{\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_{lis}}

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

q_{liq} = q_o + q_w

{\rm Y_w} = \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_i}

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

P_{wf} = P_e - \frac{1}{J_{PI}} q_o

{\rm J_{PI}} = \frac{Q}{P_e - P_{wf}} {\quad \Rightarrow \quad} P_{wf}=P_e - \frac{1}{PI}Q

{\rm J_{PIm} } = \frac{q_o}{P_e - P_{wf}}