Embed Size (px)
Citation preview
Chapter 12:Variable-discharge tests and tests in well fields
•Aquifers may be pumped at variable discharge rates either deliberately or due to characteristics of the pump. •Aquifers can be pumped step-wise (always pumped but pumping rates vary) or may be pumped intermittently (not always pumped and pumping rates can vary).
Confined Aquifers, Birsoy-Summer’s MethodBirsoy and Summers present an
analytical solution for the drawdown response in a confined aquifer that is pumped step-wise or intermittently .
They apply the principle of superposition (ch.6) to Jacob’s approximation of the Theis equation (3.7) (shown below)
Variable-discharge tests
The drawdown in the aquifer at time t during the nth pumping period of intermittent pumping is shown by the following expression:
where
Variable-discharge tests
Confined Aquifers, Birsoy-Summer’s Method
where
where
Intermittent Pumping
For step-wise (uninterrupted pumping):
Variable-discharge tests
t’(i-1) = ti, and the ‘adjusted time’ becomes
where
Confined Aquifers, Birsoy-Summer’s Method
If the intermittent pumping rate is constant (Q=Q1 =Q2=…….Qn) then the adjusted time becomes:
Dividing both sides of equation 12.1 by Qn gives an expression for drawdown:
Variable-discharge testsConfined Aquifers, Birsoy-Summer’s
Method
Step-wise Pumping
Variable-discharge testsConfined Aquifers, Birsoy-Summer’s
MethodAssumptions (from Ch.3):1.)The aquifer is confined2.)The aquifer has a seemingly infinite areal extent3.)The aquifer is homogeneous, isotropic, and of
uniform thickness over the area influenced by the test
4.)Prior to pumping, the piezometric surface is horizontal (or nearly so) over the area influenced by the test
5.)The aquifer is pumped step-wise or intermittently at a variable discharge rate or is intermittently pumped at a constant discharge rate
6.)The well penetrates the entire thickness of the aquifer and thus receives water by horizontal flow
The following conditions are added:the flow to the well is in an unsteady state
R is small and t is sufficiently large
•The sharpest decrease in discharge occurs soon after the start of pumping. Aron and Scott take this into account. They show that when:
Variable-discharge testsConfined Aquifers, Aron-Scott’s
Method
where sn=drawdown at a certain moment tn,; se=excess drawdown caused by the earlier higher discharge
Variable-discharge testsConfined Aquifers, Birsoy-Summer’s
Method
•Determine the slope of the straight line
Confined Aquifers, Aron-Scott’s Method
Variable-discharge tests
If the fully developed drawdown is considered to extend to the distance ri at which
then the se (excess drawdown) can be approximated by:
Assumptions:All same as in chapter 3, except:5.)The discharge rate
decreases with time, the sharpest decrease occurring soon after pumping
the following condition is added:
Variable-discharge testsConfined Aquifers, Aron-Scott’s
Method
Free-Flowing Wells
Based on the conditions that the drawdown in the well is constant and discharge decreases with time.
To satisfy these conditions, the well is shut until pressure becomes static, then at t=0 the well is opened and the water level in the well drops instantaneously to a constant drawdown level which is equal to the outflow. The well discharges at a decreasing rate.
Confined aquifer, unsteady-state flow, Hantush’s Method
where
Free-flowing wells
AssumptionsAll same as in chapter 3, except:5.)At the start of the test
(t=0), the water level in the free-flowing well drops instantaneously. At t>0, the drawdown in the well is constant, and its discharge is variable.
The following condition is added:the flow to the well is in an
unsteady state
Free-flowing wellsConfined aquifer, unsteady-state flow, Hantush’s Method
Leaky aquifer, steady-state flow, Hantush-DeGlee’s method
where
Free-flowing wells
AssumptionsAll assumptions that underlie the
standardmethods for leaky aquifers, except:5.)At the beginning of the test
(t=0), the water level in the well drops instantaneously. At t>0, the drawdown in the well is constant, and it’s discharge is variable.
Well-fields
