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\frac{d Q_{WAQ}}{dt} + \frac{1}{\tau} Q_{WAQ} = J \cdot ( p_i - p(t))


The aquifer productivity index can be further related to basic reservoir properties:

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J = \frac{2 \pi \sigma}{\ln \frac{A_{AQ}}{A_e} - \frac{3}{4} }



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titleDerivation

Const PI expansion:

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q_{WAQ} = \frac{d Q_{WAQ}}{dt} = J \cdot ( p_{AQ} - p(t))


Finite-volume reservoir PSS depletion:

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p_{AQ} = p_i - \frac{Q_{WAQ}}{V_{WAQ} c_t}


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