Page 92 - Water Engineering Hydraulics, Distribution and Treatment

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Chapter 3
Water Sources: Groundwater
3.14 CHARACTERISTICS OF WELLS
value of specific capacity is obtained, but also the duration
The drawdown in a well being pumped is the difference
of pumping. Determination of specific capacity from a short-
between the static water level and the pumping water level.
term acceptance test of a few hours’ duration can give mis-
The well drawdown consists of two components:
leading results, particularly in aquifers having low hydraulic
diffusivity, that is, low transmissivity and high storage
1. Formation loss, that is, the head expended in over-
coefficients.
coming the frictional resistance of the medium from
the outer boundary to the face of the well, which
is directly proportional to the velocity if the flow is
3.14.2 Partial Penetration
laminar.
2. Well loss, which includes (a) the entrance head loss
The specific capacity of a well is affected by partial pene-
tration. A well that is screened only opposite a part of an
caused by the flow through the screen and (b) the head It is important to state not only the discharge at which a
loss due to the upward axial flow of water inside aquifer will have a lower discharge for the same drawdown
the screen and the casing up to the pump intake. or larger drawdown for the same discharge, that is, a smaller
This loss is associated with the turbulent flow and specific capacity. The ratio of the specific capacity of a par-
is approximately proportional to the square of the tially penetrating well to the specific capacity of a completely
velocity. penetrating well in homogeneous artesian aquifers is given
by the Kozeny formula, which is valid for steady-state con-
The well drawdown D can be expressed as ditions using either the US customary units or the SI units:
w
D = BQ + CQ 2 (3.39a)
w 1∕2
(Q∕s )(Q∕s) = K {1 + 7[r ∕(2K b)] cos( K ∕2)}
p
p
p
w
p
where B summarizes the resistance characteristics of the for-
(3.41)
mation and C represents the characteristics of the well.
For unsteady flow in a confined aquifer, from Eq. (3.18),
where Q∕s = specific capacity of a partially penetrating
p
3
well, gpm/ft or m /d/m; Q∕s = specific capacity of a com-
2
3
B = (264∕T) log(0.3 Tt∕r S) (3.39b) pletely penetrating well, gpm/ft or m /d/m; r = effective
w
w
well radius, ft or m; b = aquifer thickness, ft or m; and K =
p
This shows that the resistance of an extensive artesian
ratio of length of screen to saturated thickness of the aquifer.
aquifer increases with time as the area of influence of the
If the right-hand side of Eq. (3.41) is denoted by F ,the
p
well expands. For relatively low pumping rates, the well loss
equation may be written as
may be neglected, but for higher rates of discharge it can
represent a sizable proportion of the well drawdown. Q∕s = (Q∕s)F (3.42)
p p
The formula is not valid for small b, large K , and
p
3.14.1 Specific Capacity of a Well
large r .
w
The productivity and efficiency of a well is generally A graph of F versus K for various values of b/r is
w
p
p
expressed in terms of specific capacity, defined as the dis- given in Fig. 3.12 within the valid range of the formula.
charge per unit drawdown, that is, the ratio of discharge to
well drawdown:
3.14.3 Effective Well Radius
Q∕D = 1∕(B + CQ) (3.40a)
w
The effective radius of a well is seldom equal to its nominal
The specific capacity of a well depends on the forma- radius. Effective radius is defined as that distance, measured
tion constants and hydrogeologic boundaries of the aquifer, radially from the axis of a well, at which the theoretical
on well construction and design, and on test conditions. It is drawdown equals the actual drawdown just at the surface
sometimes useful to distinguish between theoretical specific of the well. Depending on the method of construction and
capacity, which depends only on formation characteristics development and the actual condition of the intake portion
and ignores well losses, and actual specific capacity. The for- of the well, the effective radius may be greater than, equal
mer is a measure of the productivity. The difference between to, or less than the nominal radius. The transmissivity of the
the two, or their ratio, is a measure of the efficiency of the material in the immediate vicinity of a well is the controlling
well. factor. If the transmissivity of the material surrounding the
For unsteady flow in a confined aquifer, well is higher than that of the aquifer, the effective well radius
will be greater than the nominal radius. On the other hand,
2
Q∕D = 1∕{(264∕T) log[(0.3 Tt)∕(r S)] + CQ} (3.40b) if the material around the well has a lower transmissivity
w
w
Hence the specific capacity is not a fixed quantity, but due to caving or clogging because of faulty construction, the
decreases with both the period of pumping and the discharge. effective radius will be less than the nominal radius.