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The model equation is:
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| anchor | J57KHQCRM |
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| alignment | left |
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p_n(t) = p_n(0) - \tau_n / \gamma_n \cdot \big[ q^{\uparrow}_n(t) - q^{\uparrow}_n(0) \big] - \gamma_n^{-1} \cdot Q^{\uparrow}_n (t) + \gamma_n^{-1} \cdot \sum_m f_{nm} Q^{\downarrow}_m(t) |
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\tau_n \geq 0 , \quad \gamma_n \geq 0, \quad f_{nm} \geq 0 , \quad \sum_i^{N^{\uparrow}} f_{ij} \leq 1, \quad p_{nr}(0) > 0 |
where
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p_{nr}(0) = p_n(0) + (\tau_n / \gamma_n) \cdot q^{\uparrow}_n(0) |
is the initial formation pressure.
The equation
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can be re-written with explicit form of initial formation pressure:| LaTeX Math Block |
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p_n(t) = p_{nr}(0) + (\tau_n / \gamma_n) \cdot q^{\uparrow}_n(t) - \gamma_n^{-1} \cdot Q^{\uparrow}_n (t) + \gamma_n^{-1} \cdot \sum_m f_{nm} Q^{\downarrow}_m(t) |
If
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| body | --uriencoded--p_%7Bnr%7D(0) |
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is known then it can be fixed during the search loop which normally improves the quality of future production forecasts.See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Capacitance Resistance Model (CRM)
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