Asymptotic analysis of pollution filtration through thin random fissures between two porous media

We describe the asymptotic behaviour of a filtration problem from a contaminated porous medium to a non-contaminated porous medium through thin vertical fissures of fixed height h>0, of random thinness of order {\epsilon} and which are $\epsilon$-periodically distributed. We compute the limit velocity of the flow and the limit flux of pollutant at the interfaces between the two porous media and the intermediate one

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

Development and implementation of the generalized continuum model for transport in porous media

Fluid flow phenomena in porous media have always attracted a lot of attention of scientists and engineers. Attempts to quantify the average transport in homogeneous media with a simple partial differential equation with constant coefficients disclosed significant inconsistencies comparing to experiments. Modern numerical simulations of porous networks confirmed that those inconsistencies are systematic and not caused by the observation error. The error appeared as a result of the, so called, anomalous or non-Fickian transport, which was in contrast to the normal regime, described by the Fick’s laws. The problem has been addressed through the introduction of more complex and substantial models to describe the phenomena. Although, these new approaches have resolved the problem of quantification, they have raised another question for researchers and engineers, how to choose the most suitable approach and, if it is possible, to parametrize the modeling choice at all. The models general lack of physical consistency makes it difficult to distinguish the model parameters. This leaves judging of suitability to the general accuracy of quantification only, which is often not the most important criterion. In other words, the model parameters are typically estimated by fitting the model to the experimental data, and are often not related to the real properties of the medium. Therefore, a model is often chosen a priory, based only on the experience of the researcher. In this work, we address the problem of model selection by introducing a new model: the Generalized Continuum Transport model. This model transforms into existing models at certain limits and, therefore, constrains the modeling choice through the introduction of the parameter space. It is shown that the Generalized Continuum Transport model limits to the advection-dispersion equation, the Continuous Time Random Walk, the Multi-Rate Mass Transfer and the Multiple-Porosity models, when corresponding configurations of the parameter space are applied. The model’s accuracy is studied by quantifying the breakthrough curves obtained from a fine scale porous network modeldemonstrating significant appearance of anomalous transport phenomena. The results show that the error of quantification is smaller than the error of the existing models. It is discussed that the parameters of the Generalized Continuum Transport model are related to the physical properties of porous media. Finally, it is presented that the parameter space of GCT can be constrained and related to the transport phenomena studied. Hence, the limits of GCT are controlled by the transport complexity and the desired accuracy and the modeling choice can be parametrized

Contaminant transport in a fractured chalk aquifer at Sigerslev, Denmark, as characterised by tracer techniques

