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Item Open Access Two-phase flow processes with dynamic effects in porous media - parameter estimation and simulation(2006) Manthey, Sabine; Helmig, Rainer (Prof. Dr.-Ing.)This study contributes to the understanding of dynamic effects in the capillary pressure-saturation relationship on the local scale and macroscale as well as giving an assessment as to when these effects might need to be taken into account for the evaluation of two-phase flow processes. In a general form, the rate-dependent Pc-Sw relationship as analysed here postulates that the difference between the non-wetting and wetting phase pressure minus the equilibrium capillary pressure is a linear function of the rate of change of saturation, introducing the factor of proportionality tau. This extended Pc-Sw relationship is examined in this study under three aspects. In order to identify flow regimes where dynamic effects might be of importance, a dimensional analysis of the two-phase balance equations being closed with the extended Pc-Sw relationship is carried out. In the dimensionless equations the well-known capillary and gravitational number, Ca and Gr, evolve. Moreover, the new dimensionless number Dy appears as a factor. Dy quantifies the ratio of the 'dynamic capillary force' to the viscous force. Relating Dy to Ca or Gr yields DyC, the ratio of the dynamic to the capillary equilibrium force, and DyG, the ratio of the dynamic capillary to the gravitational force. The influence of the dynamic capillary force decreases with increasing characteristic length scale in relation to the equilibrium capillary, viscous or gravitational force. Moreover, with increasing transient flow velocity, the dynamic capillary force gains in importance. A second part of this study deals with the determination of the coefficient tau on the basis of primary drainage laboratory experiments performed by GeoDelft, The Netherlands and numerical experiments. Using the laboratory experiments tau was calculated to vary between 11.0 kPas and 154.7 kPas depending on the water saturation. The coefficient increases with decreasing water saturation. For the determination of tau using numerical experiments first homogeneous domains were considered in order to test the averaging approach. The coefficient tau was found to scale proportionally to the porosity, the (saturation-weighted average) viscosity, and the squared averaging length, as well as inversely proportional to the intrinsic permeability. Parameters that describe the equilibrium Pc-Sw relationship have a minor influence on the coefficient tau. The dependence of tau on the averaging length poses a problem as its magnitude is thus not clearly bounded, making it impossible to define an REV. As a consequence, either the averaging length should relate to a bounded property or the averaging of the phase pressures as applied in this study has to be reconsidered. Moreover, two heterogeneous domains were studied, one being a simple pattern of two fine sand lenses in a coarse sand and the other a spatially-correlated random field. An influence resulting from the simple heterogeneity pattern on the coefficient is only noticeable in case the fine sand lenses are drained. The heterogeneity stemming from the spatially-correlated random field does not affect the magnitude of the coefficient. Finally, the impact on the numerical solution of the balance equations being closed with an extended Pc-Sw relationship is assessed with simulations of imbibition processes. The dimensionless numbers Dy and DyC can be consulted to assess the impact on the solution. The front width should be applied as the characteristic length scale. It is observed that for a dominance of the dynamic capillary over the viscous force, the rate of change of saturation is dampened and thus a retardation effect with respect to the cumulative mass occurs. Locally, accelerating and slowing down of the displacement can flatten a front in comparison to a reference case. Moreover, for a high influx of wetting phase a process reversal from imbibition to drainage and back occurred. If additionally the equilibrium capillary forces are diminished, oscillations in the solution might occur for a large viscosity ratio.Item Open Access Optimierung der Grundwasserbewirtschaftung unter Berücksichtigung der Belange der Wasserversorgung, der Landwirtschaft und des Naturschutzes(2006) Schneck, Alexander; Kobus, Helmut (Prof. Dr. h.c. Dr.-Ing. E.h. Ph.D.)Grundwasserentnahmen zum Zwecke der öffentlichen Trinkwasserversorgung führen in den Wassergewinnungsgebieten zur Absenkung der natürlichen Grundwasserstände und können sich daher negativ auf andere Grundwassernutzer auswirken. Sie bewirken beispielsweise Änderungen in den Standortbedingungen für die grundwasserabhängige Tier- und Pflanzenwelt und die landwirtschaftliche Nutzung. Bei der Existenz mehrerer Gewinnungsanlagen lässt sich die Gesamtentnahme auf die verschiedenen Brunnen verteilen, so dass hier eine Möglichkeit zur aktiven Steuerung der Förderraten gegeben ist. Dadurch ist es möglich, die Eingriffsintensität der Entnahme auf die anderen Nutzer zu minimieren. Doch durch die Entnahme aus verschiedenen Brunnen ergeben sich auch für die Wasserversorgung Anforderungen, beispielsweise hinsichtlich der Qualität des Mischwassers. Vor diesem Hintergrund gilt es, ein Werkzeug zu