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• Pumping tests in heterogeneous aquifers: An analytical study of what can be obtained from their interpretation using Jacob's Method

  X. Sánchez-Vila, P. Meier, J. Carrera

  Water Resources Research (1999). Vol. 35 (4), pp. 943-952

  
  

  Abstract

  Interpretation of pumping tests to estimate hydraulic parameter values is typically based on the assumption of aquifer homogeneity. The applicability of the traditional methods of interpretation in real aquifers can be questioned, since the evaluation of the drawdown curves observed at different locations in a single test may not result in one consistent set of hydraulic parameters. Thus most hydrogeologists tend to look at estimated transmissivities (T) as some average property of the medium, while estimated storativities (S) are disregarded in some cases, particularly when they are obtained from data measured at the pumping well. An analytical study of drawdown under radially convergent flow toward a single point in heterogeneous aquifers shows that large time drawdown values form a straight line on a drawdown versus log time plot. Jacob's method consists of obtaining estimates for T and S from the slope and intercept of this line. We find that even in a heterogeneous field, these estimates provide valuable information about the aquifer. Estimated T values for different observation points tend to converge to a single value, which corresponds to the effective T derived under parallel flow conditions. Estimated storativities, however, display higher variability, but the geometric mean of the Sest values can be used as an unbiased estimator of the actual S. Thus it appears that although Jacob's method was originally derived for homogeneous media, it can provide valuable information in real aquifers

  Abstract
  Interpretation of pumping tests to estimate hydraulic parameter values is typically based on the assumption of aquifer homogeneity. The applicability of the traditional [...]

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• Upscaling transmissivity under radially convergent flow in heterogeneous media

  X. Sánchez-Vila, C. Axness, J. Carrera

  Water Resources Research (1999). Vol. 104 (3), pp. 613-621

  
  

  Abstract

  Most field methods used to estimate transmissivity values rely on the analysis of drawdown under convergent flow conditions. For a single well in a homogeneous and isotropic aquifer and under steady state flow conditions, drawdown s is directly related to the pumping rate Q through transmissivity T. In real, nonhomogeneous aquifers, s and Q are still directly related, now through a value called equivalent transmissivity Teq. In this context, Teq is defined as the value that best fits Thiem's equation and would, for example, be the transmissivity assigned to the well location in the classical interpretation of a steady state pumping test. This equivalent or upscaled transmissivity is clearly not a local value but is some representative value of a certain area surrounding the well. In this paper we present an analytical solution for upscaling transmissivities under radially convergent steady state flow conditions produced by constant pumping from a well of radius rw in a heterogeneous aquifer based upon an extension of Thiem's equation. Using a perturbation expansion, we derive a second‐order expression for Teq given as a weighted average of the fluctuations in log T throughout the domain. This expression is compared to other averaging formulae from the literature, and differences are pointed out. Teq depends upon an infinite series which may be expressed in terms of coefficients of the finite Fourier transform of the log transmissivity function. Sufficient conditions for convergence of this series are examined. Finally, we show that our solution agrees with existing analytical ones to second order and test the solution with a numerical example

  Abstract
  Most field methods used to estimate transmissivity values rely on the analysis of drawdown under convergent flow conditions. For a single well in a homogeneous and isotropic [...]

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• An evaluation of Jacob's Method for the interpretation of pumping tests in heterogeneous formations

  P. Meier, J. Carrera, X. Sánchez-Vila

  Water Resources Research (1995). Vol. 34 (5), pp. 1011-1025

  
  

