extremely important process, since it constitutes a dominant part of the terrestrial water and energy balance and is actively involved in a variety of climatic processes. On the one hand, evaporation processes are decisively influenced by the prevailing ambient conditions, such as flow velocity, temperature and air humidity, and, on the other hand, by the porous-medium system with its fluid and solid properties and flow dynamics. A good understanding of the ongoing processes and elaborate modeling tools are crucial for climate modeling and water resources management, particularly in arid regions. The main focus of this thesis is on this environmental application: the modeling and analysis of evaporation processes from porous media like bare soils or sands which are exposed to an adjacent free flow. The objectives of this study are on one hand the development of a detailed coupled model which allows the simulation of a two-phase porous-medium system in conjunction with a single-phase free flow, and on the other hand to conduct a comprehensive analysis of the relevant processes for the mass, momentum and energy transfer of the two flow compartments. A major goal is to advance the development of an elaborate model for evaporation processes from porous media on the REV scale. This model has to take the mutual influence of the two flow compartments and the processes occurring at the common interface into account to allow for a detailed analysis of the influencing quantities. Theoretical and experimental evidence suggests that the interface between free flow and porous medium plays a crucial role for modeling evaporation processes on the REV scale.
Open Access
Modeling water transport at the interface between porous GDL and gas distributor of a PEM fuel cell cathode
(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2022) Michalkowski, Cynthia; Helmig, Rainer (Prof. Dr.-Ing.)
Operating vehicles with polymer electrolyte membrane (PEM) fuel cells is a promising technology for reducing traffic-related greenhouse gas emissions. In a PEM fuel cell, hydrogen and oxygen react producing water, electric energy, and heat. Oxygen is consumed on the cathode side of the cell, while the excess water must be removed to prevent the so-called flooding (blockage of the transport paths). A sophisticated water management is crucial for improved operating conditions of a PEM fuel cell. Therefore, it is necessary to understand the transport mechanisms of water throughout the cell constituents, where an intelligent use and drainage of the water buffer can be used to enhance the performance of the fuel cell. Pore-scale modeling of gas diffusion layers (GDLs) and the gas distributor has been established as a favorable technique to investigate the ongoing processes. A particular challenge is the investigation of the interface between the GDL and the gas distributor. Here, multi-phase flow in the porous material of the GDL is combined with the free flow in the gas distributor resulting in strong interaction. Different interface processes occur based on the pore-local structural properties, such as surface wettability and interaction with the gas flow in the gas distributor. At the interface between hydrophobic porous GDL and the hydrophilic side walls of the gas distributor, the fluids interact with the differently wetting surfaces. This results in complex pore-scale transport processes in the pores located at the interface. In the channels of the gas distributor, drops emerging from the porous domain at the interface have a strong influence on the exchange of mass, momentum, and energy between the two flow regimes. Additionally, we also consider transport processes of the gas phase between the GDL and the gas distributor, where no water breakthrough occurs.
Open Access
Modellierung von Kluftaquifersystemen: Geostatistische Analyse und deterministisch-stochastische Kluftgenerierung
(2002) Silberhorn-Hemminger, Annette; Helmig, Rainer (Prof. Dr.-Ing.)
