Compositional Description of Three-Phase Flow Model in a Gas-Lifted Well with High Water-Cut
Oil & Gas Science and Technology - Rev. IFP Energies nouvelles, Vol.
Compositional Description of Three-Phase Flow Model in a Gas-Lifted Well with High Water-Cut
M. Mahmudi 0
M. Taghi Sadeghi 0
0 Process Simulation and Control Research Lab., Department of Chemical Engineering, University of Science and Technology (IUST) , Narmak 16844, Tehran - Iran
- Compositional Description of Three-Phase Flow Model in a Gas-Lifted Well with High Water-Cut - Gas-lift technique is part of a long-term production sustainability solution in oil fields amid increasing water cuts and depleting reservoir energy. A three-phase compositional model describing the continuous gas-lift process for an operational oilfield experiencing high water-cut is developed. Field data with different water-cut values was considered to compare a three-phase black-oil model against its compositional counterpart. Results show that significant deviation may encounter when compositional method is employed in contrast to the black-oil model as water-cut increases. Due to different properties of the injection gas and produced gas in separators, the compositional treatment would be necessary for modeling the gas-lift process. Moreover, three-phase equilibrium calculations for hydrocarbon-water flow mixtures in the gas-lifted well with moderate and high water-cut are required.
List of symbols
fi Fugacity of component i
K Equilibrium constant
Nc Number of components
P Pressure (bar)
xi Mole fraction of component i in liquid phase
yi Mole fraction of component i in vapor phase
z Feed composition
O Hydrocarbon-rich liquid phase fraction
V Vapor phase fraction
Vs Superficial velocity (m/s)
W Water-rich liquid phase fraction
Øi Fugacity coefficient of component i
Hydrocarbon-rich phase indicator Vapor phase indicator Water-rich phase indicator
One of the most important issues in oil fields is a high water
production that may lead to well killing and reduction of oil
production rate. The continuous gas-lift process is widely
used to improve the production from these oil fields. In this
process, high-pressure natural gas is injected into the
wellbore to lighten the column of fluid allowing the reservoir
pressure to force the fluid to the surface . The fluids in
gas-lift process consist of different components including
hydrocarbons and water distributed in three phases
(waterrich liquid, hydrocarbon-rich liquid and vapor). The accuracy
and speed of computation for the continuous gas-lift model
depend directly on the complexity of the thermodynamic
description of the fluids involved. Most studies such as
Guanren , Shi et al. , Cazarez-Candiaa and
VasquezCruz  and Hasan et al.  performed hydrocarbon-water
system calculations based on the simplified black-oil equations.
The basic assumption in the black-oil approach is to consider
hydrocarbon-water fluids as three pseudo-components
namely oil, gas and water. The black-oil model assumes that
no mass transfer occurs between the water phase and the other
two phases. Moreover, only two components are considered
in the hydrocarbon system. The oil component (stock-tank
oil) refers to the residual liquid at atmospheric pressure left
after differential vaporization, while the gas component is the
remaining fluid . In the black-oil model, the gas can be
dissolved in the oil phase. A three-phase black-oil model
usually treats PVT properties of hydrocarbon-water phases as
a mere function of pressure and temperature. Hence, oil, gas
and water properties are computed by experimental correlations
at each pressure and temperature. The effect of the compositions
on pressure and temperature changes is neglected in the
The main question in using black-oil approach is its validity.