  Abstract

  Most pumping tests are interpreted using the classical Theis assumption of large‐scale homogeneity with various corrections to account for early time behavior of drawdown curves. When drawdowns are plotted versus log time, late time data often delineate a straight line, which is consistent with Jacob's approximation of Theis' solution but may seem surprising in view of the heterogeneity of natural media. The aim of our work is to show that Jacob's method leads to a good approximation of the effective transmissivity of heterogeneous media when constrained to late time data. A review of several multiwell pumping tests demonstrates that when drawdown curves from each observation well are interpreted separately, they produce very similar transmissivity T estimates. However, the corresponding estimates for storativity span a broad range. This behavior is verified numerically for several models of formation heterogeneity. A very significant finding of the numerical investigation is that T values estimated using simulated drawdown from individual observation wells are all very close to the effective T value for parallel flow. This was observed even in nonmultiGaussian T fields, where high T zones are well connected and where the effective T is larger than the geometric average of point values. This implies that Jacob's method can be used for estimating effective T values in many, if not most, formations.

  Abstract
  Most pumping tests are interpreted using the classical Theis assumption of large‐scale homogeneity with various corrections to account for early time behavior of drawdown [...]

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• On matrix diffusion: formulations, solution methods and qualitative effects

  J. Carrera, X. Sánchez-Vila, I. Benet, A. Medina, G. Galarza, J. Guimerà

  Journal of Hydrology (1997). Vol. 6, pp. 178-190

  
  

  Abstract

  Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φ m 2 R m D m  / L m 2, whereas late-time behavior (long tracer tests) depends only on φ m R m , and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them.

  Abstract
  Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. [...]

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• Radially convergent flow in heterogeneous media

  X. Sánchez-Vila

  Water resources research (1997). Vol. 33 (7), pp. 1633-1641

  
  

  Abstract

  We present an analytical solution for apparent effective transmissivity under radially convergent steady state flow conditions, produced by constant pumping from a single well of finite radius, rw. Apparent effective transmissivity, Te, is defined as the value that relates the expected values of flow and head gradient at a certain location. The domain is two‐dimensional, of annular shape, and the size of the pumping well is explicitly taken into account. The solution for the steady state heads is obtained by solving the perturbed flow equation and substituting it into Darcy's law to obtain a consistent second‐ order expansion for Te. We show that apparent effective transmissivity is a scalar for any choice of isotropic covariance model, with an expression given in integral form. Our main result is that Te in a heterogeneous, statistically isotropic random field, under radial steady state flow conditions, is a monotonie increasing function of r (distance from the well) that rises from the harmonic mean of the point transmissivity values (close to the well) and tends asymptotically towards the geometric mean (far from the well). The asymptotic value is reached at a distance of a few integral scales (1.5–2 for the Gaussian model and 3–5 for the exponential one). The apparent effective transmissivity versus normalized r curves are in excellent agreement with previously published numerical work carried out using Monte Carlo method

  Abstract
  We present an analytical solution for apparent effective transmissivity under radially convergent steady state flow conditions, produced by constant pumping from a single [...]

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• Directional effects on convergent flow tracer tests

  X. Sánchez-Vila, J. Carrera

  Mathematical geology (1997). Vol. 29 (4), pp. 551-569

  
  

  Abstract

  Convergent flow tracer tests constitute a convenient way of characterizing hydraulic parameters in an aquifer. Interpretation of tracer breakthrough curves from convergent flow tests normally is made under the assumption of radial symmetry. Nevertheless, these curves may display directional dependence; that is when tracers are injected at several points located at the same distance, both arrival times and estimated dispersivities may be significantly different. This result is why some authors attribute a tensorial nature to porosity or, equivalently, talk about directional porosity when trying to explain the variations in computed porosity depending on the relative orientation of pumping and injection wells. Our main ponit is that this directional effect is nothing but an artifact of an inappropriate selection of a conceptual model, where anisotropy (local of statistical) in hydraulic conductivity is not properly characterized. To illustrate this point, we first consider the situation of a simple homogeneous and anisotropic model of the medium. We prove analytically that this model leads to arrival time being proportional to the square root of directional hydraulic conductivity. Using a stochastic approach, we determine the same directional behavior of arrival time for a locally isotropic hydraulic conductivity field with statistical anisotropy caused by an anisotropic correlation structure. A statistical anisotropic covariance model for hydraulic conductivity is consistent with field evidence.

