This presentation file was created to provide a quick refresher on the fundamentals of gas-liquid horizontal pipe sizing.

1. Two-phase fluid flow
GUIDELINE TO PIPE SIZING FOR TWO-PHASE FLOW (LIQUID-
GAS)
AUTHOR: VIKRAM SHARMA
DATE: 2nd MARCH 2017

2. Table of Contents
 What is two-phase flow?
 Types of Gas-Liquid flow
 Baker’s map for gas-liquid flow
 Calculation methodology
 References

3. What is two-phase flow?
 Single-phase flow → fluid flow in a single state
 Multiphase flow → simultaneous flow of several
fluid phases
 Common multiphase flow are (i) gas-liquid, (ii)
liquid-liquid or (iii) liquid-solid.
 Why is it so important? Severity of pressure drop
problems that may result to operational problems in
a process

4. Types of Gas-Liquid flow
Bubble flow:
 Bubbles (gas) are dispersed throughout the liquid
& moves along the upper part of the pipe due to
their buoyancy.
 Velocity of the bubble of gas ≈ velocity of the liquid
 Occurs when the gas content is 0.3 wt. frac. of the
total volumetric flow & at high mass flow rates
 Linear vel. of the liq. = 1.5-4.8 m/s (typical)
 Linear vel. 0f the vap. = 0.15-0.61m/s (typical)

5. Types of Gas-Liquid flow
(cont’d)
Plug flow:
 Intermittent type two-phase flow
 Alternate plugs of liq. & gas where the gas portion
moves along the upper part of the pipe.
 Liq. → along the bottom part of the pipe
 Expected to occur when liq phase is at 0.61 m/s
and vapour phase is < 1.22 m/s

6. Types of Gas-Liquid flow
(cont’d)
Stratified flow:
 2 phases separated frm. by a common interface
 Liq phase stratified at the bottom of the piping due
to gravity
 Seen in horizontal & slightly inclined pipelines
 ↓ gas flow: smooth fluid interface or possible
rippling by small capillary waves of a few mm
lengths
 ↑ gas flow: waves of small amplitude appears,
droplets can be entrained, deposited at the wall or
interface
 Liq. vel < 0.15 m/s, gas vel: 0.15-3.05 m/s (typical)

7. Types of Gas-Liquid flow
(cont’d)
Wave flow
 Similar to stratified flow, gas flow at ↑ velocity
 ↓ gas vel. – gas-liq. Interface is flat
 As gas vel. increases – interface becomes
unstable due to small disturbances & waves are
seen
 Shape & size of waves α pipeline geometry & fluids
flow rates

8. Types of Gas-Liquid flow
(cont’d)
Slug flow
 Liq. rich slugs - may or may not cover the entire
inner section of a pipe
 Observed when the rapidly moving gas created
waves & form froth slugs
 This slugs travel along the pipeline @ vel. Higher
than ave. liq. Vel.
 Vibrations are due to ↑ vel. travelling against
fittings
 Liq. vel ≈ 4.58 m/s
 Gas vel.: 4.58-15.24 m/s

9. Types of Gas-Liquid flow
(cont’d)
Annular flow
 Gas vel. further increases resulting to gas flow
through the liq. Flow
 Liq. Film @ the bottom of the pipe is thicker due to
gravity
 Liq vel. < 0.15 m/s
 Gas vel. > 6.1 m/s

10. Types of Gas-Liquid flow
(cont’d)
Dispersed flow
 Liq. entrained as the fine droplets by the gas phase
in the gas-liq flow
 The dispersed phase in both gas-liq. / liq.-liq. - flow
rates of both phases as the interface is deformable
 The dispersed phase of the dispersed flow
coalesces & become continuous phase with ↑ flow
rate
 Occur when the gas content is > 30% of the total
weight flow rate

11. Baker’s map for two phase
flow
 Liq. entrained as the fine droplets by the gas phase
in the gas-liq flow

12. Calculation procedure
 Obtain physical properties of the fluid (mass
flowrate, density, viscosity and surface tension) for
both gas and liquid.
 Obtain piping layout. Piping is to be divided into
segments as fluid regime and properties varies
along the piping route
 Determine the flow regime for 1st pipe segment
 Perform ΔPfriction, ΔPelev. & Δpfittings
 Repeat the above calculations for other pipe
segments

13. Calculation procedure (cont’d)
 Break the pipe into a couple of segments.
 For Segment 0-1, determine the fluid flow regime
by calculating Bx and By (refer to Slide #11).
 Intersection of Bx and By gives the fluid flow regime
 The next step is to calculate the ΔP of individual
phase (ΔPL, bar/100m & ΔPG,bar/100m)
1 2 3 4 5 6 n
Fluid in Fluid out
𝑚 𝐿, 𝑚 𝐺
𝜌 𝐿, 𝜌 𝐺
𝜇 𝐿, 𝜇 𝐺
𝜎𝐿, 𝜎 𝐺
0

14. Calculation procedure (cont’d)
 The next step is to calculate the ΔP of individual
phase (ΔPL, bar/100m & ΔPG,bar/100m) (cont’d)
 Darcy friction factor (fD) is expressed as:
 fD can calculate for both laminar and turbulent flows

15. Calculation procedure (cont’d)
 Lockhart-Martinelli (LM) parameter, X is the ratio of
liquid and gas pressure drop.
 It is a function of mass fluxes, densities, viscosities
of the liq.. & gas and pipe diameter.
 We have to determine the frictional pressure drop
multipliers for both liq. (φ2
L) and gas (φ2
G).
 The multipliers are a factor of fluid Reynolds number
(turbulent, laminar (viscous)).
 Transitional flow is considered as TURBULENT.

