Homogeneous Gas-Liquid Pressure Profile Calculator

Integrate an isothermal no-slip gas/liquid screening profile with friction, elevation and gas-expansion acceleration, checked against momentum closure.

Results

Calculate to view linked results. Default values are examples, not recommended operating inputs.

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Worked explanations, controlled studies and printable exercises connected to this calculation.

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Calculation sequence

Set inlet absolute pressure, constant temperature, pipe ID, uphill inclination and length measured along flow. Enter conserved gas and liquid mass rates, not standard gas volume or stock-tank liquid rates. At least one rate must be positive; single-phase endpoints are accepted for limiting-case checks. Select gas molecular mass and a constant Z appropriate to the supplied state; no fluid composition or phase flash is inferred.
A homogeneous mixture has one shared velocity: local gas volume changes with absolute pressure while liquid density stays constant. The volume-specific mixture relation follows conservation of each phase mass. The chart and table update pressure, density, velocity and gas volume fraction along the interval. No-slip volume fraction is not a separately predicted liquid-holdup correlation.
Supply a constant Darcy friction factor appropriate to a screening comparison. Darcy is four times Fanning: the NASA source's f = 0.079 Re^-0.25 uses the Fanning convention, and that number must not be entered as a Darcy factor. This implementation does not apply that source correlation or invent a mixture-viscosity rule. Friction uncertainty remains a user assumption throughout the interval.
The implemented steady momentum equation combines Darcy wall friction, upward gravitational head and acceleration from gas expansion. ODEX integrates normalized pressure plus cumulative friction and hydrostatic components, samples 51 stations, then repeats at tighter tolerances. The acceleration component is calculated independently from endpoint momentum flux. A refinement difference above 1e-7 of inlet pressure or momentum closure above 1e-8 is rejected.

Worked check

The default synthetic case uses 5 MPa absolute, 320 K, 0.1-m ID, 1,000 m at 10 degrees uphill, 0.05 kg/s gas and 5 kg/s liquid, liquid density 850 kg/m3, molecular mass 20 kg/kmol, Z = 0.9 and Darcy factor 0.02. Outlet pressure is about 3.75582 MPa absolute. Friction, hydrostatic and acceleration losses are approximately 59,441.53 Pa, 1,184,706.49 Pa and 32.47 Pa: their sum recovers the total 1,244,180.49 Pa drop within numerical tolerance. These are reproducible synthetic checks, not field-calibrated performance data.

Synthetic examples for reproducibility, not measured field results.

Assumptions and limitations

This is explicitly a homogeneous no-slip isothermal screening model, not Beggs-Brill, Hagedorn-Brown, drift-flux, a mechanistic flow-regime solver or three-phase PVT. It does not model slugging, slip, actual liquid holdup, gas liberation/dissolution, phase change, heat transfer, compositional properties or flow assurance.
One constant-ID interval, 0 to 90 degrees uphill from horizontal, constant phase masses, liquid density, Z, temperature and Darcy factor. Downhill flow, fittings and changes of direction/area are not supported. The zero-friction and single-phase options exist for limiting checks, not as recommended operating assumptions.
All evaluated pressures must remain at least 0.1 MPa absolute, and the acceleration parameter must remain below 0.2, well away from the model's singular limit at one. These are conservative software bounds, not physical safety limits or a choking prediction. A successful numerical solve is not validation of no-slip behavior in a real petroleum system.

Implemented equations

No-slip mixture and gas closure

\begin{aligned}x&=\frac{\dot m_g}{\dot m_g+\dot m_l}\\G&=\frac{\dot m_g+\dot m_l}{A}\\c_g&=\frac{ZRT}{M}\\\rho_g&=p/c_g\\v&=\frac{1-x}{\rho_l}+\frac{xc_g}{p}\\\rho_m&=1/v,\quad u=Gv\end{aligned}

Steady pressure ODE with acceleration

\begin{aligned}a_p&=\frac{G^2xc_g}{p^2}\\F&=\frac{f_DG^2}{2D\rho_m}\\H&=\rho_mg\sin\theta\\-\frac{dp}{ds}&=\frac{F+H}{1-a_p}\\\Delta p_{acc}&=G^2xc_g\left(\frac1{p_{out}}-\frac1{p_{in}}\right)\end{aligned}

Sources and maintenance

Published by PetroCalcHub Team. Implementation and source checks: 2026-10-14. This does not claim independent expert review.

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