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.

Reactive transport modeling has become an important tool to study and understand the transport and fate of solutes in the subsurface. However, the accurate simulation of reactive transport represents a formidable challenge because of the characteristics of flow, transport and chemical reactions that govern the migration of solutes in geological formations. In particular, solute transport in natural porous media is advection-controlled and dispersion is higher in the direction of flow than in the transverse direction. Both characteristics create difficulties for traditional numerical schemes that result in numerical dispersion and/or spurious oscillations. While these errors can often be tolerated in conservative transport simulations, they can be amplified in presence of chemical reactions resulting in much larger errors or unstable solutions. In this thesis, new Lagrangian based methods to simulate conservative and reactive transport in porous media are investigated. First, the derivation of a new meshless approximation based on smoothed particle hydrodynamics (SPH) to simulate conservative multidimensional solute transport, including advection and anisotropic dispersion, is presented. Second, a hybrid scheme that combines some of the advantages of streamline-based simulations and meshless methods and that allows simulating longitudinal and transverse dispersion without requiring a background grid is also derived. The numerical properties of both methods are analyzed analytical and numerically. Furthermore, both formulations are compared with existing numerical techniques in a set of two- and three-dimensional benchmark problems. It is demonstrated that the proposed schemes provide accurate and efficient solutions of physical transport processes in heterogeneous porous media and overcome most of the issues in existing numerical formulations. The new methods have the potential to remove or minimize numerical dispersion and grid orientation effects and, in the case o.

Teaches the application of Reactive Transport Modeling (RTM) for subsurface systems in order to expedite the understanding of the behavior of complex geological systems This book lays out the basic principles and approaches of Reactive Transport Modeling (RTM) for surface and subsurface environments, presenting specific workflows and applications. The techniques discussed are being increasingly commonly used in a wide range of research fields, and the information provided covers fundamental theory, practical issues in running reactive transport models, and how to apply techniques in specific areas. The need for RTM in engineered facilities, such as nuclear waste repositories or CO2 storage sites, is ever increasing, because the prediction of the future evolution of these systems has become a legal obligation. With increasing recognition of the power of these approaches, and their widening adoption, comes responsibility to ensure appropriate application of available tools. This book aims to provide the requisite understanding of key aspects of RTM, and in doing so help identify and thus avoid potential pitfalls. Reactive Transport Modeling covers: the application of RTM for CO2 sequestration and geothermal energy development; reservoir quality prediction; modeling diagenesis; modeling geochemical processes in oil & gas production; modeling gas hydrate production; reactive transport in fractured and porous media; reactive transport studies for nuclear waste disposal; reactive flow modeling in hydrothermal systems; and modeling biogeochemical processes. Key features include: A comprehensive reference for scientists and practitioners entering the area of reactive transport modeling (RTM) Presented by internationally known experts in the field Covers fundamental theory, practical issues in running reactive transport models, and hands-on examples for applying techniques in specific areas Teaches readers to appreciate the power of RTM and to stimulate usage and application Reactive Transport Modeling is written for graduate students and researchers in academia, government laboratories, and industry who are interested in applying reactive transport modeling to the topic of their research. The book will also appeal to geochemists, hydrogeologists, geophysicists, earth scientists, environmental engineers, and environmental chemists.