Given. The present Vogel AOF directly, plus PVT/relative-permeability data at both the present and the depleted future reservoir pressure.
Present $\bar P_R$ / future $\bar P_R$
3000 psig / 1500 psig
Present $(q_o)_{max}$
2000 STB/day
Present: $k_{ro},\mu_o,B_o$
0.85, 3.0 cp, 1.18 bbl/STB
Future: $k_{ro},\mu_o,B_o$
0.60, 3.70 cp, 1.12 bbl/STB
Find. The well's oil producing capacity (future AOF) at $\bar P_R=1500$ psi.
Approach. Standing's future-IPR method scales the productivity index by the change in the oil mobility ratio $k_{ro}/(\mu_o B_o)$ between the two pressures, then re-applies Vogel's relation $(q_o)_{max}=J^*\bar P_R/1.8$ at the future pressure.
Present ideal productivity index. From Vogel's relation at $P_{wf}=0$: $J^*_{present}=1.8\,(q_o)_{max}/\bar P_R=1.8\times2000/3000$. $\boxed{J^*_{present}=1.2\ \text{STB/day/psi}}$.
Oil mobility at present and future conditions. $\left(\dfrac{k_{ro}}{\mu_oB_o}\right)_{present}=\dfrac{0.85}{3.0\times1.18}=0.2401$; $\left(\dfrac{k_{ro}}{\mu_oB_o}\right)_{future}=\dfrac{0.60}{3.70\times1.12}=0.1448$.
Scale the productivity index. $J^*_{future}=J^*_{present}\times\dfrac{0.1448}{0.2401}=1.2\times0.6030$. $\boxed{J^*_{future}=0.7236\ \text{STB/day/psi}}$.
Future absolute open flow. $(q_o)_{max,future}=J^*_{future}\,\bar P_{R,future}/1.8=0.7236\times1500/1.8$. $\boxed{(q_o)_{max,future}=603\ \text{STB/day}}$ — the well's oil producing capacity once the reservoir has declined to 1500 psi.
Check: the future data set also reports GOR $=800$ scf/STB and $f_w=0.5$ at 1500 psi; these describe the future produced gas and water streams but are not inputs to Standing's oil-mobility scaling itself (the method needs only $k_{ro},\mu_o,B_o$), so they are not used further here — they would enter a full three-phase composite-IPR/nodal analysis if the well's total liquid or gas handling were being sized, which was not asked.
Fig. 5 — Present ($\bar P_R=3000$ psi, $(q_o)_{max}=2000$ STB/day, blue) vs. future ($\bar P_R=1500$ psi, $(q_o)_{max}=603$ STB/day, red) Vogel IPR curves, showing how both the reservoir energy and the oil mobility loss (rising water saturation, falling $k_{ro}$) shrink the deliverability as the reservoir depletes.
Quantity
Value
Present ideal productivity index, $J^*_{present}$
1.20 STB/day/psi
Oil mobility ratio, future/present
0.603
Future ideal productivity index, $J^*_{future}$
0.724 STB/day/psi
Future oil producing capacity at $\bar P_R=1500$ psi