entwickeln, mit dessen Hilfe die optimalen Förderraten schnell errechnet werden können, wobei die verschiedenartigen Anforderungen der Wasserversorgung, der Landwirtschaft und des Naturschutzes berücksichtigt werden. Gleichzeitig muss aber auch der Frage nachgegangen werden, welche Gesamtförderrate optimal im Sinn einer nachhaltigen Entwicklung des Wassergewinnungsgebietes ist. Dazu wird in der vorliegenden Arbeit ein Bewertungs- und Optimierungssystem für die Grundwasserbewirtschaftung entwickelt und anhand des Langenauer Donaurieds seine Praxistauglichkeit unter Beweis gestellt. Das System nutzt die Rechenergebnisse von numerischen Grundwassermodellen und wertet diese zusammen mit anderen ökologischen und sozioökonomischen Bewertungskriterien aus. Der errechnete Gesamtnutzwert einer Bewirtschaftungsalternative erlaubt nun eine Aussage darüber, wie nah man der angestrebten nachhaltigen Lösung ist und macht verschiedene Alternativenbewertungen direkt miteinander vergleichbar. Mit Hilfe eines gekoppelten Optimierungsalgorithmus‘ lässt sich so schnell die bestmögliche Bewirtschaftungsstrategie unter vorgegebenen Randbedingungen ermitteln. Eine solch umfassende Betrachtung der Auswirkungen von Grundwasserentnahmen erfordert den Einsatz eines multikriteriellen Bewertungssystems. Bei den durchgeführten Untersuchungen hat sich das Bewertungsverfahren Composite Programming als am besten geeignet für die vorliegende Fragestellung dargestellt. Die Arbeit stellt Schritt für Schritt dar, wie die einzelnen Bewertungskriterien und Zielvorgaben zu ermitteln sind, wie die einzelnen Teilbewertungen zu einer nachvollziehbaren Gesamtbewertung gebündelt werden und wie die gewonnenen Informationen genutzt werden können, um die Grundwasserbewirtschaftung zu optimieren. Umfassend wird in der Arbeit die Sensitivität der Bewertungs- und Optimierungsergebnisse auf die einwirkenden Randbedingungen untersucht und dargestellt. Aus den Untersuchungsergebnissen werden weiterhin Hinweise zum Umgang mit den nicht objektivierbaren Parametern abgeleitet, um die Anwendbarkeit und Übertragbarkeit auf andere Gebiete zu erleichtern. Als Ergebnis der Arbeit steht ein Werkzeug zur Verfügung, mit dessen Hilfe Grundwasserentnahmen zukünftig für die Nutzergruppen Wasserversorgung, Landwirtschaft und Natur verträglicher gestaltet werden können. Ein solches Werkzeug ist insbesondere vor dem Hintergrund der in den kommenden Jahren umzusetzenden EU-Wasserrahmenrichtlinie (Vermeidung signifikanter Schädigungen grundwasserabhängiger Landökosysteme) dringend notwendig.Item Open Access Bedload transport estimation in mountainous intermittent rivers and streams(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2023) Sadid, Najibullah; Wieprecht, Silke (Prof. Dr.-Ing.)Rivers and streams with the flow, sediment, and habitat seasonality are termed as intermittent rivers and streams (IRS). IRS are the main water bodies in arid and semi-arid regions of the world but are also found in the temperate and humid environment, where they are particularly draining headwater streams. Thus, a large part of headwater streams in the mountainous regions behave as intermittent water bodies, where the steep channel slope and a wide variety of sediment sizes add to their hydrosedimentological complexity. Bedload transport as an important sedimentological characteristic of mountainous IRS and essential for planning sediment management strategies, is far from being well understood. Often the knowledge of lowland perennial rivers is adapted to steep IRS, which may lead to an overestimation of bedload transport mainly due to the overestimation of near-bed flow characteristics. Despite the development of numerous methods for modifying near-bed flow parameters for steep IRS such as Double-averaging of Navier-Stokes equation and flow resistance methods modifications for steep IRS, their application is limited to small domains and laboratory conditions. In this research, the flow resistance, main determinant of near-bed flow characteristic is estimated using a regime channel approach. In this approach, the flow resistance is estimated on reach-scale based on the channel’s regime dimension, slope and bankfull discharge assuming an IRS is in regime state (equilibrium condition). A channel’s regime state represents a long-term average characteristic of a river and does not significantly change over time. A channel reach of a constant slope develops a certain flow resistance during its regime state development to resist the change imposed by bankfull discharge and maintain a specific regime geometry, slope, and sediment grain size. 2D- hydromorphological computer simulations are employed to simulate the development of channel regime state for several cases of initial geometries, slopes, and grain sizes by steering the flow resistance. This modifies the riverbed shear stress by the ratio of total flow resistance to grain resistance also known as relative flow resistance µ in order to account for flow energy dissipation on resistance sources such as macro-roughness elements (MRE), and bedforms. Alternatively, two cases of MRE as a main flow resistance inducer is built as non-erodible trapezoidal shapes (i) randomly distributed over the channel bed, and (ii) arranged in cascade bedforms are used in regime channel simulations. MRE protects the channel by reducing the exposed riverbed to erosion and changing