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{\rm VRR_{cum}} = \frac{B_w \, Q_{WI}}{B_w \, Q_W + B_o \, Q_O + B_g Q_G - B_g R_s Q_O}

{\rm VRR_{inst}} = \frac{B_w \, q_{WI}}{B_w \, q_W + B_o \, q_O + B_g (q_G - R_s Q_O)}

{\rm RF} = \frac{Q_O}{V_{STOIIP}}

{\rm Y_w} = \frac{q_W}{q_{LIQ}}

{\rm GOR} = \frac{q_g}{q_o}

q_{LIQ} = q_O + q_W

{\rm Y_wm} = \frac{1}{1 + \frac{K_{ro}}{K_{rw}} \cdot \frac{\mu_w}{\mu_o} \cdot \frac{B_w}{B_o}}

{\rm PIR} = \frac{Q_O}{Q_{WI}}

{\rm PIR_m} = { \frac{1}{VRR} }*{ \frac{1-Y_w}{ Y_w + (1-Y_w) \bigg[ \frac{B_o}{B_w} - \frac{B_g}{B_w}(GOR - R_s) \bigg] } }

{\rm J_{O}} = \frac{q_O}{P_e - P_{wf}} {\quad \Rightarrow \quad} P_{wf} = P_e - \frac{1}{J_O} q_O

{\rm J_t} = \frac{q_t}{P_e - P_{wf}}

{\rm J_{tm} } = \frac{2 \pi \sigma}{\ln \frac{r_e}{r_w} +0.5 + S}