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Documents published in Scipedia

• 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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• On the meaning of the transmissivity values obtained from recovery tests

  M. Willmann, J. Carrera, X. Sánchez-Vila, E. Vázquez-Suñé

  Hydrogeology Journal (2007). Vol. 15 (5), pp. 833-842

  
  

  Abstract

        Recovery tests are based on estimating transmissivity, T, from the heads that rebound after pumping has stopped. Recovery tests can be performed in wells where conventional constant-rate pumping tests would not be possible. Test interpretation is based on the simple Theis recovery method, related to late time drawdown in an infinite homogeneous aquifer. Yet, field data often cannot be explained by the homogeneous theory. Because T is heterogeneous over an evolving range of scales, it is important to evaluate the support scale of hydraulic tests. Numerical simulations are performed to show that heterogeneity in T can explain these field observations. It is also shown that the local T value around the well can be inferred from early time-recovery data, assuming ideal conditions, whereas late time data yield a large-scale (regional) representative value. Even when recovery is observed for a short time, indirect information about the regional value can also be obtained. A method for the interpretation of recovery tests is proposed based on the Theis recovery method that takes into account the heterogeneity of aquifers. Finally, some guidelines are provided for best test performance depending on the scale of the problem.  

  Abstract
        Recovery tests are based on estimating transmissivity, T, from the heads that rebound after pumping has stopped. Recovery tests [...]

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• A mixing ratios‐based formulation for multicomponent reactive transport

  M. Simoni, X. Sánchez-Vila, M. Saaltink

  Water Resources Research (2007). Vol. 43 (7), pp. 1-10

  
  

  Abstract

  Chemical reactions are driven by disequilibrium, which is often caused by mixing. Therefore quantification of the mixing rate is essential for evaluating the fate of solutes in natural systems, such as rivers, lakes, and aquifers. We propose a novel mixing ratios‐based formulation to evaluate solute concentrations and reaction rates when equilibrium aqueous reactions and precipitation/dissolution of minerals are driven by mixing of different end‐members. Each end‐member corresponds to a water from a given source with a specific chemical signature. The approach decouples the solute transport and chemical speciation problems, so that mixing ratios can be first obtained from the solution of conservative transport and then be used in general speciation codes to obtain the concentration of reacting species. One key finding is a general expression for reaction rates which demonstrates that the amount of reactants evolving into products depends on the rate at which solutions mix. Our formulation constitutes a general framework according to which one can design and interpret experimental analyses devoted to study mixing‐driven reactive processes and obtain transverse dispersion coefficients. The formulation is also proposed as a useful tool to derive analytical solutions of reactive transport problems and may result computationally advantageous when compared to previous approaches to reactive transport modeling. We apply the developed formulation to provide an analytical solution of the reactive transport process resulting from mixing different CaCO3‐saturated waters in a two‐dimensional setup

  Abstract
  Chemical reactions are driven by disequilibrium, which is often caused by mixing. Therefore quantification of the mixing rate is essential for evaluating the fate of solutes [...]

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• Quasi-horizontal circulation cells in 3D seawater intrusion

  E. Abarca, J. Carrera, X. Sánchez-Vila, C. Voss

  Journal of Hydrology (2007). Vol. 339 (3-4), pp. 118-129

  
  

  Abstract

  The seawater intrusion process is characterized by the difference in freshwater and seawater density that causes freshwater to float on seawater. Many confined aquifers have a large horizontal extension with respect to thickness. In these cases, while buoyancy acts in the vertical direction, flow is confined between the upper and bottom boundaries and the effect of gravity is controlled by variations of aquifer elevation. Therefore, the effective gravity is controlled by the slope and the shape of the aquifer boundaries. Variability in the topography of the aquifer boundaries is one case where 3D analysis is necessary. In this work, density-dependent flow processes caused by 3D aquifer geometry are studied numerically and specifically, considering a lateral slope of the aquifer boundaries. Sub-horizontal circulation cells are formed in the saltwater entering the aquifer. The penetration of the saltwater can be quantified by a dimensionless buoyancy number that measures the lateral slope of the aquifer relative to freshwater flux. The penetration of the seawater intrusion wedge is controlled more by this slope than by the aquifer thickness and dispersivity. Thus, the slope must be taken into account in order to accurately evaluate seawater intrusion.

  Abstract
  The seawater intrusion process is characterized by the difference in freshwater and seawater density that causes freshwater to float on seawater. Many confined aquifers have [...]

