Saturated‐unsaturated flow to a well with storage in a compressible unconfined aquifer

Abstract

Mishra and Neuman (2010) developed an analytical solution for flow to a partially penetrating well of zero radius in a compressible unconfined aquifer that allows inferring its saturated and unsaturated hydraulic properties from responses recorded in the saturated and/or unsaturated zones. Their solution accounts for horizontal as well as vertical flows in each zone. It represents unsaturated zone constitutive properties in a manner that is at once mathematically tractable and sufficiently flexible to provide much improved fits to standard constitutive models. In this paper we extend the solution of Mishra and Neuman [2010] to the case of a finite diameter pumping well with storage; investigate the effects of storage in the pumping well and delayed piezometer response on drawdowns in the saturated and unsaturated zones as functions of position and time; validate our solution against numerical simulations of drawdown in a synthetic aquifer having unsaturated properties described by the van Genuchten [1980]–Mualem [1976] model; use our solution to analyze 11 transducer‐measured drawdown records from a seven‐day pumping test conducted by University of Waterloo researchers at the Canadian Forces Base Borden in Ontario, Canada; validate our parameter estimates against manually‐measured drawdown records in 14 other piezometers at Borden; and compare (a) our estimates of aquifer parameters with those obtained on the basis of all these records by Moench [2008], (b) on the basis of 11 transducer‐measured drawdown records by Endres et al. [2007], (c) our estimates of van Genuchten–Mualem parameters with those obtained on the basis of laboratory drainage data from the site by Akindunni and Gillham [1992], and (d) our corresponding prediction of how effective saturation varies with elevation above the initial water table under static conditions with a profile based on water contents measured in a neutron access tube at a radial distance of about 5 m from the center of the pumping well. We also use our solution to analyze 11 transducer‐measured drawdown records from a 7 day pumping test conducted by University of Waterloo researchers at the Canadian Forces Base Borden in Ontario, Canada. We validate our parameter estimates against manually measured drawdown records in 14 other piezometers at Borden. We compare our estimates of aquifer parameters with those obtained on the basis of all these records by Moench (2008) and on the basis of 11 transducer‐measured drawdown records by Endres et al. (2007), and we compare our estimates of van Genuchten–Mualem parameters with those obtained on the basis of laboratory drainage data from the site by Akindunni and Gillham (1992); finally, we compare our corresponding prediction of how effective saturation varies with elevation above the initial water table under static conditions with a profile based on water contents measured in a neutron access tube at a radial distance of about 5 m from the center of the pumping well.

3‐D transient hydraulic tomography in unconfined aquifers with fast drainage response

“…That said, while the standard saturated‐flow MODFLOW approximations are useful and can result in faster model runtimes, such an approach is expected to be inaccurate for estimating long‐term specific yield when delayed drainage in the vadose zone is important and unaccounted for [see, e.g., Nwankwor et al , 1984; Narasimhan and Zhu , 1993; Endres et al , 2007; Tartakovsky and Neuman , 2007; Moench , 2008; Mishra and Neuman , 2010, 2011]. In this case of important delayed drainage, short‐term pumping tests such as those discussed herein are expected to return low estimates of true aquifer specific yield and may be thought of as an “effective” specific yield, representative of volume balances only at “early times” [ Nwankwor et al , 1984], i.e., time scales comparable to the 3DTHT pumping tests.…”

Improved predictions of saturated and unsaturated zone drawdowns in a heterogeneous unconfined aquifer via transient hydraulic tomography: Laboratory sandbox experiments

“…Mishra and Neuman (2010) also presented an approximate analytical solution for flow to a partially penetrating well in a compressible unconfined aquifer that infers saturated and unsaturated hydraulic properties from drawdowns recorded in the saturated and/or unsaturated zone. More recently, Mishra and Neuman (2011) extended the solution of Mishra and Neuman (2010) to consider a finite diameter pumping well with storage and the effects of delayed piezometer response. Neuman's (2010, 2011) solutions are an extension of the solution developed by Tartakovsky and Neuman (2007) and adds: (i) a more flexible representation of unsaturated constitutive properties; and (ii) a finite thickness for the unsaturated zone.…”

Recent advances in modeling of well hydraulics

“…Mishra and Neuman [212] improved the solution of Tartakovsky and Neuman [33] by introducing four-parameter representation of the hydraulic conductivity and water content functions and allowing the unsaturated zone to have a finite thickness. Mishra and Neuman [213] further considered the case of a finite diameter pumping well with storage and explored the effects of wellbore storage and delayed piezometer response on drawdowns in the unsaturated-saturated flow system.…”