Motivation
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| Aquifer Drive |
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| Aquifer Drive |
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| nopanel | true |
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Inputs & Outputs
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Q^{\downarrow}_{AQ}| --uriencoded--Q%5e%7B\downarrow%7D_%7BAQ%7D(t) |
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Cumulative q^{\downarrow}_{AQ}| --uriencoded--q%5e%7B\downarrow%7D_%7BAQ%7D(t) = \ |
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frac{dQ^{\downarrow}_{AQ}}{dt}Subsurface water flowrate from aquifer | | LaTeX Math Inline |
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body |
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Assumptions
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Physical Model
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| A_e | cross-sectional area in | LaTeX Math Inline |
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body | =p_i = Aquifer pressure is constant | | LaTeX Math Inline |
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body | J \rm constAquifer Productivity Index is constant | ...
Mathematical Model
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1| Fetkovich_PSS | | alignment | left |
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| \tau \cdot \frac{d |
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QQ^{\downarrow}_{AQ}}{dt} + |
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\frac1}{tau QJс_t \, V_\phi \cdot \left[ |
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()J 2\pi \sigma}{\ln \frac{AA_e} - \frac{3}{4} } which can be explicitly integrated:
1| Fetkovich_PSS | | alignment | left |
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q=\frac{d Q(t) = J_{AQ} \, \exp \left( -\frac{t}{ |
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dt} where
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water influx from aquifer at time moment
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| LaTeX Math Inline |
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| body | \displaystyle \tau = \frac{V_{AQ} \, c_t}{J} |
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\tau} \right) \, \int_0^t \big[ p_i - p(\xi) \big] \, \exp \left( \frac{\xi}{\tau} \right) \, d \xi |
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| Expand |
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| Expand |
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Const PI expansion: | LaTeX Math Block |
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| q_{AQ} = \frac{d Q_{ |
WAQAQ}}{dt} = J_{AQ} \cdot ( p_{AQ}(t) - p(t)) |
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Finite-volume reservoir PSS depletion
Assumption #2 = Pseudo Steady State Flow: | LaTeX Math Block |
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| p_{AQ}(t) = p_i - \frac{Q_{ |
WAQ{WAQ} c_t}
Eliminating one arrives to | LaTeX Math Block Reference |
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. |
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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-PA. http://dx.doi.org/10.2118/2603-PA
