# Two-fluid flow Gas Liquid ```Multiphase flow
Gas-liquid
General - multiphase flow

Multiphase flow includes all combinations which have at
least two phases: solid, liquid or gaseous.

Multiphase flow is common in many industries, and mostly
in the petrochemical industry.

Particularly important are the pipelines that transport gas
and oil from oil rigs.
Example
Nam Con Son pipeline in Vietnam.
Transports gas and condensate from the Lan Tay gas
production platform in Block 6.1, 370 km offshore south
eastern Vietnam, to an onshore gas processing terminal
and a 28 km-long onshore pipeline to customers.


Benefits of two-phase flow:



3
no extraction on the platform,
except water separation;
easier and cheaper,
only one pipeline.
General

Multiphase flow combinations:




Gas-Liquid
Solid-Liquid
Solid-Gas
Liquid-Liquid
Two-phase flow (Gas-Liquid)
G-L
5
Two-phase flow G-L

The presence of the gas phase during the flow of the
liquid alters the properties of the original single-phase
liquid flow.

This is a result of interaction of the two phases, and
various physical properties of each phase.

The gaseous phase generally flows faster than liquid, so
there would be a different ratio of phases through the
cross-section of the pipe over time.
6
Two-phase flow G-L

Both phases can flow in turbulent or laminar regime.

Turbulent two-phase flow begins at the lower value of the
Reynolds number than single-phase flow (Re = 2320).

In the two-phase flow it is considered that the flow is
turulent if Re &gt; 1000.

WHY?
The second phase is always disturbing steady linear
motion of the liquid.

7
Horizontal flow patterns
Different velocity ratio of the gaseous and liquid phase
forms various types of two-phase flow.
Horizontal flow


gas
liquid
Plug flow
Bubble flow
Stratified flow
Wavy flow
8
Slug flow
Annular flow
Mist flow
Horizontal flow patterns
Bubble flow



Low flow rate of gas.
Bubbles of gas appear in the upper part of the pipe.
Stratified flow




Low velocity of the liquid and gas.
The fluid of higher density is always at the bottom of the pipe.
Fluids are separated into layers, and the interfacial area is flat.
Wavy flow



9
Fluids are separated into layers.
Due to an increase in gas velocity it makes waves on the liquid
surface.
Horizontal flow patterns

Plug flow



It occurs after the bubble flow when the velocity of the liquid
is reduced, and the gas flow rate is increased.
Gas bubbles merge into larger and form the so-called plugs
that flow in the upper part of the pipe .
Slug flow


10
Gaseous phase flows much faster than liquid which causes the
waves that rise to the upper wall of the pipe.
Very unstable flow which can cause damage to the pipeline .
Horizontal flow patterns

Annular flow



Kapljevina struji uz stijenku cijevi stvarajući prsten, a plin i
raspršena kapljevina u središnjem dijelu cijevi.
It occurs by increasing the flow velocity of the gas phase.
Liquid flows along the wall of the pipe, creating a ring, and gas
with a dispersed liquid flows in the central part of the pipe.
Mist flow



11
The highest content and velocity of the gas phase.
Due to the high gas velocity liquid is dispersed into tiny
droplets.
Vertical flow patterns

Vertical flow
gas flow rate increases
gas
liquid
Bubble flow Plug flow Churn flow
12
Wispyannular
flow
Annular
flow
Flow patterns



The energy and momentum transfer between gas and
liquid phase depends on the geometry of the system,
interfacial area and two-phase flow regime/pattern.
For example, the pressure drop or the amount of heat
transferred will vary for bubbly flow (gas dispersed in a
liquid) and the annular flow (liquid along the wall, the gas
in the middle).
This leads to different models that describe mass transfer,
as well as momentum and energy transfer. The most
important task at the two-phase flow is precisely predict
flow regime as well as the characteristics of the fluid that
may lead to transitional areas .
13
Flow pattern/regime maps

Method of displaying results of the visual determination of
the flow patterns.

Charts with fluid velocities of flux of both phases on axes.

When all values are recorded, lines representing the
boundaries between different forms of flow are drawn
into the chart.
14
Flow pattern/regime maps
aL – cross sectional
area of the pipe
occupied by liquid
vL – liquid velocity
VL
a L  vL  vs 
A
surface velocity
of the liquid
15
Flow pattern/regime maps

Baker diagram – flow in horizontal pipe
1
 2
 G   L


 





W 
 A
  

 W
L

 L
 W
1
2 3

 
 W  
 L  

ṁG,A, ṁL,A– flux, gas and liquid, kg m-2 s-1
 – density, kg m-3
 – surface tension, N m-1
 – viscosity, Pa s
G – gas
A – air at 20 &deg;C and 101 325 Pa
L – liquid
W – water at 20 &deg;C
16
Flow pattern/regime maps

Hewitt-Roberts diagram – flow in vertical pipe
17
Pressure drop models



Homogeneous Gas-Liquid Models
Separated Flow Models
Fenomenological Models
18
Homogeneous Gas-Liquid Models




