Modeling non-equilibrium mass transport in biologically reactive porous media.

We develop a one-equation non-equilibrium model to describe the Darcy-scale transport of a solute undergoing biodegradation in porous media. Most of the mathematical models that describe the macroscale transport in such systems have been developed intuitively on the basis of simple conceptual schemes. There are two problems with such a heuristic analysis. First, it is unclear how much information these models are able to capture; that is, it is not clear what the model's domain of validity is. Second, there is no obvious connection between the macroscale effective parameters and the microscopic processes and parameters. As an alternative, a number of upscaling techniques have been developed to derive the appropriate macroscale equations that are used to describe mass transport and reactions in multiphase media. These approaches have been adapted to the problem of biodegradation in porous media with biofilms, but most of the work has focused on systems that are restricted to small concentration gradients at the microscale. This assumption, referred to as the local mass equilibrium approximation, generally has constraints that are overly restrictive. In this article, we devise a model that does not require the assumption of local mass equilibrium to be valid. In this approach, one instead requires only that, at sufficiently long times, anomalous behaviors of the third and higher spatial moments can be neglected; this, in turn, implies that the macroscopic model is well represented by a convection–dispersion–reaction type equation. This strategy is very much in the spirit of the developments for Taylor dispersion presented by Aris (1956). On the basis of our numerical results, we carefully describe the domain of validity of the model and show that the time-asymptotic constraint may be adhered to even for systems that are not at local mass equilibrium

Upscaling of reactive flows

The thesis deals with the upscaling of reactive flows in complex geometry. The reactions which may include deposition or dissolution take place at a part of the boundary and depending on the size of the reaction domain, the changes in the pore structure that are due to the deposition process may or may not be neglected. In mathematical terms, the models are defined in a fixed, respectively variable geometry, when the deposition layer generates a free boundary at the pore scale. Specifically, for the chemical vapor deposition (CVD) process on a trenched geometry, we have developed mathematical models for both situations. For the multi-scale computations, numerical methods inspired from domain decomposition ideas have been proposed and the convergence of the scheme has been proved. Computing the full solution in a domain with oscillating boundary requires a lot of computational effort, as one has to achieve an accuracy that agrees with the scale of oscillations. To approximate these solutions, one defines equations in a simpler domain, where flat boundaries but modified boundary conditions approximate the rough one. The two situations mentioned before were considered: the fixed geometry case, and the time dependent geometry at the microscale (free boundaries). We have derived an approximating (effective) model where a flat boundary is replacing the oscillatory boundary, but defining an effective boundary condition. In the fixed geometry case, we provide rigorous mathematical proofs for the upscaling procedure. The second case, when we take into account the geometry changes at the microscale, is more involved, and we use formal asymptotic methods to derive these boundary conditions. Our contributions in this respect are in dealing with non-Lipschitz reactive terms on the boundary in the fixed geometry case and the formal asymptotic approach for the moving boundary. Both add to the present literature. Next, to understand the flow in a domain with variable geometry, we have considered a thin strip with reactions taking place at the lateral boundaries of the strip under dominant transport conditions. Reactions take place at the lateral boundaries of the strip (the walls), where the reaction product can deposit in a layer with a non-negligible thickness compared to the width of the strip. This leads to a free boundary problem, in which the moving interface between the fluid and the deposited (solid) layer is explicitly taken into account. Using asymptotic expansion methods, we derive an upscaled, one-dimensional model by averaging in the transversal direction. The upscaled equations are similar to the Taylor dispersion and we have performed numerical simulations to compare the upscaled equations with other simpler upscaled equations and the transversally averaged, two-dimensional solution. The derivation introduces new terms originating from the changing geometry. The numerical computations also provide an insight into the regimes where such an upscaling is useful. We have further studied the rigorous homogenization process for the reactive flows for a periodic array of cells and proved the validity of upscaled equations. These reactive flows model the precipitation and dissolution processes in a porous medium. We define a sequence of microscopic solutions u" and obtain the upscaled equations as the limit of e \ 0. We adopt the 2-scale framework to achieve this. The challenges are in dealing with the low regularity of microscopic solutions and particular non-linearities in the reaction term. This rigorous derivation closes the gap of the rigorous transition from a given pore scale model to the heuristically proposed macroscopic model. In addition, numerical methods to compute the solution for an upscaled model have been proposed. The upscaled model describes the reactive flow in a porous medium. The reaction term, especially, the dissolution term has a particular, multi-valued character, which leads to stiff dissolution fronts. We have considered both the conformal and mixed schemes for the analysis including both the semi-discrete (time-discretization) and the fully discrete (both in space and time) cases. The fully discrete schemes correspond to the finite element method and the mixed finite element method for conformal, respectively mixed schemes. The numerical schemes have been analyzed and the convergence to the continuous formulation has been proved. Apart from the proof for the convergence, this also yields an existence proof for the solution of the upscaled model. Numerical experiments are performed to study the convergence behavior. The challenges are in dealing with the specific non-linearities of the reaction term. We deal with them by using the translation estimates which are adapted to the specific numerical scheme. The applications are in the development of all-solid state rechargeable batteries having a high dtorage capacity. Such devices have a complex 3D geometry for the electrodes to enhance the surface area. The challenges are in the development of the appropriate technologies for the formation of these electrodes. In particular we focus on chemical vapor deposition processes (CVD), with the aim of getting a deeper understanding of the reactions taking place in a complex geometry. Other applications include flows in porous media, bio-film growth etc

