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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Q^{\downarrow}_{AQ}| --uriencoded--Q%5e%7B\downarrow%7D_%7BAQ%7D(t) |
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Cumulative q^{\downarrow}_{AQ}Subsurface | --uriencoded--q%5e%7B\downarrow%7D_%7BAQ%7D(t) = \ |
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frac{dQ^{\downarrow}_{AQ}}{dt}| frac%7BdQ%5e%7B\downarrow%7D_%7BAQ%7D%7D%7Bdt%7D |
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| subsurface |
{AQ}
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Physical Model
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| | LaTeX Math Inline |
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| LaTeX Math Block |
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| J_{AQ} = \frac{q |
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body | J_{AQ}}{p_{AQ}(t)-p(t)} = \rm const |
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| Pseudo Steady State Flow | | LaTeX Math Block |
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| p_{AQ}(t) = p_i - \frac{Q_{AQ}(t)}{V_{AQ} \cdot c_t} |
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Mathematical Model
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1| Fetkovich_PSS | | alignment | left |
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| \tau \cdot \frac{d Q^{\downarrow}_{AQ}}{dt} + |
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\frac{1}{\tau}Jс_t \, V_\phi \cdot \left[ |
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() | | 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_{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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| Expand |
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Const PI expansion | Assumption #1 = Const Productivity Index Aquifer: | 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_{AQ}}{c_t \, V_\phi} |
Eliminating c_t} 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