Der Schwerpunkt der vorliegenden Arbeit liegt in der Untersuchung des räumlichen Verhaltens von Klüften unter Anwendung einer geostatistischen Analyse sowie in der Entwicklung eines Kluftgenerators zur dreidimensionalen deterministisch - stochastischen Simulation von Kluft - Strukturmodellen. Diese Strukturmodelle dienen als Basis für eine anschließende numerische Modellierung der Strömungs- und Transportprozesse in einem Kluftaquifersystem. Zunächst gilt es, Kriterien und Eigenschaften festzulegen, mit deren Hilfe ein geklüftetes Gestein charakterisiert werden kann. Diese Kriterien und Eigenschaften müssen im Feld oder im Labor qualitativ und quantitativ zu erfassen und beispielsweise durch einen funktionalen Zusammenhang zu beschreiben sein. Für den Aufbau eines Strukturmodells ist in erster Linie die geometrische Beschreibung eines Kluftsystems von Interesse. Hierzu wird das Kluftsystem bzw. die Kluft in einzelne Komponenten zerlegt. Man muss dabei beachten, dass die ursprüngliche "Einheit" eines Kluftsystems durch diese Vorgehensweise aufgegeben wird. Eine univariate statistische Analyse der einzelnen Kluftparameter liefert keinen Hinweis auf die räumliche Variabilität der einzelnen Parameter. Eine zusätzliche geostatistische Analyse bietet die Möglichkeit, weitere Informationen, insbesondere bzgl. des räumlichen Verhaltens der Klüfte, erlangen zu können. Dadurch ist eine umfassendere Charakterisierung des Kluftsystems gegeben. Am Beispiel der geostatistischen Analyse des Kluftaquifersystems Pliezhausen werden die Oberflächenkartierungen der Kluftspuren des Feldversuchsblocks hinsichtlich ihrer räumlichen Variabilität untersucht und die Ergebnisse vorgestellt. Der entwickelte 3D - Kluftgenerator FRAC3D, mit dem Kluft - Strukturmodelle, die die Basis für die diskrete Modellierung von Strömungs- und Transportvorgängen im geklüfteten Gestein darstellen, generiert werden können, wird vorgestellt. Die Kluftgenerierung hat hierbei die Aufgabe, basierend auf den im Feld und im Labor aufgenommenen Strukturinformationen, ein diskretes Strukturmodell zu erstellen. Sie stellt dabei das Bindeglied zwischen der Natur und dem numerischen Modell dar. Anhand ausgewählter Beispielrechnungen wird die erfolgreiche Modellbildung mit den Teilschritten Kluftgenerierung, Netzgenerierung sowie Strömungs- und Transportsimulationen von Kluftaquifersystemen aufgezeigt.
Open Access
Modelling and analysis of multicomponent transport at the interface between free- and porous-medium flow - influenced by radiation and roughness
(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2021) Heck, Katharina Klara; Helmig, Rainer (Prof. Dr.-Ing.)
Open Access
Modelling of biofilm growth and its influence on CO2 and water (two-phase) flow in porous media
(2009) Ebigbo, Anozie; Helmig, Rainer (Prof. Dr.-Ing.)
Bacterial biofilms are groups of microbial cells attached to surfaces and to each other. Cells in a biofilm are protected from adverse external conditions. In natural environments, this attached mode of growth is more successful than the suspended mode, and a major portion of microbial activity takes place at surfaces. In porous media, biofilms are used as bioreactors (e.g, in wastewater treatment) and as biobarriers (e.g., in enhanced oil recovery). They are also used in the containment and degradation of contaminants in groundwater aquifers. It has been proposed that biofilms be used as biobarriers for the mitigation of carbon dioxide (CO2) leakage from a geological storage reservoir. The concentration of greenhouse gases -- particularly carbon dioxide (CO2) -- in the atmosphere has been on the rise in the past decades. One of the methods which have been proposed to help reduce anthropogenic CO2 emissions is the capture of CO2 from large, stationary point sources and storage in deep geological formations. The caprock is an impermeable geological layer which prevents the leakage of stored CO2, and its integrity is of utmost importance for storage security. As mentioned above, biofilms could be used as biobarriers which help prevent the leakage of CO2 through the caprock in injection well vicinity. Due to the high pressure build-up during injection, the caprock in the vicinity of the well is particularly at risk of fracturing. The biofilm could also protect well cement from corrosion by CO2-rich brine. The goal of this work is to develop and test a numerical model which is capable of simulating the development of a biofilm in a CO2 storage reservoir. This involves the description of the growth of the biofilm, flow and transport in the geological formation, and the interaction between the biofilm and the flow processes. Important processes which are accounted for in the model include the effect of biofilm growth on the permeability of the formation, the hazardous effect of supercritical CO2 on suspended and attached bacteria, attachment and detachment of biomass, and two-phase fluid flow processes. The partial differential equations which describe the system are discretised in space with a vertex-centered finite volume method, and an implicit Euler scheme is used for time discretisation. The model is tested by comparing simulation results to experimental data. In a test case simulation, the model predicts the extent of biomass accumulation near an injection well and its effect on the permeability of the formation. The simulations show that the biobarrier is only effective for a limited amount of time. Regular injection of nutrients would be necessary to sustain the biofilm. In future work, the model could be extended to account for the active precipitation of minerals by the biofilm which would lead to a more enduring barrier. The model also needs to be extended to account for more than one growth-limiting factor. This would allow for the simulation of injection strategies which aim at growing a biofilm at some distance from the injection well.