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Motivation

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

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Excerpt Include
Aquifer Drive
Aquifer Drive
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Inputs & Outputs

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InputsOutputs

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Q_{WAQ}

p(t)

water influx from aquifer

field-average formation pressure at time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
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J

Q^{\downarrow}_{AQ}(t)

aquifer productivity index at time moment
Cumulative subsurface water influx from aquifer

LaTeX Math Inline
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body

p_i

initial formation pressure

LaTeX Math Inline
body

p

q^{\downarrow}_{AQ}(t)

field-average formation pressure at time moment LaTeX Math Inlinebodyt

= \frac{dQ^{\downarrow}_{AQ}}{dt}

Subsurface water flowrate from aquifer

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body\sigma

aquifertransmissibility





LaTeX Math Inline
body\chi

aquiferdiffusivity

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bodyA_e

pay area


Physical Model

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LaTeX Math Inline
bodyQ_{WAQ}(t)

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

















Fig. 1. Carter-Tracy aquifer drive schematic



Mathematical Model

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titleDerivation

Const PI expansion:

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LaTeX Math Block
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\frac{d Q_{

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AQ}}{dt} = J_{AQ}(t) \cdot ( p_

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i - p(t))

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Finite-volume reservoir PSS depletion:



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J_{AQ}(t) = 

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\frac{4 \pi \sigma}{ \ln \frac{

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1.781 \cdot A_e^2}{ 4 \pi \chi 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