Nodal Analysis — Natural Flow Check and Gas-Lift Design: 24-Pet-A5 Petroleum Production Operations, December 2018, Q3

Question 3: Nodal Analysis — Natural Flow Check and Gas-Lift Design (25 points)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A nodal-analysis problem: reservoir inflow (IPR) must be matched against the tubing's vertical lift performance (VLP) to reach the required wellhead pressure.

Productivity index, $J$ (liquid basis)	0.5 STBL/day/psi
Static reservoir pressure, $\bar P_R$	2800 psi
Bubble-point pressure, $P_b$	3000 psi
Tubing length, ID	4000 ft, 2.441 in
Required wellhead pressure, $P_{wh}$	160 psi
Natural producing GLR	100 SCF/STBL
Water cut, $f_w$	50%
Oil gravity / gas gravity	35°API / 0.65
Water specific gravity	1.07
Average flowing temperature	150°F

Find. (a) Whether 400 STBO/day flows naturally to 160 psi at the wellhead; (b) the gas injection rate needed to reach 500 STBO/day.

Check: with no gradient-curve chart supplied, the tubing pressure traverse is computed with a homogeneous, no-slip (liquid+gas mixed, no relative velocity) black-oil mixture: liquid volume from $f_w$ (oil and water both taken near-incompressible, $B_o\approx B_w\approx1$ since neither is given), free-gas volume from the real-gas law with $z$ from a Standing pseudo-critical fit, marched in small increments so the local gas density updates with pressure. Friction is neglected (no roughness/velocity data given) — this is a hydrostatic-dominated approximation appropriate to the data provided, not a full mechanistic (Hagedorn–Brown/Poettmann–Carpenter) correlation.

Approach. (a) Get $P_{wf}$ from the straight-line IPR at the total liquid rate, then march the no-slip mixture gradient up the tubing from that $P_{wf}$ and compare the resulting wellhead pressure with the 160 psi requirement. (b) Repeat at the higher rate, then bisect on the total (natural + injected) GLR until the traverse lands exactly on 160 psi at surface; the injected gas is the difference from the natural GLR.

Part (a) — inflow at 400 STBO/day. With $f_w=0.5$, total liquid rate $q_L=400/(1-0.5)=800$ STBL/day. IPR: $P_{wf}=\bar P_R-q_L/J=2800-800/0.5=2800-1600$. $\boxed{P_{wf}=1200\ \text{psi}}$.
Part (a) — VLP check. Marching the no-slip mixture gradient upward from $P_{wf}=1200$ psi over 4000 ft at the natural GLR of 100 SCF/STBL gives a computed wellhead pressure of only $\boxed{P_{wh,computed}\approx138\ \text{psi}}$ — short of the 160 psi required (the reservoir can only support a $P_{wf}$ high enough to give 160 psi at surface if $P_{wf}\ge1255$ psi, about 55 psi more than the 1200 psi the IPR actually delivers at 400 STBO/day). $\boxed{\text{Answer (a): No, the well will NOT flow naturally at 400 STBO/day}}$ — it falls just short and needs artificial lift assistance.
Part (b) — inflow at 500 STBO/day. $q_L=500/(1-0.5)=1000$ STBL/day; $P_{wf}=2800-1000/0.5=2800-2000$. $\boxed{P_{wf}=800\ \text{psi}}$ (even less BHP available than in part a, since the higher rate pulls $P_{wf}$ down further).
Part (b) — required total GLR. Bisecting the total GLR (natural + injected) so the marched traverse from $P_{wf}=800$ psi over 4000 ft lands exactly on $P_{wh}=160$ psi gives $\boxed{\text{GLR}_{total}=229.5\ \text{SCF/STBL}}$.
Part (b) — injection rate. Injected GLR $=229.5-100=129.5$ SCF/STBL; at $q_L=1000$ STBL/day, $Q_{inj}=129.5\times1000$. $\boxed{Q_{inj}\approx1.295\times10^5\ \text{SCF/day}\ (0.130\ \text{MMscf/day})}$, injected at the tubing intake to lighten the column enough to reach the required 500 STBO/day.

Fig. 3 — Well schematic: 4000 ft of 2 7/8 in tubing, natural GLR (100 SCF/STBL) insufficient at $P_{wf}=1200$ psi (part a), gas-lift assisted at $P_{wf}=800$ psi (part b).

Quantity	Value
(a) $P_{wf}$ from IPR at 400 STBO/day	1200 psi
(a) Computed $P_{wh}$ at natural GLR	≈138 psi (< 160 required)
(a) Will it flow naturally?	No
(b) $P_{wf}$ from IPR at 500 STBO/day	800 psi
(b) Required total GLR	229.5 SCF/STBL
(b) Required gas injection rate	≈129,500 SCF/day

Topic: Nodal analysis — matching inflow performance (IPR) against vertical lift performance (VLP) to test natural flow and design gas-lift assistance.

Key relations: IPR: $q_L=J(\bar P_R-P_{wf})$; no-slip mixture gradient: $dP/dz=\rho_{mix}/144$, $\rho_{mix}=\dfrac{m_{liquid}+m_{gas}}{V_{liquid}+V_{gas}(P,T)}$, with $V_{gas}$ via $B_g=0.00504\,zT/P$.

Why this works: a well only flows where its IPR and VLP curves intersect at or above the required $P_{wh}$; injecting gas lightens the column (lowers $\rho_{mix}$), which lowers the VLP curve and lets a lower $P_{wf}$ (i.e. a higher IPR-delivered rate) still reach the surface requirement.

Common pitfall: checking only the IPR-side pressure and forgetting the column must still physically lift the fluid to $P_{wh}$ — a reservoir can deliver plenty of drawdown and the well can still fail to flow if the column is too heavy, exactly the case in part (a) here.

Source: Beggs, Production Optimization Using Nodal Analysis, 2nd ed., Ch. 3–5; Brown, The Technology of Artificial Lift Methods, Vol. 2a.

Question 3 of 5: Nodal Analysis — Natural Flow Check and Gas-Lift Design

Question 3: Nodal Analysis — Natural Flow Check and Gas-Lift Design (25 points)