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titleDetailing


Detailing Inputs

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bodyB = A_e \cdot h_a \cdot \phi_a \cdot c_t

water influx constant

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



Assumptions

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Const Productivity Index Aquifer

Pseudo Steady State Flow

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J_{AQ} = \frac{q_{AQ}}{p_{AQ}(t)-p(t)} = \rm const
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p_{AQ}(t) = p_i - \frac{Q_{AQ}(t)}{V_{AQ} \cdot c_t}
Approximation to van Everdingen-Hurst (VEH)



Equations

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\frac{d Q^{\downarrow}_{AQ}}{dt_D} = \frac{ B \cdot (p_i - p(t_D)) - Q_{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}



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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} }



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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} }



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t_D= \frac{\pi \, \chi \, t}{A_e}



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