In fact, the effect of the compositions on pressure profile and
fluid flow properties should be taken into account when the
flowing liquid and gas are composed of more than one
component. The wise approach to predict the phase behavior is a
compositional description in which all components are
allowed to distribute between the phases. The most common
way was to perform a two-phase equilibrium calculation
combined with a steam table instead of a real three-phase
equilibrium calculation [7, 8]. Essentially, the equilibrium
calculation is performed first without water to get phase
distribution and compositions for the hydrocarbon-rich phase as
well as the vapor phase. Next, water is taken into account
using a steam table; this approach is fast but not consistent,
since adding water breaks equilibrium and may result in over
or underestimation of evaporation or condensation . The
development of compositional modeling with equation of
state formulations has received an increasing attention in
recent years . Such formulations require three-phase flash
calculations in each time step. Iranshahr et al.  presented
a three-phase flash method admitting an additional
assumption, in which the solubility of water in the hydrocarbon-rich
liquid phase is neglected. Recently, Lapene et al. 
presented a free-water flash method that assumes the solubility
of hydrocarbon components in the water-rich liquid phase is
negligible, which means this phase consists of pure water.
In this paper, we present a three-phase compositional
gaslift model based on the free-water flash algorithm proposed
by Lapene et al.  to model a gas-lift process with high
water-cut. A real field data case study with different
watercut value is modeled based on the compositional model.
Results are compared with a three-phase black-oil model
showing how the compositional approach is important and
when the black-oil approximation model is accurate.
1 PRESSURE DROP CALCULATION
Pressure drop in the gas-lifted well can lead to a loss of oil
production at the toe or overproduction at the heel. In order
to model the gas-lift process, accurate well flow models must
be incorporated into reservoir model. In the gas-lift process,
the gas injection leads to more flow pattern variety through
the well. Within the context of petroleum engineering, two
types of two-phase flow models most commonly used are
empirical correlations and mechanistic models. The empirical
correlations can yield good results but only limited to the
same conditions as the experiments. Furthermore, many
empirical flow maps exhibit large discontinuities at the flow
pattern transitions and this can cause convergence problems
in pressure gradient integration through the well. Compared
to empirical correlations, the mechanistic modeling approach
is more rigorous and has the potential of providing more
reliable predictions of liquid hold-up and pressure gradients for
gas and liquid flow in the wells. Mechanistic flow maps are
developed from the analysis of physical mechanisms, which
are produced by fundamental mass and momentum balance
equations. In mechanistic models, the effects of system
parameters are incorporated. Therefore, they can be applied over
a range of geometry and fluid conditions. For most of the
observed flow patterns, one or more empirical closure
relationships are required. In this study, a mechanistic flow map
and correlations based on the solution of the mass and
momentum equations developed by Petalas and Aziz 
was employed to predict flow regimes and pressure gradient
in the gas-lifted well. The procedure of Petalas and Aziz 
mechanistic model for flow pattern determination begins
with the assumption that a particular flow pattern exists and
is followed by an examination of the various criteria that
establish the stability of the flow regime. If the regime is
shown to be unstable, a new flow pattern is assumed and the
procedure is repeated. The procedure for flow pattern
determination is illustrated in Figure 1. It can be seen that the
examination of the dispersed bubble flow regime is the first
to be considered.
1.1 Dispersed Bubble Flow
The dispersed bubble flow region is bounded by two criteria.
The first is based on the transition to slug flow where a
transition from intermittent flow occurs when the liquid fraction
in the slug is less than the value associated with the
maximum volumetric packing density of the dispersed bubbles
(0.52). A transition from dispersed bubble flow to froth flow
can also occur when the maximum volumetric packing density
of the dispersed gas bubbles is exceeded. If these two criteria
are not satisfied, dispersed bubble flow is not possible and
the possibility of stratified flow is examined next.
1.2 Stratified Flow
The present model limits stratified flow to horizontal and
downhill angles only. This approach is also supported by the
fact that stratified flow is only observed for small upward
angles in large-diameter pipes. Determining the stability of
the stratified flow regime requires the calculation of the liquid
height, which can be obtained by writing the momentum
balance equations for the gas and the liquid phases. At
downward inclinations, transitions from stratified flow to other
flow can occur when the gas velocity at which waves on the
liquid surface are large enough to bridge the pipe and/or
liquid droplets are sheared off from the wavy interface and
deposited on the upper pipe wall, eventually developing into
an annular film.
