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

Zech, Alraune; Müller, Sebastian; Mai, Juliane; Heße, Falk; Attinger, Sabine

doi:10.1002/2015wr018509

Cited by 27 publications

(31 citation statements)

References 39 publications

(56 reference statements)

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“…Zech and Attinger () recently showed that for heterogeneous aquifers, steady state estimates of T (using the Theim equation) are biased. Zech and Attinger () and Zech et al () presented pumping drawdown equations for the unbiased estimation of T and drawdown within heterogeneous aquifers and which included parameters for the spatial variance and spatial correlation in T . Synthetic applications show that unbiased local and aquifer average T values can be derived.…”

Section: Discussionmentioning

confidence: 99%

Joint Estimation of Gross Recharge, Groundwater Usage, and Hydraulic Properties within HydroSight

Peterson

Fulton

2019

Groundwater

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Groundwater management decisions are often founded upon estimates of aquifer hydraulic properties, recharge and the rate of groundwater usage. Too often hydraulic properties are unavailable, recharge estimates are very uncertain, and usage is unmetered or infrequently metered over only recent years or estimated using numerical groundwater models decoupled from the drivers of drawdown. This paper extends the HydroSight groundwater time‐series package ( http://peterson-tim-j.github.io/HydroSight/) to allow the joint estimation of gross recharge, transmissivity, storativity, and daily usage at multiple production bores. A genetic evolutionary scheme was extended from estimating time‐series model parameters to also estimating time series of usage that honor metered volumes at each production bore and produces (1) the best fit with the observed hydrograph and (2) plausible estimates of actual evapotranspiration and hence recharge. The reliability of the approach was rigorously tested. Repeated calibration of models for four bores produced estimates of transmissivity, storativity, and mean recharge that varied by a factor of 0.22‐0.32, 0.13‐0.2, and 0.03‐0.48, respectively, when recharge boundary effects were low and the error in monthly, quarterly, and biannual metered usage was generally <10%. Application to the 30 observation bores within the Warrion groundwater management area (Australia), produced a coefficient of efficiency of ≥0.80 at 22 bores and ≥0.90 at 12 bores. The aquifer transmissivity and storativity were reasonably estimated, and were consistent with independent estimates, while mean gross recharge may be slightly overestimated. Overall, the approach allows greater insights from the available data and provides opportunity for the exploration of usage and climatic scenarios.

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Section: Discussionmentioning

confidence: 99%

Joint Estimation of Gross Recharge, Groundwater Usage, and Hydraulic Properties within HydroSight

Peterson

Fulton

2019

Groundwater

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“…This latter paper 125 also discusses the quantity and spatial coverage of the data needed to obtain reliable 126 estimates of the statistical parameters of the transmissivity field. Zech et al (2016) extended 127 the analysis to transient flow and showed that the number of measurements needed to obtain 128 reliable estimates of the transmissivity spatial structure is reduced compared to steady state 129 pumping tests. 130…”

Section: Copty and Findikakis (2004a) Examined The Sensitivity Of Tramentioning

confidence: 99%

Bayesian estimation of the transmissivity spatial structure from pumping test data

Demir

Copty

Trinchero

et al. 2017

Advances in Water Resources

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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.Peer ReviewedPostprint (author's final draft

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“…In case of non-fractal media, Gaussian correlation functions of the log-hydraulic conductivity field Y are often used, due to their simple mathematical treatment (Dagan 1988;Gelhar 1993;Dentz et al 2000a;Zech et al 2012Zech et al , 2016. In a d-dimensional isotropic medium they have the form…”

Section: Correlation Function For Isotropic Fractal Mediamentioning

confidence: 99%

Ensemble and effective dispersion in three-dimensional isotropic fractal media

Ross

Heße

Musuuza

et al. 2019

Stoch Environ Res Risk Assess

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We determine the time-dependent behavior of the dispersion coefficient for transport in formations with isotropic logconductivity fields showing fractal behavior. We consider two different dispersion coefficients for point-like injection: (1) the ensemble dispersion coefficients, defined as half the rate of change of the second central moments of the ensembleaveraged concentration distribution and (2) the effective dispersion, which is half the rate of change of the expected second central moments. Our results show, that the two longitudinal macrodispersion coefficients steadily grow with time and remain different at all times in a fully fractal regime, indicating that no Fickian transport regime is ever reached. The resulting effective longitudinal transport model is consequently a fractional advection-dispersion equation. In the semifractal regime, a Gaussian transport regime is reached eventually. However, compared to the case of a classic non-fractal regime, the transient non-Gaussian regime lasts much longer. In the transverse direction, the two dispersion coefficients approach the same large-time limit also in fractal media highlighting the fundamental difference between longitudinal and transverse dispersion.

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

Cited by 27 publications

References 39 publications

Joint Estimation of Gross Recharge, Groundwater Usage, and Hydraulic Properties within HydroSight

Joint Estimation of Gross Recharge, Groundwater Usage, and Hydraulic Properties within HydroSight

Bayesian estimation of the transmissivity spatial structure from pumping test data

Ensemble and effective dispersion in three-dimensional isotropic fractal media

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