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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
body\sigma

aquifertransmissibility





LaTeX Math Inline
body\chi

aquiferdiffusivity

LaTeX Math Inline
bodyA_e

pay area

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Physical Model

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Radial Composite Reservoir



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Infinite Acting Radial Flow Aquifer


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J_{AQ}(t) = \frac{4 \pi \sigma}{ \ln \frac{1.781 \cdot A_
e^2
e}{ 4 \pi \chi t} }

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Fig. 1. Carter-Tracy aquifer drive schematic



Mathematical Model

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



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

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titleEditor

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titleDerivation

Const PI expansion:

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



Finite-volume reservoir PSS depletion:

LaTeX Math Block
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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