7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
On the Simulation of WaterinOil Emulsions in Gravity Separators using an Eulerian
ThreePhase Flow Model
Djamel Lakehal, Chidambaram Narayanan, Mathieu Labois
ASCOMP GmbH
Technoparkstr. 1, Zurich, CH8005 Switzerland
Email: lakehal@ascomp.ch
Keywords: Oil separators, Threephase flow, level set method
Abstract
The aim of this contribution is to introduce a new modeling and simulation approach for the threephase flow (oil, gas, and
water) separation processes used in crude oil production. The system considered here is based on gravity separation, where oil
well stream is injected in large tanks where the three phases (gas, oil and water) separate under the action of inertia and gravity.
Use is made of the interface tracking technique combined with the EulerEuler model available in the Computational
MultiFluid Dynamics (CMFD) software package TransAT of ASCOMP. The dynamics of the flow is based on interface
tracking between gas and oilinwater liquid mixture. The diffusive process between the oil and water is taken into account by
solving an additional scalar transport equation for water drops, taken as the dispersed phase, the settling of which is accounted
for here by introducing various particle settling velocity models. The viscosity changes and nonNewtonian behavior of the oil
are also taken into account. The simulation work was performed to help design such systems by testing variable flow entry
procedures, with the objective to increase the liquid capacity of the vessels. It is shown that the Interface Tracking Technique 
level set method (accounting for gas separation), can predict this type of flow when combined with an emulsion model
accounting for the settling of the dispersed water phase in the oil phase. This model has some advantages over the TwoFluid
model, even coupled with the nonhomogeneous population balance models, particularly when comparing the computational
overhead. Real prototype models have recently been tested, some of which will be shown in the oral presentation.
Introduction
Primary separation is employed to remove water from oil.
The water can be naturally present or injected to enhance
production by forcing oil to the surface, in particular as oil
becomes difficult to extract. Both formation and injected
water eventually arrive to the wellbore and are produced
at the wellhead along with desired hydrocarbons. The
bulk of suspended oil in produced water is free oil, and
can be removed by means of gravity separation as the
primary step of treatment, although the process may not
be as effective for emulsified hydrocarbons. The presence
of gas in the production stream from the wellhead
generates a threephase flow, which needs then to be
separated into a gas phase for recovery, an oil phase for
dehydration and transport, and a water phase for treatment.
Gravity separation of gas, oil, water and suspended solids
can be performed simultaneously in one vessel, the size of
which is determined by the diameter of the particle
desired to be fully separated.
This class of flow is thus made rather complex by the
various facets of the multifluid flow dynamics, featuring
freesurface motion (between gas and oil/water phases),
mixing and interpenetration of oil and water, sc'lil,
particle deposition, and nonNewtonian behaviour of oil.
The situation becomes even more complex if the water
emulsifies or the free surface embodies surfactants.
Clearly, there is an incentive to resort to new CMFD
(Computational MultiFluid Dynamics) to help design
more efficient vessels with knowledgebased optimization,
optimizing oil resident time, which should eventually
benefit to daily production rate and storage.
We introduce for this purpose, a new modeling strategy
for hydrocarbon threephase flow separation processes
based on gravity. Use is made of the level set method to
separate gas from oilinwater mixture, combined with the
EulerEuler model available in the CMFD code TransAT
to treat the separation of the water emulsion from the oil.
The physics of emulsions is simplified and reduced to an
interpenetrating mixture featuring molecular diffusion
together with settling of the water droplets. This is taken
into account by solving an additional scalar transport
equation for the dispersed water phase, the deposition of
which is modeled by a settling velocity. Alternatively, the
emulsion can be treated by a multipleclass model in
which several concentration equations are solved at the
time to reflect the composition spectrum width, with
source terms dealing with flocculation, or coalescence and
breaking. Viscosity changes and nonNewtonian behavior
of the oil can also be taken into account easily. In the
absence of detailed measurement data, we discuss in this
paper selected examples simulated using TransAT code.
