Documents published in 2020 : Scipedia

Shock capturing techniques for hp-adaptive finite elements
A. Hierro, S. Badia, P. Kus

Computer Methods in Applied Mechanics and Engineering (2016). Vol. 309, pp. 532-553 (Preprint)

Abstract
The aim of this work is to propose an hp-adaptive algorithm for discontinuous Galerkin methods that is capable to detect the discontinuities and sharp layers and avoid the spurious oscillation of the solution around them. In order to control the spurious oscillations, artificial viscosity is used with the particularity that it is only applied around the layers where the solution changes abruptly. To do so, a novel troubled-cell detector has been developed in order to mark the elements around those layers and to impose linear order in them. The detector takes advantage of the evolution of the value of the gradient through the adaptive process.
Abstract
The aim of this work is to propose an hp-adaptive algorithm for discontinuous Galerkin methods that is capable to detect the discontinuities and sharp layers and avoid the [...]
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Segregated Runge-Kutta methods for the incompressible Navier-Stokes equations
O. Colomés, S. Badia

International Journal for Numerical Methods in Engineering (2015). Vol. 105 (5), pp. 372-400 (Preprint)

Abstract
In this work, we propose Runge-Kutta time integration schemes for the incompressible Navier-Stokes equations with two salient properties. First, velocity and pressure computations are segregated at the time integration level, without the need to perform additional fractional step techniques that spoil high orders of accuracy. Second, the proposed methods keep the same order of accuracy for both velocities and pressures. The segregated Runge-Kutta methods are motivated as an implicit-explicit Runge-Kutta time integration of the projected Navier-Stokes system onto the discrete divergence-free space, and its re-statement in a velocity-pressure setting using a discrete pressure Poisson equation. We have analysed the preservation of the discrete divergence constraint for segregated Runge-Kutta methods and their relation (in their fully explicit version) with existing half-explicit methods. We have performed a detailed numerical experimentation for a wide set of schemes (from first to third order), including implicit and IMEX integration of viscous and convective terms, for incompressible laminar and turbulent flows. Further, segregated Runge-Kutta schemes with adaptive time stepping are proposed
Abstract
In this work, we propose Runge-Kutta time integration schemes for the incompressible Navier-Stokes equations with two salient properties. First, velocity and pressure computations [...]
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An approach to verification and validation of MHD codes for fusion applications
S. Smolentsev, S. Badia, R. Bhattacharyay, L. Bühler, L. Chen, Q. Huang, H. Jin, D. Krasnov, D. Lee, E. Valls, C. Mistrangelo, R. Munipalli, M. Ni, D. Pashkevich, A. Patel, G. Pulugundla, P. Satyamurthy, A. Snegirev, V. Sviridov, P. Swain, T. Zhou, O. Zikanov

Fusion Engineering and Design (2015). Vol. 100 (11/2015), pp. 65-72 (Preprint)

Abstract
We propose a new activity on verification and validation (V&V) of MHD codes presently employed by the fusion community as a predictive capability tool for liquid metal cooling applications, such as liquid metal blankets. The important steps in the development of MHD codes starting from the 1970s are outlined first and then basic MHD codes, which are currently in use by designers of liquid breeder blankets, are reviewed. A benchmark database of five problems has been proposed to cover a wide range of MHD flows from laminar fully developed to turbulent flows, which are of interest for fusion applications: (A) 2D fully developed laminar steady MHD flow, (B) 3D laminar, steady developing MHD flow in a non-uniform magnetic field, (C) quasi-two-dimensional MHD turbulent flow, (D) 3D turbulent MHD flow, and (E) MHD flow with heat transfer (buoyant convection). Finally, we introduce important details of the proposed activities, such as basic V&V rules and schedule. The main goal of the present paper is to help in establishing an efficient V&V framework and to initiate benchmarking among interested parties. The comparison results computed by the codes against analytical solutions and trusted experimental and numerical data as well as code-to-code comparisons will be presented and analyzed in companion paper/papers
Abstract
We propose a new activity on verification and validation (V&V) of MHD codes presently employed by the fusion community as a predictive capability tool for liquid metal [...]
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On discrete maximum principles for discontinuous Galerkin methods
S. Badia, A. Hierro

Computer Methods in Applied Mechanics and Engineering (2015). Vol. 286, pp. 107-122 (Preprint)

Abstract
The aim of this work is to propose a monotonicity-preserving method for discontinuous Galerkin (dG) approximations of convection–diffusion problems. To do so, a novel definition of discrete maximum principle (DMP) is proposed using the discrete variational setting of the problem, and we show that the fulfilment of this DMP implies that the minimum/maximum (depending on the sign of the forcing term) is on the boundary for multidimensional problems. Then, an artificial viscosity (AV) technique is designed for convection-dominant problems that satisfies the above mentioned DMP. The noncomplete stabilized interior penalty dG method is proved to fulfil the DMP property for the one-dimensional linear case when adding such AV with certain parameters. The benchmarks for the constant values to satisfy the DMP are calculated and tested in the numerical experiments section. Finally, the method is applied to different test problems in one and two dimensions to show its performance.
Abstract
The aim of this work is to propose a monotonicity-preserving method for discontinuous Galerkin (dG) approximations of convection–diffusion problems. To do so, a novel [...]
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Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem
S. Badia, A. Martín, R. Planas

Journal of Computational Physics (2014). Vol. 274, pp. 562-591

Abstract
The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 x 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.
Abstract
The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic [...]
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Convergence towards weak solutions of the Navier-Stokes equations for a finite element approximation with numerical subgrid-scale modelling
S. Badia, J. Gutiérrez-Santacreu

IMA Journal of Numerical Analysis (2014). Vol. 34 (3), pp. 1193-1221

Abstract
Residual-based stabilized finite element (FE) techniques for the Navier-Stokes equations lead to numerical discretizations that provide convection stabilization as well as pressure stability without the need to satisfy an inf-sup condition. They can be motivated by using a variational multiscale (VMS) framework, based on the decomposition of the fluid velocity into a resolvable FE component plus a modelled subgrid-scale component. The subgrid closure acts as a large eddy simulation turbulence model, leading to accurate under-resolved simulations. However, even though VMS formulations are increasingly used in the applied FE community, their numerical analysis has been restricted to a priori estimates and convergence to smooth solutions only, via a priori error estimates. In this work, we prove that some versions of these methods (based on dynamic and orthogonal closures) also converge to weak (turbulent) solutions of the Navier-Stokes equations. These results are obtained by using compactness results in Bochner-Lebesgue spaces.
Abstract
Residual-based stabilized finite element (FE) techniques for the Navier-Stokes equations lead to numerical discretizations that provide convection stabilization as well as [...]
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On monotonicity-preserving stabilized finite element approximations of transport problems
S. Badia, A. Hierro

SIAM Journal on Scientific Computing (2014). Vol. 36 (6), pp. A2673-A2697

Abstract
The aim of this work is to design monotonicity-preserving stabilized finite element techniques for transport problems as a blend of linear and nonlinear (shock-capturing) stabilization. As linear stabilization, we consider and analyze a novel symmetric projection stabilization technique based on a local Scott--Zhang projector. Next, we design a weighting of the aforementioned linear stabilization such that, when combined with a finite element discretization enjoying a discrete maximum principle (usually attained via nonlinear stabilization), it does not spoil these monotonicity properties. Then, we propose novel nonlinear stabilization schemes in the form of an artificial viscosity method where the amount of viscosity is proportional to gradient jumps at either finite element boundaries or nodes. For the nodal scheme, we prove a discrete maximum principle for time-dependent multidimensional transport problems. Numerical experiments support the numerical analysis and we show that the resulting methods provide excellent results. In particular, we observe that the proposed nonlinear stabilization techniques do an excellent job eliminating oscillations around shocks
Abstract
The aim of this work is to design monotonicity-preserving stabilized finite element techniques for transport problems as a blend of linear and nonlinear (shock-capturing) [...]
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Adaptive finite element simulation of incompressible flows by hybrid continuous-discontinuous Galerkin formulations
S. Badia, J. Baiges

SIAM journal on scientific computing (2013). Vol. 35 (1), pp. A491-A516 (Preprint)

Abstract
In this work we design hybrid continuous-discontinuous finite element spaces that permit discontinuities on nonmatching element interfaces of nonconforming meshes. Then we develop an equal-order stabilized finite element formulation for incompressible flows over these hybrid spaces, which combines the element interior stabilization of SUPG-type continuous Galerkin formulations and the jump stabilization of discontinuous Galerkin formulations. Optimal stability and convergence results are obtained. For the adaptive setting, we use a standard error estimator and marking strategy. Numerical experiments show the optimal accuracy of the hybrid algorithm for both uniformly and adaptively refined nonconforming meshes. The outcome of this work is a finite element formulation that can naturally be used on nonconforming meshes, as discontinuous Galerkin formulations, while keeping the much lower CPU cost of continuous Galerkin formulations.
Abstract
In this work we design hybrid continuous-discontinuous finite element spaces that permit discontinuities on nonmatching element interfaces of nonconforming meshes. Then we [...]
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Unconditionally stable operator splitting algorithms for the incompressible magnetohydrodynamics (MHD) system discretized by a stabilized finite element formulation based on projections
S. Badia, R. Planas, J. Gutiérrez-Santacreu

International Journal for Numerical Methods in Engineering (2013). Vol. 93 (3), pp. 302-328

Abstract
In this article, we propose different splitting procedures for the transient incompressible magnetohydrodynamics (MHD) system that are unconditionally stable. We consider two levels of splitting, on one side we perform the segregation of the fluid pressure and magnetic pseudo‐pressure from the vectorial fields computation. At the second level, the fluid velocity and induction fields are also decoupled. This way, we transform a fully coupled indefinite multi‐physics system into a set of smaller definite ones, clearly reducing the CPU cost. With regard to the finite element approximation, we stick to an unconditionally convergent stabilized finite element formulation because it introduces convection stabilization, allows to circumvent inf‐sup conditions (clearly simplifying implementation issues), and is able to capture non‐smooth solutions of the magnetic subproblem. However, residual‐based finite element formulations are not suitable for segregation, because they lose the skew‐symmetry of the off‐diagonal blocks. Therefore, in this work, we have proposed a novel term‐by‐term stabilization of the MHD system based on projections that is still unconditionally convergent.
Abstract
In this article, we propose different splitting procedures for the transient incompressible magnetohydrodynamics (MHD) system that are unconditionally stable. We consider [...]
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On stabilized finite element methods based on the Scott-Zhang projector: circumventing the inf-sup condition for the Stokes problem
S. Badia

Computer Methods in Applied Mechanics and Engineering (2012). Vol. 247-248, pp. 65-72

Abstract
In this work we propose a stabilized nite element method that permits us to circumvent discrete inf-sup conditions, e.g. allowing equal order interpolation. The type of method we propose belongs to the family of symmetric stabilization techniques, which are based on the introduction of additional terms that penalize the di erence between some quantities, i.e. the pressure gradient in the Stokes problem, and their nite element projections. The key feature of the formulation we propose is the de nition of the projection to be used, a non-standard Scott-Zhang projector that is well-de ned for L1() functions. The resulting method has some appealing features: the projector is local and nested meshes or enriched spaces are not required.
Abstract
In this work we propose a stabilized nite element method that permits us to circumvent discrete inf-sup conditions, e.g. allowing equal order interpolation. The type [...]
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An Overview on Numerical Analyses of Nematic Liquid Crystal Flows
S. Badia, F. Guillén-González, J. Gutiérrez-Santacreu

Archives of Computational Methods in Engineering (2011). Vol. 18 (3), pp. 285-313

Abstract
The purpose of this work is to provide an overview of the most recent numerical developments in the field of nematic liquid crystals. The Ericksen-Leslie equations govern the motion of a nematic liquid crystal. This system, in its simplest form, consists of the Navier-Stokes equations coupled with an extra anisotropic stress tensor, which represents the effect of the nematic liquid crystal on the fluid, and a convective harmonic map equation. The sphere constraint must be enforced almost everywhere in order to obtain an energy estimate. Since an almost everywhere satisfaction of this restriction is not appropriate at a numerical level, two alternative approaches have been introduced: a penalty method and a saddle-point method. These approaches are suitable for their numerical approximation by finite elements, since a discrete version of the restriction is enough to prove the desired energy estimate.
Abstract
The purpose of this work is to provide an overview of the most recent numerical developments in the field of nematic liquid crystals. The Ericksen-Leslie equations govern [...]
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Finite element approximation of nematic liquid crystal flows using a saddle-point structure
S. Badia, F. Guillén-González, J. Gutiérrez-Santacreu

Journal of Computational Physics (2011). Vol. 230 (4), pp. 1686-1706
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Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction
S. Badia, A. Quaini, A. Quarteroni

Journal of Computational Physics (2009). Vol. 228 (21), pp. 7986-8014

Abstract
The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier–Stokes equations with the Biot system. The finite element approximation of this problem is involved due to the fact that both subproblems are indefinite. In this work, we first design residual-based stabilization techniques for the Biot system, motivated by the variational multiscale approach. Then, we state the monolithic Navier–Stokes/Biot system with the appropriate transmission conditions at the interface. For the solution of the coupled system, we adopt both monolithic solvers and heterogeneous domain decomposition strategies. Different domain decomposition methods are considered and their convergence is analyzed for a simplified problem. We compare the efficiency of all the methods on a test problem that exhibits a large added-mass effect, as it happens in hemodynamics applications.
Abstract
The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier–Stokes equations with the Biot system. The finite element [...]
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Robin-Robin preconditioned Krylov methods for fluid-structure interaction problems
S. Badia, F. Nobile, C. Vergara

Computer Methods in Applied Mechanics and Engineering (2009). Vol. 198 (33-36), pp. 2768-2784

Abstract
In this work, we propose a Robin–Robin preconditioner combined with Krylov iterations for the solution of the interface system arising in fluid–structure interaction (FSI) problems. It can be seen as a partitioned FSI procedure and in this respect it generalizes the ideas introduced in [S. Badia, F. Nobile, C. Vergara, J. Comput. Phys. 227 (2008) 7027–7051]. We analyze the convergence of GMRES iterations with the Robin–Robin preconditioner on a model problem and compare its efficiency with some existing algorithms. The method is shown to be very efficient for many challenging fluid–structure interaction problems, such as those characterized by a large added-mass effect or by enclosed fluids. In particular, the possibility to solve balloon-type problems without any special treatment makes this algorithm very appealing compared to the computationally intensive existing approaches.
Abstract
In this work, we propose a Robin–Robin preconditioner combined with Krylov iterations for the solution of the interface system arising in fluid–structure [...]
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Modular vs non-modular preconditioners for fluid-structure systems with large added-mass effect
S. Badia, A. Quaini, A. Quarteroni

Computer Methods in Applied Mechanics and Engineering (2008). Vol. 197 (49-50), pp. 4216-4232

Abstract
In this article we address the numerical simulation of fluid–structure interaction (FSI) problems featuring large added-mass effect. We analyze different preconditioners for the coupled system matrix obtained after space–time discretization and linearization of the FSI problem. The classical Dirichlet–Neumann preconditioner has the advantage of “modularity” because it allows to reuse existing fluid and structure codes with minimum effort (simple interface communication). Unfortunately, its performance is very poor in case of large added-mass effects. Alternatively, we consider two non-modular approaches. The first one consists in preconditioning the coupled system with a suitable diagonal scaling combined with an ILUT preconditioner. The system is then solved by a Krylov method. The drawback of this procedure is that the combination of fluid and structure codes to solve the coupled system is not straightforward. The second non-modular approach we consider is a splitting technique based on an inexact block-LU factorization of the linear FSI system. The resulting algorithm computes the fluid velocity separately from the coupled pressure–structure system at each iteration, reducing the computational cost. Independently of the preconditioner, the efficiency of semi-implicit algorithms (i.e., those that treat geometric and fluid nonlinearities in an explicit way) is highlighted and their performance compared to the one of implicit algorithms. All the methods are tested on three-dimensional blood-vessel systems. The algorithm combining the non-modular ILUT preconditioner with Krylov methods proved to be the fastest.
Abstract
In this article we address the numerical simulation of fluid–structure interaction (FSI) problems featuring large added-mass effect. We analyze different preconditioners [...]
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Fluid-structure partitioned procedures based on Robin transmission conditions
S. Badia, F. Nobile, C. Vergara

Journal of Computational Physics (2008). Vol. 227 (14), pp. 7027-7051

Abstract
In this article we design new partitioned procedures for fluid–structure interaction problems, based on Robin-type transmission conditions. The choice of the coefficient in the Robin conditions is justified via simplified models. The strategy is effective whenever an incompressible fluid interacts with a relatively thin membrane, as in hemodynamics applications. We analyze theoretically the new iterative procedures on a model problem, which represents a simplified blood-vessel system. In particular, the Robin–Neumann scheme exhibits enhanced convergence properties with respect to the existing partitioned procedures. The theoretical results are checked using numerical experimentation
Abstract
In this article we design new partitioned procedures for fluid–structure interaction problems, based on Robin-type transmission conditions. The choice of the coefficient [...]
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On atomistic-to-continuum coupling by blending
S. Badia, M. Parks, P. Bochev, M. Gunzburger, R. Lehoucq

Multiscale modeling and simulation (2008). Vol. 7 (1), pp. 381-406

Abstract
A mathematical framework for the coupling of atomistic and continuum models by blending them over a subdomain subject to a constraint is developed. Using the framework, four classes of atomistic-to-continuum (AtC) blending methods are established, their consistency is studied, and their relative merits are discussed. In addition, the framework helps clarify the origin of ghost forces and formalizes the notion of a patch test. Numerical experiments with the AtC methods are used to illustrate the theoretical results.
Abstract
A mathematical framework for the coupling of atomistic and continuum models by blending them over a subdomain subject to a constraint is developed. Using the framework, [...]
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Splitting methods based on algebraic factorization for fluid-structure interaction
S. Badia, A. Quaini, A. Quateroni

SIAM journal on scientific computing (2008). Vol. 30 (4), pp. 1778-1805

Abstract
We discuss in this paper the numerical approximation of fluid-structure interaction (FSI) problems dealing with strong added-mass effect. We propose new semi-implicit algorithms based on inexact block-$LU$ factorization of the linear system obtained after the space-time discretization and linearization of the FSI problem. As a result, the fluid velocity is computed separately from the coupled pressure-structure velocity system at each iteration, reducing the computational cost. We investigate explicit-implicit decomposition through algebraic splitting techniques originally designed for the FSI problem. This approach leads to two different families of methods which extend to FSI the algebraic pressure correction method and the Yosida method, two schemes that were previously adopted for pure fluid problems. Furthermore, we have considered the inexact factorization of the fluid-structure system as a preconditioner. The numerical properties of these methods have been tested on a model problem representing a blood-vessel system.
Abstract
We discuss in this paper the numerical approximation of fluid-structure interaction (FSI) problems dealing with strong added-mass effect. We propose new semi-implicit algorithms [...]
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Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force
J. Fish, M. Nuggehally, M. Shephard, C. Picu, S. Badia, M. Parks, M. Gunzburger