Over the past three decades, the primary interest of hydrogeological investigations has shifted from problems of water supply to water quality issues. Contamination of aquifers is a growing and demanding problem. In the context of assessment studies for feasible radioactive waste disposal sites contaminant transport in fractured aquifers has re-ceived a great attention. Transport processes in fractured aquifer are characterised by a couple of transport mechanisms within the fracture and the neighbouring matrix. In order to investigate the dominant transport mechanisms, various laboratory experi-ments with nitrate as a representative for agricultural contaminants compared to various hydrogeological tracers were performed in Danish chalk samples. The characteristics of the Danish chalk such as it’s sorptive and diffusive properties were evaluated by batch and through-diffusion experiments. The chalk exhibits linear sorption isotherms and low sorption capacities. This was ex-pected due to the high purity of the Danish chalk with a low content of clay minerals and organic matter. Based on a series of through-diffusion experiments a chalk specific ex-ponent m of 2.2 was derived for Archie’s law. According to the results of batch and dif-fusion experiments, nitrate as well as the other used tracers showed a low retardation in the Danish chalk. To understand the possible transport mechanisms of tracers in a frac-tured chalk block, laboratory single- and multi-tracer tests were carried out in two blocks under defined boundary conditions. The breakthrough curves (BTC’s) of the tracers are governed by sharp peaks due to advective transport and dispersive respectively diffu-sive transport processes in the tailing part of the BTC’s. The simulation of the BTC’s with the single fissure dispersion model could not reasonably fit the BTC’s. A multi-channel SFDM with the superposition of BTC’s of at least two different flow paths, re-sulted in an acceptable fit (by calculating the cumulative tracer breakthrough and recov-ery curves). Those simulations indicate the existence of flow channelling effects within the fracture. Comparing the BTC’s of nitrate, uranin and lithium implied possible adsorp-tion and/or degradation of nitrate within the fracture and the chalk matrix. The results showed that matrix diffusion process plays only a minor role in the determination of the fate of nitrate in the groundwater aquifers. The key factor controlling the fate of nitrate in the groundwater is the redox process. Reduction of nitrate is of particular importance for natural remediation process in the case of contaminated aquifers in agricultural areas. Flow and transport behaviour of different solutes in a fractured chalk blocks were visual-ized and showed that flow and transport is concentrated in a few distinct channels. The description of the observed BTC`s with a multi-channel model is still a theoretical sug-gestion and needs more investigations to be confirmed. Those investigations include quantifying and measuring the fracture aperture with different techniques such as NMR and MRI.Stoff Transport in einem geklüfteten Kreide Aquifer in Sigersler; Dänemark; charakterisiert durch Tracer-Techniken Seit den letzten drei Jahrzehnten konzentriert sich das Interesse bei hydrogeologischen Untersuchungen zur Wasserversorgung auf die Sicherung der Wasserqualität. Die wachsende Gefährdung der Grundwasserleiter durch Kontamination stellt hierbei ein wichtiges Problem dar. Besondere Beachtung finden dabei die Prozesse des Schadstofftransports in geklüfteten und porösen Medien, darunter vor allem die Beurteilung von Deponien und Endlagern sowie der Wasserqualität in Kluftaquiferen. Um die physikalischen Mechanismen beim Transport in der Kluft und der benachbarten Matrix zu untersuchen, wurden im Labor Diffusions- und Tracer-Experimente mit Nitrat (repräsentativ für eine Kontamination aus der Landwirtschaft) simultan mit verschiedenen hydrogeologischen Tracern durchgeführt. Anhand von Batch- und Diffusionsexperimenten wurden die Soprtions- und Diffusionseigenschaften der Dänischen Kreide bestimmt. Bedingt durch die hohe Reinheit der Dänischen Kreide und ihres geringen Gehaltes an Tonmineralen und organischem Material wurden bei den Batch-Tests lineare Sorptionsisothermen (Henry-Isothermen) mit geringer Sorptionskapazität ermittelt. Entsprechend dem Gesetz von Archie beträgt der Wert des Kreidespezifischen Exponenten m bei den Diffusionsexperimenten 2,2. Basierend auf diesem Exponenten kann die effektive Diffusion in abhangigkeit von der relativen Diffusivität und der Porosität der Kreideproben ermittelt werden. Die Ergebnisse aus den Batch- und Diffusionsexperimenten an der Dänischen Kreide zeigen sowohl bei Nitrat als auch bei den anderen verwendeten Tracern (Uranin, Pyranin Eosin, Chlorid und Lithium) eine geringe Retardation. Die Durchführung von Einzel- und Multitracer-Tests in zwei Kreideblöcken bei definierten Randbedingungen im Labor tragen zu einem besseren Verständnis der Transportmechanismen in Einzelklüften bei. Die Durchbruchskurven (Breakthrough curves = BTC’s) aus den Tracer-Tests zeigen scharfe Peaks mit einem deutlichen tailing, das auf Dispersion und Matrixdiffusion beruht. Da die Simulation der BTC’s mit einem eindimensionalen Dispersionsmodell keine gute Anpassung der Tracer- Konzentrationskurve ergibt, wurde ein Multichannel-Modell entwickelt um so eine akzeptable Übereinstimmung durch die Berechnung einer kumulativen Tracer-Kurve zu erreichen. Diese Simulationen zeigen deutlich, dass die BTC eine Überlagerung von mindestens zwei verschieden Fliesspfaden ist. Dies deutet eine mögliche Existenz von „flow channeling“-Effekten in der Kluft an. Die Ergebnisse aus den Nitrate Tracer-Tests im Vergleich zu Uranin, Eosin und Lithium zeigen, dass eine Adsorption und Degradation von Nitrat in der Klüftung und in der Matrix stattfinden. Mit diesem Ergebnissen können das Fliess- und Transportverhalten der untersuchten Kluft eindeuting beschrieben werden. Eindeutig ist, dass das Fliess- und Transportfeld sehr unregelmäßig verteilt ist und sich auf wenige bestimmte Fliesskanäle. Die Beschreibung der beobachteten BTC’s mit dem einem Multi-Channel-Modell ist ein theoretischer Ansatz, der noch weiteren Untersuchungen bedarf. Dazu gehören auch Methoden zur verbesserten Quantifizierung und Messung von Kluftöffnungen wie z.B. NMR- und MRI-Technologien. Der mögliche Effekt von Diffusion und Channeling in geklüfteten Medien bedarf ebenfalls weiterer Forschung

