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





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


where

LaTeX Math Inline
bodyQ_{WAQ}(t)

water influx from aquifer at time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
body\sigma

aquifertransmissibility

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bodyJ = \rm const

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body\displaystyle \tau = \frac{V_{WAQ} \, c_t}{J}


LaTeX Math Inline
bodyp_i

initial formation pressure

LaTeX Math Inline
bodyA_{AQ}

aquifer area

LaTeX Math Inline
bodyp(t)

field-average formation pressure at time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
body\sigma

aquifer transmissibility

LaTeX Math Inline
bodyA_{AQ}

aquifer area

LaTeX Math Inline
bodyA_e

pay area


This model is based on assumptions:

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