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3.14 Characteristics of Wells 95
3.14.1 Specific Capacity of a Well

The productivity and efficiency of a well is generally expressed in terms of specific ca-
pacity, defined as the discharge per unit drawdown, that is, the ratio of discharge to well
drawdown:
Q>D w l>(B CQ) (3.40a)
The specific capacity of a well depends on the formation constants and hydrogeologic
boundaries of the aquifer, on well construction and design, and on test conditions. It is
sometimes useful to distinguish between theoretical specific capacity, which depends only
on formation characteristics and ignores well losses, and actual specific capacity. The for-
mer is a measure of the productivity. The difference between the two, or their ratio, is a
measure of the efficiency of the well.
For unsteady flow in a confined aquifer,
Q>D w l>{(264>T) log[(0.3 Tt)>(r w S)] CQ} (3.40b)
2
Hence the specific capacity is not a fixed quantity, but decreases with both the period
of pumping and the discharge. It is important to state not only the discharge at which a
value of specific capacity is obtained, but also the duration of pumping. Determination of
specific capacity from a short-term acceptance test of a few hours’ duration can give mis-
leading results, particularly in aquifers having low hydraulic diffusivity, that is, low trans-
missivity and high storage coefficients.

3.14.2 Partial Penetration

The specific capacity of a well is affected by partial penetration. A well that is screened
only opposite a part of an aquifer will have a lower discharge for the same drawdown or
larger drawdown for the same discharge, that is, a smaller specific capacity. The ratio of
the specific capacity of a partially penetrating well to the specific capacity of a completely
penetrating well in homogeneous artesian aquifers is given by the Kozeny formula, which
is valid for steady-state conditions using either the U.S. customary units or the SI units:
(Q>s p )>(Q>s) K p {1 7[r w >(2K p b)] 1>2 cos( K p >2)} (3.41)
3
where Q>s p specific capacity of a partially penetrating well, gpm/ft or m /d/m; Q>s
3
specific capacity of a completely penetrating well, gpm/ft or m /d/m; r w effective well
radius, ft or m; b aquifer thickness, ft or m; and K p ratio of length of screen to sat-
urated thickness of the aquifer.
If the right-hand side of Eq. 3.41 is denoted by F p , the equation may be written as
Q>s p (Q>s)F p (3.42)

The formula is not valid for small b, large K p , and large r w.
A graph of F p vs. K p for various values of b>r w is given in Fig. 3.12 within the valid
range of the formula.

3.14.3 Effective Well Radius

The effective radius of a well is seldom equal to its nominal radius. Effective radius is de-
fined as that distance, measured radially from the axis of a well, at which the theoretical
drawdown equals the actual drawdown just at the surface of the well. Depending on the
method of construction and development, and the actual condition of the intake portion of