Computer Methods in Applied Mechanics and Engineering (2007). Vol. 196 (45-48), pp. 4548-4560

Abstract
A concurrent atomistic to continuum (AtC) coupling method is presented in this paper. The problem domain is decomposed into an atomistic sub-domain where fine scale features need to be resolved, a continuum sub-domain which can adequately describe the macroscale deformation and an overlap interphase sub-domain that has a blended description of the two. The problem is formulated in terms of equilibrium equations with a blending between the continuum stress and the atomistic force in the interphase. Coupling between the continuum and the atomistics is established by imposing constraints between the continuum solution and the atomistic solution over the interphase sub-domain in a weak sense. Specifically, in the examples considered here, the atomistic domain is modeled by the aluminum embedded atom method (EAM) inter-atomic potential developed by Ercolessi and Adams [F. Ercolessi, J.B. Adams, Interatomic potentials from first-principles calculations: the force-matching method, Europhys. Lett. 26 (1994) 583] and the continuum domain is a linear elastic model consistent with the EAM potential. The formulation is subjected to patch tests to demonstrate its ability to represent the constant strain modes and the rigid body modes. Numerical examples are illustrated with comparisons to reference atomistic solution.
Abstract
A concurrent atomistic to continuum (AtC) coupling method is presented in this paper. The problem domain is decomposed into an atomistic sub-domain [...]
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A force-based blending model for atomistic-to-continuum coupling
S. Badia, P. Bochev, R. Lehoucq, M. Parks, J. Fish, M. Nuggehally, M. Gunzburger

International Journal for Multiscale Computational Engineering (2007). Vol. 5 (5), pp. 387-406

Abstract
A method for coupling atomistic and continuum models across a subdomain, or bridge region, is presented. Coupling is effected through a force-based blending model. The method properly accounts for the the atomistic and continuum contributions to the force balance at points in the bridge region. Simple patch tests and computational experiments are used to study the method and its properties in one dimension. A discussion of implementation issues in higher dimensions is provided.
Abstract
A method for coupling atomistic and continuum models across a subdomain, or bridge region, is presented. Coupling is effected through a force-based blending model. The method [...]
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Collapse of the Pilcomayo River
J. Martí-Vide, M. Amarilla, F. Zarate

Geomorphology (2014). Vol. 205, pp. 155-136

Abstract
The Pilcomayo River flows south-eastwards from the Bolivian Andes across the Chaco Plains, setting the border between Argentina and Paraguay. It flows down along 1000 km, in principle, to finally join the Paraguay River. It spills over the plains during the rainy season from January to March. The sediment load of the Pilcomayo is one of the largest in the world: 140 million tons per year, which is mostly wash load from the upland Andes. The mean concentration of suspended sediment is 15 g/l. The maximum recorded concentration is as high as 60 g/l. The river has built a large fan covering a surface of 210,000 km2, with many abandoned channels. Today, it is a river prone to avulsion, raising border disputes between the two lowland countries, Argentina and Paraguay. Moreover, the very special feature of Pilcomayo River is that it does not actually flow into the Paraguay River. Very far upstream of the mouth in the Paraguay the channel blocks itself with sediment and wood debris forcing water and sediment to spread across the plains. Moreover, the point of blockage has moved hundreds of kilometers upstream throughout the 20th century. Many environmental issues arise because of this collapse (channel discontinuity), not the least of them is the migration of fish. The future of the river concerns Bolivia and the two lowland countries.
Abstract
The Pilcomayo River flows south-eastwards from the Bolivian Andes across the Chaco Plains, setting the border between Argentina and Paraguay. It flows down along 1000 km, [...]
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Nonlinear Regular Wave Generation in Numerical and Physical Flumes
T. Oliveira, X. Cobos, A. Sánchez-Arcilla, J. Sierra, M. Celigueta

Journal of coastal research (2009). Vol. 2 (SI:56), pp. 1025-1029

Abstract
The generation of nonlinear waves in a numerical wave using first-order wavemaker theory is discussed comparing numerical results with free Surface data from large scale physical tests (CIEM wave flume) and Stokes wave theories. A general formulation for the analysis of fluid-structure interaction problems is employed to simulate the numerical wave flume using the Particle Finite Element (PFEM). This method uses a Lagrangian description to model the motion of particles in both the fluid and the structure domains. With this work we can conclude that PFEM formulation simulate the generation of natyrally-occurring nonlinear waves with different types for varied wave conditions and at different scales. Like in physical flumes if we use first-order wavemaker theory in numerical flumes unwanted nonlinearities can be found for some wave conditions.The generation of nonlinear waves in a numerical wave using first-order wavemaker theory is discussed comparing numerical results with free Surface data from large scale physical tests (CIEM wave flume) and Stokes wave theories. A general formulation for the analysis of fluid-structure interaction problems is employed to simulate the numerical wave flume using the Particle Finite Element (PFEM). This method uses a Lagrangian description to model the motion of particles in both the fluid and the structure domains. With this work we can conclude that PFEM formulation simulate the generation of natyrally-occurring nonlinear waves with different types for varied wave conditions and at different scales. Like in physical flumes if we use first-order wavemaker theory in numerical flumes unwanted nonlinearities can be found for some wave conditions.
Abstract
The generation of nonlinear waves in a numerical wave using first-order wavemaker theory is discussed comparing numerical results with free Surface data from large scale physical [...]
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Modeling the fate of UV filters in subsurface: co-metabolic degradation and the role of biomass in sorption processes
P. Rodríguez-Escales, X. Sánchez-Vila

Water Resources Research (2020). Vol. 168, pp. 115192:1-115192:11

Abstract
Ultraviolet filters (UVFs) are emerging organic compounds found in most water systems. They are constituents of personal care products, as well as industrial ones. The concentration of UVFs in the water bodies in space and time is mostly determined by degradation and sorption, both processes being determinant of their bioavailability and toxicity to ecosystems and humans. UVFs are a wide group of compounds, with different sorption behavior expected depending on the individual chemical properties (pKa,Koc,Kow). The goal of this work is framed in the context of improving our understanding of the sorption processes of UVFs occurring in the aquifer; that is, to evaluate the role of biomass growth, solid organic matter (SOM) and redox conditions in the characterization of sorption of a set of UVFs. We constructed a conceptual and a numerical model to evaluate the fate of selected UV filters, focused on both sorption and degradation. The models were validated with published data by Liu et al. (2013), consisting in a suite of batch experiments evaluating the fate of a cocktail of UVs under different redox conditions. The compounds evaluated included ionic UV filters (Benzophenone-3; 2-(3-t-butyl-2-hydroxy-5-methylphenyl)5-chloro-benzotriazole; 2-(2'-hydroxy-5'-octylphenyl)-benzotriazole) and neutral ones (octyl 4-methoxycinnamatte; and octocrylene).
Abstract
Ultraviolet filters (UVFs) are emerging organic compounds found in most water systems. They are constituents of personal care products, as well as industrial ones. The concentration [...]
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What are the main factors influencing the presence of faecal bacteria pollution in groundwater systems in developing countries?
N. Ferrer, A. Folch, G. Masó, S. Sánchez, X. Sánchez-Vila

Journal of Contaminant Hydrology (2020). Vol. 228, pp. 103556:1-103556:11

Abstract
Groundwater is the major source of drinking water in most rural areas in developing countries. This resource is threatened by the potential presence of faecal bacteria coming from a variety of sources and pollution paths, the former including septic tanks, landfills, and crop irrigation with untreated, or insufficiently treated, sewage effluent. Accurately assessing the microbiological safety of water resources is essential to reduce diseases caused by waterborne faecal exposure. The objective of this study is to discern which are the most significant sanitary, hydrogeological, geochemical, and physical variables influencing the presence of faecal bacterial pollution in groundwater by means of statistical multivariate analyses. The concentration of Escherichia coli was measured in a number of waterpoints of different types in a rural area located in the coast of Kenya, assessing both a dry and a wet season. The results from the analyses reaffirm that the design of the well and their maintenance, the distance to latrines, and the geological structure of the waterpoints are the most significant variables affecting the presence of E. coli. Most notably, the presence of faecal bacteria in the study area correlates negatively with the concentration of ion Na+ (being an indirect indicator of fast recharge in the study site), and also negatively with the length of the water column inside the well.
Abstract
Groundwater is the major source of drinking water in most rural areas in developing countries. This resource is threatened by the potential presence of faecal bacteria coming [...]
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Particle density estimation with grid-projected and boundary-corrected adaptive kernels
G. Sole-Mari, D. Bolster, D. Fernàndez-García, X. Sánchez-Vila

Advances in Water Resources (2019). Vol. 131, pp. 103382:1-103382:13

Abstract
The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk particle tracking (RWPT) simulations, particle density is directly linked to solute concentrations, which is normally the main variable of interest, not just for visualization and post-processing of the results, but also for the computation of non-linear processes, such as chemical reactions. Previous works have shown the improved nature of kernel density estimation (KDE) over other methods such as binning, in terms of its ability to accurately estimate the “true” particle density relying on a limited amount of information. Here, we develop a grid-projected KDE methodology to determine particle densities by applying kernel smoothing on a pilot binning; this may be seen as a “hybrid” approach between binning and KDE. The kernel bandwidth is optimized locally. Through simple implementation examples, we elucidate several appealing aspects of the proposed approach, including its computational efficiency and the possibility to account for typical boundary conditions, which would otherwise be cumbersome in conventional KDE.
Abstract
The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) [...]
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A bilayer coarse-fine infiltration system minimizes bioclogging: the relevance of depth-dynamics
N. Perujo, A. Romaní, X. Sánchez-Vila

Science of the total environmental (2019). Vol. 669, pp. 559-569

Abstract
Bioclogging is a main concern in infiltration systems as it may significantly shorten the service life of these low-technology water treatment methods. In porous media, biofilms grow to clog partially or totally the pore network. Dynamics of biofilm accumulation (e.g., by attachment, detachment, advective transport in depth) and their impact on both surface and deep bioclogging are still not yet fully understood. To address this concern, a 104 day-long outdoor infiltration experiment in sand tanks was performed, using secondary treated wastewater and two grain size distributions (GSDs): a monolayer system filled with fine sand, and a bilayer one composed by a layer of coarse sand placed on top of a layer of fine sand. Biofilm dynamics as a function of GSD and depth were studied through cross-correlations and multivariate statistical analyses using different parameters from biofilm biomass and activity indices, plus hydraulic parameters measured at different depths. Bioclogging (both surface and deep) was found more significant in the monolayer fine system than in the bilayer coarse-fine one, possibly due to an early low-cohesive biofilm formation in the former, driven by lower porosity and lower fluxes; under such conditions biomass is favorably detached from the top layer, transported and accumulated in depth, so that new biomass might colonize the surface. On the other hand, in the bilayer system, fluxes are highest, and the biofilm is still in a growing phase, with low biofilm detachment capability from the top sand layer and high microbial activity in depth, resulting in low bioclogging. Overall, the bilayer coarse-fine system allows infiltrating higher volume of water per unit of surface area than the monolayer fine one, minimizing surface and deep bioclogging, and thus increasing the longevity and efficiency of infiltration systems. Bioclogging is a main concern in infiltration systems as it may significantly shorten the service life of these low-technology water treatment methods. In porous media, biofilms grow to clog partially or totally the pore network. Dynamics of biofilm accumulation (e.g., by attachment, detachment, advective transport in depth) and their impact on both surface and deep bioclogging are still not yet fully understood. To address this concern, a 104¿day-long outdoor infiltration experiment in sand tanks was performed, using secondary treated wastewater and two grain size distributions (GSDs): a monolayer system filled with fine sand, and a bilayer one composed by a layer of coarse sand placed on top of a layer of fine sand. Biofilm dynamics as a function of GSD and depth were studied through cross-correlations and multivariate statistical analyses using different parameters from biofilm biomass and activity indices, plus hydraulic parameters measured at different depths. Bioclogging (both surface and deep) was found more significant in the monolayer fine system than in the bilayer coarse-fine one, possibly due to an early low-cohesive biofilm formation in the former, driven by lower porosity and lower fluxes; under such conditions biomass is favorably detached from the top layer, transported and accumulated in depth, so that new biomass might colonize the surface. On the other hand, in the bilayer system, fluxes are highest, and the biofilm is still in a growing phase, with low biofilm detachment capability from the top sand layer and high microbial activity in depth, resulting in low bioclogging. Overall, the bilayer coarse-fine system allows infiltrating higher volume of water per unit of surface area than the monolayer fine one, minimizing surface and deep bioclogging, and thus increasing the longevity and efficiency of infiltration systems.
Abstract
Bioclogging is a main concern in infiltration systems as it may significantly shorten the service life of these low-technology water treatment methods. In porous media, biofilms [...]
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Are dominant microbial sub-surface communities affected by water quality and soil characteristics?
C. Barba, A. Folch, X. Sánchez-Vila, M. Martínez-Alonso, N. Gaju-Ricart

Journal of environmental management (2019). Vol. 237, pp. 332-343

Abstract
Subsurface microorganisms must deal with quite extreme environmental conditions. The lack of light, oxygen, and potentially nutrients are the main environmental stresses faced by subsurface microbial communities. Likewise, environmental disruptions providing an unbalanced positive input of nutrients force microorganisms to adapt to varying conditions, visible in the changes in microbial community diversity. In order to test microbial community adaptation to environmental changes, we performed a study in a surface Managed Aquifer Recharge facility, consisting of a settlement basin (two-day residence time) and an infiltration pond. Data on groundwater hydrochemistry, soil texture, and microbial characterization was compiled from surface water, groundwater, and soil samples at two distinct recharge operation conditions. Multivariate statistics by means of Principal Component Analysis (PCA) was the technique used to map the relevant dimensionality reduced combinations of input variables that properly describe the system behavior. The methodology selected allows including variables of different nature and displaying very different range values. Strong differences in the microbial assemblage under recharge conditions were found, coupled to hydrochemistry and grain-size distribution variables. Also, some microbial groups displayed correlations with either carbon or nitrogen cycles, especially showing abundant populations of denitrifying bacteria in groundwater. A significant correlation was found between Methylotenera mobilis and the concentrations of NO3 and SO4, and also between Vogesella indigofera and the presence of DOC in the infiltrating water. Also, microbial communities present at the bottom of the pond correlated with representative descriptors of soil grain size distribution.
Abstract
Subsurface microorganisms must deal with quite extreme environmental conditions. The lack of light, oxygen, and potentially nutrients are the main environmental stresses faced [...]
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A simple contaminant fate and transport modelling tool for management and risk assessment of groundwater pollution from contaminated sites
L. Locatelli, P. Binning, X. Sánchez-Vila, G. Sondergaard, L. Rosenberg, P. Bjerg

Journal of Contaminant Hydrology (2019). Vol. 221, pp. 35-49

Abstract
Contaminated sites pose a significant threat to groundwater resources. The resources that can be allocated by water regulators for site investigation and cleanup are limited compared to the large number of contaminated sites. Numerical transport models of individual sites require large amounts of data and are labor intensive to set up, and thus they are likely to be too expensive to be useful in the management of thousands of contaminated sites. Therefore, simple tools based on analytical solutions of contaminant transport models are widely used to assess (at an early stage) whether a site might pose a threat to groundwater. We present a tool consisting of five different models, representing common geological settings, contaminant pathways, and transport processes. The tool employs a simplified approach for preliminary, conservative, fast and inexpensive estimation of the contamination levels of aquifers. This is useful for risk assessment applications or to select and prioritize the sites, which should be targeted for further investigation. The tool is based on steady-state semi-analytical models simulating different contaminant transport scenarios from the source to downstream groundwater, and includes both unsaturated and saturated transport processes. The models combine existing analytical solutions from the literature for vertical (from the source to the top of the aquifer) and horizontal (within the aquifer) transport. The effect of net recharge causing a downward migration and an increase of vertical dispersion and dilution of the plume is also considered. Finally, we illustrate the application of the tool for a preliminary assessment of two contaminated sites in Denmark and compare the model results with field data. The comparison shows that a first preliminary assessment with conservative, and often non-site specific parameter selection, is qualitatively consistent with broad trends in observations and provides a conservative estimate of contamination.
Abstract
Contaminated sites pose a significant threat to groundwater resources. The resources that can be allocated by water regulators for site investigation and cleanup are limited [...]
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Microbial community changes induced by Managed Aquifer Recharge activities: linking hydrogeological and biological processes
C. Barba, A. Folch, N. Gaju, X. Sánchez-Vila, M. Carrasquilla, A. Grau-Martínez, M. Martínez-Alonso

Hydrology and Earth system sciences (2019). Vol. 23 (1), pp. 139-154

Abstract
Managed Aquifer Recharge (MAR) is a technique used worldwide to increase the availability of water resources. We study how MAR modifies microbial ecosystems and its implications for enhancing biodegradation processes to eventually improve groundwater quality. We compare soil and groundwater samples taken from a MAR facility located in NE Spain during recharge (with the facility operating continuously for several months) and after 4 months of no recharge. The study demonstrates a strong correlation between soil and water microbial prints with respect to sampling location along the mapped infiltration path. In particular, managed recharge practices disrupt groundwater ecosystems by modifying diversity indices and the composition of microbial communities, indicating that infiltration favors the growth of certain populations. Analysis of the genetic profiles showed the presence of nine different bacterial phyla in the facility, revealing high biological diversity at the highest taxonomic range. In fact, the microbial population patterns under recharge conditions agree with the intermediate disturbance hypothesis (IDH). Moreover, DNA sequence analysis of excised denaturing gradient gel electrophoresis (DGGE) band patterns revealed the existence of indicator species linked to MAR, most notably Dehalogenimonas sp., Nitrospira sp. and Vogesella sp.. Our real facility multidisciplinary study (hydrological, geochemical and microbial), involving soil and groundwater samples, indicates that MAR is a naturally based, passive and efficient technique with broad implications for the biodegradation of pollutants dissolved in water.
Abstract
Managed Aquifer Recharge (MAR) is a technique used worldwide to increase the availability of water resources. We study how MAR modifies microbial ecosystems and its implications [...]
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Ecological and soil hydraulic implications of microbial responses to stress: a modeling analysis
A. Carles-Brangari, D. Fernàndez-García, X. Sánchez-Vila, S. Manzoni

