Fluid flow, solute transport, and chemical reactions in porous media are highly relevant for multiple applications and in several fields of knowledge. Aquifers are a typical example of porous media, but many others exist, like for instance biological tissues or wastewater treatment filters. Modeling and simulation of transport processes in porous media can be done through Lagrangian methods, which have certain advantages with respect to classical Eulerian methods. Among these advantages, a key one is that the solution of the advective transport term does not generate any numerical dispersion or instabilities, not even in those cases that are strongly dominated by advection, as opposed to what happens with classical Eulerian methods. However, the incorporation of chemical reaccions in the Lagrangian modeling context involves additional challenges and considerations with respect to conservative transport modeling. In this thesis, which is presented as a compendium of publications, new techniques are developed for modeling reactive transport of solutes in porous media from a Lagrangian perspective. Throghout the thesis, two different types of numerical particles are studied: mass-particles and fluid-particles. In both cases, continuum-scale dispersion (or at least part of it) is represented by random walks of numerical particles. Also in both cases, reactive transport simulations require interaction between nearby particles, either for directly computing reactions (when mass-particles are used) or for exchanging solutes (in the fluid-particle case). For this reason, a large part of this thesis revolves around the study of kernel functions, whose purpose is to mathematically represent the support volume of (and interaction between) particles. In this thesis it is shown that these functions, optimized using statistical theories of Kernel Density Estimation (KDE), may be used to simulate all kinds of nonlinear reactions with the mass-particle method known as Random Walk Particle Tracking (RWPT). Then, a new approach is developed for locally optimizing the particles' support volume (represented by the kernel bandwidth), such that it adapts its size and shape in time and space to minimize error. Thereafter, this technique is implemented in a hybrid manner in combination with a spatial discretization (binning) to improve its computational efficiency and to allow the incorporation of boundary conditions. Regarding fluid-particles, in this thesis it is shown that two methods that exist in Lagrangian modeling literature (Smoothed Particle Hydrodynamics or SPH, and Mass Transfer Particle Tracking) are mathematically equivalent, and they only differ in the choice of kernel used for the solute exchange between particles, which simulates dispersive transport. Finally, a novel Lagrangian fluid-particle method is developed, with an algorithm based on Multi-Rate Interaction by Exchange with the Mean (MRIEM), which enables to account for local-scale concentration fluctuation effects, as well as their generation, transport and decay. The method is shown capable of reproducing experimental results of reactive transport in a porous medium with locally mixing-limited conditions.

Random walk particle tracking methods are a computationally efficient family of methods to solve reactive transport problems. While the number of particles in most realistic applications is in the order of 10̂6 - 10̂9, the number of reactive molecules even in diluted systems might be in the order of fractions of the Avogadro number. Thus, each particle actually represents a group of potentially reactive molecules. The use of a low number of particles may result not only in loss of accuracy, but also may lead to an improper reproduction of the mixing process, limited by diffusion. Recent works have used this effect as a proxy to model incomplete mixing in porous media. The main contribution of this thesis is to propose a reactive transport model using a Kernel Density Estimation (KDE) of the concentrations that allows getting the expected results for a well-mixed solution with a limited number of particles. The idea consists of treating each particle as a sample drawn from the pool of molecules that it represents; this way, the actual location of a tracked particle is seen as a sample drawn from the density function of the location of molecules represented by that given particle, rigorously represented by a kernel density function. The probability of reaction can be obtained by combining the kernels associated with two potentially reactive particles. We demonstrate that the observed deviation in the reaction vs time curves in numerical experiments reported in the literature could be attributed to the statistical method used to reconstruct concentrations (fixed particle support) from discrete particle distributions, and not to the occurrence of true incomplete mixing. We further explore the evolution of the kernel size with time, linking it to the diffusion process. Our results show that KDEs are powerful tools to improve computational efficiency and robustness in reactive transport simulations, and indicates that incomplete mixing in diluted systems should be modeled based on alternative mechanistic models and not on a limited number of particles. Motivated by this potential, we extend the KDE model to simulate nonlinear adsorption which is a relevant process in many fields, such as product manufacturing or pollution remediation in porous materials. We show that the proposed model is able to reproduce the results of the Langmuir and Freundlich isotherms and to combine the features of these two classical adsorption models. In the Langmuir model, it is enough to add a finite number of sorption sites of homogeneous sorption properties, and to set the process as the combination of the forward and the backward reactions, each one of them with a pre-specified reaction rate. To model the Freundlich isotherm instead, typical of low to intermediate range of solute concentrations, there is a need to assign a different equilibrium constant to each specified sorption site, provided they are all drawn from a truncated power-law distribution. Both nonlinear models can be combined in a single framework to obtain a typical observed behavior for a wide range of concentration values. This approach opens up a new way to predict and control an adsorption-based process using a particle-based method with a finite number of particles. Finally, by classifying the particles to mobile and immobile states and employing transition probabilities between these two states, we take into account the porosity of the diluted system in the KDE model. The state of a particle is an attribute that defines the domain at which the particle is present at a given time within the porous medium. The transition probabilities are controlled by two parameters which implicitly determine the porosity. Simulations results show a good agreement with the analytical solutions of complete and incomplete mixing solutions, independent of the number of particles.