The simplest method for calculating the pressure drop is
to find mean values of fluid properties (density, viscosity,
etc.) and then calculating the pressure drop as it is a
single-phase systems.
Assumption: both phases have the same velocities.
The biggest problem is the calculation of the viscosity of
the two-phase system.
19
Homogeneous Gas-Liquid Models

Properties of two-phase system:
1
TP

x
G

1 x
L
VTP  x  VG  (1  x )  VL
1
TP


x
G

1 x
x – mass content of gas
(1-x) – mass content of liquid
 – viscosity, Pa s
TP – two-phase system
G – gas
L – liquid
L
Mean values of two-phase system are introduced into
Darcy-Weissbach equation:
2
v
 TS

p
1
 
     
l TS
d
2
20
Separated Flow Models

Assumptions:




Each phase occupies a certain cross sectional area of the pipe.
There may be differences in the phase velocities.
There are numerous models proposed in the literature,
but the simplest is considered the &quot;classical&quot; LockhartMartinelli method (1949)
According to this method, the total pressure drop is
obtained by the pressure drop in one phase multiplied by
Lockhart-Martinelli multiplier, .
 p 
2  p 
   L   
l TP
l L
21
 p 
2  p 
   G   
l TP
l G
Separated Flow Models

Lockhart-Martinelli multiplier  depends on Martinelli
parameter X.

Martinelli parameter is calculated from the pressure drop
of each phase:
  p  
  l  
L
X
  p  
  l  
G

22
0,5
 mL, A   L G 
X 
  

 mG, A   G L 
0,5
Separated Flow Models

Lockhart-Martinelli multiplier  is calculated according to:
C 1
 1  2
X X
2
L
G2  1  C  X  X 2
23
Kapljevina
Plin
Oznaka
C
Turbulent
Turbulent
tt
20
Laminar
Turbulent
vt
12
Turbulent
Laminar
tv
10
Laminar
Laminar
vv
5
Separated Flow Models

Lockhart-Martinelli multiplier 
24
Review of methods
– Homogeneous
Gas-Liquid Model
1

x

1 x
1
L
TP

Find viscosity and density for TP.

Reynolds number and friction factor (64/Re or Moody diagram)
Re 

G
x
G

1 x
L
mtotal,A  d
TP
muk
v
A  TP
Pressure drop:
1 v 2  TP
 p 
     
l TP
d
2
25
TP

x – mass content of gas
(1-x) – mass content of liquid
 – viscosity, Pa s
ṁtotal,A – total flux, kg m-2 s-1
ṁtotal – total mass flow rate, kg s-1
TP – two-phase system
G – gas
L – liquid
Review of methods
Lockhart-Martinelli

Reynolds number and friction factor of each phase.
ReL 

– Separated Flow Model
mtotal,A  1  x   d
L
ReG 
mtotal,A  x  d
x – mass content of gas
(1-x) – mass content of liquid
 – viscosity, Pa s
ṁtotal,A – total flux, kg m-2 s-1
ṁtotal – total mass flow rate, kg s-1
TP – two-phase system
G – gas
L – liquid
G
Find flow regime for each phase.
Re &lt; 1000 – laminar; Re &gt; 2000 – turbulent
 mL, A   L G 
X 
     
m
 G, A   G L 

Calculate X

Find L ili G (equation, chart)
26
0,5
L2  1 
C 1

X X2
G2  1  C  X  X 2
Review of methods
Lockhart-Martinelli

Calculate pressure drop of a single phase:
1 vL2  L
 p 
   L  
l L
d
2

– Separated Flow Model
2
1 mG,A
 p 
   G  
l G
d 2  G
Calculate pressure drop for two-phase flow
 p 
2  p 
   L   
l TP
l L
27
x – mass content of gas
(1-x) – mass content of liquid
 – viscosity, Pa s
ṁtotal,A – total flux, kg m-2 s-1
ṁtotal – total mass flow rate, kg s-1
TP – two-phase system
G – gas
L – liquid
Moody diagram
Laminar
flow
5x10– 4
Absolute roughness
depends on material and
surface characteristics.
(Tables)
2x10– 4
Complete turbulence
5x10– 5
Smooth Pipe
Reynolds number, Re
28
5x10– 6
relative roughness, e/d
friction factor, 
Transition region
Equations

Mass balance
x – mass content of gas
(1-x) – mass content of liquid
 – viscosity, Pa s
ṁtotal,A – total flux, kg m-2 s-1
ṁtotal – total mass flow rate, kg s-1
TP – two-phase system
G – gas
L – liquid
mtotal  mL  mG
mL  1  x   muk
mG  x  muk

Velocity
vL 
vG 
29
1  x   mtotal  1  x   mtotal,A
A  L
x  mtotal x  mtotal,A

A  G
G
L
Equations

Reynolds number
ReL 

1  x   mtotal  d  1  x   mtotal,A  4  1  x   mtotal
A  L
Pressure drop
2
1 mL,A
 p 
   L  
l L
d 2  L
30
L
d    L
x – mass content of gas
(1-x) – mass content of liquid
 – viscosity, Pa s
ṁtotal,A – total flux, kg m-2 s-1
ṁtotal – total mass flow rate, kg s-1
TP – two-phase system
G – gas
L – liquid
```