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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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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) |
The objective function is:
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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_m^{\downarrow}(t) |
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XCRM – Liquid-Control Cross-well Capacitance Resistance Model
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 Model
See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Capacitance Resistance Model (CRM)
Production – Injection Pairing @ model
[ Slightly compressible Material Balance Pressure @model ]
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