the flow characteristics in their vicinity. Regime channel simulations are performed on artificial channels of initial slopes between 0.0% to 10% and initial dimensions of 5.5 m x 200 m and 16.5 m x 200 m resembling a fixed (laboratory) and an extended-width (natural wide channel) condition. Three channel slope combination cases representing a natural channel reach which can be composed of one or more constant slope stretch are also studied beside single slope channels. Steady state simulations are performed for six sediment grain size (GSD) sets, which cover a wide spectrum of naturally occurring sediment sizes. The simulation results show a power-law relationship between µ and regime channel slopes for all channel dimensions, reach combinations, GSD, initial slopes and with (R1) and without sediment feeding (R). The increase in relative flow resistance (µ) with regime channel slope is well reproduced in form of bedforms. Regime channels developed step-pool to cascade bedforms for steep slopes and plane- to riffle bed for gentle slopes channels. The relationship between µ and regime slope derived using regime channel simulation approach exhibits good agreement with some field measurement of flow resistance for mountainous rivers and streams. The approach is applied on two IRS case studies with observed data in Kabul River basin, Afghanistan to estimate bedload transport. The relative flow resistance resulted from models calibration showed good agreement with those derived from test channels regime development simulation. The outcome of channel regime simulation with presence of MRE as geometrical shapes produced a logarithmic-law with a horizontal asymptote relationship between MRE concentrations and channel regime slopes. Similar results are also reported from flume experiments that the ratio of drag to total shear stress increases rapidly when the MRE are sufficiently distant. Regime channels develop micro-channels around MRE, where the bulk of bedload transport occur. For MRE arrangements as cascades, the results show a power-law relationship between channel regime slope and step-pool dimensions λ = LD/DB. The results obtained are in good agreement with field measurement of naturally occurring and artificially built λ relationship with SR. Future studies can further enrich the validation of this approach by applying it to other study sites. Present modelling tools have their limitations when dealing with strong geometries which is often the case for mountain rivers, therefore, improvement in modelling techniques is required to flexibly deal with abrupt changes in riverbed geometry for instance when implementing MRE as main flow resistance inducer.Item Open Access Seasonal dynamics of gaseous CO2 concentrations in a karst cave correspond with aqueous concentrations in a stagnant water column(2023) Class, Holger; Keim, Leon; Schirmer, Larissa; Strauch, Bettina; Wendel, Kai; Zimmer, MartinDissolved CO2 in karst water is the key driving force of karstification. Replenishment of CO2 concentrations in karst water occurs by meteoric water that percolates through the vadose zone, where CO2 produced from microbial activity is dissolved. CO2 can thus be transported with the percolating water or in the gas phase due to ventilation in karst systems. We measured seasonally fluctuating CO2 concentrations in the air of a karst cave and their influence on aqueous CO2 concentrations in different depths of a stagnant water column. The observed data were compared to numerical simulations. The data give evidence that density-driven enhanced dissolution of gaseous CO2 at the karst water table is the driving force for a fast increase of aqueous CO2 during periods of high gaseous concentrations in the cave, whereas during periods of lower gaseous concentrations, the decline of aqueous CO2 is limited to shallow water depths in the order of 1 m. This is significant because density-driven CO2 dissolution has not been previously considered relevant for karst hydrology in the literature. Attempts at reproducing the measured aqueous CO2 concentrations with numerical modeling revealed challenges related to computational demands, discretization, and the high sensitivity of the processes to tiny density gradients.Item Open Access Modeling of evaporation-driven multiple salt precipitation in porous media with a real field application(2020) Mejri, Emna; Helmig, Rainer; Bouhlila, RachidaSoil and groundwater salinization are very important environmental issues of global concern. They threaten mainly the arid and semiarid regions characterized by dry climate conditions and an increase of irrigation practices. Among these regions, the south of Tunisia is considered, on the one hand, to be a salt-affected zone facing a twofold problem: The scarcity of water resources and the degradation of their quality due to the overexploitation of the aquifers for irrigation needs. On the other hand, this Tunisian landform is the only adequate area for planting date palm trees which provide the country with the first and most important exportation product. In order to maintain the existence of these oases and develop the date production, a good understanding of the salinization problem threatening this region, and the ability to predict its distribution and evolution, should not be underestimated. The work presented in this paper deals with the Oasis of Segdoud