1.3 Annular-Mist Flow
The model is based on the assumption of a constant film
thickness and accounts for the entrainment of the liquid in the
gas core. Slip between the liquid droplets in the gas core and
the gas phase is not accounted for. The transition from annular
flow is based on two conditions. The first of the transitions is
based on the observation that the minimum interfacial shear
stress is associated with a change in the direction of the
velocity profile in the film. When the velocity profile
becomes negative stable annular flow cannot be maintained
and the transition to intermittent flow occurs. This transition
mechanism is only relevant during uphill flow. The second
mechanism occurs when the supply of liquid in the film is
sufficient to cause blockage of the gas core by bridging the
pipe. This is said to take place when the in situ volume
fraction of liquid exceeds one half of the value associated with
the maximum volumetric packing density of uniformly sized
gas bubbles (0.52).
1.4 Bubble Flow
When the liquid fraction in the slug is greater than 0.48 and
the stratified, annular and dispersed bubble flow regimes
have been eliminated, the flow will either be intermittent,
froth or bubble flow. Bubble flow is encountered in steeply
inclined pipes and is characterized by a continuous liquid
phase containing a dispersed phase of mostly spherical gas
bubbles. It can exist if the Taylor bubble velocity exceeds the
bubble velocity and the angle of inclination is large enough
to prevent migration of bubbles to the top wall of the pipe.
The transition to bubble flow from intermittent flow occurs
when the gas void fraction (during slug flow) drops below
the critical value of 0.25.
1.5 Intermittent Flow
The intermittent flow model includes the slug and elongated
bubble flow patterns. It is characterized by alternating slugs
of liquid trailed by long bubbles of gas. The liquid slug may
contain dispersed bubbles and the gas bubbles have a liquid
film below them. A transition from intermittent flow occurs
when the liquid fraction in the slug exceeds the value
associated with the maximum volumetric packing density of the
dispersed bubbles. The same mechanism can occur at low
liquid rates when sufficient liquid is not available for slug
formation. The elongated bubble flow regime is defined as
the portion of intermittent flow for which the liquid slug
contains no dispersed bubbles of gas. The liquid volume fraction
may be determined by writing an overall liquid mass balance
over a slug-bubble unit.
1.6 Froth Flow
When none of the transition criteria listed above is met, the
flow pattern is designated as “Froth” implying a transitional
state between the other flow regimes.
ELs < 0.48
θ ≤ 0
EL A – M ≤ 0.24
∼δL < δLmax
ELs ≥ 0.48
Begin mechanistic model Yes
2 THERMODYNAMIC DESCRIPTION OF THE FLUID
Pressure gradient over a step length of the gas-lifted well
depends on the local fluid properties including the phase
densities, viscosities and inter-phase surface tension. The phase
properties of the fluid can be obtained via a compositional
treatment or a black-oil model approach.
The compositional treatment is based on a cubic equation of
state calculation for the phase equilibrium of the fluid. Thus,
given the temperature, pressure, composition and overall flow
of the fluid, the phase densities, viscosities and inter-phase
surface tension can be computed. However, in case of the black-oil
thermodynamic description, the fluid properties are calculated
from empirical correlations using merely the pressure values.
Hydrocarbon properties together with those for water are
then passed into a two-phase flow model to find the pressure
drop along the gas-lifted well in a pressure traverse calculation
3 BLACK-OIL MODEL
In the three-phase black-oil model, two pseudo components
namely oil and gas are used to describe the hydrocarbon fluid
system. A third pseudo component is also used to describe
the water. The pseudo components are usually defined as
phases at standard conditions. For example, the gas (vapor)
and oil (liquid) at surface conditions are labeled as the gas
and oil pseudo components, respectively. In the generalized
black-oil formulation, each hydrocarbon phase (gas and oil)
at reservoir conditions can be made up of two pseudo
components. One can associate a component with a master phase. In
the standard black-oil model, only the gas component is
allowed to dissolve in the oil phase. For a given reservoir
temperature, the gas solubility is usually expressed as the
gas-oil-ratio and a function of pressure. In addition to the
solubility, the black-oil model employs the concept of formation
volume factor, which is defined as the ratio of the fluid phase
volume at reservoir conditions to standard conditions.
