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titlePIR equation deduction
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Y_w=\frac{q_W}{q_W + q_O} \rightarrow \frac{q_O}{q_W} = \frac{1-Y_w}{Y_w}
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VRR = \frac{B_w \, q_{WI}}{B_w \, q_W + B_O \, q_O + B_g \, [ q_G - R_s \, q_O] } =  \frac{B_w \, q_{WI}}{B_w \, q_W + B_O \, q_O + B_g \, [ GOR - R_s] q_O } 
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PIR=\frac{q_W}{q_{WI}}
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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) ] } }

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