Engineering lesson
Holdup versus flowing gas fraction
Flowing gas fraction is based on phase volumetric rates. Gas holdup is the fraction of local pipe volume occupied by gas. They coincide only under a compatible no-slip assumption.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Give the fractions their own denominators
The no-slip flowing fraction is jg/(jg + jl), where superficial velocities use the full pipe area. In-situ gas velocity is jg/αg when gas holdup αg is known.
A drift closure can give αg = jg/[C0(jg + jl) + vd]. The distribution parameter and drift velocity introduce a model for phase motion.
Keep the local property state
Gas density and local gas volumetric rate depend on pressure and temperature. A standard-rate fraction cannot be substituted directly into a local holdup relation.
The explorer uses the supported vertical drift-flux profile and varies its explicit drift-velocity assumption. It is not a universal flow-regime calibration.
Understand the pressure consequence
Holdup changes in-situ mixture density and therefore hydrostatic pressure. A no-slip and a slip model can predict different pressure profiles even at the same phase mass rates.
Check the closure's domain, pressure margin and numerical warnings before interpreting a computed endpoint.
Explore the example
Original recorded synthetic cases solved with the site's vertical-drift-flux-pressure-profile engine. The full inputs, outputs and diagnostic rows are in the downloadable JSON. These are discrete solved states; the lesson does not interpolate a new solve.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Calibrated upward drift velocity (m/s) = 0.3. Outlet liquid holdup (dimensionless): 0.851738475; Drift-flux outlet absolute pressure (MPa): 3.52561111; No-slip comparison outlet pressure (MPa): 3.62785081.
- Outlet liquid holdup (dimensionless)
Worked example
Vertical Drift-Flux Gas-Liquid Pressure Profile Calculator
Fixed controls: Inlet absolute pressure = 5 MPa; Constant absolute temperature = 320 K; Pipe inside diameter = 0.1 m; Vertical upward interval length = 200 m; Gas mass flow rate = 0.05 kg/s; Liquid mass flow rate = 5 kg/s; Constant liquid density = 850 kg/m3; Gas molecular mass = 20 kg/kmol; Constant gas Z-factor = 0.9 dimensionless; Calibrated constant Darcy factor = 0.02 dimensionless; Calibrated distribution parameter = 1.2 dimensionless.
Relation and unit basis
jk = mass_rate_k/(A*rho_k); ug = C0*(jg+jl)+vd; alpha = jg/ug; ul = jl/(1-alpha); rhoh = alpha*rhog+(1-alpha)*rhol; rhog = p*M/(Z*8314.46261815324*T).; Pi = alpha*rhog*ug^2+(1-alpha)*rhol*ul^2; G = total_mass_rate/A; F = fD*G^2/(2*D*rhoh); -dp/ds = (F+rhoh*g)/(1+dPi/dp); acceleration loss = Pi_out-Pi_in. Darcy factor fD = 4*Fanning factor.
Calibrated upward drift velocity is varied within the supported input range. Steady, vertical upward, co-current, isothermal gas/liquid screening only. No downward, counter-current, horizontal or inclined slip model; no regime selection, empirical Shi/Hagedorn-Brown/Beggs-Brill implementation, phase flash, dissolution, heat transfer, slug transients or reservoir coupling. This is a reduced model, not the full T2Well simulator.
1. Define the baseline
Calibrated upward drift velocity (m/s) = 0.3
Fixed controls: Inlet absolute pressure = 5 MPa; Constant absolute temperature = 320 K; Pipe inside diameter = 0.1 m; Vertical upward interval length = 200 m; Gas mass flow rate = 0.05 kg/s; Liquid mass flow rate = 5 kg/s; Constant liquid density = 850 kg/m3; Gas molecular mass = 20 kg/kmol; Constant gas Z-factor = 0.9 dimensionless; Calibrated constant Darcy factor = 0.02 dimensionless; Calibrated distribution parameter = 1.2 dimensionless.
2. Select the relation
jk = mass_rate_k/(A*rho_k); ug = C0*(jg+jl)+vd; alpha = jg/ug; ul = jl/(1-alpha); rhoh = alpha*rhog+(1-alpha)*rhol; rhog = p*M/(Z*8314.46261815324*T).; Pi = alpha*rhog*ug^2+(1-alpha)*rhol*ul^2; G = total_mass_rate/A; F = fD*G^2/(2*D*rhoh); -dp/ds = (F+rhoh*g)/(1+dPi/dp); acceleration loss = Pi_out-Pi_in. Darcy factor fD = 4*Fanning factor.
Calibrated upward drift velocity is varied within the supported input range. Steady, vertical upward, co-current, isothermal gas/liquid screening only. No downward, counter-current, horizontal or inclined slip model; no regime selection, empirical Shi/Hagedorn-Brown/Beggs-Brill implementation, phase flash, dissolution, heat transfer, slug transients or reservoir coupling. This is a reduced model, not the full T2Well simulator.
3. Substitute the values
v_d = 0.3 m/s; with the fixed controls above, the workflow evaluates Outlet liquid holdup = 0.851738475 dimensionless; Drift-flux outlet absolute pressure = 3.52561111 MPa; No-slip comparison outlet pressure = 3.62785081 MPa
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Outlet liquid holdup (dimensionless) = 0.851738475; Drift-flux outlet absolute pressure (MPa) = 3.52561111; No-slip comparison outlet pressure (MPa) = 3.62785081
C0, drift velocity, Z, Darcy factor and liquid density remain constant over the interval. The wall-friction closure is one specified mixture approximation, not a universal multiphase friction correlation. A Darcy factor must not be entered as a Fanning factor. Field use requires independent calibration and validation; numerical balance alone is not accuracy evidence. Software envelopes: 1 <= C0 <= 1.5, 0 <= drift velocity <= 3 m/s, positive rates for both phases, gas less dense than liquid, pressure >= 0.1 MPa absolute and 0 < gas void fraction <= 0.95 throughout. Both profiles must have acceleration parameter below 0.2; choking and near-critical solutions are rejected, not extrapolated. These are implementation limits, not universal correlation ranges.
