### Abstract

The properties of heterogeneous media vary spatially in a manner that can seldom be described with certainty. It may, however, be possible to describe the spatial variability of these properties in terms of geostatistical parameters such as mean, integral (spatial correlation) scale, and variance. Neuman et al. (2004) proposed a graphical method to estimate the geostatistical parameters of (natural) log transmissivity on the basis of quasi-steady state head data when a randomly heterogeneous confined aquifer is pumped at a constant rate from a fully penetrating well. They conjectured that a quasi-steady state, during which heads vary in space-time while gradients vary only in space, develops in a statistically homogeneous and horizontally isotropic aquifer as it does in a uniform aquifer. We confirm their conjecture numerically for Gaussian log transmissivities, show that time-drawdown data from randomly heterogeneous aquifers are difficult to interpret graphically, and demonstrate that quasi-steady state distance-drawdown data are amenable to such interpretation by the type curve method of Neuman et al. The method yields acceptable estimates of statistical log transmissivity parameters for fields having either an exponential or a Gaussian spatial correlation function. These estimates are more robust than those obtained using the graphical time-drawdown method of Copty and Findikakis (2003, 2004a). We apply the method of Neuman et al. (2004) simultaneously to data from a sequence of pumping tests conducted in four wells in an aquifer near Tübingen, Germany, and compare our transmissivity estimate with estimates obtained from 312 flowmeter measurements of hydraulic conductivity in these and eight additional wells at the site. We find that (1) four wells are enough to provide reasonable estimates of lead log transmissivity statistics for the Tübingen site using this method, and (2) the time-drawdown method of Cooper and Jacob (1946) underestimates the geometric mean transmissivity at the site by 30-40%.

Original language | English (US) |
---|---|

Article number | W10421 |

Journal | Water Resources Research |

Volume | 43 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2007 |

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### ASJC Scopus subject areas

- Environmental Science(all)
- Environmental Chemistry
- Aquatic Science
- Water Science and Technology

### Cite this

*Water Resources Research*,

*43*(10), [W10421]. https://doi.org/10.1029/2007WR005871

**Type curve interpretation of late-time pumping test data in randomly heterogeneous aquifers.** / Neuman, Shlomo P; Blattstein, Ayelet; Riva, Monica; Tartakovsky, Daniel M.; Guadagnini, Alberto; Ptak, Thomas.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 43, no. 10, W10421. https://doi.org/10.1029/2007WR005871

}

TY - JOUR

T1 - Type curve interpretation of late-time pumping test data in randomly heterogeneous aquifers

AU - Neuman, Shlomo P

AU - Blattstein, Ayelet

AU - Riva, Monica

AU - Tartakovsky, Daniel M.

AU - Guadagnini, Alberto

AU - Ptak, Thomas

PY - 2007/10

Y1 - 2007/10

N2 - The properties of heterogeneous media vary spatially in a manner that can seldom be described with certainty. It may, however, be possible to describe the spatial variability of these properties in terms of geostatistical parameters such as mean, integral (spatial correlation) scale, and variance. Neuman et al. (2004) proposed a graphical method to estimate the geostatistical parameters of (natural) log transmissivity on the basis of quasi-steady state head data when a randomly heterogeneous confined aquifer is pumped at a constant rate from a fully penetrating well. They conjectured that a quasi-steady state, during which heads vary in space-time while gradients vary only in space, develops in a statistically homogeneous and horizontally isotropic aquifer as it does in a uniform aquifer. We confirm their conjecture numerically for Gaussian log transmissivities, show that time-drawdown data from randomly heterogeneous aquifers are difficult to interpret graphically, and demonstrate that quasi-steady state distance-drawdown data are amenable to such interpretation by the type curve method of Neuman et al. The method yields acceptable estimates of statistical log transmissivity parameters for fields having either an exponential or a Gaussian spatial correlation function. These estimates are more robust than those obtained using the graphical time-drawdown method of Copty and Findikakis (2003, 2004a). We apply the method of Neuman et al. (2004) simultaneously to data from a sequence of pumping tests conducted in four wells in an aquifer near Tübingen, Germany, and compare our transmissivity estimate with estimates obtained from 312 flowmeter measurements of hydraulic conductivity in these and eight additional wells at the site. We find that (1) four wells are enough to provide reasonable estimates of lead log transmissivity statistics for the Tübingen site using this method, and (2) the time-drawdown method of Cooper and Jacob (1946) underestimates the geometric mean transmissivity at the site by 30-40%.

AB - The properties of heterogeneous media vary spatially in a manner that can seldom be described with certainty. It may, however, be possible to describe the spatial variability of these properties in terms of geostatistical parameters such as mean, integral (spatial correlation) scale, and variance. Neuman et al. (2004) proposed a graphical method to estimate the geostatistical parameters of (natural) log transmissivity on the basis of quasi-steady state head data when a randomly heterogeneous confined aquifer is pumped at a constant rate from a fully penetrating well. They conjectured that a quasi-steady state, during which heads vary in space-time while gradients vary only in space, develops in a statistically homogeneous and horizontally isotropic aquifer as it does in a uniform aquifer. We confirm their conjecture numerically for Gaussian log transmissivities, show that time-drawdown data from randomly heterogeneous aquifers are difficult to interpret graphically, and demonstrate that quasi-steady state distance-drawdown data are amenable to such interpretation by the type curve method of Neuman et al. The method yields acceptable estimates of statistical log transmissivity parameters for fields having either an exponential or a Gaussian spatial correlation function. These estimates are more robust than those obtained using the graphical time-drawdown method of Copty and Findikakis (2003, 2004a). We apply the method of Neuman et al. (2004) simultaneously to data from a sequence of pumping tests conducted in four wells in an aquifer near Tübingen, Germany, and compare our transmissivity estimate with estimates obtained from 312 flowmeter measurements of hydraulic conductivity in these and eight additional wells at the site. We find that (1) four wells are enough to provide reasonable estimates of lead log transmissivity statistics for the Tübingen site using this method, and (2) the time-drawdown method of Cooper and Jacob (1946) underestimates the geometric mean transmissivity at the site by 30-40%.

UR - http://www.scopus.com/inward/record.url?scp=36749004941&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749004941&partnerID=8YFLogxK

U2 - 10.1029/2007WR005871

DO - 10.1029/2007WR005871

M3 - Article

AN - SCOPUS:36749004941

VL - 43

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 10

M1 - W10421

ER -