in southern Tunisia, with the objective of modeling the evaporation-driven salt precipitation processes at the soil profile scale and under real climatic conditions. The model used is based on the one developed and presented in a previous work. In order to fulfil the real field conditions, a further extension of the geochemical system of the existing model was required. The precipitated salts considered in this work were halite (NaCl), gypsum (CaSO4) and thenardite (Na2SO4). The extended model reproduces very well the same tendencies of the physico-chemical processes of the natural system in terms of the spatio-temporal distribution and evolution of the evaporation and multiple-salt precipitation. It sheds new lights on the simulation of sequences of salt precipitation in arid regions. The simulation results provide an analysis of the influence of salt precipitation on hydrodynamic properties of the porous medium (porosity and permeability). Moreover, the sensitivity analysis done here reveals the influence of the water table level on the evaporation rate.Item Open Access River models for transport of matter and heat(1980) Kobus, Helmut; Grimm-Strele, JostInsufficient quality of water-supply may become the imiting factor for growth and development particularly in highly industrialized regions. A deterioration of water quality may result, aside from natural sources, from excessive municipal or industrial waste-water or cooling water discharges. Assessment of the environmental impact of such discharges requires adequate knowledge of the mixing and transport processes to which the introduced substances are subjected. Such phenomena are investigated in hydraulic models. A decisive distinction between mixing- and conventional models is the requirement to simulate turbulent transport processes correctly, which necessitates an exact reproduction of the local velocity distribution in the model. This results in more sophisticated requirements for model similarity. The main task of mixing models including intake- or outlet structures is usually the determination of the effluent concentration field in the water body, which is a prerequisite for the evaluation of possible negative consequences on the river ecology and on other water users located downstream. The model experiment gives answers to the question of how changes in the design of the outlet structure can influence the mixing pattern. Such questions are primarily important for large rivers and reservoirs, where incomplete mixing and stratification are likely to occur. For small rivers or creeks, the main problem is longitudinal dispersion, since cross-sectional mixing is quickly achieved because of the large ratio of effluent- to river flow rate. Similarly, the effect of very small waste-water discharges is easily evaluated as long as they do not produce a noticeable disturbance of the river flow.Item Open Access Comparison of multivariate spatial dependence structures of DPIL and flowmeter hydraulic conductivity data sets at the MADE site(2019) Xiao, Bo; Haslauer, Claus; Bohling, GeoffreyItem Open Access Hydraulische Möglichkeiten zur Grundwassersanierung im Bereich von Altablagerungen(1983) Kobus, Helmut; Rinnert, BerndEine moderne Industriegesellschaft wie die der Bundesrepublik Deutschland benötigt neben einer Vielzahl von Grundstoffen vor allem auch eine ausreichende Versorgung mit qualitativ hochwertigem Wasser sowohl für industrielle Zwecke als auch für die Trinkwasserversorgung. Wegen der starken Verschmutzung der meisten Oberflächengewässer wird hierzu vorrangig auf die vorhandenen Grundwasserreserven zurückgegriffen. Aus der zunehmenden Raumnutzung resultiert jedoch auch eine wachsende Gefährdung der Grundwasserbeschaffenheit. Gerade in industriellen Ballungsgebieten werden immer häufiger Fälle von Grundwasserverschmutzung festgestellt. Neben der Verschmutzung durch industrielle Einleiter wird das Grundwasser vor allem durch das Eindringen von Schadstoffen aus .Ablagerungen gefährdet. Eine besondere Gefahr geht dabei von den Altablagerungen sowie den sogenannten "wilden" Müllkippen aus. Im Gegensatz zum Abfallbeseitigungsverfahren "Geordnete Deponie", bei dem mit großem technischem Aufwand ein Eindringen von Schadstoffen in den Grundwasserleiter weitgehend verhindert wird, fehlen bei Altablagerungen häufig und bei "wilden" Ablagerungen in der Regel bauliche oder hydraulische Maßnahmen zum Schutz des Grundwassers. Dadurch können über viele Jahrzehnte Schad- oder Giftstoffe kontinuierlich in den Grundwasserleiter gelangen und so zu einer stetig wachsenden Kontaminierung der Grundwasservorkommen führen.Item Open Access Learning groundwater contaminant diffusion‐sorption processes with a finite volume neural network(2022) Praditia, Timothy; Karlbauer, Matthias; Otte, Sebastian; Oladyshkin, Sergey; Butz, Martin V.; Nowak, WolfgangImproved understanding of complex hydrosystem processes is key to advance water resources research. Nevertheless, the conventional way of modeling these processes suffers from a high conceptual uncertainty, due to almost ubiquitous simplifying assumptions used in model parameterizations/closures. Machine learning (ML) models are considered as a potential alternative, but their generalization abilities remain limited. For example, they normally fail to predict accurately across different boundary conditions. Moreover, as a black box, they