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q^{\uparrow}_n (t) =\exp(-t/\tau_n) \cdot \left[ \ q^{\uparrow}_n (0) + \tau_n^{-1} \cdot \int_0^t \exp(s/\tau_n) \left[ \sum_m f_{nm} \cdot q^{\downarrow}_m(s) - \gamma_n \frac{dp_n}{ds} \right] ds \ \right] |
The objective function is:
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XCRM – Liquid-Control Cross-well Capacitance Resistance Model
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p_n(t) = p_{nr}(0) + (\tau_n / \gamma_n) \cdot q_n(t) - \gamma_n^{-1} \cdot Q_n (t) + \gamma_n^{-1} \cdot
\sum_{m \neq n}f_{nm} \
- \frac{B_o - R_s \, B_g}{1- R_s \, R_v} \cdot \, Q^{\uparrow}_O + \frac{ B_g - R_v \, B_o}{1- R_s \, R_v} \cdot \, \left( Q^{\downarrow}_G - Q^{\uparrow}_G + Q^{\downarrow}_{GCAP} \right) + B_w \, \left( Q^{\downarrow}_W - Q^{\uparrow}_W + Q^{\downarrow}_{WAQ} \right) |
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Q_m(t) = \int_0^t q_m(t) \, dt |
Some extensions to conventional CRM model can be found in XCRM – Liquid-Control Cross-well Capacitance Resistance Model @model.
ELPM – Explicit Linear Production Model
Some extensions to conventional CRM model can be found in Explicit Linear Production ModelIn regular case , the initial formation pressure at datum is the same for all wells: LaTeX Math Inline
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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