Nodal Analysis: IPR Meets VLP
Pick a node - usually the bottomhole - and plot what the reservoir can deliver against what the tubing can lift. Where the two curves cross, supply meets demand, and that crossing is the one rate and pressure at which the well actually produces.
Plot what the reservoir can deliver against what the tubing can lift - where the two curves cross is the one rate and pressure at which the well actually produces.
Pick a Node, Plot Two Curves
A producing well is a chain of components - reservoir, near-wellbore zone, tubing, wellhead, surface choke - and each one relates pressure to rate in its own way. Nodal analysis simplifies that chain by picking a single point, the node - almost always the bottomhole - and looking at what flows into it and what flows out of it. From below, the inflow curve is the reservoir's IPR: the rate the formation can deliver to the node as the bottomhole pressure is drawn down. From above, the outflow curve is the tubing's VLP: the bottomhole pressure needed to carry that rate from the node up to surface. Plotted together against rate, the two curves describe the whole producing system on one graph - supply from below, demand from above.
The Operating Point: Where Supply Meets Demand
The reservoir will only deliver what the tubing can lift, and the tubing will only lift what the reservoir supplies - so the well must settle where the two agree. That place is the operating point: the unique rate and bottomhole flowing pressure at which inflow equals outflow, the intersection of the IPR and VLP curves. At any other rate the curves disagree - supply would exceed demand, or demand exceed supply - and the well cannot stay there. The power of nodal analysis is that anything that shifts either curve moves the operating point: a bigger tubing lowers the VLP, a lower wellhead pressure lowers the VLP, a higher productivity index raises the IPR, and adding artificial lift reshapes the outflow curve entirely. To predict what a change does to production, shift the curve and read the new intersection.
- At the operating point inflow equals outflow: $3000 - q = 1000 + 0.001\,q^2$.
- Rearrange: $0.001\,q^2 + q - 2000 = 0$, or multiplying by 1,000, $q^2 + 1000\,q - 2{,}000{,}000 = 0$.
- Solve the quadratic: $q = \dfrac{-1000 + \sqrt{1000^2 + 4(2{,}000{,}000)}}{2} = \dfrac{-1000 + \sqrt{9{,}000{,}000}}{2} = \dfrac{-1000 + 3000}{2}$.
- $q = 2000/2 = 1{,}000$ STB/d.
- Operating pressure from the IPR: $p_{wf} = 3000 - 1000 = 2{,}000$ psi (check with the VLP: $1000 + 0.001 \times 1000^2 = 1000 + 1000 = 2{,}000$ psi).
The whole point of nodal analysis is seeing how a shifted curve moves the operating point - and the best way to feel that is to move the curves yourself. This module's interactive IPR/VLP nodal-analysis plot lets you slide the reservoir pressure and productivity index (which reshape the inflow IPR) and the tubing head and friction (which reshape the outflow VLP), and watch the operating point slide along to a new rate and pressure. Try raising the productivity index $J$ (lifts the IPR) and watch the operating rate climb; try lowering the tubing head or friction, as gas lift would, and watch it climb further. The worked example above is exactly the kind of intersection the tool computes - and displays - in real time.
Check your understanding
- Nodal analysis picks a node (usually the bottomhole) and plots inflow (the IPR, reservoir delivering to the node) and outflow (the VLP, tubing lifting from the node) against rate.
- The intersection of the two curves is the operating point - the unique rate and bottomhole flowing pressure at which supply equals demand; anything that shifts either curve moves it.
- For the worked well (IPR p_wf = 3000 - q, VLP p_wf = 1000 + 0.001 q^2), the operating point is q = 1,000 STB/d at p_wf = 2,000 psi.