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Motivation


Excerpt Include
Aquifer Drive
Aquifer Drive
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Inputs & Outputs


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} = \frac{2 \pi \sigma}{\ln \frac{A_{AQ}}{A_e}+0.75}

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

aquifer total compressibility

LaTeX Math Inline
bodyV_{AQ}

aquifer volume

LaTeX Math Inline
bodyA_{AQ}

aquifer area

LaTeX Math Inline
bodyA_e

pay area


Assumptions


Const PI

Pseudo Steady State Flow


LaTeX Math Inline
bodyJ_{AQ} = \rm const
Aquifer Productivity Index is constant


LaTeX Math Block
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p_{AQ}(t) = p_i - \frac{Q_{AQ}}{V_{AQ} c_t}





Equations


LaTeX Math Block
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\frac{d Q^{\downarrow}_{AQ}}{dt} + \frac{1}{\tau} Q^{\downarrow}_{AQ} = J \cdot ( p_i - p(t))



LaTeX Math Block
anchor1
alignmentleft
q^{\downarrow}_{AQ}(t)=\frac{d Q^{\downarrow}_{AQ}}{dt}



Expand
titleDerivation

Const PI expansion:

LaTeX Math Block
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q_{AQ} = \frac{d Q_{WAQ}}{dt} = J_{AQ} \cdot ( p_{AQ} - p(t))


Finite-volume reservoir PSS depletion:

LaTeX Math Block
alignmentleft
p_{AQ}(t) = p_i - \frac{Q_{AQ}}{V_{WAQ} c_t}



See Also

Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling / Aquifer Drive / Aquifer Drive @model

Reference

 1.   Fetkovich, M.J. 1971. A Simplified Approach to Water Influx Calculations—Finite Aquifer Systems. J Pet Technol 23 (7): 814–28. SPE-2603-PA. http://dx.doi.org/10.2118/2603-PA