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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:

image-20250112-102738.png

where:

image-20250112-102808.png
image-20250112-102826.png

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) :image-20250112-102919.png

J0,1 : Bessel functions 0th, 1st order 1st degree [-]

Y0,1 :Bessel functions 0th, 1st order 2nd degree [-]

rs : Radius of well screen [m]

rc : Radius of casing [m]

By numerical integration, COOPER et al. (1967) compiled five tables with h(t)/h0 and ß for varying image-20250112-103714.png. 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.

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