Contents preface (VII) introduction 1—37

4.5.3. Well Interference
If the zone of influence of two adjacent wells overlap (i.e., the wells are spaced at distances smaller than the sum of their radii of influence), the wells affect each other’s drawdown and discharge. This effect is due to what is known as well interference. As a result of well interference, even though the total output (i.e., the discharge) of a multiple well system increases, the efficiency of each well (measured in terms of the discharge per unit drawdown) of the system decreases. Since the equation of flow in a confined aquifer is a linear one, one can use the principle of superposition to obtain the resulting drawdown at a point in a well field in which number of wells are being pumped simultaneously. This means, if s_i is the total drawdown at i^th observation well on acount of pumping of N wells located in the well field, then

N
si = ∑ ^sij	(4.30)

j = 1
in which, s_ij is the drawdown at i^th observation well on account of pumping of j^th well as if there were no interference effects.
Considering steady flow conditions for two wells in a confined aquifer located distance B apart, the drawdown in the two wells s_w1 and s_w2 can be expressed as

s

=

^Q1

ln

r0

+

^Q2

ln

r0

,

(4.31)

w1

2 π T

^rw

2 πT

B

s

=

^Q1

ln

^r0

+

^Q2

ln

^r0

(4.32)

w2

2 π T

B

2 πT

rw

If Q1 = Q2 = Q, then

Q

r 2

s

= s

= h – h

w

=

ln

0

w1

w2

0

2 πT

Brw

This means,

Q

=

2 πT

(4.33)

h

− h

r ^2

0

w

ln

0

Br

w

Since,

_ln ^r0² _{> ln} ^r0 _,

Br_w r_w
it is obvious that the efficiency of an individual well has reduced. On the other hand, Eq. (4.33) can also be written as

2 Q	=	2 πT	(4.34)
h0 − hw
	ln [ r0 / ( Brw ) ^0.5 ]

138 IRRIGATION AND WATER RESOURCES ENGINEERING
Since (Br_w)^0.5 >> r_w, the value of (h₀ – h_w) is relatively less for a discharge of 2 Q compared to the value of (h₀ – h_w ) when only a single well were to pump a discharge of 2 Q. This shows that the efficiency of a multiple well system is higher compared to that of a single well. But, the efficiency of an individual well in a multiple well system is reduced.