## Two Phase Flow - Horizontal Pipe

Sun, 30 Aug 2015

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

Pressure drop for each of the phases are calculated assuming that the total mixture flows as either liquid or gas based on procedure provided for single phase flow.

````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

Pressure drop for each of the phases are calculated explicitly assuming that either liquid or gas is flowing through the pipe based on procedure provided for single phase flow.

````(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 )````

where gc is gravitational constant. Friction factor for each of the phases are calculated assuming that the total mixture flows as either liquid or gas based on procedure provided for single phase flow.

````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)0.7`
`F = 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``

### References

1. Pressure Drop, Two Phase Flow at Thermopedia.com
2. Horizontal 2-Phase Flow Correlations at Cheresources.com
3. Chemical Process Equipment : Selection and Design, Stanley M. Walas, 2nd Edition

Beggs & Brill Method Pipe Fitting Losses