Lecture 23
Flow in a Leaky Confined
Aquifer - Hantush Method
Fetter 7.4.3.4
If vertical recharge across upper confining layer.
Figure 7.3 Fully penetrating well in an aquifer overlain by a semipermeable confining layer.
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| K’ = Vertical hydraulic conductivity of leaky layer (L/T) | |
| b’ = Thickness of leaky layer (L) | |
| h = head (L) | |
| r = Radial distance from pumped well (L) | |
| t = time (T) | |
| S = Storativity | |
| T = Transimissivity (L2/T) | |
| h0-h = drawdown (L) |
M.S.Hantush (1956) developed first solution-
| All water from | ||
| (1.) Elastic storage in confined aquifer. | ||
| (2.) Leakage across confining layer. | ||
| No water from storage in confining layer. | ||
| Assumption | |
| (1.) Aquifer is bounded by leaky confining layer. | |
| (2.) The leaky confining layer is overlain by unconfined aquifer (source bed). | |
| (3.) Water table in source bed is initially horizontal. | |
| (4.) Water table in source bed does not change during pumping. | |
| (5.) Ground-water flow in leaky confining layer is vertical. | |
| (6.) Aquifer is compressible, no water drains instantaneously with a decline in head. | |
| (7.) Leaky confining layer is compressible, no water released from storage when aquifer is pumped. |
Assumption 4
| Requires recharge to upper unconfined aquifer | ||
| is valid if the following conditions are met. | ||
or b’’K’’ > 100bK |
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Assumption 7 Leaky Confining Layer- no water from storage
| Effect of storage negligible if... | ||
 Specific storage |
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| Equations valid for any well diameter if- | ||
t > |
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| rw = radius pumped well | ||
Solution - Hantush- Jacob Formula-
h0
- h =  |
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u =  |
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B =  |
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| Q = pumping rate (L3/T) | ||
| h0- h = drawdown in leaky confined aquifer (L) | ||
| T = Transimissivity (L2/T) | ||
| W(u,r/B) = Leaky confined well function. | ||
| r = radial distance from pumped well to observation well (L). | ||
| S = storativity | ||
| t = time since pumping began (T) | ||
| B = Leakage factor (L) | ||
| b’ = thickness of leaky layer (L) | ||
| K’ = hydraulic conductivity of leaky layer. (L/T) | ||
All water from leakage across confining layer when
t >  |
Walton Graphical Method- For Hantush-Jacob Formulas.
| Leaky, confined Aquifer with no storage in LCL | |
| Use data from aquifer tests to determine properties of aquifer and leaky layer. |
W.C. Walton (1962, 1960)
(1.) Type curves for W(u, r/B) as a function of 1/u for various values 1/B and r/B
| IF r/B = 0 ® Theis type curve (reverse) |
(2.) Plot field data as drawdown vs. time. log-log paper.
(3.) Overlay type curves - keep axes parallel.
| Match to field data ( may match to interploted curve) | |
| Early time falls on Theis | |
| Late time, leakage, follows r/B curve. |
(4.) Pick match point
| W(u, r/B) , | 1/u | Type Curve | |
| r/B | Type Curve | ||
| t, s | Field Data |
(5.) Calculate
T =  |
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S =  |
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r/B =  |
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K’ =
 |
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| Q = Pumping rate (ft3/d) | ||
| T = Tramissivity (ft2/d) | ||
| t = time since pumping (d) | ||
| S = Storativity | ||
| r = radial distance to observation well (ft) | ||
| K’ = Vertical K of leaky confining layer (ft/d) | ||
| b’ = Thickness of leaky confining layer (ft) | ||
| B = leakage factor | ||
Walton Leaky Confined aquifer type curves.
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