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InputsOutputs

LaTeX Math Inline
bodyp(t)

field-average formation pressure at time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyQ^{\downarrow}_{AQ}(t)

Cumulative subsurface water influx from aquifer

LaTeX Math Inline
bodyp_i

initial formation pressure

LaTeX Math Inline
bodyq^{\downarrow}_{AQ}(t) = \frac{dQ^{\downarrow}_{AQ}}{dt}

Subsurface water flowrate from aquifer

LaTeX Math Inline
bodyJ_{AQ}(t)

aquifer Productivity Index

LaTeX Math Inline
body\displaystyle \tau = \frac{V_{AQ} \, c_t}{J}

aquifer relaxation time
Detailing Inputs

LaTeX Math Inline
body\sigma

aquifertransmissibility





LaTeX Math Inline
bodyc_t=c_r +c_w\chi

aquifer total compressibilitydiffusivity

mathinline
LaTeX Math Inline
bodyV_{AQ}

aquifer volume

bodyA_{AQ}

aquifer area

LaTeX Math Inline
bodyA_e

pay area

where

LaTeX Math Inline
bodyJ(t)

aquifer productivity index at time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyp_i

initial formation pressure

LaTeX Math Inline
bodyp(t)

field-average formation pressure at time moment

LaTeX Math Inline
bodyt

LaTeX Math Inlinebody
\sigmaaquifer transmissibility

LaTeX Math Inline
body\chi

aquifer diffusivity


Assumptions

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LaTeX Math Block
Infinite Acting Radial Flow Aquifer

Slow variation of water influx 

LaTeX Math Inline
bodyQ_{WAQ}(t)
 in time


LaTeX Math Block
anchor2
alignmentleft
p
J_{AQ}(t) =
p_i -
 \frac{4 \pi \sigma}{ \ln \frac{
Q_{AQ}(t)}{V_{AQ} \cdot c_t}
1.781 \cdot A_e^2}{ 4 \pi \chi t} }




Equations

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LaTeX Math Block
anchor1
alignmentleft
\frac{d Q_{AQ}}{dt} = J__{AQ}(t) \cdot ( p_i - p(t))



LaTeX Math Block
anchor2
alignmentleft
J_{AQ}(t) = \frac{4 \pi \sigma}{ \ln \frac{1.781 \cdot A_e^2}{ 4 \pi \chi t} }


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