GGU-SLUGTEST: COOPER et al. approach to the solution

For the water level in a well, COOPER et al. (1967) arrived at the following solution:

where:

and

h₀ : Water level in well at time t = 0 [m]

h(t) : Water level in well at time t [m]

T : Transmissivity [m²]

S : Storage coefficient [-]

u : Integration constant [-]

f(u) :

J_0,1 : Bessel functions 0^th, 1^st order 1^st degree [-]

Y_0,1 :Bessel functions 0^th, 1^st order 2^nd degree [-]

r_s : Radius of well screen [m]

r_c : Radius of casing [m]

By numerical integration, COOPER et al. (1967) compiled five tables with h(t)/h₀ and ß for varying . If the table values are graphically represented in a semi-logarithmic format, one arrives at type curves which allow the transmissivity to be determined in a similar manner to that using the Theis type curve method.