Essentially, the black-oil approach employs a simple model
to represent the PVT behavior of the fluids and ignores the
mass transfer occurring between the water phase and the
other two phases. In the black-oil model, the fluid properties
can be supplied as functions of pressure and temperature via
data tables or they can be calculated from built-in
correlations. The built-in correlations for oil PVT properties should
be tuned to match the data measured at bubble point,
separator and reservoir conditions. The PVT behavior may be based
on a number of experimentally measurable parameters such
as the gas-oil ratio, the formation volume factors for oil, gas
and water. The basic correlations utilized to generate the
physical properties for the black-oil model are given in Table 1
and were tuned to match the measured physical properties.
Compositional model deals with a quite large number of
components in which dependence of the PVT phase behavior
on composition is modeled. The physical properties of a fluid
depend on whether the fluid is present as a single phase or
splits into several equilibrium phases. Flash calculation is
therefore required to determine the number of equilibrium
phases as well as their amounts and compositions. Here,
Lapene et al.  free-water flash method is used based on
Peng-Robinson equation of state. It assumes negligible
solubility of hydrocarbon components in water-rich liquid phase
and pure water for water phase. In this method, equilibrium
state for each species in the three-phase mixture of vapor,
hydrocarbon-rich liquid and water is expressed as following.
Physical and thermodynamic properties must be evaluated
as a function of pressure, temperature and composition at
each point. Component distribution among the various
phases is determined by phase-equilibrium calculations. This
requires the molar-balance constraint to be preserved, the
chemical potentials of each component be the same for all
phases, and the Gibbs free energy at constant temperature
and pressure be minimized. These can be described for a
mixture of hydrocarbon-water fluid having Nc components
fiO = fiV = fiW : i = 1, Nc
and using fugacity coefficients as:
PØiO xio = PØiV yi = PØiW xiW : i = 1, Nc
The two equilibrium ratios are defined as:
KiI = xyiOi = ØØiiVO : i = 1, Nc
: i = 1, Nc
In a free-water system, water is distributed over the three
phases while the rest of other components present only in
vapor and hydrocarbon (non-aqueous) phases. This assumption
Thus, Equation (
) is simplified for the water component
and takes the following form:
and from Equation (
xi=w = 1; xi≠w = 0
yw = K II
When thermodynamic treatment of c is described by a
compositional model, the hydrocarbon-water fluid properties
are computed from a phase equilibrium calculation. Moreover,
the density of oil (ρO), vapor (ρV) and water (ρW) are
computed from the following relations:
MwO = ∑iN=c1 xio Mwi
MwV = ∑i=1 yi Mwi
ρW = MwW (
where Mw and v are the weight of one mole and the volume
of one mole of each phase respectively. The molar weights of
oil and vapor are found as follows:
In compositional model, the oil and gas viscosities are found
from the Lohrenz, Bray and Clark correlation, using the phase
composition and molar volume in addition to component
critical properties. Moreover, the water viscosity is calculated
from Beal’s correlation. The surface tension between oil and
gas may be computed from the MacLeod-Sugden relation
that requires component parachors in addition to the phase
equilibrium calculation .
5 RESULTS AND DISCUSSION
An illustrative example based on a mature oil field was used to
demonstrate the effect of different thermodynamic approaches
on three-phase pressure drop calculation in a gas-lifted well
with high water-cut. The reservoir characteristics and initial
conditions are shown in Tables 2 and 3. The particular well
considered in this study had a depth of 1 800 m equipped
with a gas-lift valve at 80 m above the sand face. The
temperature of the wellbore was assumed to fall linearly from the
reservoir temperature to that at the surface. The fluid from
the well entered a common manifold and was directed to a
train of three separators placed in series.
