Drainage of a horizontal Boussinesq aquifer with a power law hydraulic conductivity profile
نویسندگان
چکیده
[1] Solutions to the Boussinesq equation describing drainage into a fully penetrating channel have been used for aquifer characterization. Two analytical solutions exist for earlyand 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, 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, 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 1. Similar to discharge, water table height h in late time can be expressed as dh/dt = ch, where d = 2 for constant k and d ! 1 as n ! 1. 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 earlyor 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.
منابع مشابه
On the use of the Boussinesq equation for interpreting recession hydrographs from sloping aquifers
[1] The method of recession analysis proposed by Brutsaert and Nieber (1977) remains one of the few analytical tools for estimating aquifer hydraulic parameters at the field scale and beyond. In the method, the recession hydrograph is examined as dQ/dt = f(Q), where Q is aquifer discharge and f is an arbitrary function. The observed function f is parameterized through analytical solutions to th...
متن کاملDetermination of unsaturated hydraulic conductivity by internal drainage assuming a uniform soil water profile
متن کامل
Estimation of aquifer lower layer hydraulic conductivity values through base flow hydrograph rising limb analysis
[1] The estimation of catchment-averaged aquifer hydraulic conductivity values is usually performed through a base flow recession analysis. Relationships between the first time derivatives of the base flow and the base flow values themselves, derived for small and large values of time, are used for this purpose. However, in the derivation of the short-time equations, an initially fully saturate...
متن کاملHydraulic conductivity of the High Plains Aquifer re-evaluatedusing surface drainage patterns
[1] The High Plains Aquifer (HPA), underlying parts of 8 states from South Dakota to Texas, is one of the largest fresh water aquifers in the world and accounts for 30% of the groundwater used for irrigation in the US. Determining the distribution of HPA’s hydraulic conductivity (K) is critical for water management and addressing water quality issues. K is traditionally estimated from well pump...
متن کاملMODELING OF GROUNDWATER FLOW OVER SLOPING BEDS IN RESPONSE TO CONSTANT RECHARGE AND STREAM OF VARYING WATER LEVEL
This paper presents an analytical model characterizing unsteady groundwater flow in an unconfined aquifer resting on a sloping impervious bed. The aquifer is in contact with a constant water level at one end. The other end is connected to a stream whose level is increasing form an initial level to a final level at a known exponentially decaying function of time. Moreover, the aquifer is repleni...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005