  Abstract
  Convergent flow tracer tests constitute a convenient way of characterizing hydraulic parameters in an aquifer. Interpretation of tracer breakthrough curves from convergent [...]

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• Field tracer experiment in a low permeability fractured medium: results from El Berrocal site

  M. D'Alessandro, F. Mousty, G. Bidoglio, J. Guimera, I. Benet, X. Sánchez-Vila, M. Gutiérrez, A. Llano

  Journal of Contaminant Hydrology (1997). Vol. 26 (1-4), pp. 189-201

  
  

  Abstract

  A modelling experimental activity was developed to characterise the hydraulic behaviour of water-bearing fractures in crystalline rocks. Three conservative tracers were injected into two packed-off sections of the same well, 69 m deep in a granite formation, and recovered by pumping from an isolated section of a second borehole, 46 m deep, 14 m apart. The concept of this design is to characterise separately an isolated fracture zone intersecting the lower parts of both wells from the fracture network intersecting the bulk of the rock. Before using the tracers in the field, their behaviour was studied in the laboratory under controlled conditions. Fluorescein, eosin and iodide were finally chosen as the best spikes. The field experiments were developed under strictly controlled conditions, such as (1) checking the hydraulic pressure in the packed-off sections and in other parts of circuits; (2) mixing the tracer solutions during the injection and checking their homogeneity; (3) performing a continuous and automatic monitoring of tracer concentration in the arrival well. Iodide and fluorescein were injected in one section, and eosin in the other section. The pumping rate was maintained at 2 1 min−1. The test lasted 27 d after which from 40 to 60% of the injected masses were recovered. Breakthrough curve analysis considered two conceptual models: radial advective-dispersive transport with and without matrix diffusion: the first model returns thickness-porosity values around 0.2 × 10−1 m and dispersivity around 4 m. Parameters are remarkably consistent for iodide and fluorescein, although fittings can be improved. The matrix diffusion model provides much better fittings by decreasing thickness porosity to 0.8 X 10-Z m. Dispersivities range from 0.5 to 0.9 m and the molecular diffusion term differentiates the behaviour of conservative tracers such as fluorescein and iodide.

  Abstract
  A modelling experimental activity was developed to characterise the hydraulic behaviour of water-bearing fractures in crystalline rocks. Three conservative tracers were [...]

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• Scale effects in transmissivity

  X. Sánchez-Vila, J. Carrera, J. Girardi

  Journal of Hydrology (1996). Vol. 183 (1-2), pp. 1-22

  
  

  Abstract

  Heterogeneity accounts for several paradoxes in groundwater flow and solute transport. One of the most striking observations is the emergence of scale effects in transmissivity, that is, the increase in effective transmissivity (or hydraulic conductivity, for that matter) with increasing scale of observation. Traditional stochastic approaches, where transmissivity is treated as a multilog-normal random function, lead to a large-scale effective transmissivity equal to the geometric average of local measurements. We present several field cases in which large-scale transmissivities are indeed larger than the geometric average of local tests. This suggests that the assumption of multilog-normality may not be valid in many cases, even if point T values display a log-normal distribution. We conjecture that scale dependence of T may, in part, be a consequence of high T zones being better connected than average or low T zones, a feature which may occur in many geological environments, but which is not consistent with multinormal log-T fields. We go on to generate a suite of log-T fields with a normal distribution for point values but non-multinormal spatial correlation. In all our fields, high T zones show longer correlations than average of low T zones. By simulating flow through these synthetic fields under simple boundary conditions, and estimating their effective transmissivity values, we conclude that these types of departures from the multilog-normality assumption lead consistently to scale effects.

  Abstract
  Heterogeneity accounts for several paradoxes in groundwater flow and solute transport. One of the most striking observations is the emergence of scale effects in transmissivity, [...]

