Encyclopedia of Environmental Science and Engineering, Volume I and II

442 GROUNDWATER RESOURCES

area through which flow occurs, ft^2. From the basic mass

balance equation, the resulting expression of nonequilibrium

(transient) flow forward wells can be written as follows:

1 2

r^2

s

r

s

r

S

T

s

t

TKb















, 
 (2)

where s is drawdown, ft; S is the storage coefficient; T is

the transmissibility, ft^3 /d per ft^ ; r is the radial coordinator,

ft; and t is the time, days. The solution for Equation (2) with

the pertinent initial and boundary conditions is given as

s

Q

T

e

u

du

Q

T

Wu u

S

T

r

t

u

u

 


44 4

2

pp

−

−

∞

∫ (),^ (3)

where W ( u ) is known as the “well function,” whose values

can be obtained from a standard mathematical handbook.

Equation (3) is called the Theis equation and is the expression

for the drawdown for radial flow to a well. It is perhaps the

most widely used equation for the field determination of

transmissibility and the storage coefficient. However, due to

the mathematical difficulties involved, several approximate

techniques have been developed.

The Theis Method

This is simply the graphical solution of Equation (3), also

known as the type-current method. The Theis equation can

be rewritten in the form

Wu

u

T

QS

s

rt

()

()



16 2

2

p

(4)

By plotting W ( u ) versus u and s versus r^2 / t on log-log scales,

respectively, and then overlapping these two curves with

S 2

Q 2

Q 2

Q 1

Q 1

S 1

r

r

dr

dr

m Artesian Aquifer

Differential

Control

Volume

Drawdown of

Piezometric Surface

During Pumping

Q

Non-Pumping Piezometric Surface

Circumference = 2πr

Circumference = 2π(r+dr)

 

FIGURE 3 Definition sketch for the derivation of the nonequilibrium Theis equation.

C007_003_r03.indd 442C007_003_r03.indd 442 11/18/2005 10:28:24 AM11/18/2005 10:28:24 AM