Upscaling of the acidizing process in heterogeneous porous media

Coupled fluid flow, reaction and transport in porous media has been the topic of research in various disciplines for the past few decades. Conventional approach assumes a homogeneous and isotropic porous media, and simplifies the nature of coupling between fluid and rock interactions. However, including the reality of the process, i.e. assuming heterogeneous and anisotropic porous media with fully coupled rock fluid interaction, can lead to more advanced understanding of the fundamental physics behind the problem and developing efficient industrial applications. In the oil and gas industry optimization of different well stimulation techniques such as matrix acidizing in order to enhance oil recovery requires an advanced understanding of fluid flow and also reaction in heterogeneous formations. This thesis is a contribution to development of more general governing equations describing the reactive flow and transport in heterogeneous formations.;The heterogeneity of the porous medium is introduced in the formulation through random permeability field that possess the characteristics of stationary stochastic process. The heterogeneity in permeability field affects the reservoir dynamics over a range of length and time scales by making pressure, concentration, diffusion and reaction coefficients stochastic random fields. Stochastic nature of these parameters helps us to be able to upscale the process while keeping the local information associated with heterogeneous nature of the porous media.;Conventional approaches to deal with this problem are homogenization and smoothing the heterogeneous properties of the formation using averaging based techniques such as up-gridding. However, these techniques do not carry the fundamental physics governing the process and cannot mimic the experimental observations such as acid front movement and instability of the reaction process. The local variations in rock and fluid properties are also ignored in these techniques which might lead to significant impacts in field scale application of acidizing as one of the major stimulation techniques.;In order to upscale the isothermal reaction process in a heterogeneous porous medium, according to the nature of the process, spectral-based small perturbation theory (Gelhar, 1993; Gelhar and Axness, 1983) is used among the various numerical and analytical upscaling techniques. The reaction is a nonlinear dissolution of an injected acid in a homogeneous liquid with constant density in a stationary mineral with constant porosity. In order to follow the acid front a moving coordinate is introduced. The upscaled governing equations are obtained with explicit macro-scale expressions for the coefficients and solved using time adaptive implicit finite difference technique. The results are compared with homogeneous models and sensitivity analysis of the upscaled equations is performed. Finally conclusions and results are discussed showing the importance of applying upscaling techniques to capture the impacts of heterogeneity on fluid dynamics

Confined turbulent fluid-particle flow modeling using multiple-realization particle trajectory schemes

A multiple-realization particle trajectory scheme has been developed and applied to the numerical prediction of confined turbulent fluid-particle flows. The example flows investigated include the vertical pipe upflow experimental data of Tsuji et al. and the experimental data of Leavitt for a coaxial jet flow, comprising a particle-laden central jet and a clean annular jet, into a large recirculation chamber. The results obtained from the numerical scheme agree well with the experimental data, lending confidence to the modeling approach. The multiple-realization particle trajectory turbulent flow modeling scheme is believed to be a more elegant and accurate approach to the extension of single-particle hydrodynamics to dilute multi-particle systems than the more commonly employed two-fluid modeling approach. It is also better able to incorporate additional force items such as lift, virtual mass and Bassett history terms directly into the particle equation of motion as appropriate. This makes it a suitable candidate for particle migration studies and an extension to situations involving liquid particulate phases with possible propulsion applications, such as in spray combustion, follows naturally

Simulación a microescala del flujo atmosférico y dispersión de contaminantes reactivos en ciudades