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• A Synthesis of Approaches to Upscaling of Hydraulic Conductivities

  X. Sánchez-Vila, J. Girardi, J. Carrera

  Water resources research (1995). Vol. 31 (4), pp. 867-882

  
  

  Abstract

  Simulation of flow through heterogeneous media often requires discretizing the flow domain into blocks and assigning an equivalent block conductivity value to each one of them. The process of defining block conductivities from point values is termed upscaling. A number of approaches to upscaling are available, most of which consider the uncertainty associated with any natural property, so that they cast the problem in a stochastic frame. Recently, Indelman and Dagan (1993a, b) provided a general stochastic methodology to upscaling in heterogeneous anisotropic formations by means of the dissipation energy function; unfortunately, they did not provide any “practical” method to compute block values from point ones. The objective of this work is twofold: First, we analyze different practical approaches to compute block conductivities and find that all of them provide very similar results in terms of actual computed values; second, we check that all approaches verify approximately a number of conditions stated by Indelman and Dagan (1993a). Specifically, we show analytically that for regular blocks, the methodologies of both Rubin and Gómez‐Hernández (1990) and Desbarats (1992) (which we call “practical” methodologies) satisfy the condition that the effective conductivity obtained from a field where the elementary conductivities are defined over a certain support (we call this the actual formation) is identical to that obtained from the same field with conductivities defined at a larger support (upscaled formation). The analysis is carried out by working with the logarithm of block conductivities and using a small‐perturbation expansion and thus is strictly valid for small variances. On the other hand, we show numerically that the two methodologies satisfy approximately an important condition stated in terms of the dissipation energy: that block‐averaged dissipation values computed are indeed very close to the true dissipation values in each block. The agreement is even better if we consider statistical moments instead of point values. As an important conclusion we should note that all practical methodologies considered in this work perform equally well and, more important, constitute a simple way to treat an otherwise very complex problem

  Abstract
  Simulation of flow through heterogeneous media often requires discretizing the flow domain into blocks and assigning an equivalent block conductivity value to each one of [...]

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• A discussion on validation of hydrogeological models

  J. Carrera, S. Mousavi, E. Usunoff, X. Sánchez-Vila, G. Galarza

  Reliability Engineering & System Safety (1993). Vol. 42 (2-3), pp. 201-216

  
  

  Abstract

      Groundwater flow and solute transport are often driven by heterogeneities that elude easy identification. It is also difficult to select and describe the physico-chemical processes controlling solute behavior. As a result, definition of a conceptual model involves numerous assumptions both on the selection of processes and on the representation of their spatial variability. Even if a unique conceptual model could be identified, estimation of its parameters may be highly uncertain. Using a calibrated model for making groundwater predictions involves three types of uncertainties: those associated with the correctness of the conceptual model, which may arise during model construction or during prediction; those related to the accuracy of model parameters; and those corresponding to uncertainties in future stresses. In this context, validating a numerical model by comparing its predictions with actual measurements may not be sufficient for evaluting whether or not it provides a good representation of ‘reality’. Predictions will be close to measurements, regardless of model validity, if these are taken from experiments that stress well-calibrated model modes. On the other hand, predictions will be far from measurements when model parameters are very uncertain, even if the model is indeed a very good representation of the real system. Hence, we contend that ‘classical’ validation of hydrogeological models is not possible. Rather, models should be viewed as theories about the real system. This can be proven wrong, but they cannot be proven right. In this sense, we propose to follow a rigorous modeling approach in which different sources of uncertainty are explicitly recognized. The application of one such approach is illustrated by modeling a laboratory uranium tracer test performed on fresh granite, which was used as Test Case 1b in INTRAVAL.  

  Abstract
      Groundwater flow and solute transport are often driven by heterogeneities that elude easy identification. It is also difficult to select and [...]

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