Reactive transport modeling is an important tool for the analysis of coupled physical, chemical, and biological processes in Earth systems. Observed reactive transport in heterogeneous porous media shows a different behavior than the established transport laws for homogeneous media. Natural aquifers exhibit physical and chemical heterogeneities at all scales, which leads to reaction and transport dynamics that cannot be explained by traditional reactive models based on the advection-dispersion-reaction equation (ADRE). In particular, the discrepancy is traced back to the nonuniform nature of flow velocity fields, complex spatial concentration distributions, and the degree of mixing between reactants. The role and contribution of these factors is key to provide accurate predictions of reactions. The complexity of the task lies in the enormous range of spatial and temporal scales that reactants find in natural porous media. Hence, the complete characterization of the fate of chemical reactions requires that models accounts for the basic mechanisms that govern the mixing and reaction dynamics. In this thesis, we present a novel methodology for the simulation of homogeneous chemical reactions. The proposed methodology is a random walk particle tracking approach (RWPT) coupled with reactions that simulates bimolecular chemical reactions, and is equivalent to the ADRE. Reactions among particles are determined by a reaction probability given in terms of the reaction rate coefficient, the total number of particles, and an interaction radius that describes a well-mixed support volume at which all particles have the same probability to react. The method is meshless and free of numerical dispersion. The RWPT approach is validated against analytical solutions for different flow scenarios under slow and fast reaction kinetics. We focus on the impact of the mixing degree between chemical species and its role in the global reaction behavior. We first consider a reactive displacement in a Poiseuille flow through a pore channel, this system allow us to quantify the impact of the interaction of interface deformation and diffusion on mixing and reactive transport. We observe overestimation of the global reaction efficiency by the use of the Taylor dispersion coefficient at preasymptotic times, when the system is characterized by incomplete mixing. Next, we observe features of incomplete mixing in a synthetic porous medium. Results show that macroscopic predictions using the hydrodynamic dispersion coefficient overestimates the amount of reaction. In addition, we analize the bimolecular reactive transport in a laboratory experiment, where we find that the amount of reaction is affected by the amount of mixing due to difusion, the amount of mixing due to spreading and the degree of heterogeneity of the flow field. The contributions of these factors induces that ADRE estimation of the total reaction product fails. In order to characterize incomplete mixing and provide an explicit relation between fluid deformation and its impact on the temporal evolution of the chemical reactivity, we develop the dispersive lamella approach based on the concept of effective dispersion which accurately predicts the full evolution of the product mass. Specifically, the approach captures the impact of interface deformation and diffusive coalescence. Using this methodology, we quantify the impact of flow heterogeneities on the amount of fluid mixing in a pore channel, where we observe three temporal regimes based on the production rate of the product mass. In addition, the dispersive lamella predictions capture the kinetics of the reaction in a synthetic porous medium. Results reveal that reaction behavior is controlled by the interface front between the two reactants. In the pore-scale experimental visualization, the dispersive lamella show that reaction is controlled by the deformed mixing interface at early times, and for fingering coalescence at late times.

The present work reflects a multi-disciplinary effort to address the topic of confined hydrosystems developed with a cross-fertilization panel of physics, chemists, biologists, soil and earth scientists. Confined hydrosystems include all situations in natural settings wherein the extent of the liquid phase is limited so that the solid-liquid and/or liquid-air interfaces may be critical to the properties of the whole system. Primarily, this so-called “residual” solution is occluded in pores/channels in such a way that decreases its tendency to evaporation, and makes it long-lasting in arid (Earth deserts) and hyper-arid (Mars soils) areas. The associated physics is available from domains like capillarity, adsorption and wetting, and surface forces. However, many processes are still to understand due to the close relationship between local structure and matter properties, the subtle interplay between the host and the guest, the complex intermingling among static reactivity and migration pathway. Expert contributors from Israel, Russia, Europe and US discuss the behaviour of water and aqueous solutes at different scale, from the nanometric range of carbon nanotubes and nanofluidics to the regional scale of aquifers reactive flow in sedimentary basins. This scientific scope allowed the group of participants with very different background to tackle the confinement topic at different scales. The book is organized according to four sections that include: i) flow, from nano- to mega-scale; ii) ions, hydration and transport; iii) in-pores/channels cavitation; iv) crystallization under confinement. Most of contributions relates to experimental works at different resolution, interpreted through classic thermodynamics and intermolecular forces. Simulation techniques are used to explore the atomic scale of interfaces and the migration in the thinnest angstrom-wide channels.

This RiMG (Reviews in Mineralogy & Geochemistry) volume includes contributions that review experimental, characterization, and modeling advances in our understanding of pore-scale geochemical processes. The volume had its origins in a special theme session at the 2015 Goldschmidt Conference in Prague. From a diversity of pore-scale topics that ranged from multi-scale characterization to modeling, this work summarizes the state-of-the-science in this subject. Topics include: modification of thermodynamics and kinetics in small pores. chemo-mechanical processes and how they affect porosity evolution in geological media. small angle neutron scattering (SANS) techniques. how isotopic gradients across fluid–mineral boundaries can develop and how these provide insight into pore-scale processes. Information on an important class of models referred to as "pore network" and much more. The material in this book is accessible for graduate students, researchers, and professionals in the earth, material, environmental, hydrological, and biological sciences. The pore scale is readily recognizable to geochemists, and yet in the past it has not received a great deal of attention as a distinct scale or environment that is associated with its own set of questions and challenges. Is the pore scale merely an environment in which smaller scale (molecular) processes aggregate, or are there emergent phenomena unique to this scale? Is it simply a finer-grained version of the "continuum" scale that is addressed in larger-scale models and interpretations? The scale is important because it accounts for the pore architecture within which such diverse processes as multi-mineral reaction networks, microbial community interaction, and transport play out, giving rise to new geochemical behavior that might not be understood or predicted by considering smaller or larger scales alone.