Upscaling mixing-limited reactions is one of the ongoing problems in in-situ reactive transport within the groundwater due to the intrinsic challenges in characterizing such reactions. Previous techniques did not completely solve it; the classic macrodispersion (Eulerian) model overestimates the mixing and hence the reaction zone, while the Lagrangian particle tracking does not introduce a straightforward approach to evaluate the mixing zone extent, and also the streamtube technique does not capture the actual mixing zone and ignores the intra-tube mixing. The lamella approach is a new tool that overcomes the abovementioned shortcomings by decoupling the transport and reactions within a Lagrangian frame of reference tracking the reaction front only. The approach depends on dividing the mixing front (between displacing-displaced solutions) into approximately linear patches (lamellae, in 2-D) on which the mixing-limited reactions take place and are characterized in terms of transport impacts and reactions on them. Here the approach is applied to the 2-D radial flow for testing the equilibrium reaction network and the kinetic bimolecular reaction cases, also applied to the fractal radial domain to test the bimolecular equilibrium reaction. The theoretical reaction rate found via the simplified lamella approach is compared with explicit simulation using a finite elements (COMSOL) framework fitted with the representative multicomponent equilibrium reaction network and good matching is obtained implying the successfulness of the lamella tool.

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.

Written jointly by a specialist in geophysical fluid dynamics and an applied mathematician, this is the first accessible introduction to a new set of methods for analysing Lagrangian motion in geophysical flows. The book opens by establishing context and fundamental mathematical concepts and definitions, exploring simple cases of steady flow, and touching on important topics from the classical theory of Hamiltonian systems. Subsequent chapters examine the elements and methods of Lagrangian transport analysis in time-dependent flows. The concluding chapter offers a brief survey of rapidly evolving research in geophysical fluid dynamics that makes use of this new approach.

Published by the American Geophysical Union as part of the Geophysical Monograph Series, Volume 200. Trajectory-based (“Lagrangian”) atmospheric transport and dispersion modeling has gained in popularity and sophistication over the previous several decades. It is common practice now for researchers around the world to apply Lagrangian models to a wide spectrum of issues. Lagrangian Modeling of the Atmosphere is a comprehensive volume that includes sections on Lagrangian modeling theory, model applications, and tests against observations. Published by the American Geophysical Union as part of the Geophysical Monograph Series. Comprehensive coverage of trajectory-based atmospheric dispersion modeling Important overview of a widely used modeling tool Sections look at modeling theory, application of models, and tests against observations

This book is an ensemble of six major chapters, an introduction, and a closure on modeling transport phenomena in porous media with applications. Two of the six chapters explain the underlying theories, whereas the rest focus on new applications. Porous media transport is essentially a multi-scale process. Accordingly, the related theory described in the second and third chapters covers both continuum‐ and meso‐scale phenomena. Examining the continuum formulation imparts rigor to the empirical porous media models, while the mesoscopic model focuses on the physical processes within the pores. Porous media models are discussed in the context of a few important engineering applications. These include biomedical problems, gas hydrate reservoirs, regenerators, and fuel cells. The discussion reveals the strengths and weaknesses of existing models as well as future research directions.