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Motivation

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Excerpt Include
Aquifer Drive
Aquifer Drive
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Inputs & Outputs

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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

aquifer total compressibility

LaTeX Math Inline
bodyV_{AQ}

\chi

aquiferdiffusivity aquifer volume

LaTeX Math Inline
bodyA_{AQ}

aquifer area

LaTeX Math Inline
bodyA_e

pay area

where

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LaTeX Math Inline
bodyJ(t)

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aquifer productivity index at time moment

LaTeX Math Inline
bodyt

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LaTeX Math Inline
bodyp_i

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LaTeX Math Inline
bodyp(t)

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field-average formation pressure at time moment

LaTeX Math Inline
bodyt

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LaTeX Math Inline
body\sigma

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LaTeX Math Inline
body\chi

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Physical Model

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Assumptions

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}

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1.781 \cdot A_e}{ 4 \pi \chi t} }

















Fig. 1. Carter-Tracy aquifer drive schematic



Mathematical Model

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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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groupeditors

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titleEditor

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titleDerivation

Const PI expansion:

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

Finite-volume reservoir PSS depletion:

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



See Also

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

Reference

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