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.
μ_{L}/ μ_{G} | 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.
ρ_{ave} = (Q_{G} + Q_{L})/(Q_{G} /ρ_{G} + Q_{L} /ρ_{L})
V_{ave} = (Q_{G} + Q_{L})/(ρ_{ave}(πD²/4))
μ_{ave} = (Q_{G} + Q_{L})/(Q_{G} /μ_{G} + Q_{L} /μ_{L})
Re_{ave} = 4(Q_{G} + Q_{L})/(πDμ_{ave})
where, Q_{G}, Q_{L} are gas and liquid mass flowrate. ρ_{G} and ρ_{L} are gas and liquid density. μ_{G} and μ_{L} 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 = Q_{G} + Q_{L}
(ΔP/L)_{Go} = function(G, D, μ_{G}, ρ_{G}, ε)
(ΔP/L)_{Lo} = function(G, D, μ_{L}, ρ_{L}, 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^{ 2}G^{ 0.5}, 28 < Y
Two phase correction factor is calculated as following:
φ²_{Lo} = 1+(Y²-1)[BX^{(2-n)/2}(1-X)^{(2-n)/2}+X^{2-n}]
where n is 0.25 and X is gas mass fraction. Two phase pressure drop is calculated as following:
(ΔP/L)_{TP} = φ²_{Lo} (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(Q_{G}, D, μ_{G}, ρ_{G}, ε)
(ΔP/L)_{L} = function(Q_{L}, D, μ_{L}, ρ_{L}, 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} = φ²_{L} (ΔP/L)_{L}
(ΔP/L)_{G1} = φ²_{G} (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 / ( g_{c}Dρ²_{ave} )
We = G²D / ( ρ_{ave} 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.
f_{Go} = function(G, D, μ_{G}, ρ_{G}, ε)
f_{Lo} = function(G, D, μ_{L}, ρ_{L}, ε)
Following constants are calculated -
E = (1 - X)² + X² ρ_{L}f_{Go} / (ρ_{G}f_{Lo})
H = (ρ_{L}/ρ_{G})^{0.91}(μ_{G}/μ_{L})^{0.19}(1-μ_{G}/μ_{L})^{0.7}
F = X ^{0.78} (1 -X) ^{0.24}
where, X is gas mass fraction. Two phase correction factor is calculated as following -
φ²_{Lo} = E + 3.24 FH / (Fr ^{0.045} We ^{0.035})
Two phase pressure drop is calculated as following -
(ΔP/L)_{TP} = φ²_{Lo} (ΔP/L)_{Lo}
Resources
- Web based calculation available at checalc.com
- Spreadsheet for Pipe Fitting Losses
References
- Pressure Drop, Two Phase Flow at Thermopedia.com
- Horizontal 2-Phase Flow Correlations at Cheresources.com
- Chemical Process Equipment : Selection and Design, Stanley M. Walas, 2^{nd} Edition