THREE

DIMENSIONAL COMPUTATIONS OF GRAVITATIONAL SEPARATION
OF TWO

PHASE SYSTEMS
Takhavoutdinov R. G., Farakhov M. I., Altapov A. R.
Kazan State Technological University (K. Marksa street, 68, Kazan, Russia)
e

mail to:
roustam@kstu.ru
Computer and operating system used: AMD

K7

700 Athlon, 512Mb, Windows
XP
PHOENICS version used: PHOENICS

3.3
ABSTRACT
The PHOENICS code is employed to perform numerical simulation of two

phase
systems.
The results of computations m
ade for three

dimensional domain of an oil

water
system
gravitational separation device are presented. The Virtual Reality option of
PHOENICS

3.3 was used for pre

and post

processing, which made it possible to set an
adequate geometry and sources for the
sedimentation problem and to analyze the results after
the problem was solved using PHOENICS. A built

in option of LVEL turbulence model was
used. The fields of pressure, phase volume fractions and velocities are obtained.
Residence
time distribution is ob
tained by means of computing scalar tracer concentration distribution
after its impulse injection
into the inlet.
INTRODUCTION
Separation of oil

water systems has long been an important research topic due to
industrial applications and difficulties in ap
paratus design, operation and sediment control. As
a rule, such systems are involved in the petroleum industry because raw petroleum material
may come out like emulsion together with ground water. Separating this emulsion is an
important technical problem
for industry. Mathematical modeling of the sedimentation
processes enables us make recommendations for optimal device design and operation.
Multiphase flow dynamic of these apparatus is a main phenomenon, which has great influence
on efficiency and commerc
ial compatibility of the entire process.
Similar multiphase flows are also being used for a wide range of chemical processes,
including bio

and petrochemical technologies, catalytic reactions and bubble columns.
Therefore researches of multiphase flow dy
namic have a wide range of practical applications.
Recent developments of computational fluid dynamic (CFD) and corresponding computer
codes have shown promise for adequate simulation of momentum, heat

and mass

transfer
phenomena in multiphase flows. CFD
is presently an important tool in the investigation of
multidimensional two

phase flows.
Phenomenological models, such as one

and two

dimensional dispersion models of
flow structure,
residence
time distribution function approaches (Dankwerts, 1953)
etc
,
have
earlier been widely used to describe such flows, but these simulations are not well suited for
so called “scale

up” and industrial design, since they require prior knowledge of flow
structure, obtained experimentally for the apparatus of fixed size.
More of the published
models for predicting flow characteristics of the heterogeneous regime in multiphase
chemical reactors, reviewed by Ranade (1992), are restricted to a one

dimensional approach
and require experimental information about the radial disp
ersed phase hold

up profile and
turbulent viscosity and therefore lack generality (Kumar
et al
, 1994).
By introducing more fundamental models for internal variables, an up

to

date CFD
tool may successfully simulate multiphase systems for a variety of cond
itions and pattern
sizes without using prior experimental data for the concrete apparatus.
Related to the initiatives addressing PHOENICS for modeling of sedimentation
process has been the CFD work on sediment control, which has sought to reduce the impac
t
of sedimentation on the availability and distribution of water in irrigation systems (Fish
et al
,
1986). It has continued through specific initiatives such as on vortex tube extractors
(Atkinson, 1991) and the development of a structured procedure for se
diment control.
Procedures for mathematical modeling of sediment flow at intakes using PHOENICS
software have been developed. The result was a series of comprehensive design manuals and
software packages for sediment extractors, guides on designing stable
alluvial canals and
methods for the design of low

cost sediment excluders.
The results of our original investigations on modeling sedimentation are presented
below.
PHENOMENON, SIMULATIONS AND SETTINGS
PHOENICS implemented mathematical models, equations a
nd boundary conditions
have been used, described in PHOENICS “help” called “POLIS” and no more details of
mathematical forms of these simulations are presented here.
Two principally different approaches, namely, Eulerian and Lagrangian are used to
simulate
multiphase flow. The number of disperse phase elements in the separation apparatus
is huge, and here the Eulerian approach is the most suitable. In the case of the Eulerian
approach, two different phases are modeled as two space

sharing interspersed conti
nua. The
PHOENICS code provides a few models of multiphase flows with inter

phase interaction.
The standard two

fluid option of the PHOENICS code was used for solving two complete sets
of momentum conservation equations via an interphase

slip algorithm k
nown as IPSA.
PHOENICS provides solutions to the discretized versions of sets of differential
equations having the general form:
(r
i
i
F
i
)/
琠⬠摩v⡲
i
u
i
i
F
i
–
r
i
i
grad(F
i
)) = r
i
S
i
where
t

time;
r
i

volume fraction of phase
i
;
i

density
of phase
i
;
F
i

any conserved
property of phase
i
, such as enthalpy, momentum per unit mass, mass fraction of a chemical
species, turbulence energy, etc.;
u
i

velocity vector of phase
i
;
i

exchange coefficient of the
entity
F
in phase
i
; and
S
i

sour
ce rate of
F
i
.
When time

averaged values of the various quantities are used for turbulent flows,
special expressions may have to be introduced for
i
, accounting for the correlations between
velocity, density,
F
i
, and other properties of the flow and of t
he fluid. LVEL turbulence model
was used here, which is unique to PHOENICS. Using law