Advances in Water Resources (2018). Vol. 116, pp. 178-194

Abstract
A better understanding of microbial dynamics in porous media may lead to improvements in the design and management of a number of technological applications, ranging from the degradation of contaminants to the optimization of agricultural systems. To this aim, there is a recognized need for predicting the proliferation of soil microbial biomass (often organized in biofilms) under different environments and stresses. We present a general multi-compartment model to account for physiological responses that have been extensively reported in the literature. The model is used as an explorative tool to elucidate the ecological and soil hydraulic consequences of microbial responses, including the production of extracellular polymeric substances (EPS), the induction of cells into dormancy, and the allocation and reuse of resources between biofilm compartments. The mechanistic model is equipped with indicators allowing the microorganisms to monitor environmental and biological factors and react according to the current stress pressures. The feedbacks of biofilm accumulation on the soil water retention are also described. Model runs simulating different degrees of substrate and water shortage show that adaptive responses to the intensity and type of stress provide a clear benefit to microbial colonies. Results also demonstrate that the model may effectively predict qualitative patterns in microbial dynamics supported by empirical evidence, thereby improving our understanding of the effects of pore-scale physiological mechanisms on the soil macroscale phenomena.
Abstract
A better understanding of microbial dynamics in porous media may lead to improvements in the design and management of a number of technological applications, ranging from [...]
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A risk assessment methodology to evaluate the risk failure of managed aquifer recharge in the Mediterranean Basin
P. Rodríguez-Escales, A. Canelles, X. Sánchez-Vila, A. Folch, D. Kurtzman, R. Rossetto, E. Fernández-Escalante, J. Lobo-Ferreira, M. Sapiano, J. San-sebastián, C. Schüth

Hydrology and Earth system sciences (2018). Vol. 22 (6), pp. 3213-3227

Abstract
Managed aquifer recharge (MAR) can be affected by many risks. Those risks are related to different technical and non-technical aspects of recharge, like water availability, water quality, legislation, social issues, etc. Many other works have acknowledged risks of this nature theoretically; however, their quantification and definition has not been developed. In this study, the risk definition and quantification has been performed by means of "fault trees" and probabilistic risk assessment (PRA). We defined a fault tree with 65 basic events applicable to the operation phase. After that, we have applied this methodology to six different managed aquifer recharge sites located in the Mediterranean Basin (Portugal, Spain, Italy, Malta, and Israel). The probabilities of the basic events were defined by expert criteria, based on the knowledge of the different managers of the facilities. From that, we conclude that in all sites, the perception of the expert criteria of the non-technical aspects were as much or even more important than the technical aspects. Regarding the risk results, we observe that the total risk in three of the six sites was equal to or above 0.90. That would mean that the MAR facilities have a risk of failure equal to or higher than 90¿% in the period of 2–6 years. The other three sites presented lower risks (75, 29, and 18¿% for Malta, Menashe, and Serchio, respectively). Managed aquifer recharge (MAR) can be affected by many risks. Those risks are related to different technical and non-technical aspects of recharge, like water availability, water quality, legislation, social issues, etc. Many other works have acknowledged risks of this nature theoretically; however, their quantification and definition has not been developed. In this study, the risk definition and quantification has been performed by means of "fault trees" and probabilistic risk assessment (PRA). We defined a fault tree with 65 basic events applicable to the operation phase. After that, we have applied this methodology to six different managed aquifer recharge sites located in the Mediterranean Basin (Portugal, Spain, Italy, Malta, and Israel). The probabilities of the basic events were defined by expert criteria, based on the knowledge of the different managers of the facilities. From that, we conclude that in all sites, the perception of the expert criteria of the non-technical aspects were as much or even more important than the technical aspects. Regarding the risk results, we observe that the total risk in three of the six sites was equal to or above 0.90. That would mean that the MAR facilities have a risk of failure equal to or higher than 90 % in the period of 2–6 years. The other three sites presented lower risks (75, 29, and 18 % for Malta, Menashe, and Serchio, respectively).
Abstract
Managed aquifer recharge (MAR) can be affected by many risks. Those risks are related to different technical and non-technical aspects of recharge, like water availability, [...]
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Bilayer infiltration system combines benefits from both coarse and fine sands promoting nutrient accumulation in sediments and increasing removal rates
N. Perujo, A. Romaní, X. Sánchez-Vila

Environmental science and technology (2018). Vol. 52 (10), pp. 5734-5743 (Preprint)

Abstract
Infiltration systems are treatment technologies based on water percolation through porous media where biogeochemical processes take place. Grain size distribution (GSD) acts as a driver of these processes and their rates and influences nutrient accumulation in sediments. Coarse sands inhibit anaerobic reactions such as denitrification and could constrain nutrient accumulation in sediments due to smaller specific surface area. Alternatively, fine sands provide higher nutrient accumulation but need a larger area available to treat the same volume of water; furthermore, they are more susceptible to bioclogging. Combining both sand sizes in a bilayer system would allow infiltrating a greater volume of water and the occurrence of aerobic/anaerobic processes. We studied the performance of a bilayer coarse-fine system compared to a monolayer fine one - by triplicate - in an outdoor infiltration experiment to close the C-N-P cycles simultaneously in terms of mass balances. Our results confirm that the bilayer coarse-fine GSD promotes nutrient removal by physical adsorption and biological assimilation in sediments, and further it enhances biogeochemical process rates (2-fold higher than the monolayer system). Overall, the bilayer coarse-fine system allows treating a larger volume of water per surface unit achieving similar removal efficiencies as the fine system. This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in Environmental science and technology.
Abstract
Infiltration systems are treatment technologies based on water percolation through porous media where biogeochemical processes take place. Grain size distribution (GSD) acts [...]
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Linking biofilm spatial structure to real-time microscopic oxygen decay imaging
S. Rubol, A. Freixa, X. Sánchez-Vila, A. Romaní

Biofouling (2018). Vol. 34 (2), pp. 200-211 (Preprint)

Abstract
Two non-destructive techniques, confocal laser scanning microscopy (CLSM) and planar optode (VisiSens imaging), were combined to relate the fine-scale spatial structure of biofilm components to real-time images of oxygen decay in aquatic biofilms. Both techniques were applied to biofilms grown for seven days at contrasting light and temperature (10/20°C) conditions. The geo-statistical analyses of CLSM images indicated that biofilm structures consisted of small (~100 µm) and middle sized (~101 µm) irregular aggregates. Cyanobacteria and EPS (extracellular polymeric substances) showed larger aggregate sizes in dark grown biofilms while, for algae, aggregates were larger in light-20°C conditions. Light-20°C biofilms were most dense while 10°C biofilms showed a sparser structure and lower respiration rates. There was a positive relationship between the number of pixels occupied and the oxygen decay rate. The combination of optodes and CLMS, taking advantage of geo-statistics, is a promising way to relate biofilm architecture and metabolism at the micrometric scale.
Abstract
Two non-destructive techniques, confocal laser scanning microscopy (CLSM) and planar optode (VisiSens imaging), were combined to relate the fine-scale spatial structure of [...]
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A KDE-based random walk method for modeling reactive transport with complex kinetics in porous media
G. Sole-Mari, D. Fernàndez-García, P. Rodríguez-Escales, X. Sánchez-Vila

Water Resources Research (2017). Vol. 53 (11), pp. 9919-9919 (Preprint)

Abstract
In recent years, a large body of the literature has been devoted to study reactive transport of solutes in porous media based on pure Lagrangian formulations. Such approaches have also been extended to accommodate second‐order bimolecular reactions, in which the reaction rate is proportional to the concentrations of the reactants. Rather, in some cases, chemical reactions involving two reactants follow more complicated rate laws. Some examples are (1) reaction rate laws written in terms of powers of concentrations, (2) redox reactions incorporating a limiting term (e.g., Michaelis‐Menten), or (3) any reaction where the activity coefficients vary with the concentration of the reactants, just to name a few. We provide a methodology to account for complex kinetic bimolecular reactions in a fully Lagrangian framework where each particle represents a fraction of the total mass of a specific solute. The method, built as an extension to the second‐order case, is based on the concept of optimal Kernel Density Estimator, which allows the concentrations to be written in terms of particle locations, hence transferring the concept of reaction rate to that of particle location distribution. By doing so, we can update the probability of particles reacting without the need to fully reconstruct the concentration maps. The performance and convergence of the method is tested for several illustrative examples that simulate the Advection‐Dispersion‐Reaction Equation in a 1‐D homogeneous column. Finally, a 2‐D application example is presented evaluating the need of fully describing non‐bilinear chemical kinetics in a randomly heterogeneous porous medium.
Abstract
In recent years, a large body of the literature has been devoted to study reactive transport of solutes in porous media based on pure Lagrangian formulations. Such approaches [...]
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Revisiting the analytical solution approach to mixing-limited equilibrium multicomponent reactive transport using mixing ratios: identification of basis, fixing an error, and dealing with multiple minerals
T. Ginn, L. Schreyer, X. Sánchez-Vila, M. Nassar, A. Ali, S. Krautle

Water Resources Research (2017). Vol. 53 (11), pp. 9941-9959

Abstract
Multicomponent reactive transport involves the solution of a system of nonlinear coupled partial differential equations. A number of methods have been developed to simplify the problem. In the case where all reactions are in instantaneous equilibrium and the mineral assemblage is constant in both space and time, de Simoni et al. (2007) provide an analytical solution that separates transport of aqueous components and minerals using scalar dissipation of Multicomponent reactive transport involves the solution of a system of nonlinear coupled partial differential equations. A number of methods have been developed to simplify the problem. In the case where all reactions are in instantaneous equilibrium and the mineral assemblage is constant in both space and time, de Simoni et al. (2007) provide an analytical solution that separates transport of aqueous components and minerals using scalar dissipation of "mixing ratios" between a number of boundary/initial solutions. In this approach, aqueous speciation is solved in conventional terms of primary and secondary species, and the mineral dissolution/precipitation rate is given in terms of the scalar dissipation and a chemical transformation term, both involving the secondary species associated with the mineral reaction. However, the identification of the secondary species is nonunique, and so it is not clear how to use the approach in general, a problem that is keenly manifest in the case of multiple minerals which may share aqueous ions. We address this problem by developing an approach to identify the secondary species required in the presence of one or multiple minerals. We also remedy a significant error in the de Simoni et al. (2007) approach. The result is a fixed and extended de Simoni et al. (2007) approach that allows construction of analytical solutions to multicomponent equilibrium reactive transport problems in which the mineral assemblage does not change in space or time and where the transport is described by closed-form solutions of the mixing ratios.
Abstract
Multicomponent reactive transport involves the solution of a system of nonlinear coupled partial differential equations. A number of methods have been developed to simplify [...]
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Bayesian estimation of the transmissivity spatial structure from pumping test data
M. Demir, N. Copty, P. Trinchero, X. Sánchez-Vila

Advances in Water Resources (2017). Vol. 104, pp. 174-182 (Preprint)

Abstract
Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.
Abstract
Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic [...]
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Interaction between physical heterogeneity and microbial processes in subsurface sediments: a laboratory-scale column experiment
N. Perujo, X. Sánchez-Vila, L. Proia, A. Romaní

Environmental science and technology (2017). Vol. 51 (11), pp. 6110-6119 (Preprint)

Abstract
Physical heterogeneity determines interstitial fluxes in porous media. Nutrients and organic matter distribution in depth influence physicochemical and microbial processes occurring in subsurface. Columns 50 cm long were filled with sterile silica sand following five different setups combining fine and coarse sands or a mixture of both mimicking potential water treatment barriers. Water was supplied continuously to all columns during 33 days. Hydraulic conductivity, nutrients and organic matter, biofilm biomass, and activity were analyzed in order to study the effect of spatial grain size heterogeneity on physicochemical and microbial processes and their mutual interaction. Coarse sediments showed higher biomass and activity in deeper areas compared to the others; however, they resulted in incomplete denitrification, large proportion of dead bacteria in depth, and low functional diversity. Treatments with fine sediment in the upper 20 cm of the columns showed high phosphorus retention. However, low hydraulic conductivity values reported in these sediments seemed to constraint biofilm activity and biomass. On the other hand, sudden transition from coarse-to-fine grain sizes promoted a hot-spot of organic matter degradation and biomass growth at the interface. Our results reinforce the idea that grain-size disposition in subsurface sandy sediments drives the interstitial fluxes, influencing microbial processes. This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in Environmental science and technology
Abstract
Physical heterogeneity determines interstitial fluxes in porous media. Nutrients and organic matter distribution in depth influence physicochemical and microbial processes [...]
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Improving degradation of emerging organic compounds by applying chaotic advection in Managed Aquifer Recharge in randomly heterogeneous porous media
P. Rodríguez-Escales, D. Fernàndez-García, J. Drechsel, A. Folch, X. Sánchez-Vila

Water Resources Research (2017). Vol. 53 (5), pp. 4376-4392

Abstract
Improving degradation rates of emerging organic compounds (EOCs) in groundwater is still a challenge. Although their degradation is not fully understood, it has been observed that some substances are preferably degraded under specific redox conditions. The coupling of Managed Aquifer Recharge with soil aquifer remediation treatment, by placing a reactive layer containing organic matter at the bottom of the infiltration pond, is a promising technology to improve the rate of degradation of EOCs. Its success is based on assuming that recharged water and groundwater get well mixed, which is not always true. It has been demonstrated that mixing can be enhanced by inducing chaotic advection through extraction-injection-engineering. In this work, we analyze how chaotic advection might enhance the spreading of redox conditions with the final aim of improving degradation of a mix of benzotriazoles: benzotriazole, 5-methyl-benzotriazole, and 5-chloro-benzotriazole. The degradation of the first two compounds was fastest under aerobic conditions whereas the third compound was best degraded under denitrification conditions. We developed a reactive transport model that describes how a recharged water rich in organic matter mixes with groundwater, how this organic matter is oxidized by different electron acceptors, and how the benzotriazoles are degraded attending for the redox state. The model was tested in different scenarios of recharge, both in homogenous and in heterogenous media. It was found that chaotic flow increases the spreading of the plume of recharged water. Consequently, different redox conditions coexist at a given time, facilitating the degradation of EOCs.
Abstract
Improving degradation rates of emerging organic compounds (EOCs) in groundwater is still a challenge. Although their degradation is not fully understood, it has been observed [...]
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Stochastic estimation of hydraulic transmissivity fields using flow connectivity indicator data
G. Freixas, D. Fernàndez-García, X. Sánchez-Vila

Water Resources Research (2017). Vol. 53 (1), pp. 602-618 (Preprint)

Abstract
Most methods for hydraulic test interpretation rely on a number of simplified assumptions regarding the homogeneity and isotropy of the underlying porous media. This way, the actual heterogeneity of any natural parameter, such as transmissivity ( math formula), is transferred to the corresponding estimates in a way heavily dependent on the interpretation method used. An example is a long-term pumping test interpreted by means of the Cooper-Jacob method, which implicitly assumes a homogeneous isotropic confined aquifer. The estimates obtained from this method are not local values, but still have a clear physical meaning; the estimated math formula represents a regional-scale effective value, while the log-ratio of the normalized estimated storage coefficient, indicated by math formula, is an indicator of flow connectivity, representative of the scale given by the distance between the pumping and the observation wells. In this work we propose a methodology to use math formula, together with sampled local measurements of transmissivity at selected points, to map the expected value of local math formula values using a technique based on cokriging. Since the interpolation involves two variables measured at different support scales, a critical point is the estimation of the covariance and crosscovariance matrices. The method is applied to a synthetic field displaying statistical anisotropy, showing that the inclusion of connectivity indicators in the estimation method provide maps that effectively display preferential flow pathways, with direct consequences in solute transport.
Abstract
Most methods for hydraulic test interpretation rely on a number of simplified assumptions regarding the homogeneity and isotropy of the underlying porous media. This way, [...]
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A mechanistic model (BCC-PSSICO) to predict changes in the hydraulic properties for bio-amended variably saturated soils
A. Carles-Brangari, X. Sánchez-Vila, A. Freixa, A. Romaní, S. Rubol, D. Fernàndez-García

Water Resources Research (2017). Vol. 53 (1), pp. 93-109 (Preprint)

Abstract
The accumulation of biofilms in porous media is likely to influence the overall hydraulic properties and, consequently, a sound understanding of the process is required for the proper design and management of many technological applications. In order to bring some light into this phenomenon we present a mechanistic model to study the variably saturated hydraulic properties of bio-amended soils. Special emphasis is laid on the distribution of phases at pore-scale and the mechanisms to retain and let water flow through, providing valuable insights into phenomena behind bioclogging. Our approach consists in modeling the porous media as an ensemble of capillary tubes, obtained from the biofilm-free water retention curve. This methodology is extended by the incorporation of a biofilm composed of bacterial cells and extracellular polymeric substances (EPS). Moreover, such a microbial consortium displays a channeled geometry that shrinks/swells with suction. Analytical equations for the volumetric water content and the relative permeability can then be derived by assuming that biomass reshapes the pore space following specific geometrical patterns. The model is discussed by using data from laboratory studies and other approaches already existing in the literature. It can reproduce (i) displacements of the retention curve toward higher saturations and (ii) permeability reductions of distinct orders of magnitude. Our findings also illustrate how even very small amounts of biofilm may lead to significant changes in the hydraulic properties. We, therefore, state the importance of accounting for the hydraulic characteristics of biofilms and for a complex/more realistic geometry of colonies at the pore-scale.
Abstract
The accumulation of biofilms in porous media is likely to influence the overall hydraulic properties and, consequently, a sound understanding of the process is required for [...]
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The role of advection and dispersion in the rock matrix on the transport of leaking CO2-saturated brine along a fractured zone
N. Ahmad, A. Wörman, X. Sánchez-Vila, A. Bottacin-Busolin

Advances in Water Resources (2016). Vol. 98, pp. 132-146 (Preprint)

Abstract
CO2 that is injected into a geological storage reservoir can leak in dissolved form because of brine displacement from the reservoir, which is caused by large-scale groundwater motion. Simulations of the reactive transport of leaking CO2aq along a conducting fracture in a clay-rich caprock are conducted to analyze the effect of various physical and geochemical processes. Whilst several modeling transport studies along rock fractures have considered diffusion as the only transport process in the surrounding rock matrix (diffusive transport), this study analyzes the combined role of advection and dispersion in the rock matrix in addition to diffusion (advection-dominated transport) on the migration of CO2aq along a leakage pathway and its conversion in geochemical reactions. A sensitivity analysis is performed to quantify the effect of fluid velocity and dispersivity. Variations in the porosity and permeability of the medium are found in response to calcite dissolution and precipitation along the leakage pathway. We observe that advection and dispersion in the rock matrix play a significant role in the overall transport process. For the parameters that were used in this study, advection-dominated transport increased the leakage of CO2aq from the reservoir by nearly 305%, caused faster transport and increased the mass conversion of CO2aq in geochemical reactions along the transport pathway by approximately 12.20% compared to diffusive transport.
Abstract
CO2 that is injected into a geological storage reservoir can leak in dissolved form because of brine displacement from the reservoir, which is caused by large-scale groundwater [...]
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Debates—Stochastic subsurface hydrology from theory to practice: why stochastic modeling has not yet permeated into practitioners?
X. Sánchez-Vila, D. Fernàndez-García

