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Calculator 7 - Time/Drawdown


COOPER-JACOB APPROXIMATION

An approximation of the Theissian Model for Pumping Test Interpretation

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Cooper and Jacob (1946) developed an approximation for the Theis equation and a data analysis method which does not require type-curve matching. The Cooper-Jacob calculator presented here estimates the drawdown for a given well location over time.  This calculator is good for anticipating results from pump tests.  The Cooper-Jacob approximation is given by:

COOPER-JACOB APPROXIMATION

Input

Q (pumping rate):  

t (elapsed time since the start of pumping):

delta t (time increments):

T (transmissivity):

r (radial distance from pumped well):

S (Storage Coefficient):

**KEEP UNITS CONSISTENT**

Results

Example:

A consultant is preparing to conduct a pump test at a local well field.  They have results from a pump test conducted two decades earlier, indicating a transmissivity of 1250 m2/d and a storage coefficient of 1.9x10-4.  The intention of the upcoming pump test is to double check these estimates.  With a pumping rate of 2730 m3/d, what would be the expected drawdown at a monitoring well 122 m away.  The test will run for 1 day, and monitoring will occur approximately every 3 hours.

The results should look as follows (with units of m-d):

time           drawdown
10800.0000       0.83646656
21600.0000       0.95667492
32400.0000       1.02699231
43200.0000       1.07688329
54000.0000       1.11558173
64800.0000       1.14720067
75600.0000       1.17393410
86400.0000       1.19709165
 

What would be a common error in this example?

- forgetting to keep units consistent (i.e. all in days, hours or seconds)

See our Newsletter on Cooper-Jacob Calculator and AquiferTest



You can also perform Time/Drawdown calculations with graphical display using:

AquiferWin32
Aquifer Test Software









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