Preliminary results and open issues will be discussed.
Modelling Context in TransAT
The problem is treated in two steps: First, separate gas
from oilinwater mixture using an interface tracking
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
method (ITM), then treat the separation of the oilinwater
mixture itself using the EulerEuler approach, by
considering water as a dispersed flow. Freesurface and
interfacial flows refer to twophase flow problems that
involve two or more immiscible fluids separated by sharp
interfaces.
2.1. Interface Tracking Methods (ITM)
These methods are used for the prediction of twophase
flows requiring precise interface identification. A
singlefluid set of conservation equations is solved with
variable material properties and surface forces (Lakehal et
al., 2002). This is what makes the strategy more accurate
than the twofluid formalism, which requires more
modeling assumptions. The fluid motion equations under
incompressible flow conditions expressed within the ITM
formalism take the following form:
V.u=O (1)
a,(pu)+V.(puu) =Vp+V.o+F, +F,
where p is the density, p is the pressure, and o is the
viscous stress, with a rheology dependent on the nature of
the oil. Source terms in Eq. (2) denote the surface tension
and body forces, respectively. In the Level Set technique
(Sussmann et al., 1999), the interface between immiscible
fluids is represented by a function t, representing the
distance to the interface that is set to zero on the interface,
is positive on one side and negative on the other. This way,
both fluids are identified, such that the location of the
physical interface is associated with the zero level.
Material properties, body and surface forces in Eq. (2) are
locally dependent on the level set function, the evolution
equation of which reads:
a,(0)+u.V= 0 (3)
In the level set context, the surface tension takes the form:
F,= 7Kn (O) (4)
with n standing for the interface normal vector, K is the
surface curvature, y is the surface tension coefficient of
the fluid, and 6 is a smoothed Dirac delta centred at the
interface. Mass conservation is forced using Takahira's
(2004) method. The presence of surfactants on the free
surface can be taken into account by considering the
variations of y as a function of concentration, y=f(C, T).
2.2. The EulerEuler Single Class Suspended Particles
Model (SCSP)
The SCSP approach is used to model the dispersed phase
(water) dynamics and deposition in the vessel, represented
here as a singleclass dispersed phase. The combination
with ITM's used to separate gas from liquid can also
involve different fluids; with different theological
properties (i.e. various nonNewtonian models can be
coupled). The SCSP formulation is employed in the form
of a field description of dilute suspensions (water drops)
evolving in a carrier phase (oil). The dilute suspension
settles due to the action of inertia and gravity. The density
difference between the carrier phase and the dispersed
phase is small, such that the Boussinesq hypothesis can be
invoked (< 15%). The dilute suspension is assumed to
have some characteristics of a continuous phase (the local
concentration expressed in terms of a mass fraction C) or,
when appropriate, some of a dispersed phase (e.g., the
particle number density). The governing equations for the
carrier fluid (oil) and the dilute suspension (water) are
("w" refers to the water phase):
3,(pu)+V.(puu)=Vp+V.ogCAp/p, (6)
D,(pC)+V.(p C(uW))= V.D(VC) (7)
where D is the diffusivity
waterdrops settling velocity.
coefficient and W' i
s the
r
Figure 1: Water emulsion settling in oil using Eq. (9)
The complexity of the thermodynamics of emulsions (Liu
and Li, 1999) in hydrocarbon flows forces to consider the
oilwater mixture to be somewhat continuous and
interpenetrating, with the water droplets featuring settling
properties. One could invoke Stokes Law relating the
settling velocity to particle diameter D, gravity g, density
and viscosity of the fluid /,:
Ws = WStokes g(p p)D2 (8)
18/u
In creaming oilinwater emulsions, the Stokes velocity is
modified by introducing the effect of steric hindrance due
to the presence of surrounding particles to describe their
movement, e.g., in Barnea and Mizrahi (1973):
W= WStokes ( a) (9)
(1+ a/3)exp[5a/3(1 a)]
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
where a is the volume fraction. This model assumes that
the cream layer contains a fixed concentration of one
phase dispersed in another, with thickness increasing with
time. As the model stands now, the effects of coalescence,
flocculation, electrostatic interactions and droplet packing
and deformation are not directly considered. Coalescence
and flocculation effects could be taken into account if Eq.