Water Resources Research (2016). Vol. 52 (12), pp. 9246-9258

Abstract
We address modern topics of stochastic hydrogeology from their potential relevance to real modeling efforts at the field scale. While the topics of stochastic hydrogeology and numerical modeling have become routine in hydrogeological studies, nondeterministic models have not yet permeated into practitioners. We point out a number of limitations of stochastic modeling when applied to real applications and comment on the reasons why stochastic models fail to become an attractive alternative for practitioners. We specifically separate issues corresponding to flow, conservative transport, and reactive transport. The different topics addressed are emphasis on process modeling, need for upscaling parameters and governing equations, relevance of properly accounting for detailed geological architecture in hydrogeological modeling, and specific challenges of reactive transport. We end up by concluding that the main responsible for nondeterministic models having not yet permeated in industry can be fully attributed to researchers in stochastic hydrogeology.
Abstract
We address modern topics of stochastic hydrogeology from their potential relevance to real modeling efforts at the field scale. While the topics of stochastic hydrogeology [...]
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Fate of sulfamethoxazole in groundwater: Conceptualizing and modeling metabolite formation under different redox conditions
P. Rodríguez-Escales, X. Sánchez-Vila

Water Research (Oxford) (2016). Vol. 105, pp. 540-550 (Preprint)

Abstract
Degradation of emerging organic compounds in saturated porous media is usually postulated as following simple low-order models. This is a strongly oversimplified, and in some cases plainly incorrect model, that does not consider the fate of the different metabolites. Furthermore, it does not account for the reversibility in the reaction observed in a few emerging organic compounds, where the parent is recovered from the metabolite. One such compound is the antibiotic sulfamethoxazole (SMX). In this paper, we first compile existing experimental data to formulate a complete model for the degradation of SMX in aquifers subject to varying redox conditions, ranging from aerobic to iron reducing. SMX degrades reversibly or irreversibly to a number of metabolites that are specific of the redox state. Reactions are in all cases biologically mediated. We then propose a mathematical model that reproduces the full fate of dissolved SMX subject to anaerobic conditions and that can be used as a first step in emerging compound degradation modeling efforts. The model presented is tested against the results of the batch experiments of Barbieri et al. (2012) and Nödler et al. (2012) displaying a non-monotonic concentration of SMX as a function of time under denitrification conditions, as well as those of Mohatt et al. (2011), under iron reducing conditions.
Abstract
Degradation of emerging organic compounds in saturated porous media is usually postulated as following simple low-order models. This is a strongly oversimplified, and in some [...]
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Injection of CO2-saturated brine in geological reservoir: a way to enhanced storage safety
N. Ahmad, A. Wörman, X. Sánchez-Vila, J. Jarsjö, A. Borracin-Busolin, H. Hellevang

International Journal of Greenhouse Gas Control (2016). Vol. 54 (1), pp. 129-144 (Preprint)

Abstract
Injection of free-phase supercritical CO2 into deep geological reservoirs is associated with risk of considerable return flows towards the land surface due to the buoyancy of CO2, which is lighter than the resident brine in the reservoir. Such upward movements can be avoided if CO2 is injected in the dissolved phase (CO2aq). In this work, injection of CO2-saturated brine in a subsurface carbonate reservoir was modelled. Physical and geochemical interactions of injected low-pH CO2-saturated brine with the carbonate minerals (calcite, dolomite and siderite) were investigated in the reactive transport modelling. CO2-saturated brine, being low in pH, showed high reactivity with the reservoir minerals, resulting in a significant mineral dissolution and CO2 conversion in reactions. Over the injection period of 10 yr, up to 16% of the injected CO2 was found consumed in geochemical reactions. Sorption included in the transport analysis resulted in additional quantities of CO2 mass stored. However, for the considered carbonate minerals, the consumption of injected CO2aq was found mainly in the form of ionic trapping.
Abstract
Injection of free-phase supercritical CO2 into deep geological reservoirs is associated with risk of considerable return flows towards the land surface due to the buoyancy [...]
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Modeling long term Enhanced in situ Biodenitrification and induced heterogeneity in column experiments under different feeding strategies
P. Rodríguez-Escales, A. Folch, B. Breukelen, G. Vidal-Gavilan, X. Sánchez-Vila

Journal of Hydrology (2016). Vol. 538, pp. 127-137 (Preprint)

Abstract
Enhanced In situ Biodenitrification (EIB) is a capable technology for nitrate removal in subsurface water resources. Optimizing the performance of EIB implies devising an appropriate feeding strategy involving two design parameters: carbon injection frequency and C:N ratio of the organic substrate nitrate mixture. Here we model data on the spatial and temporal evolution of nitrate (up to 1.2 mM), organic carbon (ethanol), and biomass measured during a 342 day-long laboratory column experiment (published in Vidal-Gavilan et al., 2014). Effective porosity was 3% lower and dispersivity had a sevenfold increase at the end of the experiment as compared to those at the beginning. These changes in transport parameters were attributed to the development of a biofilm. A reactive transport model explored the EIB performance in response to daily and weekly feeding strategies. The latter resulted in significant temporal variation in nitrate and ethanol concentrations at the outlet of the column. On the contrary, a daily feeding strategy resulted in quite stable and low concentrations at the outlet and complete denitrification. At intermediate times (six months of experiment), it was possible to reduce the carbon load and consequently the C:N ratio (from 2.5 to 1), partly because biomass decay acted as endogenous carbon to respiration, keeping the denitrification rates, and partly due to the induced dispersivity caused by the well developed biofilm, resulting in enhancement of mixing between the ethanol and nitrate and the corresponding improvement of denitrification rates. The inclusion of a dual-domain model improved the fit at the last days of the experiment as well as in the tracer test performed at day 342, demonstrating a potential transition to anomalous transport that may be caused by the development of biofilm. This modeling work is a step forward to devising optimal injection conditions and substrate rates to enhance EIB performance by minimizing the overall supply of electron donor, and thus the cost of the remediation strategy.
Abstract
Enhanced In situ Biodenitrification (EIB) is a capable technology for nitrate removal in subsurface water resources. Optimizing the performance of EIB implies devising an [...]
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Scale dependence of the hydraulic properties of a fractured aquifer estimated using transfer functions
D. Pedretti, A. Russian, X. Sánchez-Vila, M. Dentz

Water Resources Research (2016). (preprint) Vol. 52 (7), pp. 5008-5024

Abstract
We present an investigation of the scale dependence of hydraulic parameters in fractured media based on the concept of transfer functions (TF). TF methods provide an inexpensive way to perform aquifer parameter estimation, as they relate the fluctuations of an observation time series (hydraulic head fluctuations) to an input function (aquifer recharge) in frequency domain. Fractured media are specially sensitive to this approach as hydraulic parameters are strongly scale-dependent, involving nonstationary statistical distributions. Our study is based on an extensive data set, involving up to 130 measurement points with periodic head measurements that in some cases extend for more than 30 years. For each point, we use a single-porosity and dual-continuum TF formulation to obtain a distribution of transmissivities and storativities in both mobile and immobile domains. Single-porosity TF estimates are compared with data obtained from the interpretation of over 60 hydraulic tests (slug and pumping tests). Results show that the TF is able to estimate the scale dependence of the hydraulic parameters, and it is consistent with the behavior of estimates from traditional hydraulic tests. In addition, the TF approach seems to provide an estimation of the system variance and the extension of the ergodic behavior of the aquifer (estimated in approximately 500 m in the analyzed aquifer). The scale dependence of transmissivity seems to be independent from the adopted formulation (single or dual-continuum), while storativity is more sensitive to the presence of multiple continua.
Abstract
We present an investigation of the scale dependence of hydraulic parameters in fractured media based on the concept of transfer functions (TF). TF methods provide an inexpensive [...]
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A locally adaptive kernel regression method for facies delineation
D. Fernàndez-García, M. Barahona-Palomo, C. Henri, X. Sánchez-Vila

Journal of Hydrology (2015). Vol. 531 (Part 1), pp. 62-72 (Preprint)

Abstract
Facies delineation is defined as the separation of geological units with distinct intrinsic characteristics (grain size, hydraulic conductivity, mineralogical composition). A major challenge in this area stems from the fact that only a few scattered pieces of hydrogeological information are available to delineate geological facies. Several methods to delineate facies are available in the literature, ranging from those based only on existing hard data, to those including secondary data or external knowledge about sedimentological patterns. This paper describes a methodology to use kernel regression methods as an effective tool for facies delineation. The method uses both the spatial and the actual sampled values to produce, for each individual hard data point, a locally adaptive steering kernel function, self-adjusting the principal directions of the local anisotropic kernels to the direction of highest local spatial correlation. The method is shown to outperform the nearest neighbor classification method in a number of synthetic aquifers whenever the available number of hard data is small and randomly distributed in space. In the case of exhaustive sampling, the steering kernel regression method converges to the true solution. Simulations ran in a suite of synthetic examples are used to explore the selection of kernel parameters in typical field settings. It is shown that, in practice, a rule of thumb can be used to obtain suboptimal results. The performance of the method is demonstrated to significantly improve when external information regarding facies proportions is incorporated. Remarkably, the method allows for a reasonable reconstruction of the facies connectivity patterns, shown in terms of breakthrough curves performance.
Abstract
Facies delineation is defined as the separation of geological units with distinct intrinsic characteristics (grain size, hydraulic conductivity, mineralogical composition). [...]
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Do we really need a large number of particles to simulate bimolecular reactive transport with random walk methods? A kernel density estimation approach
M. Rahbaralam, D. Fernàndez-García, X. Sánchez-Vila

Journal of computational physics (2015). Vol. 303, pp. 95-104

Abstract
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 106–109106–109, 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. In this work, we propose 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 to 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.
Abstract
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 [...]
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Reactive transport modeling of leaking CO2-saturated brine along a fractured pathway
N. Ahmad, A. Wörman, A. Bottacin-Busolin, X. Sánchez-Vila

International Journal of Greenhouse Gas Control (2015). Vol. 42, pp. 672-689 (preprint)

Abstract
One concern regarding the underground storage of carbon dioxide (CO2) is its potential leakage from reservoirs. Over short period of time, the leakage risk is related mainly to CO2 as a separate supercritical fluid phase. However, over longer periods upon complete dissolution of injected CO2 in the fluid, the leakage risk is associated with dissolved phase CO2. Over the geological time scales, large-scale groundwater motion may cause displacement of brine containing dissolved CO2 along the conducting pathways. In this paper, we present a comprehensive modeling framework that describes the reactive transport of CO2-saturated brine along a fracture in the clay caprock based on the future, hypothetical leakage of the dissolved phase CO2. This study shows that the transport of leaked dissolved CO2 is significantly retarded by a combination of various physical and geochemical processes, such as mass exchange between conducting fracture and the neighboring rock matrix through molecular diffusion, sorption and calcite dissolution in the rock matrix. Mass stored in aqueous and adsorbed states in the rock matrix caused retention of dissolved CO2 along the leakage pathway. Calcite dissolution reaction in the rock matrix resulted in consumption of leaking dissolved CO2 and reduced its mass along the leakage pathway. Consumption and retention of dissolved CO2 along the leakage pathway have important implications for analyzing the potential reduction of CO2 fluxes from storage reservoirs over large periods and long travel pathways.
Abstract
One concern regarding the underground storage of carbon dioxide (CO2) is its potential leakage from reservoirs. Over short period of time, the leakage risk is related mainly [...]
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Vadose zone oxygen (O2) dynamics during drying and wetting cycles: An artificial recharge laboratory experiment
T. Dutta, A. Carles-Brangari, D. Fernàndez-García, S. Rubol, J. Tirado-Conde, X. Sánchez-Vila

Journal of Hydrology (2015). Vol. 527, pp. 151-159 (Preprint)

Abstract
Vadose zone oxygen dynamics control all subsurface redox reactions and play a decisive role in maintaining groundwater quality. Although drying and wetting events are common in artificial recharge, their effects on subsurface oxygen distribution are poorly documented. We monitored oxygen concentration in the unsaturated zone in a mid-scale (1 m high) laboratory soil lysimeter, which was subjected to short wetting and drying cycles that simulated a highly permeable shallow aquifer recharged by river water. Ten cycles of varying duration were performed for a period of 85 days. Measurements of oxygen in the liquid and the gas phases were recorded every 20 s using non-invasive optical fibers (PreSens). The results provided high-resolution (in time) oxygen concentration maps. The infiltration rate revealed a decreasing trend during wetting cycles associated with biological clogging. Such a decrease with time was accompanied by a depletion of O2 concentration, occurring within the first few hours of the infiltration. During drying, O2 concentrations recovered rapidly at all depths owing to air flushing, resulting in a stratified vertical profile consistent with the biological consumption of O2 along the air infiltration path. Furthermore, drying periods caused a potential recovery of the infiltration capacity while preserving the soil biological activity. Scraping also led to the recovery of the infiltration capacity of the soil but was less effective than drying. Our experiment suggests that the small-scale heterogeneity played a key role in accurately mapping pore-scale O2 concentrations and should be considered in modeling O2 fluxes of unsaturated soils under natural or managed recharge conditions.
Abstract
Vadose zone oxygen dynamics control all subsurface redox reactions and play a decisive role in maintaining groundwater quality. Although drying and wetting events are common [...]
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Improving the accuracy of risk prediction from particle-based breakthrough curves reconstructed with kernel density estimators
E. Siirila-Woodburn, D. Fernàndez-García, X. Sánchez-Vila

Water Resources Research (2015). Vol. 51 (6), pp. 4574-4591

Abstract
While particle tracking techniques are often used in risk frameworks, the number of particles needed to properly derive risk metrics such as average concentration for a given exposure duration is often unknown. If too few particles are used, error may propagate into the risk estimate. In this work, we provide a less error‐prone methodology for the direct reconstruction of exposure duration averaged concentration versus time breakthrough curves from particle arrival times at a compliance surface. The approach is based on obtaining a suboptimal kernel density estimator that is applied to the sampled particle arrival times. The corresponding estimates of risk metrics obtained with this method largely outperform those by means of traditional methods (reconstruction of the breakthrough curve followed by the integration of concentration in time over the exposure duration). This is particularly true when the number of particles used in the numerical simulation is small ( 105), and for small exposure times. Percent error in the peak of averaged breakthrough curves is approximately zero for all scenarios and all methods tested when the number of particles is 105. Our results illustrate that obtaining a representative average exposure concentration is reliant on the information contained in each individual tracked particle, more so when the number of particles is small. They further illustrate the usefulness of defining problem‐specific kernel density estimators to properly reconstruct the observables of interest in a particle tracking framework without relying on the use of an extremely large number of particles.
Abstract
While particle tracking techniques are often used in risk frameworks, the number of particles needed to properly derive risk metrics such as average concentration for a given [...]
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Mathematical equivalence between time-dependent single-rate and multirate mass transfer models
D. Fernàndez-García, X. Sánchez-Vila

Water Resources Research (2015). Vol. 51 (4), pp. 3166-3180

Abstract
The often observed tailing of tracer breakthrough curves is caused by a multitude of mass transfer processes taking place over multiple scales. Yet, in some cases, it is convenient to fit a transport model with a single-rate mass transfer coefficient that lumps all the non-Fickian observed behavior. Since mass transfer processes take place at all characteristic times, the single-rate mass transfer coefficient derived from measurements in the laboratory or in the field vary with time w(t). The literature review and tracer experiments compiled by Haggerty et al. (2004) from a number of sites worldwide suggest that the characteristic mass transfer time, which is proportional to w(t)^-1, scales as a power law of the advective and experiment duration. This paper studies the mathematical equivalence between the multirate mass transfer model (MRMT) and a time-dependent single-rate mass transfer model (t-SRMT). In doing this, we provide new insights into the previously observed scale-dependence of mass transfer coefficients. The memory function, g(t), which is the most salient feature of the MRMT model, determines the influence of the past values of concentrations on its present state. We found that the t-SRMT model can also be expressed by means of a memory function \phi(t,\tau). In this case, though the memory function is nonstationary, meaning that in general it cannot be written as \phi(t-\tau). Nevertheless, the full behavior of the concentrations using a single time-dependent rate w(t) is approximately analogous to that of the MRMT model provided that the equality w(t) = -dlng(t)/dt holds and the field capacity is properly chosen. This relationship suggests that when the memory function is a power law, g(t) \approx t^{1-k}, the equivalent mass transfer coefficient scales as w(t) \approx t^-1, nicely fitting without calibration the estimated mass transfer coefficients compiled by Haggerty et al. (2004).
Abstract
The often observed tailing of tracer breakthrough curves is caused by a multitude of mass transfer processes taking place over multiple scales. Yet, in some cases, it is convenient [...]
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The effects of sediment depth and oxygen concentration on the use of organic matter: an experimental study using an infiltration sediment tank
A. Freixa, S. Rubol, A. Carles-Brangari, A. Butturini, X. Sánchez-Vila, A. Romaní

Science of the total environmental (2015). Vol. 540, pp. 20-31 (preprint)

Abstract
Water flowing through hyporheic river sediments or artificial recharge facilities promotes the development of microbial communities with sediment depth. We performed an 83-day mesocosm infiltration experment, to study howmicrobial functions (e.g., extracellular enzyme activities and carbon substrate utilization) are affected by sediment depth (up to 50 cm) and different oxygen concentrations. Results indicated that surface sediment layers were mainly colonized bymicroorganisms capable of using awide range of substrates (although they preferred to degrade carbon polymeric compounds, as indicated by the higher ß-glucosidase activity). In contrast, at a depth of 50 cm, the microbial community became specialized in using fewer carbon substrates, showing decreased functional richness and diversity. At this depth, microorganisms picked nitrogenous compounds, including amino acids and carboxyl acids. After the 83-day experiment, the sediment at the bottomof the tank became anoxic, inhibiting phosphatase activity. Coexistence of aerobic and anaerobic communities, promoted by greater physicochemical heterogeneity, was also observed in deeper sediments. The presence of specific metabolic fingerprints under oxic and anoxic conditions indicated that the microbial community was adapted to use organic matter under different oxygen conditions. Overall the heterogeneity of oxygen concentrations with depth and in time would influence organic matter metabolism in the sediment tank.
Abstract
Water flowing through hyporheic river sediments or artificial recharge facilities promotes the development of microbial communities with sediment depth. We performed an 83-day [...]
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On the formation of multiple local peaks in breakthrough curves
E. Siirila-Woodburn, X. Sánchez-Vila, D. Fernàdez-García

