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\frac{d Q_{WAQ}}{dt} = \frac{4 \pi \sigma}{ \ln \frac{1.781 \cdot A_e^2}{ 4 \pi \chi t} } \cdot ( p_i - p(t))

where

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bodyQ_{WAQ}(t)

water influx from aquifer at time moment

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bodyt

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bodyp_i

initial formation pressure

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bodyp(t)

field-average formation pressure at time moment

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bodyt

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body\sigma

aquifer transmissibility

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body\chi

aquifer diffusivity


This model is based on assumption of:


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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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