In order to study the composition variation through the
gas-lifted well, calculations of three-phase pressure drop
based on the black-oil model and compositional free-water
flash model were compared. The pressure and temperature
at the bottom-hole were taken as 170 bar and 360 K
respectively. Pure methane was injected as a lifting gas at a
rate of 56 000 scm/day.
Effect of water-cut on the pressure profile of the gas-lifted
well is demonstrated in Figure 2. It shows the pressure of the
well at different water-cut values obtained from the black-oil
model. Figure 3 shows the profile using three-phase
compositional model at the same condition. It is evident from
Figure 2 that the pressure drop of the well is increased at high
water-cut. The pressure drops below the value of surface
pressure causing the pressure drop calculations to stop in a
section of the well.
Figure 4 compares the two sets of results obtained from
black-oil model to those of compositional model. Water-cut
values were 0, 20 and 40%. The comparison between phase
superficial velocities and pressure profiles shows that more
deviation between black-oil and compositional model
encounter at higher water-cut values. The calculated pressure
may drop below the surface separator pressure at water-cut
40 causing the pressure curve discontinuity.
The ignoring or considering the solubility of the injection
gas in the produced fluids of gas-lifted well is the major
difference of black-oil and compositional approaches in
modeling of fluid thermodynamic behavior. The black-oil
model does not take into account solution of injected gas into
the produced oil, so the gas appears as free gas beside the oil.
By contrast, compositional model allows the injected gas to
dissolve in the oil and equilibrium flash calculations determine
the amount of the free gas. From Figure 4, as in black-oil
model the injection gas is insoluble in the produced fluid, its
flow rate and superficial velocity are greater than those in
compositional approach. This point effects on the liquid and
water superficial velocities. As the pressured drop and
pressure profile in the well are calculated base on phase
superficial velocities, the calculated pressure from black-oil and
compositional models are significantly different.
In all curves of gas superficial velocities in Figure 4, there
is one point that the slope of the superficial gas velocities is
changed drastically. These points are related to the mixture
state, changing from single liquid to vapor-liquid phase. The
bubble pressures are 124.56, 1 811.1 and 18 210.7 bar for the
fluid having 0, 20 and 40% water-cut respectively.
However, the amounts of solubility of water in hydrocarbon
rich phases (liquid and vapor) are small but at a high value of
water and oil flow rates in well, the water flow rates in
hydrocarbon phases will be considerable. Figure 5 shows the
flow rates of water in hydrocarbon phases at two water-cut
values: 20 and 40%. As expected, in higher water-cut values,
more water enters the hydrocarbon phases and more deviation
is arisen between black-oil and compositional approaches.
Variation of liquid/gas/water superficial velocities and pressure with well depth at different water-cuts.
Hydrocarbon liquid phase Vapor phase 8 7
Well depth (m)
Variation of water molar flow rate in each hydrocarbon liquid and vapor phases with well depth at different water-cuts.
Results show that the three-phase black-oil model may
provide a good approximation for modeling gas-lift process
at initial production periods where the hydrocarbon fluid
contain a low value of water. The difference with the black-oil
model seems in the first instance not to great however, the
difference plays an important role when calculation of the
multi-phase flow in a gas-lift process having high water-cut
values is required.
The continuous gas-lift technique is often employed as the
reservoir pressure declines due to depletion or water-cut
increase. A three-phase compositional model based on
freewater flash method was developed to study the gas-lift
process for an oilfield having a high water-cut. A case study
with different water-cut values was considered to compare a
three-phase black-oil model against the compositional model.
It was shown that, the difference between black-oil modeling
and compositional results would increase as the water-cut
increases. Therefore, it is necessary to perform a three-phase
multi-phase flash calculation to find the extent, physical
property and superficial velocity of the phases in modeling a
gas-lifted well with moderate and/or high water-cut.
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Final manuscript received in July 2012 Published online in March 2013