(7) were solved for a multiple class of water droplets, with
appropriate source terms for interdroplet interactions.
To test the particle settling model of Eq. (9), we have
simulated a generic flow in a square cavity containing
water in the form of a dispersed phase, with droplets of
1mm diameter, mixed with a continuous oil phase. The
concentration of water is initially randomly distributed, as
shown the first panel of Fig. 1. The settling mechanism is
well illustrated in the next panels, with the thickening
process of emulsion. The calculation using Eq. (8) alone
(Stokes velocity) showed a faster settling behavior than
with Eq. (9). The model is coupled with the Level Set
method to account for the presence of gas, or alternatively
with a Lagrangian approach to track individual particles.
The Numerical Algorithm in TransAT
The CMFD code TransAT developed at ASCOMP is a
multiphysics, finitevolume code based on solving
multifluid NavierStokes equations on structured multi
block meshes. Grid arrangement is collocated and can
thus handle curvilinear skewed grids. Multiphase flows
can be tackled using Level Sets, Phase Field, VOF, and
homogeneous model. The equations are solved using the
third order of RungeKutta explicit scheme for time
integration. The convective fluxes are discretized using
the 3rd order Quick scheme (Leonard, 1977). The diffusive
fluxes are difference using the 2nd order central scheme.
Various multiphase flows were successfully treated by
TransAT (www.ascomp.ch/transat). To cope with
separation vessels of complex shapes, use is made of the
Immersed Surfaces Technology (IST) developed at
ASCOMP. The idea is to represent solid boundaries by a
solid level set function, where the solid is the second
plh.,c having its thermomechanical properties. A CAD
file describing the solid is imported and immersed into a
Cartesian grid. The approach has the advantage to solve
conjugate heat transfer problems, which can be an
important feature for the study of oil separator flows.
ThreePhase Flow Separation in a 2D Prototype
In the 2D axisymmetric test shown in Fig. 2, crude oil
containing 50% of gas and 50% of liquid, with 20% water
cut, is injected from the left. Water droplets are 1mm
diameter. Model (Eq. 9) is used to account for droplet
settling. The flow is treated as laminar. Note that with this
approach the flow should be simulated in transient
conditions, which should provide a faithful picture of
what might be expected in real conditions.
101
I~olP~N ~4n ~ l TnAT
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Figure 2. Threephase flow in a 2D axisymmetric separator.
After impinging on the momentum breaker, the flow
deviates and separates. The gas escapes from the top, and
the oil settles over the water before being extracted below.
The dispersed water phase is represented by dark blue
contours, the oil with grey, and the gas with green. Real
prototype models have recently been tested, one of which
(simplified) is discussed next.
Flow Separation in a Real Prototype Vessel
5.1. Modeling
The vessel used as a prototype for the simulations is
shown in Fig. 4, depicting the IST grid. The vessel can
collect a volume of crude oil equivalent to 100 m3/hr. The
simulations with TransAT were conducted in transient
conditions, using the ke turbulence model. Water, oil and
gas phases were considered in the simulations as
isothermal, nonmiscible incompressible fluids. The gas is
considered as a continuous phase. The flow is gravity
driven with the gravity vector directed positively in the
direction of the vertical liquid outlet pipe. Although use
was made of the ks model to treat turbulence in this
example, TransAT can treat this class of flows using the
Very LargeEddy Simulation (VLES) approach or the
MILES technique of Fureby and Grienstein (1999).
