Fluid Flow

## Two Phase Flow ‐ Horizontal Pipe

Criterion for Line size selection is generally pressure drop expressed as ΔP per 100 feet or meters of pipe. There are different type of two phase pressure drop correlations determined by viscosity ratio and mass flux.

μL/ μG Mass Flux, (kg/m².sec) Correlation
< 1000 All Friedel
> 1000 > 100 Chisolm - Baroczy
> 1000 < 100 Lockhart - Martinelli

Select a pipe and estimate inner diameter (D) based on pipe schedule. Obtain important properties for both Gas and Liquid like flowrate, density (ρ), viscosity (μ) and surface tension (σ).

Density, velocity and viscosity are averaged for the combined phases in fluid flow and two-phase Reynolds number is calculated.

ρave = (QG + QL)/(QG /ρG + QL /ρL)Vave = (QG + QL)/(ρave(πD²/4))μave = (QG + QL)/(QG /μG + QL /μL)Reave = 4(QG + QL)/(πDμave)

where, QG, QL are gas and liquid mass flowrate. ρG and ρL are gas and liquid density. μG and μL are gas and liquid viscosity.

Chisolm - Baroczy method

G = QG + QL(ΔP/L)Go = function(G, D, μG, ρG, ε)(ΔP/L)Lo = function(G, D, μL, ρL, ε)

A pressure ratio, Y is calculated -

Y² = (ΔP/L)Go / (ΔP/L)Lo

Based on pressure ratio, a constant is calculated:

B = 55 / G 0.5, 0 < Y < 9.5  = 520 / YG 0.5, 9.5 < Y < 28  = 15,000 / Y 2G 0.5, 28 < Y

Two phase correction factor is calculated as following:

φ²Lo = 1+(Y²-1)[BX(2-n)/2(1-X)(2-n)/2+X2-n]

where n is 0.25 and X is gas mass fraction. Two phase pressure drop is calculated as following:

(ΔP/L)TP = φ²Lo (ΔP/L)Lo

Lockhart - Martinelli method

(ΔP/L)G = function(QG, D, μG, ρG, ε)(ΔP/L)L = function(QL, D, μL, ρL, ε)

A pressure ratio is calculated.

X² = (ΔP/L)L / (ΔP/L)G

A separate pressure drop is calculated for each phase.

(ΔP/L)L1 = φ²L (ΔP/L)L(ΔP/L)G1 = φ²G (ΔP/L)G

Estimated two phase pressure drop is maximum of these

(ΔP/L)TP = Max((ΔP/L)L1,(ΔP/L)G1)

Friedel method

Calculate Froude and Weber number using mass flux of the total mass flowing in pipe.

Fr = G² / ( gcDρ²ave )We = G²D / ( ρave σ )
fGo = function(G, D, μG, ρG, ε)fLo = function(G, D, μL, ρL, ε)

Following constants are calculated -

E = (1 - X)² + X² ρLfGo / (ρGfLo)H = (ρL/ρG)0.91(μG/μL)0.19(1-μG/μL)0.7F = X 0.78 (1 -X) 0.24

where, X is gas mass fraction. Two phase correction factor is calculated as following -

φ²Lo = E + 3.24 FH / (Fr 0.045 We 0.035)

Two phase pressure drop is calculated as following -

(ΔP/L)TP = φ²Lo (ΔP/L)Lo

Resources

References

1. Chemical Process Equipment : Selection and Design, Stanley M. Walas, 2nd Edition