2. Introduction
Partially penetrating wells:
aquifer is so thick that a fully penetrating well is impractical
Increase velocity close to well, extra loss of head, and the effect is inversely
related to distance from well (unless the aquifer has obvious anisotropy). Strongest
well face
Anisotropic aquifers
The affect is negligible at distances r > 2D sqrt(Kb/Kv) *standard methods cannot be used at r <
2D sqrt(Kb/Kv) unless allowances are made
Assumptions Violated:
Well is fully penetrating
Flow is horizontal
3. Corrections
Different types of aquifers require different modifications
Confined and Leaky (steady-state)- Huisman method:
Observed drawdowns can be corrected for partial penetration
Confined (unsteady-state)- Hantush method:
Modification of Theis Method or Jacob Method
Leaky (unsteady-state)-Weeks method:
Based on Walton and Hantush curve-fitting methods for horizontal flow
Unconfined (unsteady-state)- Streltsova curve-fitting or Neuman curve-fitting
method
Fit data to curves
4. Confined aquifers (steady-state)
Huisman's correction method I
Equation used to correct steady-state drawdown in piezometer at r < 2D
(Sm)partially = observed steady-state drawdown
(Sm)fully = steady state drawdown that would have occurred if the well had been fully
penetrating
Zw= distance from the bottom of the well screen to the underlying
b= distance from the top of the well screen to the underlying aquiclude
Z = distance from the middle of the piezometer screen to the underlying aquiclude
D = length of the well screen
5. (Sm)partially = observed steady-
state drawdown
(Sm)fully = steady state drawdown
that would have occurred if the
well had been fully penetrating
Zw= distance from the bottom of
the well screen to the underlying
b= distance from the top of the
well screen to the underlying
aquiclude
Z = distance from the middle of the
piezometer screen to the
underlying aquiclude
D = length of the well screen
6. Re: Confined aquifers (steady-state)
Assumptions:
The assumptions listed at the beginning of Chapter 3, with the exception of the
sixth assumption, which is replaced by:
The well does not penetrate the entire thickness of the aquifer.
The following conditions are added:
The flow to the well is in steady state;
r > rew rew = effective radius of the pumped well
Remarks
Cannot be applied in the immediate vicinity of well where Huisman’s correction
method II must be used
A few terms of series behind the ∑-sign will generally suffice
7. Huisman’s Correction Method II
Huisman’s correction method- applied in the immediate vicinity of well
Expressed by:
Where:
P = d/D = the penetration ratio
d = length of the well screen
e =l/d = amount of eccentricity
I = distance between the middle of the well screen and the middle of the aquifer
ε = function of P and e
rew = effective radius of the pumped well
Account for extra drawdown if well was full penetrating
8. Huisman’s Correction method II
Assumptions:
The assumptions listed at the beginning of Chapter 3, with the exception of the
sixth assumption, which is replaced by:
The well does not penetrate the entire thickness of the aquifer.
The following conditions are added:
The flow to the well is in a steady state;
r = rew.
9. Confined Aquifers (unsteady-state):
Modified Hantush’s Method
Hantush’s modification of Theis method
For a relatively short period of pumping {t < {(2D-b-a)2(S,)}/20K, the drawdown in a
piezometer at r from a partially penetrating well is
Where
E(u,(b/r),(d/r),(a/r)) = M(u,B1) – M(u,B2) + M(u,B3) – M(u,B4)
U = (R^2 Ss/4Kt)
Ss = S/D = specific storage of aquifer
B1 = (b+a)/r (for sympols b,d, and a)
B2 = (d+a)/r
B3 = (b-a)/r
B4 = (d-a)/r
10. Where
E(u,(b/r),(d/r),(a/r)) = M(u,B1) – M(u,B2) + M(u,B3) – M(u,B4)
U = (R^2 Ss/4Kt)
Ss = S/D = specific storage of aquifer
B1 = (b+a)/r (for sympols b,d, and a)
B2 = (d+a)/r
B3 = (b-a)/r
B4 = (d-a)/r
11. Re: Confined Aquifers (unsteady-state):
Modified Hantush’s Method
Assumptions:- The assumptions listed at the beginning of Chapter 3, with the
exception of the sixth assumption, which is replaced by:
The well does not penetrate the entire thickness of the aquifer.
The following conditions are added:
The flow to the well is in an unsteady state;
The time of pumping is relatively short: t < {(2D-b-a)*(Ss)}/20K.
12. Confined Aquifers (unsteady-state):
Modified Jacob’s Method
Hantush’s modification of the Jacob method can be used if the following
assumptions and conditions are satisfied:
The assumptions listed at the beginning of Chapter 3, with the exception of the
sixth assumption, which is replaced by:
The well does not penetrate the entire thickness of the aquifer.
The following conditions are added:
The flow to the well is in an unsteady state;
The time of pumping is relatively long: t > D2(Ss)/2K.
13. Leaky Aquifers (steady-state)
The effect of partial penetration is, as a rule, independent of vertical
replenishment; therefore, Huisman correction methods I and II can also be
applied to leaky aquifers if assumptions are satisfied…
14. Leaky Aquifers (unsteady-state):
Weeks’s modification of Walton and Hantush
curve-fitting method
Pump times (t > DS/2K):
Effects of partial penetration reach
max value and then remain constant
Drawdown equation:
15. Re: Leaky Aquifers (unsteady-state):
Weeks’s modification of Walton and Hantush
curve-fitting methods
The value of f, is constant for a particular well/piezometer configuration and
can be determined from Annex 8.1. With the value of Fs, known, a family of
type curves of {W(u,r/L) + fs} or {W(u,p) + f,} versus I/u can be drawn
for different values of r/L or p. These can then be matched with the data
curve for t > DS/2K to obtain the hydraulic characteristics of the aquifer.
16. Re: Leaky Aquifers (unsteady-state):
Weeks’s modification of Walton and Hantush
curve-fitting methods
Assumptions:
The Walton curve-fitting method (Section 4.2.1) can be used if:
The assumptions and conditions in Section 4.2.1 are satisfied;
A corrected family of type curves (W(u,r/L + fs} is used instead of W(u,r/L);
Equation 10.12 is used instead of Equation 4.6.
The Hantush curve-fitting method (Section 4.2.3) can be used if:
T > DS/2K
The assumptions and conditions in Section 4.2.3 are satisfied;
A corrected family of type curves (W(u,p) + fs} is used instead of W(u,p);
Equation 10.13 is used instead of Equation 4.15.
20. Re: Unconfined Anisotropic Aquifers
(unsteady-state): Streltsova’s curve-fitting
method
Assumptions:
The Streltsova curve-fitting method can be used if the following assumptions
and conditions are satisfied:
The assumptions listed at the beginning of Chapter 3, with the exception of the
first, third, sixth and seventh assumptions, which are replaced by
The aquifer is homogeneous, anisotropic, and of uniform thickness over the area
influenced by the pumping test
The well does not penetrate the entire thickness of the aquifer;
The aquifer is unconfined and shows delayed water table response.
The following conditions are added:
The flow to the well is in an unsteady state;
SY/SA > 10.