Result and interpretation
Outlet liquid holdup (dimensionless) = 0.851738475; Drift-flux outlet absolute pressure (MPa) = 3.52561111; No-slip comparison outlet pressure (MPa) = 3.62785081
C0, drift velocity, Z, Darcy factor and liquid density remain constant over the interval. The wall-friction closure is one specified mixture approximation, not a universal multiphase friction correlation. A Darcy factor must not be entered as a Fanning factor. Field use requires independent calibration and validation; numerical balance alone is not accuracy evidence. Software envelopes: 1 <= C0 <= 1.5, 0 <= drift velocity <= 3 m/s, positive rates for both phases, gas less dense than liquid, pressure >= 0.1 MPa absolute and 0 < gas void fraction <= 0.95 throughout. Both profiles must have acceleration parameter below 0.2; choking and near-critical solutions are rejected, not extrapolated. These are implementation limits, not universal correlation ranges.
Drift velocity changes while inlet state, phase mass rates and the other closure inputs stay fixed.
Exact scenario data
Original recorded synthetic cases solved with the site's vertical-drift-flux-pressure-profile engine. The full inputs, outputs and diagnostic rows are in the downloadable JSON. These are discrete solved states; the lesson does not interpolate a new solve.
| Calibrated upward drift velocity (m/s) | Outlet liquid holdup (dimensionless) | Drift-flux outlet absolute pressure (MPa) | No-slip comparison outlet pressure (MPa) |
|---|---|---|---|
| 0 | 0.8154814 | 3.578461 | 3.627851 |
| 0.1 | 0.8294152 | 3.558006 | 3.627851 |
| 0.3 | 0.8517385 | 3.525611 | 3.627851 |
| 0.5 | 0.8688517 | 3.501099 | 3.627851 |
| 0.7 | 0.8823992 | 3.481898 | 3.627851 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Test your understanding
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. If gas moves faster than the mixture-average velocity, can its holdup be below its no-slip flowing fraction?
Show the worked answer
Yes. The same gas rate can pass through a smaller occupied fraction when its in-situ velocity is larger.
2. Reproduce the baseline Outlet liquid holdup (dimensionless) without rounding intermediate values.
Show the worked answer
v_d = 0.3 m/s; with the fixed controls above, the workflow evaluates Outlet liquid holdup = 0.851738475 dimensionless; Drift-flux outlet absolute pressure = 3.52561111 MPa; No-slip comparison outlet pressure = 3.62785081 MPa. Outlet liquid holdup (dimensionless) = 0.851738475. C0, drift velocity, Z, Darcy factor and liquid density remain constant over the interval. The wall-friction closure is one specified mixture approximation, not a universal multiphase friction correlation. A Darcy factor must not be entered as a Fanning factor. Field use requires independent calibration and validation; numerical balance alone is not accuracy evidence. Software envelopes: 1 <= C0 <= 1.5, 0 <= drift velocity <= 3 m/s, positive rates for both phases, gas less dense than liquid, pressure >= 0.1 MPa absolute and 0 < gas void fraction <= 0.95 throughout. Both profiles must have acceleration parameter below 0.2; choking and near-critical solutions are rejected, not extrapolated. These are implementation limits, not universal correlation ranges.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Calibrated upward drift velocity (m/s) changes from 0 to 0.7. Other controls remain as stated in the premise. Outlet liquid holdup (dimensionless) changes from 0.815481425 to 0.88239921.
4. What would be needed to apply this example to a different physical system?
Show the worked answer
Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. Calibrated upward drift velocity is varied within the supported input range. Steady, vertical upward, co-current, isothermal gas/liquid screening only. No downward, counter-current, horizontal or inclined slip model; no regime selection, empirical Shi/Hagedorn-Brown/Beggs-Brill implementation, phase flash, dissolution, heat transfer, slug transients or reservoir coupling. This is a reduced model, not the full T2Well simulator. C0, drift velocity, Z, Darcy factor and liquid density remain constant over the interval. The wall-friction closure is one specified mixture approximation, not a universal multiphase friction correlation. A Darcy factor must not be entered as a Fanning factor. Field use requires independent calibration and validation; numerical balance alone is not accuracy evidence. Software envelopes: 1 <= C0 <= 1.5, 0 <= drift velocity <= 3 m/s, positive rates for both phases, gas less dense than liquid, pressure >= 0.1 MPa absolute and 0 < gas void fraction <= 0.95 throughout. Both profiles must have acceleration parameter below 0.2; choking and near-critical solutions are rejected, not extrapolated. These are implementation limits, not universal correlation ranges.
Before using the result
- Use local phase rates.
- Distinguish superficial and in-situ velocity.
- Record C0 and drift velocity.
C0, drift velocity, Z, Darcy factor and liquid density remain constant over the interval. The wall-friction closure is one specified mixture approximation, not a universal multiphase friction correlation. A Darcy factor must not be entered as a Fanning factor. Field use requires independent calibration and validation; numerical balance alone is not accuracy evidence. Software envelopes: 1 <= C0 <= 1.5, 0 <= drift velocity <= 3 m/s, positive rates for both phases, gas less dense than liquid, pressure >= 0.1 MPa absolute and 0 < gas void fraction <= 0.95 throughout. Both profiles must have acceleration parameter below 0.2; choking and near-critical solutions are rejected, not extrapolated. These are implementation limits, not universal correlation ranges.
Continue learning
Start with the broader workflow guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.