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| p_e \ (t) = p_{nr} \ (0) + \gamma_n^{-1} \cdot \sum_m \left( Q^{\uparrow}_{nm} + Q^{\downarrow}_{nm} \ \right) |
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| p_{{\rm wf}, n} \ \ \ (t) = p_e \ (t) + J_n^{-1} \cdot q_n(t) |
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| Q^{\uparrow}_{nm} \ =
\ - \ f^{\uparrow}_{O,nm} \ \cdot B_{ob} \cdot \, Q^{\uparrow}_O
\ - \ f^{\uparrow}_{G,nm} \ \cdot B_{go} \cdot Q^{\uparrow}_G
\ - \ f^{\uparrow}_{W,nm} \ \cdot B_w \cdot Q^{\uparrow}_W
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| Q^{\downarrow}_{nm} \ =
f^{\downarrow}_{G,nm} \ \cdot B_{go} \cdot Q^{\downarrow}_G
\ + \ f^{\downarrow}_{W,nm} \ \cdot B_w \cdot Q^{\downarrow}_W
\ + \ B_{go} \cdot Q^{\downarrow}_{GCAP} \
\ + \ B_w \cdot Q^{\downarrow}_{WAQ}
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| Q_m(t) = \int_0^t q_m(t) \, dt |
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| B_{og} = \frac{B_o - R_s \, B_g}{1- R_s \, R_v} |
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| B_{go} = \frac{ B_g - R_v \, B_o}{1- R_s \, R_v} |
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The objective function is:
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In regular case , the initial formation pressure at datum is the same for all wells:
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| body | --uriencoded-- p_%7Bnr%7D(0) = p_i = %7B\rm const%7D, \ \forall n |
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See Also
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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 ]
