The Extended Thiem's solution: Including the impact of heterogeneity

Zech, Alraune; Schneider, Christoph; Attinger, Sabine

doi:10.1029/2012wr011852

Cited by 16 publications

(35 citation statements)

References 21 publications

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“…Similar work has been done by Zech et al (2012) for pumping tests in threedimensional porous media. The "effective well flow solution" h efw (r) describes the mean depression cone of a pumping test in two-dimensional heterogeneous media effectively.…”

Section: Introductionmentioning

confidence: 53%

“…The differences in the estimates for the drawdowns in different direction for the same realization of transmissivity shows that the parameter estimates reflect local heterogeneity in the vicinity of the well rather than the global statistical parameters of the transmissivity field. This was studied and discussed in detail for pumping tests in three-dimensional heterogeneous media by Zech et al (2015). The realization in Fig.…”

Section: Individual Pumping Test Interpretationmentioning

confidence: 99%

“…The question of the applicability of h efw (r) on limited head data is of quite complex nature. For a detailed discussion on that issue the reader is referred to Zech et al (2015).…”

Section: Numerical Pumping Testsmentioning

confidence: 99%

“…ζ is a factor of proportionality, which was determined to be ζ = 1.6, as discussed in detail by Zech et al (2012). T RCG (r) can be interpreted as an interpolating function between the representative transmissivity at the well T H = T G exp − 1 2 σ 2 to the far-field value T G depending on r, controlled by the correlation length (Fig.…”

Section: Radial Coarse Graining Transmissivitymentioning

confidence: 99%

“…The approach was further developed for three-dimensional well flow by Zech et al (2012), introducing an effective well flow solution for the hydraulic head. Similarly, the concept of radial coarse graining for two-dimensional well flow will be expanded in the following.…”

Section: Concept Of Radial Coarse Grainingmentioning

confidence: 99%

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Technical note: Analytical drawdown solution for steady-state pumping tests in two-dimensional isotropic heterogeneous aquifers

Zech

Attinger

2016

Hydrol. Earth Syst. Sci.

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Abstract.A new method is presented which allows interpreting steady-state pumping tests in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. An effective description of transmissivity is required, being a function of the radial distance to the well and including the parameters of log-transmissivity: mean, variance, and correlation length. Such a model is provided by the upscaling procedure radial coarse graining, which describes the transition of near-well to far-field transmissivity effectively. Based on this approach, an analytical solution for a steady-state pumping test drawdown is deduced. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown within an individual heterogeneous transmissivity field. The analytical form of the solution allows inversely estimating the parameters of aquifer heterogeneity. For comparison with the effective well flow solution, virtual pumping tests are performed and analysed for both cases, the ensemble mean drawdown and pumping tests at individual transmissivity fields. Interpretation of ensemble mean drawdowns showed proof of the upscaling method. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media in contrast to Thiem's solution for homogeneous media. Multiple pumping tests conducted at different locations within an individual transmissivity field are analysed, making use of the effective well flow solution to show that all statistical parameters of aquifer heterogeneity can be inferred under field conditions. Thus, the presented method is a promising tool with which to estimate parameters of aquifer heterogeneity, in particular variance and horizontal correlation length of log-transmissivity fields from steady-state pumping test measurements.

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Section: Introductionmentioning

confidence: 53%

Section: Individual Pumping Test Interpretationmentioning

confidence: 99%

“…The question of the applicability of h efw (r) on limited head data is of quite complex nature. For a detailed discussion on that issue the reader is referred to Zech et al (2015).…”

Section: Numerical Pumping Testsmentioning

confidence: 99%

Section: Radial Coarse Graining Transmissivitymentioning

confidence: 99%

Section: Concept Of Radial Coarse Grainingmentioning

confidence: 99%

See 3 more Smart Citations

Technical note: Analytical drawdown solution for steady-state pumping tests in two-dimensional isotropic heterogeneous aquifers

Zech

Attinger

2016

Hydrol. Earth Syst. Sci.

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Estimating transmissivity from single‐well pumping tests in heterogeneous aquifers

Pechstein

Attinger

Krieg

et al. 2016

Water Resources Research

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Although aquifers are naturally heterogeneous, the interpretation of pumping tests is commonly performed under the assumption of aquifer homogeneity. This yields interpreted hydraulic parameters averaged over a domain of uncertain extent which disguises their relation to the underlying heterogeneity. In this study, we numerically investigate the sensitivity of the transient drawdown at the pumping well, to nonuniform distributions of transmissivity in confined aquifers. Frechet kernels and their time derivative are used to estimate two spatially averaged transmissivities, denoted the equivalent and interpreted transmissivity, T eq and T in , respectively, for the case of single-well pumping tests. Interrelating T eq and T in is achieved by modeling T in in terms of a distance dependent, radially heterogeneous field. In weakly heterogeneous aquifers, T eq approximates T PW , the local transmissivity at the pumped well. With increasing degree of heterogeneity, T eq deviates from T PW as pumping propagates. T in starts at T PW , approaching the spatial geometric mean of transmissivity during late pumping times. Limits of the proposed spatial weighting functions are investigated by treating the interpreted storativity, S est , as an indicator for flow connectivity. It is shown numerically that the spatial weights for T eq and T in agree well to the underlying heterogeneity if S est < 1. Finally, implications for applying the concepts of T eq and T in to heterogeneous domains, and, for real world applications are discussed. It is found that time-dependent spatial averages of T in agree well with estimates of the interpreted transmissivity from the Continuous-Derivation method.

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Extending Theis' solution: Using transient pumping tests to estimate parameters of aquifer heterogeneity

Zech

Müller

Mai

et al. 2016

Water Resources Research

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A framework for interpreting transient pumping tests in heterogeneous transmissivity fields is developed to infer the overall geostatistical parameters of the medium without reconstructing the specific heterogeneous structure point wise. The methodology of Radial Coarse Graining is applied to deduce an effective radial description of multi-Gaussian transmissivity. It was used to derive an Effective Well Flow Solution for transient flow conditions including not only the storativity, but also the geometric mean, the variance, and the correlation length of log-transmissivity. This solution is shown to be appropriate to characterize the pumping test drawdown behavior in heterogeneous transmissivity fields making use of ensembles of simulated pumping tests with multiple combinations of statistical parameters. Based on the Effective Well Flow Solution, a method is developed for inferring heterogeneity parameters from transient pumping test drawdown data by inverse estimation. Thereby, the impact of statistical parameters on the drawdown is analyzed, allowing to determine the dependence of reliability of parameter estimates on location and number of measurements. It is shown, that the number of measurements can be reduced compared to steady state pumping tests. Finally, a sampling strategy for single aquifer analysis is developed, which allows to estimate the statistical parameters, in particular variance and correlation length for individual heterogeneous transmissivity fields making use of transient pumping test measurements at multiple locations.

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The Extended Thiem's solution: Including the impact of heterogeneity

Cited by 16 publications

References 21 publications

Technical note: Analytical drawdown solution for steady-state pumping tests in two-dimensional isotropic heterogeneous aquifers

Technical note: Analytical drawdown solution for steady-state pumping tests in two-dimensional isotropic heterogeneous aquifers

Estimating transmissivity from single‐well pumping tests in heterogeneous aquifers

Extending Theis' solution: Using transient pumping tests to estimate parameters of aquifer heterogeneity

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