Two-Phase Flow in Vertical Wells
Notes to Accompany
Week 5 Lab—Vertical Two-Phase Flow
Multi-Phase Flow in Wells
(see also PPS Ch. 7, pp 184 onward)
1
Multiphase Flow in Wells
• The simultaneous flow of 2 or
more phases will occur in
 Almost all oil wells
• Whenever the pressure drops
below the bubble point, gas will
evolve, and from that point to the
surface, 2-phase flow will occur
 In many gas wells
• Condensation may occur as a
result of the reduction of
pressure and temperature as
fluids flow up the well
2
Two-Phase Flow Is More Complicated Than
Single-Phase Flow
• The phases tend to separate because of
differences in density
• Shear stresses at the pipe wall are
different for each phase - different density
and viscosity
• Expansion of the highly compressible gas
phase with decreasing pressure increases
the in situ volumetric flow rate of the gas
3
Two-Phase Flow—More Complicated
• For upward flow, the less dense, more
compressible, less viscous gas phase tends
to flow at a higher velocity than the liquid
phase causing a phenomenon known as
slippage
•
•
•
•
4
Consider the 2-phase example to the right where
both α and β are flowing upwards
α is less dense than β and will move faster than β
This phenomenon is called “holdup” – that is, the
denser phase is “held-up” in the pipe relative to the
lighter phase
So, the volume of the denser phase in the pipe is
disproportionately greater than the volumetric flow
rate of the denser phase feeding into the pipe
Two-Phase Flow Regimes
• The flow regime or flow pattern is a qualitative
description of the phase distribution
• For gas-liquid, upward flow, 4 flow regimes are
generally agreed upon in the two-phase literature
 Bubble, Slug, Churn, and Annular
• These occur as a progression with increasing gas
rate for a given liquid rate
• Slug and churn flow are sometimes combined in a flow pattern called
intermittent flow
• Some investigators have named annular flow as mist or annular-mist
flow
5
Flow Regimes in Vertical, Upward Multiphase Flowing
Wells is a Qualitative description of the Phase
Distribution
Gas in the center
and liquid “hugging” or
“climbing” the walls
Increasing
Gas-Liquid Ratio
6
Intermittent Flow
Mist Flow
• The flow regime in gasliquid, vertical flow can be
predicted with a flow
regime map – a plot
relating flow regime to flow
rates of each phase, fluid
properties, and pipe size
• The chart to the right is
from Govier and Azis and
shows these flow patterns
and the approximate
regions in which they occur
as functions of gas and
liquid velocities
7
• A theoretical flow
regime map was
developed by Taitel,
Barnea, and Dukler
in 1980
• This map identifies
5 flow regions,
again based on gas
and liquid velocities
8
Taitel-Dukler Flow Regime
Map (from PPS Fig. 7-11)
Bubble Flow
• Dispersed bubbles of gas in a continuous
liquid phase
9
Slug Flow
• At higher gas rates, the bubbles coalesce
into larger bubbles, called Taylor bubbles,
that eventually fill the entire pipe cross
section
• Between the large gas bubbles are slugs
of liquid that contain smaller bubbles of
gas entrained in the liquid
10
Churn Flow
• With a further increase in gas rate, the
larger gas bubbles become unstable and
collapse, resulting in churn flow,
• Churn flow is a chaotic flow of gas and
liquid in which the shape of both the Taylor
bubbles and the liquid slugs are distorted
• It is a highly turbulent flow pattern
• Churn flow is characterized by oscillatory,
up-and-down motions of the liquid
11
Annular Flow
• At higher rates, gas becomes the
continuous phase, with liquid flowing in an
annulus coating the surface of the pipe
and with liquid droplets entrained in the
gas phase
12
Note Differences in Flow Regimes
in Horizontal Pipes—gravity effects are
important (we will look at horizontal twophase flow in Week 6 Lab)
13
14
Two-Phase Flow Models
• There are many different correlations that
have been developed to calculate gasliquid pressure gradients, most of which
are empirically derived
• Each correlation was likely derived for a
specific set of conditions, so no single
correlation will apply to all real-world cases
• Become familiar with the assumptions
inherent to each correlation and which
correlation is best to use
15
Two-Phase Flow Models
• The table at the right
compares the relative
errors of 8 different 2phase flow
correlations for
different flow
conditions
– VW = vertical wells
– DW = deviated wells
– VNH = vertical well
cases w/o Hagedorn
and Brown data
– Etc.
• In this table, the
smaller the relative
performance factor,
the more accurate is
the correlations
16
The different flow correlation models are in
the left column
Multiple Flow Regimes May Exist in a Well
Multiphase Flow Concepts
• Flow Regimes
• Velocities:
 Superficial
 Slip
 In-situ
• Holdup vs. input volume fraction
Flow Regimes: Vertical Flow
• Four flow regimes:
 Bubble
 Slug
 Churn
 Annular
• Change based on gas and liquid rate
Flow Regime Map:
Vertical Flow
Govier and Aziz
Flow Regime Map: Vertical Flow
Taitel-Dukler Flow
Regime Map (from
PPS)
Flow Regimes in
Horizontal Pipe
Good animation:
http://www.bing.com/videos/search?q=vert
ical+two+phase+flow+video+clip&mid=0C
1617DA4FC12EBA92610C1617DA4FC12
EBA9261&view=detail&FORM=VIRE7
Velocity Concepts
Velocity Differences
Holdup Vs. Input Fraction
Holdup Vs. Input Fraction
Two-Phase Flow Pressure Drop Calculation
Two-Phase Flow Models
• Several different empirical correlations:
 Separated flow models:
• Hagedorn-Brown (1965): only for vertical
wells
• Beggs-Brill (1973): any wellbore inclination
and flow direction
 Homogenous flow models:
• Poettmann-Carpenter (1952)
• Guo-Ghalambor (2005)
Two-Phase Gradient Curves
• Based on given
water/oil ratio (liquid
density) and varying
gas-liquid-ratio
• Includes friction and
potential pressure
drops
• For a fixed size
• Affected by GLR
Example of Tubing Curve Use (PPS
wh = wellhead
bh = bottom hole