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Y_wVRR = \frac{B_w \, q_W{WI}}{B_w \, q_W + B_O \, q_O + B_g \, [ q_G - R_s \, q_O] } = \rightarrow \frac{B_w \, q_O{WI}}{B_w \, q_W + B_O \, q_O + B_g \, [ GOR - R_s] q_O } = \frac{1-YB_w \, q_{WI}}{Y_wB_w \, q_W + [ B_o  + B_g \, ( GOR - R_s) ] \, q_O }

VRR = \frac{B_w \, q_{WI}q_{WI}}{q_W + \bigg[ \frac{B_o}{B_w}  + \frac{B_g}{B_w} \, ( GOR - R_s) \bigg] \, q_O }

PIR=\frac{q_W}{q_{WI}} = \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] }

PIR = \frac{q_O}{q_{WI}}={ \frac{1}{VRR} }*{ \frac{1-\gamma}{ \gamma +  [ \frac{B_o}{B_w} - \frac{B_g}{B_w}(GOR - R_s) ] } }