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Drainage of a horizontal Boussinesq aquifer with a power law hydraulic conductivity profile
Author(s) -
Rupp David E.,
Selker John S.
Publication year - 2005
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2005wr004241
Subject(s) - hydraulic conductivity , aquifer , aquifer test , water table , geology , permeability (electromagnetism) , drainage , power law , homogeneous , constant (computer programming) , geometry , drawdown (hydrology) , soil science , mathematics , geotechnical engineering , hydrology (agriculture) , mechanics , groundwater , soil water , physics , chemistry , statistics , combinatorics , ecology , biochemistry , groundwater recharge , membrane , computer science , programming language , biology
Solutions to the Boussinesq equation describing drainage into a fully penetrating channel have been used for aquifer characterization. Two analytical solutions exist for early‐ and late‐time drainage from a saturated, homogeneous, and horizontal aquifer following instantaneous drawdown. The solutions for discharge Q can be expressed as dQ / dt = − aQ b , where a is constant and b takes on the value 3 and 3/2 for early and late time, respectively. Though many factors can contribute to departures from the two predictions, we explore the effect of having permeability decrease with depth, as it is known that many natural soils exhibit this characteristic. We derive a new set of analytical solutions to the Boussinesq equation for k ∝ z n , where k is the saturated hydraulic conductivity, z is the height above an impermeable base, and n is a constant. The solutions reveal that in early time, b retains the value of 3 regardless of the value of n , while in late time, b ranges from 3/2 to 2 as n varies from 0 to ∞. Similar to discharge, water table height h in late time can be expressed as dh / dt = − ch d , where d = 2 for constant k and d → ∞ as n → ∞. In theory, inclusion of a power law k profile does not complicate aquifer parameter estimation because n can be solved for when fitting b to the late‐time data, whereas previously b was assumed to be 3/2. However, if either early‐ or late‐time data are missing, there is an additional unknown. Under appropriate conditions, water table height measurements can be used to solve for an unknown parameter.