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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
bodyB

water influx constant





LaTeX Math Inline
body\chi

aquifer diffusivity

LaTeX Math Inline
bodyA_e

net pay area


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titleDetailing


Detailing Inputs

LaTeX Math Inline
bodyB = \frac{\theta}{2\pi} \cdot A_e \cdot h_a \cdot \phi_a \cdot c_t

water influx constant

LaTeX Math Inline
body\theta

central angle of net pay area ↔ aquifer contact

LaTeX Math Inline
bodyh_a

aquifer effective thickness

LaTeX Math Inline
body\phi_a

aquifer porosity

LaTeX Math Inline
bodyc_t=c_r +c_w

aquifer total compressibility

LaTeX Math Inline
bodyc_r

aquifer pore compressibility 

LaTeX Math Inline
bodyc_w

aquifer water compressibility



Assumptions

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Transient Radial Composite Reservoir



Equations

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LaTeX Math Block
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\frac{d Q^{\downarrow}_{AQ}}{dt_D} = \frac{ B \cdot (p_i - p(t_D)) - Q^{\downarrow}_{AQ} \cdot p'_D(t)}{p_D(t) - t \cdot p'_D(t)}



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q^{\downarrow}_{AQ}(t)=\frac{d Q^{\downarrow}_{AQ}}{dt}





LaTeX Math Block
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t_D= \frac{\pi \, \chi \, t}{A_e}





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titleDerivation

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See Also

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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling / Aquifer ExpansionDrive / Aquifer expansion @modelDrive Models

Reference

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 1. van Everdingen, A.F. and Hurst, W. 1949. The Application of the Laplace Transformation to Flow Problems in Reservoirs. Trans., AIME 186, 305.

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