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| LaTeX Math Block |
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| anchor | Fetkovich_PSS |
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| alignment | left |
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| \frac{d Q^{\downarrow}_{AQ}}{dt} + \frac{1}{\tau} Q^{\downarrow}_{AQ} = B_w \, J \cdot ( p_i - p(t)) |
| | LaTeX Math Block |
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| q^{\downarrow}_{AQ}(t)=\frac{d Q^{\downarrow}_{AQ}}{dt} |
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which can be explicitly integrated:
| LaTeX Math Block |
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| anchor | Fetkovich_PSS |
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| alignment | left |
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| Q^{\downarrow}_{AQ}(t) = J \, \exp \left(-\frac{t}{\tau} \right) \, \int_0^t B_w(p) \, ( p_i - p(t)) \, \exp \left(\frac{t}{\tau} \right) \, dt |
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| Expand |
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| Panel |
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| Assumption #1 = Const Productivity Index Aquifer: | LaTeX Math Block |
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| q_{AQ} = \frac{d Q_{AQ}}{dt} = J_{AQ} \cdot ( p_{AQ}(t) - p(t)) |
Assumption #2 = Pseudo Steady State Flow: | LaTeX Math Block |
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| p_{AQ}(t) = p_i - \frac{Q_{AQ}}{V_{AQ} c_t} |
Eliminating one arrives to | LaTeX Math Block Reference |
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