6.4.1. Model Parameters
The figure below shows the drop curve of the hydraulic height due to pumping from an aquifer. The parameters used to calculate the flow ratio are also given schematically..
rw: well radius
sw: drawdown in the well
hr: hydraulic head at distance r
Η: initial hydraulic head (of aquifer when no pumping).
R: radius of influence
Rradius of influence is the distance R from the center of the well beyond which the drop of the hydraulic height due to pumping is negligible (practically zero). Note At a distance equal to the radius of influence the hydraulic inclination dh / dl is almost zero. However, the input flow to the R-cylinder around the well is equal to the pumped flow since although the specific flow is almost zero at the cylinder circumference, the peripheral surface it contributes is very large. .
Empirical estimation of radius of influence
Exercise: Let be a surface well aquifer 15m thick with an underlying impermeable limestone layer 5m thick. The aquifer consists of layers of muddy sand with K = 20 m / day (2,315 ∙ 10-4 m / s). Water was pumped from a rarely used well for 5 h and the aquifer level at the well fell by sw = 1 m. Give an estimate of the impact radius and plot the level drop curve. (Answer R = 45m)
6.4.2. Pumping from unconfined aquifers
For continuous pumping with Q flow, the aquifer was stabilized (steady flow conditions). The detailed relation that described the constant flow for the case of pumping from an aquifer is:
The relationship you use for:
(1) Find the flow Q for a given aquifer level humidity (h1, h2).
(2) Find the humidity of the aquifer for a specific pumping supply.
(3) Find the influence radius (R) for a specific pumping supply.
(3) Assessment of the hydraulic conductivity (K) of the aquifer.
There are 6 variables (Q, K, h1, h2 r1, r2). If we know the five we can calculate the 6th
Observations:
- Instead of the pairs (h1, r1) and (h2, r2) we can use (hw, rw) and (H, R). (Hw, rw) is almost always available in a pump test.
- To have values for (h1, r1) and (h2, r2) there must be wells near the pumping point which we use to monitor the level (monitoring wells).
6.4.3. Pumping from confined aquifers
For constant pumping from a limited aquifer the relationship between flow and hydraulic height change is as follows:
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6.4.1: Unconfined aquifiers. Calculation of k and R
An unconfined aquifier is 30 m thick. A constant amount of 35 L / s is pumped from a well with a diameter of 20 cm. The fall of the aquifer is measured by monitoring wells located at a distance of 10 m and 100 m and are 7.5 m and 0.5 m respectively. Calculate the hydraulic conductivity of the aquifer and the radius of influence.
6.4.2: Unconfined aquifie, Calculation of pumping rate Q
An unconfined aquifier is 50 m thick. From a well with a radius of 50 cm that extends to the lower limit of the aquifer, water is pumped with a constant flow Q. The fall of the aquifer in the well is 10 m while at a distance of 500 m the fall of the aquifer is zero. Calculate the pumping supply Q.
6.4.3: Unconfined aquifie, Calculation of pumping rate Q
Question: A well with a diameter of 0.5 m penetrates a completely limited aquifer with a thickness of 20 m and a hydraulic conductivity of 8.2 x 10-4 m / s. What is the maximum flow that can be pumped if the level drop in the well can not be more than 3m. The 3m limit may exist for example to avoid adverse environmental effects.
Input: sw=3m, K=8.2 x 10-4 m/s, b=20m, Answer: Q = 49 L/s
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