Partially Penetrating Wells By: Lauren Cameron 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 Corrections Different types of aquifers require different modifications Confined and Leaky (steady-state)- Huisman method:

Confined (unsteady-state)- Hantush method: Modification of Theis Method or Jacob Method Leaky (unsteady-state)-Weeks method: Observed drawdowns can be corrected for partial penetration Based on Walton and Hantush curve-fitting methods for horizontal flow Unconfined (unsteady-state)- Streltsova curve-fitting or Neuman curvefitting method Fit data to curves 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 (Sm)partially = observed steadystate 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 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 Huismans correction method II must be used A few terms of series behind the -sign will generally suffice Huismans Correction Method II Huismans 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 = function of P and e rew = effective radius of the pumped well

Account for extra drawdown if well was full penetrating Huismans 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. Confined Aquifers (unsteady-state): Modified Hantushs Method Hantushs 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

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 Re: Confined Aquifers (unsteadystate): Modified Hantushs 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. Confined Aquifers (unsteady-state): Modified Jacobs Method Hantushs 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. 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 Leaky Aquifers (unsteady-state): Weekss 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: Re: Leaky Aquifers (unsteady-state): Weekss 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. Re: Leaky Aquifers (unsteady-state): Weekss 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. Unconfined Anisotropic Aquifers (unsteady-state): Streltsovas curve-fitting method

Unconfined Anisotropic Aquifers (unsteady-state): Streltsovas curve-fitting method Re: Unconfined Anisotropic Aquifers (unsteady-state): Streltsovas 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. Unconfined Anisotropic Aquifers (unsteady-state): Neumans curve-fitting method