Fundamentals of air pollution engineering

Analysis and abatement of air pollution involve a variety of technical disciplines. Formation of the most prevalent pollutants occurs during the combustion process, a tightly coupled system involving fluid flow, mass and energy transport, and chemical kinetics. Its complexity is exemplified by the fact that, in many respects, the simplest hydrocarbon combustion, the methane-oxygen flame, has been quantitatively modeled only within the last several years. Nonetheless, the development of combustion modifications aimed at minimizing the formation of the unwanted by-products of burning fuels requires an understanding of the combustion process. Fuel may be available in solid, liquid, or gaseous form; it may be mixed with the air ahead of time or only within the combustion chamber; the chamber itself may vary from the piston and cylinder arrangement in an automobile engine to a 10-story-high boiler in the largest power plant; the unwanted byproducts may remain as gases, or they may, upon cooling, form small particles. The only effective way to control air pollution is to prevent the release of pollutants at the source. Where pollutants are generated in combustion, modifications to the combustion process itself, for example in the manner in which the fuel and air are mixed, can be quite effective in reducing their formation. Most situations, whether a combustion or an industrial process, however, require some degree of treatment of the exhaust gases before they are released to the atmosphere. Such treatment can involve intimately contacting the effluent gases with liquids or solids capable of selectively removing gaseous pollutants or, in the case of particulate pollutants, directing the effluent flow through a device in which the particles are captured on surfaces. The study of the generation and control of air pollutants can be termed air pollution engineering and is the subject of this book. Our goal here is to present a rigorous and fundamental analysis of the production of air pollutants and their control. The book is intended for use at the senior or first-year graduate level in chemical, civil, environmental, and mechanical engineering curricula. We assume that the student has had basic first courses in thermodynamics, fluid mechanics, and heat transfer. The material treated in the book can serve as the subject of either a full-year or a one-term course, depending on the choice of topics covered. In the first chapter we introduce the concept of air pollution engineering and summarize those species classified as air pollutants. Chapter 1 also contains four appendices that present certain basic material that will be called upon later in the book. This material includes chemical kinetics, the basic equations of heat and mass transfer, and some elementary ideas from probability and turbulence. Chapter 2 is a basic treatment of combustion, including its chemistry and the role of mixing processes and flame structure. Building on the foundation laid in Chapter 2, we present in Chapter 3 a comprehensive analysis of the formation of gaseous pollutants in combustion. Continuing in this vein, Chapter 4 contains a thorough treatment of the internal combustion engine, including its principles of operation and the mechanisms of formation of pollutants therein. Control methods based on combustion modification are discussed in both Chapters 3 and 4. Particulate matter (aerosols) constitutes the second major category of air pollutants when classified on the basis of physical state. Chapter 5 is devoted to an introduction to aerosols and principles of aerosol behavior, including the mechanics of particles in flowing fluids, the migration of particles in external force fields, Brownian motion of small particles, size distributions, coagulation, and formation of new particles from the vapor by homogeneous nucleation. Chapter 6 then treats the formation of particles in combustion processes. Chapters 7 and 8 present the basic theories of the removal of particulate and gaseous pollutants, respectively, from effluent streams. We cover all the major air pollution control operations, such as gravitational and centrifugal deposition, electrostatic precipitation, filtration, wet scrubbing, gas absorption and adsorption, and chemical reaction methods. Our goal in these two chapters, above all, is to carefully derive the basic equations governing the design of the control methods. Limited attention is given to actual equipment specification, although with the material in Chapters 7 and 8 serving as a basis, one will be able to proceed to design handbooks for such specifications. Chapters 2 through 8 treat air pollution engineering from a process-by-process point of view. Chapter 9 views the air pollution control problem for an entire region or airshed. To comply with national ambient air quality standards that prescribe, on the basis of health effects, the maximum atmospheric concentration level to be attained in a region, it is necessary for the relevant governmental authority to specify the degree to which the emissions from each of the sources in the region must be controlled. Thus it is generally necessary to choose among many alternatives that may lead to the same total quantity of emission over the region. Chapter 9 establishes a framework by which an optimal air pollution control plan for an airshed may be determined. In short, we seek the least-cost combination of abatement measures that meets the necessary constraint that the total emissions not exceed those required to meet an ambient air quality standard. Once pollutants are released into the atmosphere, they are acted on by a variety of chemical and physical phenomena. The atmospheric chemistry and physics of air pollution is indeed a rich arena, encompassing the disciplines of chemistry, meteorology, fluid mechanics, and aerosol science. As noted above, the subject matter of the present book ends at the stack (or the tailpipe); those readers desiring a treatment of the atmospheric behavior of air pollutants are referred to J. H. Seinfeld, Atmospheric Chemistry and Physics of Air Pollution (Wiley-Interscience, New York, 1986). We wish to gratefully acknowledge David Huang, Carol Jones, Sonya Kreidenweis, Ranajit Sahu, and Ken Wolfenbarger for their assistance with calculations in the book. Finally, to Christina Conti, our secretary and copy editor, who, more than anyone else, kept safe the beauty and precision of language as an effective means of communication, we owe an enormous debt of gratitude. She nurtured this book as her own; through those times when the task seemed unending, she was always there to make the road a little smoother. R. C. Flagan J. H. Seinfel