two-phase-1

MULTIPHASE FLOW

• More complicated than single phase flow.• Flow pattern is not simply laminar or turbulent.

Types of multiphase flow:Solid-fluid flows (e.g. particulate flows)Liquid-liquid flowsGas-liquid flowsThree-phase flows.

Due to density differences, horizontal flows are different than vertical flows. Cocurrent flows are different than countercurrent flows. Phase changes should be taken into account when present.

Multiphase Flow (gas-liquid) Horizontal Vertical Dispersed

Annular

Stratified

Churn or froth

Wavy

Slug

Plug

Bubble

Multiphase Flow (gas-liquid)

Note: Each phase travels with its own velocity.

Flow regime is a matter of visual interpretation and subjective to the person who takes the measurements. Transition from one regime to another is gradual.

Cocurrent Horizontal flows:Low liquid velocity: Stratified flow, wavy flow, annular flow Intermediate liquid velocity: Plug flow, slug flow, annular flow Large liquid velocity: Bubbly flow, spray or mist flow.

Gas velocity

Importance of flow regime predictions• Better predictions of P and Holdup (volume fraction), if flow regime is known.

• Flow regime prediction is not only important for reliable design, but for pipeline operability.

• Phenomena like pipe corrosion and erosion depend on flow regimes.

• Distribution of corrosion, hydrate and was inhibitors depend on flow regimes.

• Flow regime at pipe outlet affects gas-liquid separation efficiency.

Multiphase Flow (gas-liquid)

Typical Velocities (1in pipe)

Regime Liquid Velocity Vapor Velocity (ft/sec) (ft/Sec)

Dispersed Close to vapor > 200Annular <0.5 > 20Stratified <0.5 0.5-10Slug Less than vapor vel. 3-50Plug 2 < 4Bubble 5-15 0.5-2

Multiphase Flow (gas-liquid)Flow regime mapsGood for approximate prediction of flow characteristics.

WG , WL : gas or liquid mass velocity (lb/h)viscosity in cp, surface tension in dyn/cm, density in lb/ft3, area in ft2.

G

Lx W

WB

Baker plot (1954)

AWB G

y 1

GL 463.0

3/2

3/11147

L

L

Flow regime maps• and depend on the fluid property only.• BX depends on the ratio of flows (Known beforehand. Not a design parameter)• BY depends on the vapor/gas superficial velocity. This is the only parameter the designer can change (through A)• Transition boundaries are not at all that sharp.

Trajectories On The Baker Plot. How regimes change through a pipe.

As the pressure drops, the density of the vapor becomes lower.

1) ~ BX ~ BX decreases2) 1/ ~ BY ~ BY increasesThus trajectories are always "up" and "to the left"

2/1G

2/1G

2/1G

2/1G

Shortcomings of the Taitel - Dukler flow regime models

• Poor prediction of stratified flow for inclined pipes.

• Stratified flow model used for flow regime prediction contradicts pressure drop and liquid holdup data.

•Poor prediction of high pressures and low surface tension fluids.

•Near vertical flow regime better predicted than near horizontal.

• Viscosity effect not properly described.

•Out of 10,000 gas liquid flow pattern observations over the last 30 years, only 67% of all observations were predicted correctly. (Shell Research - Development, 1999)

Flow regime mapsMandhane Plot (Mandhane et al., 1974)Claimed that the Baker correlation overestimates the effect of fluid properties.Claimed that a plot with superficial velocities rather than superficial mass velocities is better.

Suggested a slight correction for fluid properties by using a corrected superficial gas velocity:

GG VyxfV ),('

225.02.0

018.04.72

0013.0GLGx

2.0

25.04.72L

Ly

Flow regime mapsWeisman Plot (Weisman et al., 1979)Found that Mandhane’s suggestion for plotting VL versus VG is a good first order approximation.Presented updated corrections for fluid properties.

This paper provides the most up-tp-date correlations for predicted flow regimes (horizontal pipes).

Note that all the experiments were for pipes 1/2in to 2in.

Weisman, J., Duncan, D., Gibson, J., and T. Crawford, Int. J. Multiphase Flow, 5, pp.437-462, 1979.

We know fairly well what happens in a 1in horizontal pipefor air and water flow.

Pressure Drop - homogeneous modelAssume:1) Zero slip between phases.2) Uniform flow.3) Phase equilibrium.4) Friction factor given by an eqn. similar to that for single phase flow.Define:x=quality, mass fraction that is vapor or gas =fraction of cross-section that is gasMixture density, H=(Mass Flow)/(Volume flow)Then:

LGH

xx

11 LGgGH 1

G

Pressure Drop - homogeneous modelComments:

1) Drops in air, uGuL

In this case: 1/2 f G uG2 (shear stress at the interface)

and =1/2 f H uG2 overpredicts

2) Bubbles in liquids:

In this case: 1/2 f L uL2

Now f (D uL L )/ L and =1/2 f H uL2 underpredicts

It might be better to use f (D uL L )/ 2-p

since H < L and 2-p < 2-p

Limitations of the homogeneous model

1) Assumption of equilibrium between phases often not correct. Only way to deal with this problem is to use a “two - fluid

model”.

2) Use of single phase equations with H and 2-p not very good.

3) There can be appreciable slip between the phases, so the calculation of from x can be incorrect. This can affect calculations of pressure drop due to hydrostatic head. The “separated flow model”, is based on calculations of slip

S=uG / uL . However, it needs more equations to calculate x and

G

G

Pressure Drop - horizontal pipesLockhart-Martinelli (1949) (exps. with 1 in pipe)Approximated 2-phase flow pressure drop from single phase flow results (when the other phase is not present).

Lockhart-Martinelli parameter:

Two phase pressure drop:

or

The factors L2 or G

2 are read from a figure (see fig 6-26 in Perry’s handbook). High predictions for stratified, wavy, slug flows.Low predictions for annular flow.

2/1

//

G

L

LPLPX

GG

p LP

LP

2

2 LL

p LP

LP

2

2

Pressure Drop - horizontal pipesLockhart-Martinelli (1949)

Two phase pressure drop:

where and X is the L-M parameter as before.

a bBubble 14.2 0.75Slug 1190 0.82Stratified 15400 1(horizontal)Plug 27.3 0.86Annular 4.8 -0.3125D 0.343-0.021D

D is the ID. If D > 12in, then use D=12 in

Gp PP 2

2 baX

Pressure Drop - horizontal pipes

Dispersed flow:

Pressure Drop - horizontal pipesWavy flow:

G

L

G

LX W

WH

G

GHWave D

WfP5

2

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