Lecture 24
Flow in an Unconfined Aquifer -
Neuman Method
Fetter 7.4.5
Neuman and Witherspoon (1969) - Equation to describe flow of water in an
unconfined aquifer to a well.
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| h = saturated thickness of aquifer (L) | |
| r = radial distance from observation well (L) | |
| z = elevation above base aquifer (L) | |
| Ss = Specific storage (1/L) | |
| Kr = radial hydraulic conductivity (L/T) | |
| Kv = vertical hydraulic conductivity (L/T) | |
| t = time (T) |
Water in unconfined aquifer
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Three responses to time- drawdown curve.
| (1.) Theis- like response aquifer compress, water expand, horizontal flow. | ||
| (2.) Water from gravity drainage. | ||
| Horizontal and vertical flow components. | ||
| Drawdown function (Kh:Kv), r, h (h = saturated thickness) | ||
| (3.) Theis-like response (late time). | ||
Shlomo Nueman developed solution-
Assumptions:
| (1.) Aquifer is unconfined. | |
| (2.) Vadose zone does not influence drawdown. | |
| (3.) Water initially pumped comes from instantaneous release of water from elastic storage. | |
| (4.) Eventually water comes from storage due to gravity drainage of interconnected pores. | |
| (5.) Drawdown is negligible compared with the saturated aquifer thickness. | |
| (6.) Specific yield is at least 10 times the elastic storativity. | |
| (7.) Aquifer may be anisotropic. |
| Kv | ||
| Kr | ||
Solutions
h0 - h = 
W(uA, uB, G ) -Well function for water-table aquifer.
uA =
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Early time drawdown | ||
uB
=  |
Late time drawdown | ||
G =  |
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| h0 - h = drawdown (ft) | |||
| Q = pumping rate (ft3/d) | |||
| T = Transmissivity (ft2/d) | |||
| r = radial distance (L) | |||
| S = Storativity (dimensionless) | |||
| Sy = Specific yield (dimensionless) | |||
| t = time (d) | |||
| Kh = Horizontal hydraulic conductivity ( L/T) | |||
| Kv = vertical hydraulic conductivity (L/T) | |||
| b = initial saturated thickness (L) | |||
Graphical method - Nonequilibrium radial flow - unconfined.
Neuman(1975) others Streltsova and Walton
T = 
W (uA, uB, G )
S =  |
Early-time drawdown |
Sy =  |
Late-time drawdown |
G =
Two sets of type curves
| Type A - early-time drawdown | ||
| -instantaneous release water storage | ||
| -gravity drainage- vertical flow | ||
| Type B - late-time drawdown | ||
| -gravity drainage effects smaller | ||
| -ends on Theis-type curve. | ||
| Values W (uA, G ) and W ( uB, G ) in appendix | ||
Method
| (1.) Overlay field data and type A curves. | |||
| Get match point for early time data | |||
| W (uA, G ), 1/uA, G ® from type Curves. | |||
| t, h0-h ® field data | |||
| Calculate | |||
| T and S (S has meaningless value) | |||
| (2.) Overlay late time drawdown data - Type B curve | |||
| use same G value | |||
| W(uB, G ) 1/uB, G | Type B curve | ||
| h0 - h and t | field data | ||
| Calculate | |||
| T (~ T from part 1) | |||
| Sy | |||
| (3.) Calculate Kh | |||
Kh
=  |
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| (4.) Calculate Kv | |||
Kv
=  |
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Drawdown must not be substantial compared to saturated thickness
If drawdown is substantial, correct it
(h0-h)’ = (h0-h) -[(h0 - h)2/2h0]
(h0-h)’ = corrected drawdown
s’ = s - [s2/2h0] initial saturated thickness.
Need Jacob’s Dewatering Correction if-
| (1.) late time data | |
| (2.) s > 10% of initial saturated thickness. |
Fairborn test and solutions to unconfined problems
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ENV 302 - Lectures