Water Resources Research (2015). Vol. 51 (4), pp. 2128-2152

Abstract
The analysis of breakthrough curves (BTCs) is of interest in hydrogeology as a way to parameterize and explain processes related to anomalous transport. Classical BTCs assume the presence of a single peak in the curve, where the location and size of the peak and the slope of the receding limb has been of particular interest. As more information is incorporated into BTCs (for example, with high-frequency data collection, supercomputing efforts), it is likely that classical definitions of BTC shapes will no longer be adequate descriptors for contaminant transport problems. We contend that individual BTCs may display multiple local peaks depending on the hydrogeologic conditions and the solute travel distance. In such cases, classical definitions should be reconsidered. In this work, the presence of local peaks in BTCs is quantified from high-resolution numerical simulations in synthetic fields with a particle tracking technique and a kernel density estimator to avoid either overly jagged or smoothed curves that could mask the results. Individual BTCs from three-dimensional heterogeneous hydraulic conductivity fields with varying combinations of statistical anisotropy, heterogeneity models, and local dispersivity are assessed as a function of travel distance. The number of local peaks, their corresponding slopes, and a transport connectivity index are shown to strongly depend on statistical anisotropy and travel distance. Results show that the choice of heterogeneity model also affects the frequency of local peaks, but the slope is less sensitive to model selection. We also discuss how solute shearing and rerouting can be determined from local peak quantification.
Abstract
The analysis of breakthrough curves (BTCs) is of interest in hydrogeology as a way to parameterize and explain processes related to anomalous transport. Classical BTCs assume [...]
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An approach to aquifer vulnerability including uncertainty in a spatial random function framework
S. Armengol, X. Sánchez-Vila, A. Folch

Journal of Hydrology (2014). Vol. 517, pp. 889-900

Abstract
We introduce a methodology to include uncertainty into DRASTIC (Aller et al., 1987), the most commonly used method to define aquifer vulnerability. For this purpose, we explore separately all seven DRASTIC indices, and analyze how uncertainty can be introduced into each one of them, by proposing a simple decision tree to select the most appropriate geostatistical methods depending on the amount and type of available data. We further analyzed the implications of introducing the concept of degree of confidence, based on the estimated point variances, into the estimates of some of the indices. The methodology is illustrated by mapping the DRASTIC indices in an aquifer located in northeast Spain. It is concluded that the final vulnerability index may vary substantially depending on the degree of confidence accepted in the analysis, indicating the possibility of extending the deterministic version of DRASTIC to a stochastic one, where uncertainty is directly accounted for.
Abstract
We introduce a methodology to include uncertainty into DRASTIC (Aller et al., 1987), the most commonly used method to define aquifer vulnerability. For this purpose, [...]
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GIS-based hydrogeochemical analysis tools (QUIMET)
V. Velasco, I. Tubau, D. Gaitanaru, E. Vázquez-Suñé, R. Gogu, M. Alcaraz, A. Serrano-Juan, D. Fernàndez-García, T. Garrido, J. Fraile, X. Sánchez-Vila

Computers & Geosciences (2014). Vol. 70, pp. 164-180

Abstract
A software platform (QUIMET) was developed to improve the sorting, analysis, calculations, visualizations, and interpretations of hydrogeochemical data in a GIS environment. QUIMET is composed of a geospatial database plus a set of tools specially designed for graphical and statistical analysis of hydrogeochemical data. The geospatial database has been designed to include organic and inorganic chemical records, as well as relevant physical parameters (temperature, Eh, electrical conductivity). The instruments for analysis cover a wide range of methodologies for querying, interpreting, and comparing groundwater quality data. They include, among others, chemical time-series analysis, ionic balance calculations, correlation of chemical parameters, and calculation of various common hydrogeochemical diagrams (Salinity, Schoeller-Berkaloff, Piper, and Stiff). The GIS platform allows the generation of maps of the spatial distribution of parameters and diagrams. Moreover, it allows performing a complete statistical analysis of the data including descriptive statistic univariate and bivariate analysis, the latter including generation of correlation matrices and graphics. Finally, QUIMET offers interoperability with other external platforms. The platform is illustrated with a geochemical data set from the city of Badalona, located on the Mediterranean coast in NE Spain.
Abstract
A software platform (QUIMET) was developed to improve the sorting, analysis, calculations, visualizations, and interpretations of hydrogeochemical data in a GIS environment. [...]
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Estimation of spatial covariance of log conductivity from particle size data
M. Riva, X. Sánchez-Vila, A. Guadagnini

Water Resources Research (2014). Vol. 50 (6), pp. 5298-5308

Abstract
We derive analytical relationships between the spatial covariance of the (natural) logarithm of hydraulic conductivity (K) and that of representative soil particle sizes and porosity. The latter quantities can be directly measured during routine sedimentological analyses of soil samples and provide a way of incorporating K estimates into groundwater flow models at a relatively modest experimental cost. Here we rely on widely used empirical formulations requiring measurements of representative particle diameters and, in some cases, of medium porosity. We derive exact formulations relating the spatial covariance of these quantities and K and present workable approximations on the basis of perturbation methods. Our formulations provide a direct link between key geostatistical descriptors of sedimentological and hydraulic parameters of heterogeneous aquifers which can be employed in classical estimation and simulation procedures. The approach and theoretical results are tested on an extensive data set comprising 411 particle size curves collected at 12 boreholes in a small-scale alluvial aquifer.
Abstract
We derive analytical relationships between the spatial covariance of the (natural) logarithm of hydraulic conductivity (K) and that of representative soil particle sizes and [...]
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Apparent directional mass-transfer capacity coefficients in three-dimensional anisotropic heterogeneous aquifers under radial convergent transport
D. Pedretti, D. Fernàndez-García, X. Sánchez-Vila, D. Bolster, D. Benson

Water Resources Research (2014). Vol. 50 (2), pp. 1205-1224

Abstract
Aquifer hydraulic properties such as hydraulic conductivity (K) are ubiquitously heterogeneous and typically only a statistical characterization can be sought. Additionally, statistical anisotropy at typical characterization scales is the rule. Thus, regardless of the processes governing solute transport at the local (pore) scale, transport becomes non‐Fickian. Mass‐transfer models provide an efficient tool that reproduces observed anomalous transport; in some cases though, these models lack predictability as model parameters cannot readily be connected to the physical properties of aquifers. In this study, we focus on a multirate mass‐transfer model (MRMT), and in particular the apparent capacity coefficient (β), which is a strong indicator of the potential of immobile zones to capture moving solute. We aim to find if the choice of an apparent β can be phenomenologically related to measures of statistical anisotropy. We analyzed an ensemble of random simulations of three‐dimensional log‐transformed multi‐Gaussian permeability fields with stationary anisotropic correlation under convergent flow conditions. It was found that apparent β also displays an anisotropic behavior, physically controlled by the aquifer directional connectivity, which in turn is controlled by the anisotropic correlation model. A high hydraulic connectivity results in large β values. These results provide new insights into the practical use of mass‐transfer models for predictive purposes.
Abstract
Aquifer hydraulic properties such as hydraulic conductivity (K) are ubiquitously heterogeneous and typically only a statistical [...]
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Geochemical modeling of arsenic release from a deep natural solid matrix under alternated redox conditions
A. Molinari, C. Ayora, M. Marcaccio, L. Guadagnini, X. Sánchez-Vila, A. Guadagnini

Environmental science and pollution research (2014). Vol. 21 (3), pp. 1628-1637

Abstract
Dissolved arsenic (As) concentrations detected in groundwater bodies of the Emilia-Romagna Region (Italy) exhibit values which are above the regulation limit and could be related to the natural composition of the host porous matrix. To support this hypothesis, we present the results of a geochemical modeling study reproducing the main trends of the dynamics of As, Fe, and Mn concentrations as well as redox potential and pH observed during batch tests performed under alternating redox conditions. The tests were performed on a natural matrix extracted from a deep aquifer located in the Emilia-Romagna Region (Italy). The solid phases implemented in the model were selected from the results of selective sequential extractions performed on the tested matrix. The calibrated model showed that large As concentrations have to be expected in the solution for low crystallinity phases subject to dissolution. The role of Mn oxides on As concentration dynamics appears significant in strongly reducing environments, particularly for large water-solid matrix interaction times. Modeled data evidenced that As is released firstly from the outer surface of Fe oxihydroxides minerals exhibiting large concentrations in water when persistent reducing conditions trigger the dissolution of the crystalline structure of the binding minerals. The presence of organic matter was found to strongly affect pH and redox conditions, thus influencing As mobility.
Abstract
Dissolved arsenic (As) concentrations detected in groundwater bodies of the Emilia-Romagna Region (Italy) exhibit values which are above the regulation limit and could be [...]
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Dynamic interactions between hydrogeological and exposure parameters in daily dose prediction under uncertainty and temporal variability
V. Kumar, F. Barros, M. Schuhmacher, D. Fernàndez-García, X. Sánchez-Vila

Journal of hazardous materials (2013). Vol. 263 (1), pp. 197-206

Abstract
We study the time dependent interaction between hydrogeological and exposure parameters in daily dose predictions due to exposure of humans to groundwater contamination. Dose predictions are treated stochastically to account for an incomplete hydrogeological and geochemical field characterization, and an incomplete knowledge of the physiological response. We used a nested Monte Carlo framework to account for uncertainty and variability arising from both hydrogeological and exposure variables. Our interest is in the temporal dynamics of the total dose and their effects on parametric uncertainty reduction. We illustrate the approach to a HCH (lindane) pollution problem at the Ebro River, Spain. The temporal distribution of lindane in the river water can have a strong impact in the evaluation of risk. The total dose displays a non-linear effect on different population cohorts, indicating the need to account for population variability. We then expand the concept of Comparative Information Yield Curves developed earlier (see de Barros et al. [29]) to evaluate parametric uncertainty reduction under temporally variable exposure dose. Results show that the importance of parametric uncertainty reduction varies according to the temporal dynamics of the lindane plume. The approach could be used for any chemical to aid decision makers to better allocate resources towards reducing uncertainty.
Abstract
We study the time dependent interaction between hydrogeological and exposure parameters in daily dose predictions due to exposure of humans [...]
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On the formation of breakthrough curves tailing during convergent flow tracer tests in three-dimensional heterogeneous aquifers
D. Pedretti, D. Fernàndez-García, D. Bolster, X. Sánchez-Vila

Water Resources Research (2013). Vol. 49 (7), pp. 4157-4173

Abstract
Anomalous transport in advection-dominated convergent flow tracer tests can occurs due to small-scale heterogeneities in aquifer hydraulic properties. These result in fluctuations of the groundwater velocity field and complex connectivity patterns between injection and extraction wells. While detailed characterization of heterogeneity is often not possible in practice, a proper understanding of what fundamental physical mechanisms can give rise to macroscopic behaviors that are measurable is essential for proper upscaling of solute transport processes. We analyze here how heavy-tailed breakthrough curves can arise in radially convergent flow to a well. The permeability fields are three-dimensional multi-Gaussian fields with varying statistical geometry and degrees of heterogeneity. We consider transport of conservative tracers from multiple injection locations by varying distance and angle from the extraction well. Anomalous power law tailing in breakthrough curves is attributed to a variety of features including the initial vertical stratification of the solute that arises due to a flux-weighted injection, the injection distance to the well relative to the depth of the aquifer, and the statistics of the heterogeneity field as defined by the correlation length and variance of the permeability. When certain conditions cooccur for a given injection, such as strong connectivity contrasts between aquifer layers, injection distances comparable to the horizontal heterogeneity integral scales, and large global variances, breakthrough curves tend to scale as a PL with unit slope at late time. These findings offer new insights to understand what physical processes must be understood to develop and choose appropriate upscaling approaches that might reproduce such anomalous transport in heterogeneous advection-dominated systems.
Abstract
Anomalous transport in advection-dominated convergent flow tracer tests can occurs due to small-scale heterogeneities in aquifer hydraulic properties. These result in fluctuations [...]
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Controlling scaling metrics for improved characterization of well-head protection regions
F. Barros, A. Guadagnini, D. Fernàndez-García, M. Riva, X. Sánchez-Vila

Journal of Hydrology (2013). Vol. 494 (28), pp. 107-115

Abstract
We addressed the value of hydrogeological information on the assessment of the risk that an operating pumping well is polluted. The work considered a heterogeneous aquifer and focused on the statistical characterization of the contaminant mass fraction from a diffused source recovered at the well and the solute arrival times. We explored the role of the key length scales that characterize and control the well capture region and its probabilistic delineation with respect to the contaminant source location and size. The impact of augmenting the data-base of hydraulic information on the reduction of uncertainty associated with the environmental scenario analyzed was then investigated. It was found that obtaining a robust characterization of the target Environmental Performance Metrics (EPMs) depends on the length scale considered. For the sampling scheme considered, the importance of conditioning on the probability distributions of solute mass fraction and travel times is strongly affected by the location of the contaminant source within the probabilistic well catchment. With reference to the characterization of the travel time distribution associated with the recovery of a given mass fraction, the worth of augmenting the hydraulic parameter data-sets tends to decrease with decreasing solute residence time within the well catchment
Abstract
We addressed the value of hydrogeological information on the assessment of the risk that an operating pumping well is polluted. The work considered a heterogeneous aquifer and [...]
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Siphon pipe Parameter Optimization of the Toilet Using CFD-DEM Coupling Method
Z. Li, X. Ge, K. Li, X. Tong

Siphon pipe Parameter Optimization of the Toilet Using CFD-DEM Coupling Method (2020). 1

Abstract
The computational fluid dynamics (CFD) and discrete element method (DEM) coupling method is used to simulate the flushing process of the toilet and this paper analyzes the influence of different structural parameters of siphon pipe on the flushing performance of the toilet. And through the adjusted-parameters toilet, tlushing experments were carried out to verify the simulations. Meanwhile the orthogonal test of different structural parameters of siphon pipes were conducted to study the flushing Performance. The research results show that the CFD-DEM coupling method can be used to study the regularity of the toilet flushing performance. The toilet can get the better flushing performance when the tilt angle of the angle of inclination is 50°, the curvature width and length are 50 mm and 220 mm, the width and height of the secondary water seal are 100 mm and 25 mm and pipe diameter is 53 mm. The method in this paper can provide a new idea for the study and design of the flushing performance of the toilet. '''Keyword:''' CFD-DEM, flushing performance, structural parameters, coupling method, adjusted-parameters toilet
Abstract
The computational fluid dynamics (CFD) and discrete element method (DEM) coupling method is used to simulate the flushing process of the toilet and this paper analyzes the [...]
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Mobility and Interaction of Heavy Metals in a Natural Soil
E. Janetti, I. Dror, M. Riva, A. Guadagnini, X. Sánchez-Vila

Transport in Porous Media (2013). Vol. 97 (3), pp. 295-315

Abstract
We study the mobility and interaction under competing conditions observed for copper ( Cu2+ Cu2+) and zinc ( Zn2+ Zn2+) ions in the context of laboratory-scale experiments performed in natural soil columns. The experiments focus on the analysis of solute breakthrough curves (BTCs) obtained after injection of an aqueous solution containing similar concentrations of the two metal ions into a soil column fully saturated with double deionized water. Transport of the competing ions is tested for the same soil under aerobic and anaerobic conditions. Measurements show that the species with lower affinity for the soil, Zn2+ Zn2+, migrates occupying all available adsorption sites, and is then progressively replaced by the ion with higher affinity, Cu2+ Cu2+. The two ions are displaced in the system with different effective retardation. The slowest species replaces the sorbed ions, resulting in observed Zn2+ Zn2+ concentrations that display a non-monotonic behavior in time and which, for a certain period, are larger than the concentration supplied continuously at the inlet. In the absence of a complete geochemical characterization of the system, we show that the measured concentrations of both metals can be interpreted through simple models based on a set of coupled partial differential and algebraic equations, involving a small subset of aqueous and adsorbed species that are present in the system. Depending on the model considered, the relationship between aqueous and adsorbed ion concentrations is described at equilibrium by a Gaines–Thomas (GT) formulation, a competitive Sheindorf–Rebhun–Sheintuch (SRS) isotherm, or an Extended Langmuir (EL) isotherm, respectively. The GT formulation provides the best interpretation of the observed behavior among the models tested. We find that employing these simple models, which account only for the main governing reactive processes, allows reasonable estimation of the observed BTCs in experiments where only partial geochemical datasets are available.
Abstract
We study the mobility and interaction under competing conditions observed for copper ( Cu2+ Cu2+) and zinc ( Zn2+ Zn2+) ions in the context of laboratory-scale [...]
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A risk‐based probabilistic framework to estimate the endpoint of remediation: Concentration rebound by rate‐limited mass transfer
F. Barros, D. Fernàndez-García, D. Bolster, X. Sánchez-Vila

Water Resources Research (2013). Vol. 49 (4), pp. 1929-1942

Abstract
Aquifer remediation is a challenging problem with environmental, social, and economic implications. As a general rule, pumping proceeds until the concentration of the target substance within the pumped water lies below a prespecified value. In this paper we estimate the a priori potential failure of the endpoint of remediation due to a rebound of concentrations driven by back diffusion. In many cases, it has been observed that once pumping ceases, a rebound in the concentration at the well takes place. For this reason, administrative approaches are rather conservative, and pumping is forced to last much longer than initially expected. While a number of physical and chemical processes might account for the presence of rebounding, we focus here on diffusion from low water mobility into high mobility zones. In this work we look specifically at the concentration rebound when pumping is discontinued while accounting for multiple mass transfer processes occurring at different time scales and parametric uncertainty. We aim to develop a risk‐based optimal operation methodology that is capable of estimating the endpoint of remediation based on aquifer parameters characterizing the heterogeneous medium as well as pumping rate and initial size of the polluted area.
Abstract
Aquifer remediation is a challenging problem with environmental, social, and economic implications. As a general rule, pumping proceeds until the concentration of the target [...]
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An analytical solution to study substrate-microbial dynamics in soils
X. Sánchez-Vila, S. Rubol, A. Carles-Brangari, D. García

Advances in Water Resources (2013). Vol. 54, pp. 181-190

Abstract
We provide an approximate analytical solution for the substrate-microbial dynamics of the organic carbon cycle in natural soils under hydro-climatic variable forcing conditions. The model involves mass balance in two carbon pools: substrate and biomass. The analytical solution is based on a perturbative solution of concentrations, and can properly reproduce the numerical solutions for the full non-linear problem in a system evolving towards a steady state regime governed by the amount of labile carbon supplied to the system. The substrate and the biomass pools exhibit two distinct behaviors depending on whether the amount of carbon supplied is below or above a given threshold. In the latter case, the concentration versus time curves are always monotonic. Contrarily, in the former case the C-pool concentrations present oscillations, allowing the reproduction of non-monotonic small-scale biomass concentration data in a natural soil, observed so far only in short-term experiments in the rhizosphere. Our results illustrate the theoretical dependence of oscillations from soil moisture and temperature and how they may be masked at intermediate scales due to the superposition of solutions with spatially variable parameters.
Abstract
We provide an approximate analytical solution for the substrate-microbial dynamics of the organic carbon cycle in natural soils under hydro-climatic variable forcing conditions. [...]
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Arsenic release from deep natural solid matrices under experimentally controlled redox conditions
A. Molinari, A. Guadagnini, M. Marcaccio, S. Straface, X. Sánchez-Vila, L. Guadagnini

