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The objective function is:
E[ \ \tau_n, \gamma_n, f_{nm} \ ] = \sum_k \sum_n \left[ {\rm w}_e \cdot \left( p_{e,n} \ \ (t_k) - \tilde p_{e,n} \ \ (t_k) \right)^2 + {\rm w}_{\rm wf} \ \ \cdot \left( p_{{\rm wf},n} \ \ (t_k) - \tilde p_{{\rm wf},n} \ \ (t_k) \right)^2 \right] \rightarrow \min |
The constraints are:
J_n \geq 0 , \quad \gamma_n \geq 0, \quad f_{nm} \ \geq 0 , \quad \sum_m f^{\uparrow}_{O, nm} \ \leq 1 , \quad \sum_m f^{\uparrow}_{G, nm} \ \leq 1, \quad \sum_m f^{\downarrow}_{W, nm} \ \leq 1, \quad \sum_m f^{\downarrow}_{G, nm} \ \leq 1 |
In regular case , the initial formation pressure at datum is the same for all wells:
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Capacitance Resistance Model (CRM) / Capacitance-Resistivity Model (CRM) @model
Production – Injection Pairing @ model
[ Slightly compressible Material Balance Pressure @model ]