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• Transport‐controlled reaction rates under local non‐equilibrium conditions

  X. Sánchez-Vila, M. Dentz, L. Donado

  Geophysical research letters (2007). Vol. 34 (10), pp. 10404

  
  

  Abstract

  Chemical reactions are driven by non‐equilibrium and can be fully described by the spatio‐temporal distribution of the reaction rate. We present an analytical approach for the computation of reaction rates under local non‐equilibrium conditions for a precipitation/dissolution problem. We derive an original non‐linear partial differential equation for the reaction rate r and present a series expansion of r for large Damköhler numbers, i.e., fast local scale reactions. The impact of local scale non‐equilibrium conditions on the transport‐controlled reaction rate is studied for reactive transport in a column.

  Abstract
  Chemical reactions are driven by non‐equilibrium and can be fully described by the spatio‐temporal distribution of the reaction rate. We present an analytical approach [...]

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• Anisotropic dispersive Henry problem

  E. Abarca, J. Carrera, X. Sánchez-Vila, M. Dentz

  Advances in Water Resources (2007). Vol. 30 (4), pp. 913-926

  
  

  Abstract

  The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. This paper seeks to modify Henry’s problem to ensure sensitivity to density variations and vertical salinity profiles that resemble field observations. In the proposed problem, the “dispersive Henry problem”, mixing is represented by means of the traditional Scheidegger dispersion tensor (dispersivity times water flux). Anisotropy in the hydraulic conductivity is acknowledged and Henry’s seaside boundary condition of prescribed salt concentration is replaced by a flux dependent boundary condition, which represents more realistically salt transport across the seaside boundary. This problem turns out to be very sensitive to density variations and its solution gets closer to reality. However, an improvement in the traditional Henry problem (gain in sensitivity and realism) can be also achieved if the value of the Peclet number is significantly reduced. Although the dispersive problem lacks an analytical solution, it can shed light on flow in coastal aquifers. It provides significant information about the factors controlling seawater penetration, width of the mixing zone and influx of seawater. The width of the mixing zone depends basically on dispersion with longitudinal and transverse dispersion controlling different parts of the mixing zone but displaying similar overall effects. Toe penetration is mainly controlled by the horizontal permeability and by the geometric mean of the dispersivities. Finally, transverse dispersivity and the geometric mean of the hydraulic conductivity are the leading parameters controlling the amount of saltwater that enters the aquifer

  Abstract
  The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. [...]

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• Ergodicity of pumping tests

  X. Sánchez-Vila, D. Tartakovsky

  Water Resources Research (2007). Vol. 43 (3), pp. 1-5

  
  

  Abstract

  Standard interpretations of pumping tests in heterogeneous formations rely on effective representations of porous media, which replace spatially varying hydraulic properties with their constant counterparts averaged over the support volume of a test. Rigorous approaches for deriving representative (effective, apparent, upscaled, etc.) parameters employ either ensemble or spatial averaging. We derive a set of conditions under which these two paradigms yield identical results. We refer to them as conditions for the ergodicity of pumping tests. This allows one to use stochastic approaches to estimate the statistics of the spatial variability of hydraulic parameters on scales smaller than the support volume of a pumping test.

  Abstract
  Standard interpretations of pumping tests in heterogeneous formations rely on effective representations of porous media, which replace spatially varying hydraulic properties [...]

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• Effective dispersion in a chemically heterogeneous medium under temporally fluctuating flow conditions

  V. Zavala-Sánchez, M. Dentz, X. Sánchez-Vila

  Advances in Water Resources (2007). Vol. 30 (5), pp. 1342-1354

  
  

  Abstract

  We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general.

  Abstract
  We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the [...]

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• Variable density flow in porous media

  M. Dentz, D. Tartakovsky, E. Abarca, A. Guadagnini, X. Sánchez-Vila, J. Carrera

  Journal of Fluid Mechanics (2006). Vol. 561, pp. 209-235

  
  

  Abstract

  We review the state of the art in modeling of variable-density flow and transport in porous media, including conceptual models for convection systems, governing balance equations, phenomenological laws, constitutive relations for fluid density and viscosity, and numerical methods for solving the resulting nonlinear multifield problems. The discussion of numerical methods addresses strategies for solving the coupled spatio-temporal convection process, consistent velocity approximation, and error-based mesh adaptation techniques. As numerical models for those nonlinear systems must be carefully verified in appropriate tests, we discuss weaknesses and inconsistencies of current model-verification methods as well as benchmark solutions. We give examples of field-related applications to illustrate specific challenges of further research, where heterogeneities and large scales are important.

  Abstract
  We review the state of the art in modeling of variable-density flow and transport in porous media, including conceptual models for convection systems, governing balance equations, [...]

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