Motivation
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| Excerpt Include |
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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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| Detailing Inputs | | LaTeX Math Inline |
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| body | \displaystyle J_{AQ} = \frac{\theta}{2\pi} \cdot \frac{2 \pi |
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| LaTeX Math Block |
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\frac{d Q_{WAQ}}{dt} + \frac{1}{\tau} Q_{WAQ} = J \cdot ( p_i - p(t)) |
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| area | | LaTeX Math Inline |
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| body | \displaystyle \tau = \frac{V_{ |
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Physical Model
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Mathematical Model
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| LaTeX Math Block |
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| anchor | Fetkovich_PSS |
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| alignment | left |
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| \tau \cdot \frac{d Q^{\downarrow}_{AQ}}{dt} + Q^{\downarrow}_{AQ} = с_t \, V_\phi \cdot \left[ p_i - p(t) \right] |
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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_{AQ} \, \exp \left( -\frac{t}{\tau} \right) \, \int_0^t \big[ p_i - p(\xi) \big] \, \exp \left( \frac{\xi}{\tau} \right) \, d \xi |
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Const PI expansion: WAQWAQAQ}}{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
