Installation — business terrible  1 part
September 8th, 2015
a. In an equilibrium type of pumping test, the well is pumped at a constant rate until the drawdown in the well and piezometers becomes stable.
b. A typical timedrawdown curve for a piezometer near a test well is plotted to an arithmetical scale in figure C5 and to a semilog scale in figure C6. (The computations in fig C6 are discussed subsequently.) Generally, a timedrawdown curve plotted to a semilog scale becomes straight after the first few minutes of pumping. If true equilibrium conditions are established, the drawdown curve will become horizontal.








Figure C6. Drawdown in an observation well versus pumping time (semilog scale).
The drawdown measured in the test well and adjacent observation wells or piezometers should always be plotted versus (log) time during the test to check the performance of the well and aquifer. Although the example presented in figure C6 shows stabilization to have essentially occurred after 500 minutes, it is considered good practice to pump artesian wells for 12 to 24 hours and to pump test wells where gruuity flow conditions exist for 2 or 3 days.
c. The drawdown in an artesian aquifer as measured by piezometers on a radial line from a test well is plotted versus (log) distance from the test well in figure C7. In a homogeneous, isotropic aquifer with artesian flow, the drawdown (Hh) versus (log) distance from the test well will plot as a straight line when the flow in the aquifer has stabilized. The drawdown H2—h2 versus (log) distance will also plot as a straight line for gruuity flow. However, the drawdown in the well may be somewhat greater than would be indicated by a projection of this straight line to the well because of well entrance losses and the effect of a “free” flow surface at gravity wells. Extension of the drawdown versus (log) distance line to zero drawdown indicates the effective source of seepage or radius of influence R, beyond which no drawdown would be produced by pumping the test well (fig, C7).
d. For flow from a circular source of seepage, the coefficient of permeability k can be computed from the formulas for fully penetrating wells.
Artesiun Flow.
2rrkD(H—h)
ln(R/r)
Gravity Flow,
_ nk(H2—h2)
4w ln(R/r)
where
Qw = flow from the well D = aquifer thickness H = initial height of groundwater table (GWT) h = height of GWT at r (Hh) or (H2—h2) = drawdown at distance r from well
R = radius of influence
An example of the determination of R and k from an equilibrium pumping test is shown in figure C7.
e. For combined artesiangravity flow, seepage from a line source and a partially penetrating well, the coefficient of permeability can be computed from wellflow formulas presented in chapter 4.


































where
r = distance from test well to observation piezometer, feet s = coefficient of storage t’ = elapsed pumping time in days The formation constants can be obtained approximately from the pumping test data using a graphical method of superposition, which is outlined below.
Step 1. Plot W(u) versus u on log graph paper, known as a “typecurve,” using table Cl as in figure c8.
Step 2. Plot drawdown (Hh) versus r2/t’ on log graph paper of same size as the typecurve in figure C8.
Step 3. Superimpose observed data curve on typecurve, keeping coordinates axes of the two curves parallel, and adjust until a position is found by trial whereby most of the plotted data fall on a segment of the typecurve as in figure C8.
Step 4. Select an arbitrary point on coincident
segment, and record coordinates of matching point (fig. C8). •
Step 5. With value of W(u), u, Hh, and r2/t’ thus determined, compute S and T’ from equations (C3) and (C4).
Step 6. T and к from the following equations:
T’
T = ^ ^ (square feet per minute) (C5)
Г
k= 1Q 77QD (feet per minute) (C6)
(2) Method 2. This method can be used as an approximate solution for nonequilibrium flow to a well to avoid the curvefitting techniques of method 1 by using the techniques outlined below.
Step 1. Plot time versus drawdown on semilog graph as in figure C9.
Step 2. Choose an arbitrary point on timedrawdown curve, and note coordinates t and Hh.
Step 3. Draw a tangent to the timedrawdown







S~ IW X 10‘) ( 103,000) =_19B x 10,
197 rVf 1.87(1.95 x 107)
(From “Ground Water Hydrology" by D. K. Todd, 1959, Wiley & Sons, Inc.
Used with permission of Wiley & Sons, Inc.)
Figure C8. Method 1 (Superposition) for solution of the nonequilibriumequation.




EXAMPLE: Q’ = 500 GPM
DISTANCE TO OBSERVATION WELL, Г 200 FT
AT POINT A: t’ = 4.0 x 10‘3 DAY
H – h = 1.55 FT
TANGENT THROUGH A: AS = 1.26 FT/LOG CYCLE of PUMPING
H – h 1 55 TIME IN DAYS
THEN F(U) =—— = ——= 1.23 [SEE FIG. C10 for F(uT]
AS 1.26 J
115 Q’ W(U) 115(5001(2.72)
T’ =—– ггг1—————— ———– = 101,000 GPD/ FT
= 2.05 X 10
(Modifiedfrom "Ground Water Hydrology" by D. K. Todd, 1959, Wiley & Sons, Inc. Used with permission of Wiley & Sons, Inc.)
Figure C9. Method 2 for solution of the nonequilibrium equation.



















where
As = drawdown in feet per cycle of (log) time – drawdown curve
to = time at zero drawdown in days An example of the use of this method of analysis in determining values of T, S, and к is given in figure C6, using the nonequilibrium portion of the timedrawdown curve.
(4) Gravity flow. Although the equations for nonequilibrium pumping tests are derived for artesian flow, they may be applied to gravity flow if the drawdown is small with respect to the saturated thickness of the aquifer and is equal to the specific yield of the dewatered portion of the aquifer plus the yield caused by compression of the saturated portion of the aquifer as a result of lowering the groundwater. The procedure for computing T’ and S for nonequilibrium gravity flow conditions is outlined below.
Step 1. Compute T’ from equation (C3).
Step 2. Compute S from equation (C4) for various elapsed pumping times during the test period, and plotS versus (log) t’.
Step 3. Extrapolate the S versus (log) t’ curve to an ultimate value for S’.
Step 4. Compute u from equation (C4), using the extrapolated S’, the originally computed T’, and the original value ofr2/t’.
Step 5. Recompute T’ from equation (C3) using
(5) Recharge. Timedrawdown curves of a test well are significantly affected by recharge or depletion of the aquifer, as shown in figure C11. Where recharge does not occur, and all water is pumped from storage, the H’ versus (log) t curve would resemble curve a. Where the zone of influence intercepts a source of seepage, the H’ versus (log) t curve would resemble curve b. There may be geological and recharge conditions where there is some recharge but not

U. S. Army Corps of Engineers
Cl 1
enough to equal the rate of well flow (e. g., curve c). In many areas, formation boundary conditions exist that limit the area1 extent of aquifers. The effect of such a boundary on an H’ versus (log) t graph is in reverse to the effect of recharge. Thus, when an impermeable boundary is encountered, the slope of the H’ versus (log) t curve steepens as illustrated by curve d. It should be noted that a nonequilibrium analysis of a pumping test is valid only for the first segment of a timedrawdown curve.