Practice and answer pack
Multiphase and thermal model selection worksheet
Select a multiphase or thermal workflow by the physical question, required state variables and supported closure. A more complex solver is useful only when its assumptions match the problem.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Write the requested output first
Pressure loss, holdup, equilibrium onset, transient wave pressure and thermal restart state require different equations and inputs.
The worksheet asks readers to identify the minimum information for each task before choosing a tool. A single pressure and temperature pair cannot determine every flow-assurance outcome.
Distinguish steady, transient and equilibrium models
A steady profile does not predict a valve-closure wave. An equilibrium solid onset does not predict deposition kinetics. A thermal-history state does not automatically supply a fluid phase model.
The baseline homogeneous pressure case provides one concrete worked path; the additional questions test when a different workflow is necessary.
Plan the verification evidence
Check units and conservation, inspect numerical diagnostics, compare limiting cases and then seek physical validation appropriate to the intended use.
Print the model-selection worksheet or reveal answers individually. The examples connect calculator capabilities to their actual scope rather than assuming one tool solves the entire system.
Explore the example
Original recorded synthetic cases solved with the site's homogeneous-multiphase-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.
Uphill angle from horizontal (deg) = 10. Total pressure drop (MPa): 0.253516638; Integrated friction loss (MPa): 0.01164336; Integrated hydrostatic loss (MPa): 0.241868043; Acceleration pressure loss (MPa): 0.00000523531475.
- Total pressure drop (MPa)
- Integrated friction loss (MPa)
- Integrated hydrostatic loss (MPa)
- Acceleration pressure loss (MPa)
Worked example
Homogeneous Gas-Liquid Pressure Profile Calculator
Fixed controls: Inlet absolute pressure = 5 MPa; Constant absolute temperature = 320 K; Pipe inside diameter = 0.1 m; Length along flow = 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; User-supplied constant Darcy factor = 0.02 dimensionless.
Relation and unit basis
x = mg/(mg+ml); G = (mg+ml)/area; cg = Z*R*T/M; rho_g = p/cg; v = (1-x)/rho_l + x*cg/p; rho_m = 1/v; u = G*v. R = 8314.46261815324 J/(kmol.K); p in Pa.; ap = G^2*x*cg/p^2; F = fD*G^2/(2*D*rho_m); H = rho_m*g*sin(theta); -dp/ds = (F+H)/(1-ap); acceleration loss = G^2*x*cg*(1/pout-1/pin). g = 9.80665 m/s2.
Uphill angle from horizontal is varied within the supported input range. 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.
1. Define the baseline
Uphill angle from horizontal (deg) = 10
Fixed controls: Inlet absolute pressure = 5 MPa; Constant absolute temperature = 320 K; Pipe inside diameter = 0.1 m; Length along flow = 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; User-supplied constant Darcy factor = 0.02 dimensionless.
2. Select the relation
x = mg/(mg+ml); G = (mg+ml)/area; cg = Z*R*T/M; rho_g = p/cg; v = (1-x)/rho_l + x*cg/p; rho_m = 1/v; u = G*v. R = 8314.46261815324 J/(kmol.K); p in Pa.; ap = G^2*x*cg/p^2; F = fD*G^2/(2*D*rho_m); H = rho_m*g*sin(theta); -dp/ds = (F+H)/(1-ap); acceleration loss = G^2*x*cg*(1/pout-1/pin). g = 9.80665 m/s2.
Uphill angle from horizontal is varied within the supported input range. 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.
3. Substitute the values
theta = 10 deg; with the fixed controls above, the workflow evaluates Total pressure drop = 0.253516638 MPa; Integrated friction loss = 0.01164336 MPa; Integrated hydrostatic loss = 0.241868043 MPa; Acceleration pressure loss = 0.00000523531475 MPa
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Total pressure drop (MPa) = 0.253516638; Integrated friction loss (MPa) = 0.01164336; Integrated hydrostatic loss (MPa) = 0.241868043; Acceleration pressure loss (MPa) = 0.00000523531475
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.
Result and interpretation
Total pressure drop (MPa) = 0.253516638; Integrated friction loss (MPa) = 0.01164336; Integrated hydrostatic loss (MPa) = 0.241868043; Acceleration pressure loss (MPa) = 0.00000523531475
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.
Use the baseline pressure example to identify its assumptions, then choose methods for the separate transient and phase questions.
Exact scenario data
Original recorded synthetic cases solved with the site's homogeneous-multiphase-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.
| Uphill angle from horizontal (deg) | Total pressure drop (MPa) | Integrated friction loss (MPa) | Integrated hydrostatic loss (MPa) | Acceleration pressure loss (MPa) |
|---|---|---|---|---|
| 0 | 0.01159435 | 0.01159412 | 0 | 2.2782e-7 |
| 5 | 0.1332767 | 0.01161846 | 0.1216555 | 2.6843e-6 |
| 10 | 0.2535166 | 0.01164336 | 0.241868 | 5.2353e-6 |
| 20 | 0.4860348 | 0.01169409 | 0.4743301 | 1.0554e-5 |
| 30 | 0.702225 | 0.01174463 | 0.6904644 | 1.6016e-5 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Practice problems and answer key
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. Which tool type is needed for a rapid valve-closure pressure history?
Show the worked answer
A transient water-hammer model with wave speed and boundary conditions, rather than a steady pressure-loss calculator.
2. Reproduce the baseline Total pressure drop (MPa) without rounding intermediate values.
Show the worked answer
theta = 10 deg; with the fixed controls above, the workflow evaluates Total pressure drop = 0.253516638 MPa; Integrated friction loss = 0.01164336 MPa; Integrated hydrostatic loss = 0.241868043 MPa; Acceleration pressure loss = 0.00000523531475 MPa. Total pressure drop (MPa) = 0.253516638. 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.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Uphill angle from horizontal (deg) changes from 0 to 30. Other controls remain as stated in the premise. Total pressure drop (MPa) changes from 0.0115943477 to 0.702225022.
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. Uphill angle from horizontal is varied within the supported input range. 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.
5. Calculate ideal Joukowsky pressure increment for ρ = 1,000 kg/m³, a = 1,000 m/s and Δv = 0.5 m/s.
Show the worked answer
ρaΔv = 500,000 Pa = 0.5 MPa. A full transient needs closure and boundary histories.
6. Does equilibrium wax appearance predict deposit thickness after a day?
Show the worked answer
No. Deposition also needs transport, wall conditions, kinetics and removal assumptions.
Before using the result
- State the requested output.
- Choose the appropriate time and phase scope.
- Inspect numerical and physical evidence separately.
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.
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.