Science of the total environment (2013). Vol. 444, pp. 231-240

Abstract
We investigated the role of iron (Fe) on arsenic (As) release from two samples of a natural deep soil collected in an aquifer body in the Emilia-Romagna Region, Italy. Each sample is representative of a different solid matrix, i.e., sand and vegetal matter. Batch experiments were performed by applying alternating aerobic/anaerobic conditions to the samples under a range of redox and pH conditions, consistent with the corresponding values measured in the field. Arsenic mobilization was triggered by abrupt and rapid changes in redox conditions and displayed a clear correlation with oxidation/reduction potential for both solid matrices. Vegetal matter showed high binding capacity and large As concentration release. Arsenic release was also correlated with Fe released from the solid matrices. Our results suggest that the environmentally critical As concentrations detected in some aquifers in the Emilia-Romagna Region are consistent with (a) the occurrence of high natural As content in the component of the host porous medium associated with vegetal matter and (b) the effect of possible sharp localized (and temporally oscillating) variations in redox conditions.
Abstract
We investigated the role of iron (Fe) on arsenic (As) release from two samples of a natural deep soil collected in an aquifer body in the Emilia-Romagna Region, Italy. Each [...]
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Formation of diclofenac and sulfamethoxazole reversible transformation products in aquifer material under denitrifying conditions: Batch experiments
M. Barbieri, J. Carrera, C. Ayora, X. Sánchez-Vila, T. Licha, K. Nödler, V. Osorio, S. Pérez, M. Köck-Schulmeyer, M. Alda, D. Barceló

Science of the Total Environment (2012). Vol. 426, pp. 265-263

Abstract
Soil-aquifer processes have proven to work as a natural treatment for the attenuation of numerous contaminants during artificial recharge of groundwater. Nowadays, significant scientific effort is being devoted to understanding the fate of pharmaceuticals in subsurface environments, and to verify if such semipersistent organic micropollutants could also be efficiently removed from water. In this context we carried out a series of batch experiments involving aquifer material, selected drugs (initial concentration of 1 μg/L and 1 mg/L), and denitrifying conditions. Diclofenac and sulfamethoxazole exhibited an unreported and peculiar behavior. Their concentrations consistently dropped in the middle of the tests but recovered toward the end, which suggest a complex effect of denitrifying conditions on aromatic amines. The transformation products Nitro-Diclofenac and 4-Nitro-Sulfamethoxazole were detected in the biotic experiments, while nitrite was present in the water. Their concentrations developed almost opposite to those of their respective parent compounds. We conjecture that this temporal and reversible effect of denitrifying conditions on the studied aromatic amines could have significant environmental implications, and could explain at least partially the wide range of removals in subsurface environments reported in literature for DCF and SMX, as well as some apparent discrepancies on SMX behavior.
Abstract
Soil-aquifer processes have proven to work as a natural treatment for the attenuation of numerous contaminants during artificial recharge [...]
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Assessing and forecasting the impacts of global change on Mediterranean rivers. The SCARCE Consolider project on Iberian basins
A. Navarro-Ortega, V. Acuña, R. Batalla, J. Blasco, C. Conde, F. Elorza, A. Elosegi, F. Francés, F. La-Roca, I. Muñoz, M. Petrovic, Y. Picó, S. Sabater, X. Sánchez-Vila, M. Schuhmacher, D. Barceló

Evironmental Science and Pollution Research (2012). Vol. 19 (4), pp. 918-933

Abstract
Introduction The Consolider-Ingenio 2010 project SCARCE, with the full title “Assessing and predicting effects on water quantity and quality in Iberian Rivers caused by global change” aims to examine and predict the relevance of global change on water availability, water quality, and ecosystem services in Mediterranean river basins of the Iberian Peninsula, as well as their socio-economic impacts. Starting in December 2009, it brought together a multidisciplinary team of 11 partner Spanish institutions, as well as the active involvement of water authorities, river basin managers, and other relevant agents as stakeholders. Methods The study areas are the Llobregat, Ebro, Jucar, and Guadalquivir river basins. These basins have been included in previous studies and projects, the majority of whom considered some of the aspects included in SCARCE but individually. Historical data will be used as a starting point of the project but also to obtain longer time series. The main added value of SCARCE project is the inclusion of scientific disciplines ranging from hydrology, geomorphology, ecology, chemistry, and ecotoxicology, to engineering, modeling, and economy, in an unprecedented effort in the Mediterranean area. The project performs data mining, field, and lab research as well as modeling and upscaling of the findings to apply them to the entire river basin. Results Scales ranging from the laboratory to river basins are addressed with the potential to help improve river basin management. The project emphasizes, thus, linking basic research and management practices in a single framework. In fact, one of the main objectives of SCARCE is to act as a bridge between the scientific and the management and to transform research results on management keys and tools for improving the River Basin Management Plans. Here, we outline the general structure of the project and the activities conducted within the ten Work Packages of SCARCE.
Abstract
Introduction The Consolider-Ingenio 2010 project SCARCE, with the full title “Assessing and predicting effects on water quantity and quality in Iberian Rivers caused [...]
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A quick and inexpensive method to quantify spatially variable infiltration capacity for artificial recharge ponds using photographic images
D. Pedretti, M. Barahona-Palomo, D. Bolster, X. Sánchez-Vila, D. Fernàdez-García

Journal of Hydrology (2012). Vol. 430-431, pp. 118-126

Abstract
The efficiency of artificial surface ponds (SPs) for managed aquifer recharge (MAR) is mostly controlled by the topmost portion of the soil. The most significant soil property controlling recharge is the infiltration capacity (Ic), which is highly variable in space. Assessing its spatial distribution in detail is prohibitive in practice due to high costs, time effort, and limited site accessibility. We present an alternative method for a quick and low-cost quantitative estimation of the spatial distribution of Ic based on satellite images. The fact that hydraulic properties of topsoils and color intensities of digital images depend on some common factors such as moisture content, nature and organization of grains, proportion of iron, and organic and clay content among others, allow us to infer infiltration capacities from color intensities. The relationship between these two variables is site specific and requires calibration. A pilot SP site in Catalonia (Spain) is used as an application example. Two high-resolution digital images of the site are provided at no cost by the local cartographic institute as well as from a popular Internet-based map server. An initial set of local infiltration experiments, randomly located, were found to correlate to color intensities of the digital images. This relationship was then validated against additional independent measurements. The resulting maps of infiltration were then used to estimate the total maximum infiltration of the artificial pond area, the results being consistent with an independent flooding test performed at the site.
Abstract
The efficiency of artificial surface ponds (SPs) for managed aquifer recharge (MAR) is mostly controlled by the topmost portion of the soil. The most significant soil property [...]
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A Bayesian approach to integrate temporal data into probabilistic risk analysis of monitored NAPL remediation
D. Fernàndez-García, D. Bolster, X. Sánchez-Vila, D. Tartakovsky

Advances in Water Resources (2012). Vol. 36, pp. 108-120

Abstract
Upon their release into the subsurface, non-aqueous phase liquids (NAPLs) dissolve slowly in groundwater and/or volatilize in the vadose zone threatening the environment and public health over extended periods of time. The failure of a treatment technology at any given site is often due to the unnoticed presence of dissolved NAPL trapped in low permeability areas and/or the remaining presence of substantial amounts of pure phase NAPL after remediation efforts. The design of remediation strategies and the determination of remediation endpoints are traditionally carried out without quantifying risks associated with the failure of such efforts. We conduct a probabilistic risk analysis (PRA) to estimate the likelihood of failure of an on-site NAPL treatment technology. The PRA integrates all aspects of the problem (causes, pathways, and receptors) without resorting to extensive modeling. It accounts for a combination of multiple mechanisms of failure of a monitoring system, such as bypassing, insufficient sampling frequency and malfunctioning of the observation wells. We use a Bayesian framework to update the likelihood of failure of the treatment technology with observed measurements of concentrations at nearby monitoring wells
Abstract
Upon their release into the subsurface, non-aqueous phase liquids (NAPLs) dissolve slowly in groundwater and/or volatilize in the vadose zone threatening the environment and [...]
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Probabilistic analysis of maintenance and operation of artificial recharge ponds
D. Pedretti, M. Barahona-Palomo, D. Bolster, D. Fernàndez-García, X. Sánchez-Vila, D. Tartakovsky

Advances in Water Resources (2012). Vol. 36, pp. 23-35

Abstract
Aquifer artificial recharge from surface infiltration ponds is often conducted to replenish depleted aquifers in arid and semi-arid zones. Physical and bio-geochemical clogging decreases the host soil’s infiltration capacity, which has to be restored with periodic maintenance activities. We develop a probabilistic modeling framework that quantifies the risk of a pond’s infiltration capacity falling below its target value due to soil heterogeneity and clogging. This framework can act as a tool to aid managers in optimally selecting and designing maintenance strategies. Our model enables one to account for a variety of maintenance strategies that target different clogging mechanisms. The framework is applied to an existing pond in Barcelona, Spain as well as to several synthetic infiltration ponds with varying statistical distributions of initial infiltration capacity. We find that physical clogging mechanisms induce the greatest uncertainty and that maintenance targeted at these can yield optimal results. However, considering the fundamental role of the spatial variability in the initial properties, we conclude that an adequate initial characterization of the surface infiltration ponds is crucial to determining the degree of uncertainty of different maintenance solutions and thus to making cost-effective and reliable decisions.
Abstract
Aquifer artificial recharge from surface infiltration ponds is often conducted to replenish depleted aquifers in arid and semi-arid zones. [...]
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Probabilistic analysis of groundwater-related risks at subsurface excavation sites
A. Jurado, F. Gaspari, V. Vilarrasa, D. Bolster, X. Sánchez-Vila, D. Fernàndez-García, D. Tartakovsky

Engineering geology (2012). Vol. 125, pp. 35-44

Abstract
Construction of underground structures (e.g., subway lines, railways and highway tunnels) is inherently hazardous, posing risks to both workers and machinery at the site and to surrounding buildings. The presence of groundwater may increase these risks. We develop a general probabilistic risk assessment (PRA) framework to quantify risks driven by groundwater to the safety of underground constructions. The proposed approach is fully compatible with standard PRA practices, employing well-developed risk analysis tools based on the fault tree analysis method. The novelty and computational challenges of the proposed approach stem from the reliance on a combination of approaches including extracting information from databases, solving stochastic differential equations, or relying on expert judgment to compute probabilities of basic events. The general framework is presented in a case study and used to estimate and minimize risks at a construction site of an underground station for a new subway line in the Barcelona metropolitan area.
Abstract
Construction of underground structures (e.g., subway lines, railways and highway tunnels) is inherently hazardous, posing risks to both [...]
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Fate of β-blockers in aquifer material under nitrate reducing conditions: Batch experiments
M. Barbieri, T. Licha, K. Nödler, J. Carrera, C. Ayora, X. Sánchez-Vila

Chemosphere (2012). Vol. 89 (11), pp. 1272-1277

Abstract
The fate of the three environmentally relevant β-blockers atenolol, metoprolol and propranolol has been studied in batch experiments involving aquifer material and nitrate reducing conditions. Results from the about 90 d long tests indicate that abiotic processes, most likely sorption, jointly with biotransformation to atenololic acid were responsible for the 65% overall removal observed for atenolol. Zero order kinetics, typical of enzyme-limited reactions, controlled the transformation of this beta blocker to its corresponding carboxylic acid. The mass balance evidences that no mineralization of atenolol occurs in the biotic experiment and that atenololic acid is more stable than its parent compound under the studied conditions. This finding stresses the importance of considering atenololic acid as target compound in the environmental studies on the fate of atenolol. For metoprolol and propranolol the results from the experiment suggest a slower sorption to be the dominant removal process, which led to final decreases in concentrations of 25–30% and 40–45%, respectively. Overall, the removals observed in the experiments suggest that subsurface processes potentially constitute an alternative water treatment for the target beta-blockers, when compared to the removals reported for conventional wastewater treatment plants.
Abstract
The fate of the three environmentally relevant β-blockers atenolol, metoprolol and propranolol has been studied in batch experiments [...]
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Microcosm experiments to control anaerobic redox conditions when studying the fate of organic micropollutants in aquifer material
M. Barbieri, J. Carrera, X. Sánchez-Vila, C. Ayora, J. Cama, M. Köck-Schulmeyer, M. Alda, D. Barceló, J. Brunet, M. García

Journal of Contaminant Hydrology (2011). Vol. 126 (3-4), pp. 330-345

Abstract
The natural processes occurring in subsurface environments have proven to effectively remove a number of organic pollutants from water. The predominant redox conditions revealed to be one of the controlling factors. However, in the case of organic micropollutants the knowledge on this potential redox-dependent behavior is still limited. Motivated by managed aquifer recharge practices microcosm experiments involving aquifer material, settings potentially feasible in field applications, and organic micropollutants at environmental concentrations were carried out. Different anaerobic redox conditions were promoted and sustained in each set of microcosms by adding adequate quantities of electron donors and acceptors. Whereas denitrification and sulfate-reducing conditions are easily achieved and maintained, Fe- and Mn-reduction are strongly constrained by the slower dissolution of the solid phases commonly present in aquifers. The thorough description and numerical modeling of the evolution of the experiments, including major and trace solutes and dissolution/precipitation of solid phases, have been proven necessary to the understanding of the processes and closing the mass balance. As an example of micropollutant results, the ubiquitous beta-blocker atenolol is completely removed in the experiments, the removal occurring faster under more advanced redox conditions. This suggests that aquifers constitute a potentially efficient alternative water treatment for atenolol, especially if adequate redox conditions are promoted during recharge and long enough residence times are ensured.
Abstract
The natural processes occurring in subsurface environments have proven to effectively remove a number of organic pollutants from water. [...]
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Assessing preferential flow through an unsaturated waste rock pile using spectral analysis
P. Trinchero, R. Beckie, X. Sánchez-Vila, C. Nichol

Water Resources Research (2011). Vol. 47 (W07532), pp. 1-11

Abstract
Waste rock piles are an outcome of open pit and underground mining operations. Unprocessed low‐grade rock is disposed of in piles from several meters high to 100 m+ high. Waste rock piles may still contain sufficient concentrations of metals to be a potential source of pollution. The evaluation of the potential risk involves properly characterizing flow through these piles under unsaturated conditions. The main flow characteristic of the piles is the presence of a large range of grain and pore sizes. Based on data from an instrumented rock pile located in Saskatchewan Canada, unsaturated flow through the pile is modeled as a linear system after separating a fast and a slow component. Water reaching the base of the pile is monitored by 16 contiguous zero‐tension lysimeters. The fast component, flowing through macropores, is assumed to be released instantaneously, while the slow component is simulated using a linear‐reservoir model that assumes the presence of an interconnected porous matrix. An empirical transfer function (TF) is computed as the ratio of the spectra of signals between the output (basal outflow) and the input (rainfall time series). Determination of a parametric transfer function model provides information on the characteristic time of water storage in the matrix and on the fraction of the water within each subsection of the experimental pile that is channeled through the macropores. An analysis of the output signal at different support scales is performed, indicating the nonlinearity of the macropore fraction scaling processes
Abstract
Waste rock piles are an outcome of open pit and underground mining operations. Unprocessed low‐grade rock is disposed of in piles from several meters high to 100 m+ high. [...]
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Combining physical-based models and satellite images for the spatio-temporal assessment of soil infiltration capacity
D. Pedretti, D. Fernàndez-García, X. Sánchez-Vila, M. Barahona-Palomo, D. Bolster

Stochastic environmental research and risk assessment (2011). Vol. 25 (8), pp. 1065-1075

Abstract
The performance of managed artificial recharge (MAR) facilities by means of surface ponds (SP) is controlled by the temporal evolution of the global infiltration capacity Ic of topsoils. Cost-effective maintenance operations that aim to maintain controlled infiltration values during the activity of the SP require the full knowledge of the spatio-temporal variability of Ic. This task is deemed uncertain. The natural reduction in time of Ic depends on complex physical, biological and chemical reactions that clog the soil pores and has been observed to decay exponentially to an asymptotic non-zero value. Moreover, the relative influence of single clogging processes depend on some initial parameters of the soil, such as the initial infiltration capacity (Ic,0). This property is also uncertain, as aquifers are typically heterogeneous and scarcely characterized in practical situations. We suggest a method to obtain maps of Ic using a geostatistical approach, which is suitable to be extended to engineering risk assessment concerning management of SP facilities. We propose to combine geostatistical inference and a temporally-lumped physical model to reproduce non-uniform clogging in topsoils of a SP, using field campaigns of local and large scale tests and additionally by means of satellite images as secondary information. We then postulate a power-law relationship between the parameter of the exponential law, k, and Ic,0. It is found that calibrating the two parameters of the power law model it is possible to fit the temporal evolution of total infiltration rate at the pond scale in a MAR test facility. The results can be used to design appropriate measures to selectively limit clogging during operation, extending the life of the infiltration pond. The performance of managed artificial recharge (MAR) facilities by means of surface ponds (SP) is controlled by the temporal evolution of the global infiltration capacity Ic of topsoils. Cost-effective maintenance operations that aim to maintain controlled infiltration values during the activity of the SP require the full knowledge of the spatio-temporal variability of Ic. This task is deemed uncertain. The natural reduction in time of Ic depends on complex physical, biological and chemical reactions that clog the soil pores and has been observed to decay exponentially to an asymptotic non-zero value. Moreover, the relative influence of single clogging processes depend on some initial parameters of the soil, such as the initial infiltration capacity (Ic,0). This property is also uncertain, as aquifers are typically heterogeneous and scarcely characterized in practical situations. We suggest a method to obtain maps of Ic using a geostatistical approach, which is suitable to be extended to engineering risk assessment concerning management of SP facilities. We propose to combine geostatistical inference and a temporally-lumped physical model to reproduce non-uniform clogging in topsoils of a SP, using field campaigns of local and large scale tests and additionally by means of satellite images as secondary information. We then postulate a power-law relationship between the parameter of the exponential law, ¿, and Ic,0. It is found that calibrating the two parameters of the power law model it is possible to fit the temporal evolution of total infiltration rate at the pond scale in a MAR test facility. The results can be used to design appropriate measures to selectively limit clogging during operation, extending the life of the infiltration pond
Abstract
The performance of managed artificial recharge (MAR) facilities by means of surface ponds (SP) is controlled by the temporal evolution of the global infiltration capacity [...]
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A divide and conquer approach to cope with uncertainty, human health risk, and decision making in contaminant hydrology
F. Pereira, D. Bolster, X. Sánchez-Vila, W. Nowak

