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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
body--uriencoded--A_e = \pi \, r_e%5e2

net pay area


Expand
titleDetailing


Detailing Inputs

LaTeX Math Inline
bodyB = \frac{\theta}{\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

aquifereffective thickness

LaTeX Math Inline
body\phi_a

aquiferporosity

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



Physical Model

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Radial Composite Reservoir

Image Modified

Transient flow
Computational approximation to van Everdingen-Hurst (VEH)









Fig. 1. Carter-Tracy aquifer drive schematic



Mathematical Model

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LaTeX Math Block
anchorCT
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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)}



LaTeX Math Block
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p_D= \frac{370.529 \, \sqrt{t_D} +137.528 \, t_D + 5.69549 \, t_D^{1.5}}
{328.834 +265.488 \, \sqrt{t_D} + 45.2157 \, t_D +  t_D^{1.5} }



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



LaTeX Math Block
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p'_D= \frac
{716.441 + 46.7984 \, \sqrt{t_D} + 270.038 \, t_D + 71.0098 \, t_D^{1.5} }
{ 1296.86 \, \sqrt{t_D} + 1204.73 \, t_D + 618.618 \, t_D^{1.5} + 538.072 \, t_D^2 + 142.41 \, t_D^{2.5} }





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




Expand
titleDerivation

Equation

LaTeX Math Block Reference
anchorCT
is not a solution of diffusion equation but an approximation of VEH model which does not involve convolution integral.

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