Two-Phase Flow Calculator
This two-phase flow calculator estimates the pressure drop, flow regime, and void fraction for simultaneous gas-liquid flow in a pipe. It computes the single-phase pressure gradients of each phase, forms the Lockhart-Martinelli parameter and two-phase multiplier, and reports a second pressure-drop estimate from the Friedel correlation. The Baker flow map classifies the regime (such as annular, slug, or stratified) and the void fraction gives the gas-filled area fraction.
Formula
Xtt = √(dpL/dpG) ; φ²_L = 1 + C/Xtt + 1/Xtt² (C = 20) ; α = 1/(1 + 0.28·Xtt^0.71)
- Xtt
- Lockhart-Martinelli parameter, the square root of the ratio of single-phase liquid to gas pressure gradients
- φ²_L
- Two-phase multiplier applied to the liquid-alone pressure gradient (C = 20 for turbulent-turbulent flow)
- dpL, dpG
- Single-phase pressure gradients of the liquid and gas flowing alone (psi/ft)
- α
- Void fraction, the fraction of the pipe cross-section occupied by gas
- x
- Mass quality = gas mass flow / total mass flow
How it works
- Enter the pipe inside diameter (in) and length (ft), and the liquid and gas mass flow rates (lb/hr).
- Enter the fluid properties: liquid and gas densities (lb/ft³), viscosities (cP), and the surface tension (dyne/cm).
- The calculator evaluates each phase as if it flowed alone, builds the Lockhart-Martinelli parameter Xtt and multiplier φ²_L, reports both the Lockhart-Martinelli and Friedel pressure drops, classifies the flow regime on the Baker map, and computes the void fraction and phase velocities.
Worked example
4-inch pipe, 100 ft long, with 50,000 lb/hr liquid (62.4 lb/ft³, 1.0 cP) and 5,000 lb/hr gas (0.5 lb/ft³, 0.012 cP), surface tension 72 dyne/cm.
- Mass quality x = 5,000 / 55,000 = 0.0909.
- Single-phase gradients give Xtt = √(dpL/dpG) ≈ 1.167.
- Two-phase multiplier φ²_L = 1 + 20/1.167 + 1/1.167² = 18.88, so dp(L-M) = dpL × 18.88 × 100 ≈ 1.171 psi.
- Void fraction α = 1 / (1 + 0.28 × 1.167^0.71) = 0.762; Baker map gives an annular-mist regime.
Xtt ≈ 1.167, φ²_L ≈ 18.88, Lockhart-Martinelli pressure drop ≈ 1.171 psi (Friedel ≈ 0.527 psi), regime annular-mist, void fraction ≈ 0.762.
Frequently asked questions
- What does the Lockhart-Martinelli parameter tell me?
- Xtt compares how much pressure drop the liquid would cause flowing alone to how much the gas would cause flowing alone. A small Xtt means gas-dominated flow and a large Xtt means liquid-dominated flow, and it sets the two-phase multiplier used to scale the pressure drop.
- Why do the Lockhart-Martinelli and Friedel pressure drops differ?
- They are two different empirical correlations. Lockhart-Martinelli is a simple, often conservative separated-flow model, while Friedel is a more detailed correlation that includes Froude and Weber number effects. Comparing both gives a sense of the uncertainty in a two-phase pressure-drop estimate.
- What is the flow regime and why does it matter?
- The flow regime describes how the gas and liquid arrange themselves (for example annular, slug, stratified, or bubble flow). The Baker map predicts the regime from the mass fluxes and fluid properties, and the regime affects pressure drop, heat transfer, and the risk of slugging in the line.
- What is void fraction?
- Void fraction α is the fraction of the pipe cross-sectional area occupied by the gas phase. It is always less than the volumetric gas fraction because the gas typically moves faster than the liquid, and it is needed to compute the actual phase velocities and the two-phase density.