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\tau_j \geq 0 , \quad \beta_j \geq 0, \quad f_{ij} \geq 0 , \quad \sum_i^{N^{\uparrow}} f_{ij} \leq 1 |
PCRM – Liquid-Control Capacitance Resistance Model
The model equation is:
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p_n(t) = p_n(0) - \tau_n / \beta_n \cdot \big[ q^{\uparrow}_n(t) - q^{\uparrow}_n(0) \big] - \beta_n^{-1} \cdot Q^{\uparrow}_n (t) + \beta_n^{-1} \cdot \sum_m f_{nm} Q^{\downarrow}_m(t) |
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Q^{\uparrow}_j (t) = \sum_i^{n_i} f_{ij} Q^{\downarrow}_i(t) - \tau_j \cdot \big[ q^{\uparrow}_j(t) - q^{\uparrow}_j(0) \big] - \beta_j \cdot \big[ p_j(t) - p_j(0) \big] |
The objective function is:
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E[\tau, \beta, f] = \sum_k \sum_j \big[ Q^{\uparrow}_j(t_k) - \tilde Q^{\uparrow}_j(t_k) \big]^2 \rightarrow \min |
The constraints are:
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\tau_j \geq 0 , \quad \beta_j \geq 0, \quad f_{ij} \geq 0 , \quad \sum_i^{N^{\uparrow}} f_{ij} \leq 1 |
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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