Two-Phase Flow Regime (Gregory–Aziz–Mandhane): 24-Pet-B2 Oil and Gas Evaluation and Economics, Undated paper, Q6

Question 6: Two-Phase Flow Regime (Gregory–Aziz–Mandhane) (10 marks)

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.

Check: this is a chart-based classification (the Mandhane flow-pattern map has no closed-form boundary equations) — the superficial velocities below are exact, but the regime call itself carries the map's usual hand-reading precision, especially since the point sits close to the plug/bubble/stratified triple region.

Given.

Quantity	Value
Pipe I.D., $d$	200 mm
$\rho_{liq}$, $\rho_{gas}$	840, 35 kg/m$^3$
$Q_{liq}$ (std), $Q_{gas}$ (std)	50, 500 m$^3$/h
Inlet $T$, $p$	40$^\circ$C, 5000 kPa
Gas $Z$, $M$	0.85, 22 kg/kmol

Find. Expected two-phase flow regime.

Approach. Convert the standard-condition gas rate to actual (flowing) conditions with the real-gas law (the liquid rate is essentially unchanged, since liquids are near-incompressible); divide both actual rates by the pipe area to get superficial velocities $V_{sl}$, $V_{sg}$; and plot the point on the Mandhane $V_{sg}$–$V_{sl}$ map.

Actual gas flow rate at pipeline conditions. $$Q_{g,actual}=Q_{g,sc}\frac{p_{sc}}{p}\frac{T}{T_{sc}}\frac{Z}{Z_{sc}}=500\left(\frac{101.325}{5000}\right)\left(\frac{313.15}{288.15}\right)(0.85)=\boxed{9.36\ \text{m}^3/\text{h}}$$ The liquid rate is taken as unchanged, $Q_{l,actual}\approx50\ \text{m}^3/\text{h}$.
Superficial velocities. Pipe area $A=\pi d^2/4=\pi(0.200)^2/4=0.03142\ \text{m}^2$: $$V_{sl}=\frac{Q_{l,actual}}{3600A}=\frac{50}{3600(0.03142)}=\boxed{0.442\ \text{m/s}}$$ $$V_{sg}=\frac{Q_{g,actual}}{3600A}=\frac{9.36}{3600(0.03142)}=\boxed{0.0828\ \text{m/s}}$$
Locate the point on the Mandhane map and classify the regime.

Gregory–Aziz–Mandhane horizontal flow-pattern map (schematic reproduction of the published boundary shapes) with the computed operating point marked.

At $V_{sg}=0.083$ m/s the gas rate is far too low to disperse the liquid or sustain a wave-driven stratified interface, while $V_{sl}=0.442$ m/s is high enough to lift the flow out of the smooth-stratified region into intermittent gas pockets moving through a continuous liquid phase — the point falls just inside the plug-flow region of the map, close to its boundaries with bubble flow (above) and stratified flow (below). Physically: the very low actual gas rate (the 500 std m$^3$/h standard-condition rate compresses to only 9.36 actual m$^3$/h at 5000 kPa) means the gas phase occupies a small fraction of the pipe and travels as discrete elongated plugs/bubbles rather than a continuous stratified layer or a fully dispersed slug/annular pattern.

Quantity	Result
Actual gas rate, $Q_{g,actual}$	9.36 m$^3$/h
Superficial liquid velocity, $V_{sl}$	0.442 m/s
Superficial gas velocity, $V_{sg}$	0.0828 m/s
Expected flow regime	Plug flow (bordering bubble/stratified)

Topic: Two-phase horizontal-pipe flow-pattern prediction.

Key relations: real-gas volume conversion $Q_{actual}=Q_{sc}(p_{sc}/p)(T/T_{sc})(Z/Z_{sc})$; superficial velocity $V_{sj}=Q_j/A$; Mandhane map coordinates ($V_{sg}$, $V_{sl}$).

Why this works: Flow-pattern maps are empirical because no single mechanistic model captures every transition; Mandhane, Gregory & Aziz's 1974 map remains the standard first-pass screening tool precisely because it needs only the two superficial velocities computed here, with no iterative mechanistic closure.

Common pitfall: Plotting the map with the STANDARD-condition gas rate instead of converting to actual flowing conditions first — here that error would overstate $V_{sg}$ by a factor of $\sim$53, pushing the point across several regime boundaries into slug or annular-mist territory.

Source: Mandhane, Gregory & Aziz (1974), Int. J. Multiphase Flow 1(4); Brill & Mukherjee, Multiphase Flow in Wells, Ch. 3.

Question 6 of 7: Two-Phase Flow Regime (Gregory–Aziz–Mandhane)

Question 6: Two-Phase Flow Regime (Gregory–Aziz–Mandhane) (10 marks)