Water Resources Research (2011). Vol. 47 (W05508), pp. 1-13

Abstract
Assessing health risk in hydrological systems is an interdisciplinary field. It relies on the expertise in the fields of hydrology and public health and needs powerful translation concepts to provide decision support and policy making. Reliable health risk estimates need to account for the uncertainties and variabilities present in hydrological, physiological, and human behavioral parameters. Despite significant theoretical advancements in stochastic hydrology, there is still a dire need to further propagate these concepts to practical problems and to society in general. Following a recent line of work, we use fault trees to address the task of probabilistic risk analysis and to support related decision and management problems. Fault trees allow us to decompose the assessment of health risk into individual manageable modules, thus tackling a complex system by a structural divide and conquer approach. The complexity within each module can be chosen individually according to data availability, parsimony, relative importance, and stage of analysis. Three differences are highlighted in this paper when compared to previous works: (1) The fault tree proposed here accounts for the uncertainty in both hydrological and health components, (2) system failure within the fault tree is defined in terms of risk being above a threshold value, whereas previous studies that used fault trees used auxiliary events such as exceedance of critical concentration levels, and (3) we introduce a new form of stochastic fault tree that allows us to weaken the assumption of independent subsystems that is required by a classical fault tree approach. We illustrate our concept in a simple groundwater‐related setting
Abstract
Assessing health risk in hydrological systems is an interdisciplinary field. It relies on the expertise in the fields of hydrology and public health and needs powerful translation [...]
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Quantitative comparison of impeller-flowmeter and particle-size-distribution techniques for the characterization of hydraulic conductivity variability
M. Barahona-Palomo, M. Riva, X. Sánchez-Vila, E. Vázquez-Suñé, A. Guadagnini

Hydrogeology Journal (2011). Vol. 19 (3), pp. 603-612

Abstract
Hydraulic conductivities associated with measurement scale of the order of 10–1 m and collected during an extensive field campaign near Tübingen, Germany, are analyzed. Estimates are provided at coinciding locations in the system using: (1) the empirical Kozeny-Carman formulation, providing conductivity values, K GS, based on particle-size distribution, and (2) borehole impeller-type flowmeter tests, which infer conductivity, K FM, from measurements of vertical flows within a borehole. Correlation between the two sets of estimates is virtually absent. However, statistics of the natural logarithm of K GS and K FM at the site are similar in terms of mean values (averages of ln K GS being slightly smaller) and differ in terms of variogram ranges and sample variances. This is consistent with the fact that the two types of estimates can be associated with different (albeit comparable) measurement (support) scales. It also matches published results on interpretations of variability of geostatistical descriptors of hydraulic parameters on multiple observation scales. The analysis strengthens the idea that hydraulic conductivity values and associated key geostatistical descriptors inferred from different methodologies and at similar observation scales (of the order of tens of cm) are not readily comparable and should not be embedded blindly into a flow (and eventually transport) prediction model.
Abstract
Hydraulic conductivities associated with measurement scale of the order of 10–1 m and collected during an extensive field campaign near Tübingen, Germany, [...]
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Inferring spatial distribution of the radially integrated transmissivity from pumping tests in heterogeneous confined aquifers
N. Copty, P. Trinchero, X. Sánchez-Vila

Water Resources Research (2011). vol. 47 (W05526), pp. 1-11

Abstract
Hydrologists routinely analyze pumping test data using conventional interpretation methods that are based on the assumption of homogeneity and that, consequently, yield single estimates of representative flow parameters. However, natural subsurface formations are intrinsically heterogeneous, and hence, the flow parameters influencing the drawdown vary as the cone of depression expands in time. In this paper a novel procedure for the analysis of pumping tests in heterogeneous confined aquifers is developed. We assume that a given heterogeneous aquifer can be represented by a homogeneous system whose flow parameters evolve in time as the pumping test progresses. At any point in time, the interpreted flow parameters are estimated using the ratio of the drawdown and its derivative observed at that particular time. The procedure is repeated for all times, yielding time‐dependent estimates of transmissivity Ti(t) and storativity, Si(t). Based on the analysis of the sensitivity of drawdown to inhomogeneities in the T field, the time‐dependent interpreted transmissivity values are found to be a good estimate of Tg(r), the geometric mean of the transmissivity values encompassed within a progressively increasing radius r from the well. The procedure is illustrated for Gaussian heterogeneous fields with ln(T) variances up to a value of 2. The impact of the separation distance between the pumping well and observation point on data interpretation is discussed. The results show that information about the spatial variability of the transmissivity field can be inferred from time‐drawdown data collected at a single observation point
Abstract
Hydrologists routinely analyze pumping test data using conventional interpretation methods that are based on the assumption of homogeneity and that, consequently, yield single [...]
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Optimal reconstruction of concentrations, gradients and reaction rates from particle distributions
D. Fernàndez-García, X. Sánchez-Vila

Journal of Contaminant Hydrology (2011). Vol. 120-121 (c), pp. 99-114

Abstract
Random walk particle tracking methodologies to simulate solute transport of conservative species constitute an attractive alternative for their computational efficiency and absence of numerical dispersion. Yet, problems stemming from the reconstruction of concentrations from particle distributions have typically prevented its use in reactive transport problems. The numerical problem mainly arises from the need to first reconstruct the concentrations of species/components from a discrete number of particles, which is an error prone process, and then computing a spatial functional of the concentrations and/or its derivatives (either spatial or temporal). Errors are then propagated, so that common strategies to reconstruct this functional require an unfeasible amount of particles when dealing with nonlinear reactive transport problems. In this context, this article presents a methodology to directly reconstruct this functional based on kernel density estimators. The methodology mitigates the error propagation in the evaluation of the functional by avoiding the prior estimation of the actual concentrations of species. The multivariate kernel associated with the corresponding functional depends on the size of the support volume, which defines the area over which a given particle can influence the functional. The shape of the kernel functions and the size of the support volume determines the degree of smoothing, which is optimized to obtain the best unbiased predictor of the functional using an iterative plug-in support volume selector. We applied the methodology to directly reconstruct the reaction rates of a precipitation/dissolution problem involving the mixing of two different waters carrying two aqueous species in chemical equilibrium and moving through a randomly heterogeneous porous medium
Abstract
Random walk particle tracking methodologies to simulate solute transport of conservative species constitute an attractive alternative for their computational efficiency [...]
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Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation
X. Sánchez-Vila, D. Fernàndez-García, A. Guadagnini

Water Resources Research (2010). Vol. 46 (w12510), pp. 1-7

Abstract
We provide a quantitative interpretation of the column experiment reported by Gramling et al. (2002). The experiment involves advection‐dominated transport in porous media of three dissolved species, i.e., two reactants undergoing a fast irreversible reaction and the resulting product. The authors found that their observations could not be properly fitted with a model based on an advection‐dispersion‐reaction equation (ADRE) assuming the reaction was instantaneous, the actual measured total reaction product being lower than predictions for all times. The data have been recently well reproduced by Edery et al. (2009, 2010) by means of a particle tracking approach in a continuous time random walk framework. These and other authors have questioned the use of partial differential equation (PDE)–based approaches to quantify reactive transport because of the difficulty in capturing local‐scale mixing and reaction. We take precisely this approach and interpret the experiments mentioned by means of a continuum‐scale model based on the ADRE. Our approach differs from previous modeling attempts in that we imbue effects of incomplete mixing at the pore scale in a time‐dependent kinetic reaction term and show that this model allows quantitative interpretation of the experiments in terms of both reaction product profiles and time‐dependent global production rate. The time dependence of the kinetic term presented accounts for the progressive effects of incomplete mixing due to pore‐scale rate‐limited mass transfer, and follows a power law, which is consistent with the compilation of existing experiments reported by Haggerty et al. (2004). Our interpretation can form the basis for further research to assess the potential use of PDE approaches for the interpretation of reactive transport problems in moderately heterogeneous media
Abstract
We provide a quantitative interpretation of the column experiment reported by Gramling et al. (2002). The experiment involves advection‐dominated transport in porous media [...]
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A solution for multicomponent reactive transport under equilibrium and kinetic reactions
X. Sánchez-Vila, L. Donado, A. Guadagnini, J. Carrera

Water Resources Research (2010). Vol. 46 (7), pp. 1-13

Abstract
Analysis of the space‐time evolution of reactive solutes in porous systems is complex owing to the presence of different types of chemical reactions. The complete description of a reactive transport scenario entails calculating the spatial and temporal distribution of species concentrations and reaction rates. Here we develop an exact explicit expression for the space‐time distribution of reaction rates for a scenario where the geochemical system can be described by an arbitrary number of equilibrium (fast) reactions and one kinetic (slow) reaction, in the absence of non‐constant‐activity immobile species. The key result is that the equilibrium reaction rate is the sum of two terms representing the availability of reactants. One term involves diffusion and dispersion and represents the contribution of mixing. The other term includes the contribution of the kinetic reaction. The approach also yields the local concentrations of all dissolved species. Yet the latter are not needed for the direct computation of equilibrium reaction rates. We illustrate the approach by means of a simple reactive transport scenario, involving a common ion effect in the presence of a kinetic and an equilibrium reaction leading to precipitation and dissolution processes within a one‐dimensional fully saturated porous medium. The example highlights the highly nonlinear and nonmonotonic response of the system to the controlling input parameters
Abstract
Analysis of the space‐time evolution of reactive solutes in porous systems is complex owing to the presence of different types of chemical reactions. The complete description [...]
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Coupling of mass transfer and reactive transport for nonlinear reactions in heterogeneous media
M. Willmann, J. Carrera, X. Sánchez-Vila, O. Silva, M. Dentz

Water Resources Research (2010). Vol. 46 (w07515), pp. 1-15

Abstract
Fast chemical reactions are driven by mixing‐induced chemical disequilibrium. Mixing is poorly represented by the advection‐dispersion equation. Instead, effective dynamics models, such as multirate mass transfer (MRMT), have been successful in reproducing observed field‐scale transport, notably, breakthrough curves (BTCs) of conservative solutes. The objective of this work is to test whether such effective models, derived from conservative transport observations, can be used to describe effective multicomponent reactive transport in heterogeneous media. We use a localized formulation of the MRMT model that allows us to solve general reactive transport problems. We test this formulation on a simple three‐species mineral precipitation problem at equilibrium. We first simulate the spatial and temporal distribution of mineral precipitation rates in synthetic hydraulically heterogeneous aquifers. We then compare these reaction rates to those corresponding to an equivalent (i.e., same conservative BTC) homogenized medium with transport characterized by a nonlocal in time equation involving a memory function. We find an excellent agreement between the two models in terms of cumulative precipitated mass for a broad range of generally stationary heterogeneity structures. These results indicate that mass transfer models can be considered to represent quite accurately the large‐scale effective dynamics of mixing controlled reactive transport at least for the cases tested here, where individual transport paths sample the full range of heterogeneities represented by the BTC.
Abstract
Fast chemical reactions are driven by mixing‐induced chemical disequilibrium. Mixing is poorly represented by the advection‐dispersion equation. Instead, effective dynamics [...]
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An approach to identify urban groundwater recharge
E. Vázquez-Suñé, J. Carrera, I. Tubau, X. Sánchez-Vila, A. Soler

Hydrology and Earth system sciences (2010). Vol. 14 (10), pp. 2085-2097

Abstract
Evaluating the proportion in which waters from different origins are mixed in a given water sample is relevant for many hydrogeological problems, such as quantifying total recharge, assessing groundwater pollution risks, or managing water resources. Our work is motivated by urban hydrogeology, where waters with different chemical signature can be identified (losses from water supply and sewage networks, infiltration from surface runoff and other water bodies, lateral aquifers inflows, ...). The relative contribution of different sources to total recharge can be quantified by means of solute mass balances, but application is hindered by the large number of potential origins. Hence, the need to incorporate data from a large number of conservative species, the uncertainty in sources concentrations and measurement errors. We present a methodology to compute mixing ratios and end-members composition, which consists of (i) Identification of potential recharge sources, (ii) Selection of tracers, (iii) Characterization of the hydrochemical composition of potential recharge sources and mixed water samples, and (iv) Computation of mixing ratios and reevaluation of end-members. The analysis performed in a data set from samples of the Barcelona city aquifers suggests that the main contributors to total recharge are the water supply network losses (22%), the sewage network losses (30%), rainfall, concentrated in the non-urbanized areas (17%), from runoff infiltration (20%), and the Besòs River (11%). Regarding species, halogens (chloride, fluoride and bromide), sulfate, total nitrogen, and stable isotopes (18O, 2H, and 34S) behaved quite conservatively. Boron, residual alkalinity, EDTA and Zn did not. Yet, including these species in the computations did not affect significantly the proportion estimations.
Abstract
Evaluating the proportion in which waters from different origins are mixed in a given water sample is relevant for many hydrogeological problems, such as quantifying total [...]
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Conditional stochastic mapping of transport connectivity
D. Fernàndez-García, P. Trinchero, X. Sánchez-Vila

Water Resources Research (2010). Vol. 46 (10), pp. 1-14

Abstract
We present a method for the stochastic simulation of point‐to‐point transport connectivity honoring data from three types of information: (1) travel time estimates obtained from field tracer tests; (2) estimates of flow connectivity indicators obtained from the relatively fast or slow flow response that is observed at a point location given the flow impulse at another location, and (3) measurements of transmissivity at a local scale. The method thus efficiently integrates data obtained from different hydraulic tests, each sampling different areas within the aquifer. To achieve this, we first extend the concept of point‐to‐point flow connectivity and transport connectivity, mathematically formulated by Trinchero et al. (2008) for pumping conditions, to support a more general flow configuration. Interestingly, point‐to‐point flow connectivity can be generally seen as a weighted integral of transmissivity over the entire domain, the weighting function being proportional to the sensitivity of heads with respect to the natural log of transmissivity per unit of aquifer volume. On the contrary, point‐to‐point transport connectivity is a weighted integral along the particle path of the solute mass that involves two variables: transmissivity and flow connectivity. Each variable has its own distinct weighting function. The weighting function of transmissivity is inversely proportional to both the homogeneous travel time and the point velocity sampled along the travel path. On this basis, we show how to generate conditional point‐to‐point transport connectivity maps. The method avoids the inference of cross‐covariance functions between variables measured over different scales and sampled areas (which cannot be otherwise estimated with a few data measurements) by expressing them as a function of the local transmissivity covariance function. An example of the method is provided to evaluate the worth of including tracer data to delineate capture zones of abstraction wells originally defined from local transmissivity measurements. Monte Carlo simulations reveal that the impact of including tracer data is a maximum when the travel time data are obtained at a location different than that of transmissivity measurements. The reason is that weighting functions give larger weights to the injection location, so introducing tracer test data at points where transmissivity is already known is somewhat redundant
Abstract
We present a method for the stochastic simulation of point‐to‐point transport connectivity honoring data from three types of information: (1) travel time estimates obtained [...]
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An analytical approach to transient homovalent cation exchange problems
X. Sánchez-Vila, D. Bolster

Journal of Hydrology (2009). Vol. 378 (3-4), pp. 281-289

Abstract
Cation exchange in groundwater is one of the dominant surface reactions that occurs in nature and it carries with it many important environmental implications. The mass transfer of cation exchanging pollutants in groundwater can be described by a series of coupled partial differential equations, involving both aqueous and adsorbed species. The resulting system is mathematically challenging due to the complex nonlinearities that arise, which in turn complicates analytical approaches. While some analytical solutions for simplified problems exist, these typically lack the mechanisms that allow the waters to change their global chemical signature (in terms of total cations present in aqueous form) over time. We propose a methodology to solve the problem of exchanging two homovalent cations by deriving the driving equation for one of the aqueous species. This equation incorporates explicitly a retardation factor and a decay term, both with parameters that can vary in space and time. While the full solution can only be obtained numerically, we provide a solution in terms of a perturbative approach, where the leading terms can be obtained explicitly. The resulting solution provides physical explanations for the possible existence of non-monotonic concentrations for a range of parameters governing cation exchange processes
Abstract
Cation exchange in groundwater is one of the dominant surface reactions that occurs in nature and it carries with it many important environmental implications. The mass transfer [...]
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Effect of sorption heterogeneity on moments of solute residence time in convergent flows
M. Riva, A. Guadagnini, X. Sánchez-Vila

Mathematical geosciences (2009). Vol. 41 (8), pp. 835-853

Abstract
In this paper, we analyze the impact of physical and chemical heterogeneity on solute travel time to a pumping well. We consider a solute undergoing reversible linear instantaneous equilibrium sorption. Both the distribution coefficient, K d , and the transmissivity field, T, are considered spatially variable, and are modeled as partially correlated spatial random functions. Groundwater flow and solute transport are then solved within the context of a numerical Monte Carlo framework. The results are analyzed on the basis of dimensional analysis techniques. Simple and compact expressions characterizing the dependence of the target travel time moments on relevant dimensionless groups are proposed. The functional form of these expressions is inspired by, and is consistent with, the previous works of Sanchez-Vila and Rubin (Water Resour. Res. 39(4):1086, 2003) and Riva et al. (J. Contam. Hydrol. 82:23–43, 2006) A key result is that the effects of the chemical and physical heterogeneities on the mean travel time can be decoupled consistently with existing analytical results. The relative role of physical and geochemical heterogeneities in travel time variance is more complex, and such a decoupling is not observed. Potential uses of this work include the assessment of aquifer reclamation time by means of a single pumping well
Abstract
In this paper, we analyze the impact of physical and chemical heterogeneity on solute travel time to a pumping well. We consider a solute undergoing reversible linear instantaneous [...]
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Probabilistic risk analysis of groundwater remediation strategies
D. Bolster, M. Barahona, M. Dentz, D. Fernàndez-García, X. Sánchez-Vila, P. Trinchero, C. Valhondo, D. Tartakovsky

Water Resources Research (2009). Vol. 45 (6), pp. 1-10

Abstract
Heterogeneity of subsurface environments and insufficient site characterization are some of the reasons why decisions about groundwater exploitation and remediation have to be made under uncertainty. A typical decision maker chooses between several alternative remediation strategies by balancing their respective costs with the probability of their success or failure. We conduct a probabilistic risk assessment (PRA) to determine the likelihood of the success of a permeable reactive barrier, one of the leading approaches to groundwater remediation. While PRA is used extensively in many engineering fields, its applications in hydrogeology are scarce. This is because rigorous PRA requires one to quantify structural and parametric uncertainties inherent in predictions of subsurface flow and transport. We demonstrate how PRA can facilitate a comprehensive uncertainty quantification for complex subsurface phenomena by identifying key transport processes contributing to a barrier's failure, each of which is amenable to uncertainty analysis. Probability of failure of a remediation strategy is computed by combining independent and conditional probabilities of failure of each process. Individual probabilities can be evaluated either analytically or numerically or, barring both, can be inferred from expert opinion
Abstract
Heterogeneity of subsurface environments and insufficient site characterization are some of the reasons why decisions about groundwater exploitation and remediation have to [...]
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Characterization of mixing and spreading in a bounded stratified medium
V. Zavala-Sánchez, M. Dentz, X. Sánchez-Vila

