Given. A stabilized test and a build-up test bracket the well's inflow performance; the pump swap only changes where on this same IPR the well is asked to operate.
Test rate, $q_{test}$
120 STB/day
Test flowing pressure, $P_{wf,test}$
600 psi
Static (average) reservoir pressure, $\bar P_R$
1200 psi
Bubble-point pressure, $P_b$
300 psi
Find. $J$; AOF; $P_{wf}$ for $q=150$ STB/D; $q$ at $P_{wf}=350$ psi; the IPR curve.
Check: every $P_{wf}$ this question asks about (600, 450, 350 psi) sits above $P_b=300$ psi, so the well is producing single-phase (undersaturated) liquid throughout — a straight-line, constant-$J$ IPR is the physically correct model here, not a simplification of convenience.
Approach. Since the test point lies above the bubble point, apply the straight-line productivity-index relation $q_o=J(\bar P_R-P_{wf})$ directly to back out $J$, then use it for every other part.
Absolute open flow (AOF). Extending the straight line to $P_{wf}=0$ at constant $J$ (as instructed): $q_{max}=J\,\bar P_R=0.2\times1200$. $\boxed{\text{AOF}=240\ \text{STB/day}}$.
Flowing pressure for 150 STB/day. Rearranging: $P_{wf}=\bar P_R-\dfrac{q}{J}=1200-\dfrac{150}{0.2}=1200-750$. $\boxed{P_{wf}=450\ \text{psi}}$. This is above $P_b$, so the straight line is still valid at this rate.
Rate at $P_{wf}=350$ psi. $q=J(\bar P_R-P_{wf})=0.2\times(1200-350)=0.2\times850$. $\boxed{q=170\ \text{STB/day}}$ — this is the rate the larger pump should deliver once it pulls $P_{wf}$ down to 350 psi.
Fig. 1 — IPR straight line ($J=0.2$ STB/day/psi) from the 1200 psi static pressure to the 240 STB/day AOF, with the original test point and the two computed operating points (c) and (d) marked.