do not add to our process understanding or to discover improved parameterizations/closures. To tackle this issue, we propose the hybrid modeling framework FINN (finite volume neural network). It merges existing numerical methods for partial differential equations (PDEs) with the learning abilities of artificial neural networks (ANNs). FINN is applied on discrete control volumes and learns components of the investigated system equations, such as numerical stencils, model parameters, and arbitrary closure/constitutive relations. Consequently, FINN yields highly interpretable results. We demonstrate FINN's potential on a diffusion‐sorption problem in clay. Results on numerically generated data show that FINN outperforms other ML models when tested under modified boundary conditions, and that it can successfully differentiate between the usual, known sorption isotherms. Moreover, we also equip FINN with uncertainty quantification methods to lay open the total uncertainty of scientific learning, and then apply it to a laboratory experiment. The results show that FINN performs better than calibrated PDE‐based models as it is able to flexibly learn and model sorption isotherms without being restricted to choose among available parametric models.Item Open Access Stochastic and hydrological modelling for climate change prediction in the Lima region, Peru(2015) Chamorro Chávez, Alejandro; Bárdossy, András (Prof. Dr. rer. nat. Dr.-Ing.)Climate change has been an important field of research in the past years and certainly is a major concern in the present time. It involves a broad spectrum of subjects and significant different time scales, ranging from decades to thousands or millions of years. Generally speaking, in a climate change scenario a change in the pattern, average or extreme conditions of some variables is observed, and this can be due to many different causes as changing processes in the earth, human activities or extra terrestrial induced factors. This study concentrates on the influences on the climate due to human activities and focuses on the hydrological response to these influences or changes as a primarily goal, for the next few decades. The main motivation is the vulnerability and scarcity of the water availability in the capital of Peru, Lima, and how the area under study will respond to a change in the climate. An important focus of analysis in order to reduce the uncertainty in the predictions is the errors that appears when modeling a given variable or set of variables. This issue is addressed first in regionalization of precipitation and second in the calibration of hydrological models in which a robust parameter estimation is performed. In the first issue concerning to regionalization, External Drift Kriging is applied. In this part of the work the results of regionalization are analyzed with focus on the errors and systematic errors which appear during the modeling. The main goal here is the reduction of these errors through some proposed transformations. Here, three approaches are suggested, namely smoothing of the digital elevation model (DEM) considering a symmetric area, power transformation and smoothing considering a non symmetric area. The second issue concerning the uncertainty in the estimations (discharge) was addressed two-fold, namely by optimizing the objective function by means of a heuristic optimization procedure based on Monte Carlo simulation, and by means of a robust parameter estimation (ROPE) algorithm developed quite recently by Bárdossy and Singh, which in general terms can be used as a general multivariate optimization procedure. The algorithm offers a way of finding a set of “good” parameter vectors, which among other characteristics, are transferable in time. The final result comprises an ensemble of estimations for expected discharge variations accounting for the uncertainty in parameterization and processes description in the models. In this study HVB and HYMOD models are used. The assessment of the impact of climate change in precipitation and temperature is carried out by a statistical downscaling procedure based on a quantil-quantil transformation. Here the information given by the Global Climate Models (GCMs) outputs are transferred to the local scale. Two different GCMs and three scenarios are used in this step. This permitted the definition of a range for the expected future variations for temperature and precipitation. The last chapter of the study addresses the assessment of the discharge in the short term. The goal here is to “infer” the outcome of a random variable (discharge) in the next time step by taking information from past observations (previous steps). As we can regard the observations (time series) as a realization generated from a stochastic process, we can address this issue from a stochastic point of view. The task is addressed first by considering some of the existing autoregressive models (AR process), and second by considering a Copula-based autoregressive model. In order to perform the Copula-based autoregressive model, a given time series (modelled discharge) was transformed into three vectors representing the same original time series but shifted in time. A three dimensional Copula was then fitted to the univariate distributions. For this, a Gaussian model as well as a Beta kernel model expressed in terms of the Beta function was considered.