Advances in Water Resources (2008). Vol. 32 (5), pp. 635-648

Abstract
Matheron and de Marsily [Matheron M, de Marsily G. Is the transport in porous media always diffusive? A counter-example. Water Resour Res 1980;16:901–17] studied transport in a perfectly stratified infinite medium as an idealized aquifer model. They observed superdiffusive solute spreading quantified by anomalous increase of the apparent longitudinal dispersion coefficient with the square root of time. Here, we investigate solute transport in a vertically bounded stratified random medium. Unlike for the infinite medium at asymptotically long times, disorder-induced mixing and spreading is uniquely quantified by a constant Taylor dispersion coefficient. Using a stochastic modeling approach we study the effective mixing and spreading dynamics at pre-asymptotic times in terms of effective average transport coefficients. The latter are defined on the basis of local moments, i.e., moments of the transport Green function. We investigate the impact of the position of the initial plume and the initial plume size on the (highly anomalous) pre-asymptotic effective spreading and mixing dynamics for single realizations and in average. Effectively, the system “remembers” its initial state, the effective transport coefficients show so-called memory effects, which disappear after the solute has sampled the full vertical extent of the medium. We study the impact of the intrinsic non-ergodicity of the confined medium on the validity of the stochastic modeling approach and study in this context the transition from the finite to the infinite medium
Abstract
Matheron and de Marsily [Matheron M, de Marsily G. Is the transport in porous media always diffusive? A counter-example. Water Resour Res 1980;16:901–17] studied transport [...]
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Application of a mixing-ratios based formulation to model mixing-driven dissolution experiments
A. Guadagnini, X. Sánchez-Vila, M. Saaltink, M. Bussini, B. Berkowitz

Advances in Water Resources (2009). Vol. 32 (5), pp. 756-766

Abstract
We address the question of how one can combine theoretical and numerical modeling approaches with limited measurements from laboratory flow cell experiments to realistically quantify salient features of complex mixing-driven multicomponent reactive transport problems in porous media. Flow cells are commonly used to examine processes affecting reactive transport through porous media, under controlled conditions. An advantage of flow cells is their suitability for relatively fast and reliable experiments, although measuring spatial distributions of a state variable within the cell is often difficult. In general, fluid is sampled only at the flow cell outlet, and concentration measurements are usually interpreted in terms of integrated reaction rates. In reactive transport problems, however, the spatial distribution of the reaction rates within the cell might be more important than the bulk integrated value. Recent advances in theoretical and numerical modeling of complex reactive transport problems [De Simoni M, Carrera J, Sanchez-Vila X, Guadagnini A. A procedure for the solution of multicomponent reactive transport problems. Water Resour Res 2005;41:W11410. doi: 10.1029/2005WR004056, De Simoni M, Sanchez-Vila X, Carrera J, Saaltink MW. A mixing ratios-based formulation for multicomponent reactive transport. Water Resour Res 2007;43:W07419. doi: 10.1029/2006WR005256] result in a methodology conducive to a simple exact expression for the space–time distribution of reaction rates in the presence of homogeneous or heterogeneous reactions in chemical equilibrium. The key points of the methodology are that a general reactive transport problem, involving a relatively high number of chemical species, can be formulated in terms of a set of decoupled partial differential equations, and the amount of reactants evolving into products depends on the rate at which solutions mix. The main objective of the current study is to show how this methodology can be used in conjunction with laboratory experiments to properly describe the key processes that occur in a complex, geochemically-active system under chemical equilibrium conditions. We model three CaCO3 dissolution experiments reported in Singurindy et al. [Singurindy O, Berkowitz B, Lowell RP. Carbonate dissolution and precipitation in coastal environments: Laboratory analysis and theoretical consideration. Water Resour Res 2004;40:W04401. doi: 10.1029/2003WR002651, Singurindy O, Berkowitz B, Lowell RP. Correction to Carbonate dissolution and precipitation in coastal environments: laboratory analysis and theoretical consideration. Water Resour Res 2005;41:W11701. doi: 10.1029/2005WR004433], in which saltwater and freshwater were mixed in different proportions. The integrated reaction rate within the cell estimated from the experiments are modeled independently by means of (a) a state-of-the-art reactive transport code, and (b) the uncoupled methodology of [12, 13], both of which use dispersivity as a single, adjustable parameter. The good agreement between the results from both methodologies demonstrates the feasibility of using simple solutions to design and analyze laboratory experiments involving complex geochemical problems
Abstract
We address the question of how one can combine theoretical and numerical modeling approaches with limited measurements from laboratory flow cell experiments to realistically [...]
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Multicomponent reactive transport in multicontinuum media
L. Donado, X. Sánchez-Vila, M. Dentz, J. Carrera

Water Resources Research (2009). Vol. 45 (W11402), pp. 1-11

Abstract
Multicomponent reactive transport in aquifers is a highly complex process, owing to a combination of variability in the processes involved and the inherent heterogeneity of nature. To date, the most common approach is to model reactive transport by incorporating reaction terms into advection-dispersion equations (ADEs). Over the last several years, a large body of literature has emerged criticizing the validity of the ADE for transport in real media, and alternative models have been presented. One such approach is that of multirate mass transfer (MRMT). In this work, we propose a model that introduces reactive terms into the MRMT governing equations for conservative species. This model conceptualizes the medium as a multiple continuum of one mobile region and multiple immobile regions, which are related by kinetic mass transfer processes. Reactants in both the mobile and immobile regions are assumed to always be in chemical equilibrium. However, the combination of local dispersion in the mobile region and the various mass transfer rates induce a global chemical nonequilibrium. Assuming this model properly accounts for transport of reactive species, we derive explicit expressions for the reaction rates in the mobile and immobile regions, and we study the impact of mass transfer on reactive transport. Within this framework, we observe that the resulting reaction rates can be very different from those that arise in a system governed by an ADE-type equation.
Abstract
Multicomponent reactive transport in aquifers is a highly complex process, owing to a combination of variability in the processes involved and the inherent heterogeneity of [...]
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Transport upscaling in heterogeneous aquifers: What physical parameters control memory functions?
M. Willmann, J. Carrera, X. Sánchez-Vila

Water Resources Research (2008). Vol. 44 (12), pp. 1-13

Abstract
Power law tailing is often observed in the breakthrough curves (BTCs) of tracer tests. Tailing is attributed to heterogeneity of aquifer properties and cannot be properly modeled by means of the homogeneous advection‐dispersion equation. Mass transfer models (e.g., continuous time random walk method, multirate mass transfer, or fractional‐order advection‐dispersion equations) using memory have been widely applied for reproducing observed tails. The relationship between memory parameters obtained from BTC fitting and the parameters characterizing the heterogeneity of hydraulic properties is still unclear. Here we investigate the conditions under which heterogeneity produces the type of tailing observed in the field and how memory functions are influenced by measurable heterogeneity parameters (e.g., variance, variogram, or integral scale of the underlying transmissivity field). We find that the slope of a BTC in a log‐log plot is mainly influenced by the connectivity of the underlying permeability field but is insensitive to its variance. The slope BTC reaches asymptotically 2 as connectivity increases. We conclude that an appropriate choice of the memory function allows reproducing the spreading caused by hydraulic heterogeneity but not necessarily the rate of mixing.
Abstract
Power law tailing is often observed in the breakthrough curves (BTCs) of tracer tests. Tailing is attributed to heterogeneity of aquifer properties and cannot be properly [...]
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Point-to-point connectivity, an abstract concept or a key issue for risk assessment studies?
P. Trinchero, X. Sánchez-Vila, D. Fernàndez-García

Advances in Water Resources (2008). Vol. 31 (12), pp. 1742-1753

Abstract
Connectivity of high/low-permeability areas has been recognized to significantly impact groundwater flow and solute transport. The task of defining a rigorous quantitative measure of connectivity for continuous variables has failed so far, and thus there exist a suite of connectivity indicators which are dependent on the specific hydrodynamic processes and the interpretation method. Amongst the many existing indicators, we concentrate on those characterizing connectivity between the points involved in a hydraulic or tracer test. The flow connectivity indicator used here is based on the time elapsed for hydraulic response in a pumping test (e.g., the storage coefficient estimated by the Cooper–Jacob method, Sest). Regarding transport, we select the estimated porosity from the breakthrough curve (ϕest). According to Knudby and Carrera [Knudby C, Carrera J. On the relationship between indicators of geostatistical, flow and transport connectivity. Adv Water Resour 2005;28(4):405–21] these two indicators measure connectivity differently, and are poorly correlated. Here, we use perturbation theory to analytically investigate the intrinsic relationship between Sest and ϕest. We find that ϕest can be expressed as a weighted line integral along the particle trajectory involving two parameters: the transmissivity point values, T, and the estimated values of Sest along the particle path. The weighting function is linear with the distance from the pumping well, thus the influence of the weighting function is maximum at the injection area, whereas the hydraulic information close to the pumping well becomes redundant (null weight). The relative importance of these two factors is explored using numerical simulations in a given synthetic aquifer and tested against intermediate-scale laboratory tracer experiments. We conclude that the degree of connectivity between two points of an aquifer (point-to-point connectivity) is a key issue for risk assessment studies aimed at predicting the travel time of a potential contaminant.
Abstract
Connectivity of high/low-permeability areas has been recognized to significantly impact groundwater flow and solute transport. The task of defining a rigorous quantitative [...]
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Influence of heterogeneity on the interpretation of pumping test data in leaky aquifers
N. Copty, P. Trinchero, X. Sánchez-Vila, M. Sarioglu, A. Findikakis

Water Resources Research (2008). Vol. 44 (11), 1-15

Abstract
Pumping tests are routinely interpreted from the analysis of drawdown data and their derivatives. These interpretations result in a small number of apparent parameter values which lump the underlying heterogeneous structure of the aquifer. Key questions in such interpretations are (1) what is the physical meaning of those lumped parameters and (2) whether it is possible to infer some information about the spatial variability of the hydraulic parameters. The system analyzed in this paper consists of an aquifer separated from a second recharging aquifer by means of an aquitard. The natural log transforms of the transmissivity, ln T, and the vertical conductance of the aquitard, ln C, are modeled as two independent second‐order stationary spatial random functions (SRFs). The Monte Carlo approach is used to simulate the time‐dependent drawdown at a suite of observation points for different values of the statistical parameters defining the SRFs. Drawdown data at each observation point are independently used to estimate hydraulic parameters using three existing methods: (1) the inflection‐point method, (2) curve‐fitting, and (3) the double inflection‐point method. The resulting estimated parameters are shown to be space dependent and vary with the interpretation method since each method gives different emphasis to different parts of the time‐drawdown data. Moreover, the heterogeneity in the pumped aquifer or the aquitard influences the estimates in distinct manners. Finally, we show that, by combining the parameter estimates obtained from the different analysis procedures, information about the heterogeneity of the leaky aquifer system may be inferred
Abstract
Pumping tests are routinely interpreted from the analysis of drawdown data and their derivatives. These interpretations result in a small number of apparent parameter values [...]
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Relative importance of geostatistical and transport models in describing heavily tailed breakthrough curves at the Lauswiesen site
M. Riva, A. Guadagnini, D. Fernàndez-García, X. Sánchez-Vila, T. Ptak

Journal of Contaminant Hydrology (2008). Vol. 101 (1-4), pp. 1-13

Abstract
We analyze the relative importance of the selection of (1) the geostatistical model depicting the structural heterogeneity of an aquifer, and (2) the basic processes to be included in the conceptual model, to describe the main aspects of solute transport at an experimental site. We focus on the results of a forced-gradient tracer test performed at the “Lauswiesen” experimental site, near Tübingen, Germany. In the experiment, NaBr is injected into a well located 52 m from a pumping well. Multilevel breakthrough curves (BTCs) are measured in the latter. We conceptualize the aquifer as a three-dimensional, doubly stochastic composite medium, where distributions of geomaterials and attributes, e.g., hydraulic conductivity (K) and porosity (ϕ), can be uncertain. Several alternative transport processes are considered: advection, advection–dispersion and/or mass-transfer between mobile and immobile regions. Flow and transport are tackled within a stochastic Monte Carlo framework to describe key features of the experimental BTCs, such as temporal moments, peak time, and pronounced tailing. We find that, regardless the complexity of the conceptual transport model adopted, an adequate description of heterogeneity is crucial for generating alternative equally likely realizations of the system that are consistent with (a) the statistical description of the heterogeneous system, as inferred from the data, and (b) salient features of the depth-averaged breakthrough curve, including preferential paths, slow release of mass particles, and anomalous spreading. While the available geostatistical characterization of heterogeneity can explain most of the integrated behavior of transport (depth-averaged breakthrough curve), not all multilevel BTCs are described with equal success. This suggests that transport models simply based on integrated measurements may not ensure an accurate representation of many of the important features required in three-dimensional transport models.
Abstract
We analyze the relative importance of the selection of (1) the geostatistical model depicting the structural heterogeneity of an aquifer, and (2) the basic processes [...]
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Reaction rates and effective parameters in stratified aquifers
D. Fernàndez-García, X. Sánchez-Vila, A. Guadagnini

Advances in Water Resources (2008). Vol. 31 (10), pp. 1364-1376

Abstract
Chemical species are advected by water and undergo mixing processes due to effects of local diffusion and/or dispersion. In turn, mixing causes reactions to take place so that the system can locally equilibrate. In general, a multicomponent reactive transport problem is described through a system of coupled non-linear partial differential equations. Under instantaneous chemical equilibrium, a complex geochemical problem can be highly simplified by fully defining the system in terms of conservative quantities, termed master species or components, and the space–time distribution of reaction rates. We investigate the parameters controlling reaction rates in a heterogeneous aquifer at short distances from the source. Hydraulic conductivity at this scale is modeled as a random process with highly anisotropic correlation structure. In the limit for very large horizontal integral scales, the medium can be considered as stratified. Upon modeling transport by means of an ADE (Advection Dispersion Equation), we derive closed-form analytical solutions for statistical moments of reaction rates for the particular case of negligible transverse dispersion. This allows obtaining an expression for an effective hydraulic conductivity, , as a representative parameter describing the mean behavior of the reactive system. The resulting is significantly smaller than the effective conductivity representative of the flow problem. Finally, we analyze numerically the effect of accounting for transverse local dispersion. We show that transverse dispersion causes no variation in the distribution of (ensemble) moments of local reaction rates at very short travel times, while it becomes the dominant effect for intermediate to large travel times.
Abstract
Chemical species are advected by water and undergo mixing processes due to effects of local diffusion and/or dispersion. In turn, mixing causes reactions to take place so [...]
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Conditional probability density functions of concentrations for mixing-controlled reactive transport in heterogeneous aquifers
X. Sánchez-Vila, A. Guadagnini, D. Fernández-García

Mathematical geosciences (2008). Vol. 41 (3), pp. 323-351

Abstract
This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes (and associated reaction rates) evolving in a randomly heterogeneous aquifer. Most existing approaches to solute transport in heterogeneous media focus on providing expressions for space–time moments of concentrations. In general, only low order moments (unconditional or conditional mean and covariance) are computed. In some cases, this allows for obtaining a confidence interval associated with predictions of local concentrations. Common applications, such as risk assessment and vulnerability practices, require the assessment of extreme (low or high) concentration values. We start from the well-known approach of deconstructing the reactive transport problem into the analysis of a conservative transport process followed by speciation to (a) provide a partial differential equation (PDE) for the (conditional) pdf of conservative aqueous species, and (b) derive expressions for the pdf of reactive species and the associated reaction rate. When transport at the local scale is described by an Advection Dispersion Equation (ADE), the equation satisfied by the pdf of conservative species is non-local in space and time. It is similar to an ADE and includes an additional source term. The latter involves the contribution of dilution effects that counteract dispersive fluxes. In general, the PDE we provide must be solved numerically, in a Monte Carlo framework. In some cases, an approximation can be obtained through suitable localization of the governing equation. We illustrate the methodology to depict key features of transport in randomly stratified media in the absence of transverse dispersion effects. In this case, all the pdfs can be explicitly obtained, and their evolution with space and time is discussed.
Abstract
This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes [...]
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A New Method for the Interpretation of Pumping Tests in Leaky Aquifers
P. Trinchero, X. Sánchez-Vila, N. Copty, A. Findikakis

Ground water (2008). Vol. 46 (1), pp. 133-143

Abstract
A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is based on the analysis of the first and second derivatives of the drawdown with respect to log time for the estimation of the flow parameters. Like commonly used analysis procedures, such as the type‐curve approach developed by Walton (1962) and the inflection point method developed by Hantush (1956), the mathematical development of the DIP method is based on the assumption of homogeneity of the leaky aquifer layers. However, contrary to the two methods developed by Hantush and Walton, the new method does not need any fitting process. In homogeneous media, the two classic methods and the one proposed here provide exact results for transmissivity, storativity, and leakage factor when aquifer storage is neglected and the recharging aquifer is unperturbed. The real advantage of the DIP method comes when applying all methods independently to a test in a heterogeneous aquifer, where each method yields parameter values that are weighted differently, and thus each method provides different information about the heterogeneity distribution. Therefore, the methods are complementary and not competitive. In particular, the combination of the DIP method and Hantush method is shown to lead to the identification of contrasts between the local transmissivity in the vicinity of the well and the equivalent transmissivity of the perturbed aquifer volume.
Abstract
A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is [...]
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Gestión de los recursos hídricos: los modelos hidrogeológicos como herramienta auxiliar
X. Sánchez-Vila, D. Fernández

Enseñaza de las ciencias de la Tierra (2007). Vol. 15 (3), pp. 250-255

Abstract
Water is scarce, and thus must be managed adequately in order to satisfy the global demand within a water resources integral planning. Management can act either on offer or demand. Proper management implies an accountability system capable both of reproducing the existing situation and quantifying the effect of management scenarios upon resources quantity and quality. The need for quantification makes indispensable numerical models in general, and hydrogeological models in particular. We present some of the elements that are included in a hydrogeological model, including the need for managing huge amounts of data and some technical aspects on discretization and calibration of numerical models. Hydrogeological models must be included into management models that account for conjunctive use of all available resources.
Abstract
Water is scarce, and thus must be managed adequately in order to satisfy the global demand within a water resources integral planning. Management can act either on offer or [...]
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