16. Calculation procedure (cont’d)
 Transitional flow is considered as TURBULENT (cont’d)
 φ2
L decreases with increasing X, φ2
G increases with
increasing X
 Extracting data is cumbersome, may lead to
inaccurate date.

17. Calculation procedure (cont’d)
 Extracting data is cumbersome, may lead to
inaccurate date (cont’d).
 Chisholm (1967) incorporated the effect of
interfacial shear forces in the LM correlation.
 New correlation ensures engineers to determine
the hydraulic diameters of the phases more
accurately compared to LM.
 It do not require the use of graph (refer to Slide
#16)
 Chisholm (1967) correlations in terms of Lockhart-
Martinelli (1949):

18. Calculation procedure (cont’d)
 Chisholm (1967) correlations in terms of Lockhart-
Martinelli (1949) (cont’d)
 The frictional pressure drop can be calculated
based on either liquid phase or gas phase.
 The next step is to calculate the ΔPstatic due to
elevation

19. Calculation procedure (cont’d)
 The next step is to calculate the ΔPstatic due to
elevation (cont’d)
 We have to include pressure drop due top fittings.
 We rely on equivalent length method to determine
the pressure drop.
 This method approximates the pressure drop of
fittings based on hypothetical piping length

20. Calculation procedure (cont’d)
 The next step is to calculate the ΔPstatic due to
elevation (cont’d)
 We have to include pressure drop due top fittings.
 We rely on equivalent length method to determine
the pressure drop.
 This method approximates the pressure drop of
fittings based on hypothetical piping length

21. Calculation procedure (cont’d)
 This method approximates the pressure drop of fittings
based on hypothetical piping length (cont’d)
 Consider the effect of erosion-corrosion on piping.
 In certain flow regimes, liq vel approach or exceed gas
vel & this leads to erosion-corrosion
 Determine if erosion-corrosion may occur at a particular
velocity.
 Total pressure drop is:
 P1 of Segment 0-1 is obtained: ΔP0 – ΣPTP..

22. Calculation procedure (cont’d)
 P1 of Segment 0-1 is obtained: ΔP0 – ΣPTP.. (cont’d)
 The properties for Segment 1-2 is based on Point
1. Repeat the above calculations to determine the
total pressure drop of horizontal pipe straight
length.
 Do not segmentized pipe fittings! Choose your
segments appropriately.

23. References
 Akiwi, S. (2010, September 7). Dispersed Flow. Retrieved
February 23, 2017, from THERMOPEDIA: A-to-Z Guide to
Thermodynamics, Heat & Mass Transfer, and Fluids
Engineering: http://www.thermopedia.com/content/5/
 Alain, L., & Fabre, J. (2011, February 9). Stratified Gas-Liquid
Flow. Retrieved February 21, 2017, from THERMOPEDIA: A-
to-Z Guide to Thermodynamics, Heat & Mass Transfer, and
Fluids Engineering: http://www.thermopedia.com/content/266/
 Coker. (2007). Fluid Flow. In Applied Process Design for
Chemicals and Petrochemical Plants (4th ed., Vol. 1, pp. 133-
302). Burlington: Elsevier Inc.
 Hewitt, G. F., & Taylor-Hall, N. S. (2013). Flow regimes in
horizontal and inclined flow. In Annular Two-Phase Flow (p.
7). Oxford: Elsevier.
 McCready, M. J. (n.d.). Flow regimes in gas-liquid flows.
Retrieved February 22, 2017, from
https://www3.nd.edu/~mjm/flow.regimes.html

24. References
 Mekisso, H. M. (2004). Comparison of Frictional Pressure Drop
Correlations for Isothermal Two-Phase Horizontal Flow.
Stillwater: Oklahoma State University.
 Sreenivas, J. (2011, February 11). Wavy Flow. Retrieved
February 21, 2017, from THERMOPEDIA: A-to-Z Guide to
Thermodynamics, Heat & Mass Transfer, and Fluids
Engineering: http://www.thermopedia.com/content/269/
 Szilas, A. P. (1975). Selected topics in flow mechanics. In
Production and Transport of Oil and Gas (p. 54). New York:
Elsevier.
 Thermal-FluidsCentral. (2010, July 9). Frictional pressure drop
correlations based on the separated flow model. Retrieved
March 1, 2017, from
http://www.thermalfluidscentral.org/encyclopedia/index.php/Fricti
onal_pressure_drop_correlations_based_on_the_separated_flo
w_model
 Thome, J. R. (n.d.). 1: Two-Phase Flow Patterns and Flow
Pattern Maps Chapter 12 (in Databook III) [Lecture Notes].
Retrieved February 14, 2017, from Two-Phase Flows and Heat
Transfer:
http://ltcm.epfl.ch/files/content/sites/ltcm/files/shared/import/migr
ation/COURSES/TwoPhaseFlowsAndHeatTransfer/lectures/Cha