Table 1. Fluid/flow properties
Gas Oil Water
m[kg/m.s] 0.000165 0.0012 0.00089
r [kg/m3] 4.614 794 997.0
Form Gas Liquid Liquid
Fluids Continuous Continuous Dispersed
D [mm] 1
5.2. Problem Setup
In TransAT simulations, use was made of the IST method
described previously to grid the vessel, Fig, 4. The CAD
file of the vessel was immersed in a Cartesian grid, which
was refined automatically at the vessel edges and near
impermeable walls.
'4
Figure 4. The grid of the 3D vessel using IST in TransAT.
The final grid consists of 2.15 million Cartesian cells; a
preliminary grid with half resolution was not sufficient to
resolve the gas bubbling inside the liquid. The ke model
combined with wallfunctions was used, accounting
further for nearinterface turbulence damping as
recommended by Liovic and Lakehal (2007). Two inlet
boundary conditions were used: The first was set for the
inlet pipe where the static pressure was specified together
with a 20% water cut; the second was set at the gas inlet
port, with a specified static pressure and a 100% gas
volume fraction (pure gas). Three outlet boundary
conditions were specified: The velocity of the mixture
was given at each of the three outlet ports without
specifying the fluid properties at the outlet. Therefore, the
volume fractions of the fluid phases at the outlet ports
result from the computation. Noslip boundary conditions
were applied at the walls, for all phases.
The results discussed next correspond to a total crudeoil
volume rate in the vessel of 100m3/hr. The unsteady
simulations took 48 hours computing time on an eight
CPU PC Linux cluster for simulating six seconds of real
time. VLES simulations were also performed, but
statistical steadystate conditions were difficult to achieve.
5.3. Discussion of the Results
The 3D result obtained by TransAT and shown in Fig. 5
corresponds to the early stage of crude oil injection into
the vessel. The three phases are not distinctly shown. The
deformations and wrinkling of the sheared surface
separating between the gas and liquid phases (water and
oil are not separately colored) is clearly visible in the
Figure. In the unsteady approach, the interface dynamics
due to gas bubbling processes is well captured. The flow
was previously simulated (by the Saudi Aramco Research
Center) with CFX code, using the EulerEuler twofluid
model in steady state.
Figure 5. A snapshot of the flow obtained by TransAT.
Figure 6. Density distribution at 4 crosssections.
The results of CFX reveal indeed the separation of phases,
but with little details concerning gas bubbling, since the
gas phase was treated as dispersed. Also, the steadystate
prediction delivers reasonable phase separation, but in the
time averaged approach the dynamic processes in the
separator flow cannot be captured. Figure 6 shows the
density as predicted by the TransAT interface tracking
method. The first plane corresponds to the plane
intersecting the inflow pipe; the other thee planes
correspond to the successive planes in the streamwise
direction. Considerable separation is not yet visible with
the unsteady model, for the time simulated.
Conclusions
A modelling approach for threephase flow gravitydriven
.. Ar411W
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
separation used in crude oil production has been presented.
Use was made of the Level Set method combined with the
Euler model (SCSP) available in the CMFD software
package TransAT. The settling of the water droplets in oil
can be accounted for by introducing various settling
velocity models. The oil can feature nonNewtonian
behaviours with various theological models implemented.
It is shown that the Level Set Technique can predict this
type of flow when combined with an Eulerian model
accounting for the settling of the water dispersed phase in
oil. This model has some advantages over the TwoFluid
model, even when coupled with the nonhomogeneous
population balance approach. The treatment of two phases
as dispersed phases using the EulerEuler model in CFX
(Lakehal et al., 2010) limits its predictive performance for
bubbling and reentrainment processes. The next step in
this study is to use the MultipleClass Suspended Particle
Approach of TransAT. Our model can help the design of
separation systems within a reasonable computing time on
PC clusters.
Acknowledgements
This work was partially sponsored by the Saudi Aramco
Research Center.
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