Tesis de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, leída el 09/06/2017Air quality is nowadays a priority environmental concern in the cities. High pollution levels have been often observed in urban areas, where both emissions and population are concentrated. The NOx, namely NO and NO2, are the primary trac-related pollutants in gas-phase, but only the NO2 is legislated given that it is the harmful to human health. Despite the environmental policies adopted in the recent years, the limit values established by the European Union (EU) and the World Health Organization (WHO) are widely exceeded across Europe, especially in urban areas. Accordingly, exhaustive studies are required to manage and plan mitigation strategies for the abatement of urban air pollution. The complexity of atmospheric processes in urban environments hinders the assessment of air quality in the streets using both monitoring techniques and numerical models. The vast number of obstacles found in an urban area (buildings, vegetation, vehicles...) lead to complex ow patterns in the streets. Additionally, the heterogeneity of pollutant emissions, mainly from road trac, across the city, gives rise to strong gradients of concentration. Hence the irregular distribution among buildings can only be captured by maps of high spatial resolution. In this sense, the Computational Fluid Dynamics (CFD) models are powerful tools for reproducing the dispersion of pollutants considering realistic features of urban environments...La calidad del aire es, hoy en día, una de las principales preocupaciones ambientales en las ciudades, donde se concentra la mayor parte de la poblacion y se registran niveles altos de contaminantes, especialmente debido al tráfico. Los NOx (oxidos de nitrogeno), es decir, NO (oxido ntrico) y NO2 (dioxido de nitrogeno), son unos de los contaminantes mas importantes asociados a las emisiones del tráfico rodado. Sin embargo, solo esta legislado el NO2, por ser perjudicial para la salud. A pesar de las políticas medioambientales adoptadas en los ultimos años, los valores límite establecidos por la Union Europea (EU, en ingles) y la Organizacion Mundial de la Salud (WHO, en ingles) son ampliamente superados a lo largo de Europa, especialmente en las zonas urbanas. Por este motivo se necesita llevar acabo estudios exhaustivos, que ayuden a gestionar y planificar estrategias de mitigacion para reducir la contaminacion atmosferica urbana. La complejidad de los procesos atmosfericos en las zonas urbanas dificulta la evaluacion de la calidad del aire, tanto a traves de tecnicas de monitorizacion como de modelos numericos. El gran numero de obstaculos existentes en la ciudad (edificios, vegetacion, vehículos...) generan complejas distribuciones del flujo de viento en las calles. Esto unido a la heterogeneidad de las emisiones a lo largo de la ciudad, producen fuertes gradientes de concentracion. Por esta razon es necesario resolver con alta resolucion espacial los fenomenos atmosfericos urbanos. En este sentido, los modelos de mecanica de fluidos (CFD, en ingles), son herramientas potentes capaces de reproducir en detalle la dispersion de contaminantes en zonas urbanas. Por contra, estas simulaciones requieren un elevado numero de puntos de malla (varios millones), que conlleva un alto coste computacional...Fac. de Ciencias FísicasTRUEunpu

Analysis and upscaling of a reactive transport model in fractured porous media involving nonlinear a transmission condition

We consider a reactive transport model in a fractured porous medium. The particularity appears in the conditions imposed at the interface separating the block and the fracture, which involves a nonlinear transmission condition. Assuming that the fracture has thickness e, we analyze the resulting problem and prove the convergence towards a reduced model in the limit e ¿ 0. The resulting is a model defined on an interface (the reduced fracture) and acting as a boundary condition for the equations defined in the block. Using both formal and rigorous arguments, we obtain the reduced models for different flow regimes, expressed through a moderate, or a high Péclet number. Keywords: Fractured porous media; Upscaling; Reactive transport; Nonlinear transmission condition

Analysis and upscaling of a reactive transport model in fractured porous media involving nonlinear a transmission condition

We consider a reactive transport model in a fractured porous medium. The particularity appears in the conditions imposed at the interface separating the block and the fracture, which involves a nonlinear transmission condition. Assuming that the fracture has thickness e, we analyze the resulting problem and prove the convergence towards a reduced model in the limit e ¿ 0. The resulting is a model defined on an interface (the reduced fracture) and acting as a boundary condition for the equations defined in the block. Using both formal and rigorous arguments, we obtain the reduced models for different flow regimes, expressed through a moderate, or a high Péclet number. Keywords: Fractured porous media; Upscaling; Reactive transport; Nonlinear transmission condition