Re “two

equation”
K

models of
turbulence is expected to be the next stage of our investigation that will be published later.
The mass

continuity equation for phase
i
is
obtained by setting
F
i
to unity in the above
differential equation, with the result:
∂
(r
i
i
)/
∂
t + div(r
i
u
i
I
) = r
i
S
m i
Here
S
m
represents the mass inflow rate into the phase
i
, per unit volume of space, for
example by transfer from another phase wi
th which it is intermingled. We don’t consider any
inter

phase heat or mass

transfer in this work; therefore the right part of the equation is zero,
and
F
i
stands for momentum per unit mass in phases. Source rate of momentum includes
gradient of pressure,
gravitational force and inter

phase friction. The inter

phase friction
source vector term is
S=f u
s
,
where
u
s
is the slip velocity between the phases
1
an
2
:
u
s
= u
1

u
2
,
and
f
is the inter

phase drag coefficient for volume
V
:
f=0.5 C a
1
r
1
u
s
V
,
whe
re the low index
1
means continuous phase, and
a
is the projected area of particles per
unit volume. For incompressible flow
C
depends only on particle diameter
d
and the Reynolds
number
Re=u
s
d /
,
were
楳⁴桥楮敭 瑩c慭楮a爠癩獣潳楴y映瑨f潮瑩nu
潵猠灨o獥⸠
S瑯步猠摲ag 牥g業e⁷a猠瑨攠灲潰o爠潮e潲⁴ e慪潲楴y映瑨 ca獥猠睥湶 獴sga瑥携t
C=24/Re
.
Dispersed solid drag models like Stokes regime are also suitable for dispersed droplets
provided that surface

tension effects are negligible, as a
re the cases for small liquid droplets
of emulsion. We also used the standard drag curve (Clift
et al
(1978)) and the dispersed fluid
"dirty

water" drag model of Kuo and Wallis (1988):
C=16/Re
for
Re<0.49
,
C=20.68/Re
0.643
for
0.49<R
e<100
,
C=6.3/Re
0.385
for
Re>100
.
This model allows for the complete range of
Re
and the various shape regimes. It may be used
for droplets provided that the Weber number
We
is not
> 8
, as droplets then start breaking up.
As a rule,
Re<1
fo
r the gravitational separation of oil

water systems, so Stokes drag for
Re<1
and also universal models, that cover wide range of
Re
, including
Re<1,
like the standard drag
curve and the "dirty

water" drag model of Kuo and Wallis (1988), may be successfully
used
for simulating the inter

phase friction. Taking into account the fact that the liquid

liquid inter

phase surface is mobile, the "dirty

water" drag model may be more suitable than Stokes
model and the standard drag curve originally obtained for fixed
inter

phase surfaces of liquid

solid or gas

solid systems.
The two

phase flow enters into the apparatus via a tube
(figure 1)
. The dom
ain size is
2m x 0.2m x 0.375m.
The carrier phase is water: constant density 1000kg/m
3
and constant viscosity 10

6
m
2
/s
were set. The dispersed phase is oil: constant density 800kg/m
3
and particle diameter 0.0002m
were set. Inlet velocities along the longitudinal coordinate axis and volume fractions are set in
the area
IN
, shown in
figure 1
. PHOENICS built

in wall boundary
conditions for the LVEL
turbulence model are set on solid surfaces, assuming that the solid surface velocity is zero.
Outlet boundary conditions for this problem are set on the upper horizontal surface of the
domain. This way of setting outlet boundary con
ditions is based on consideration that
elements of the dispersed phase of the emulsion immediately disappear after they contact the
upper surface of the apparatus. At the same time, the carrier phase of emulsion is not allowed
to pass through the upper sur
face of the apparatus. Slip without friction is set as boundary
conditions for carrier phase in the upper suffice of the domain. The case corresponds to the
real situation, if there is an air layer over the emulsion. The real behavior of separation of the
phases near the upper surface of the device is very complicated, as the dispersed phase
elements first gather like a closed packed layer near the surface and then an inversion of the
dispersed phase takes place after that the former dispersed phase flows t
owards the outlet like
continuous phase.
These assumptions are quiet realistic, as the inlet volume fraction of the dispersed
phase of emulsion is low, for example, 1% in the cases investigated in this work, and the
height of inversed phase of emulsion und
er the upper surface and its velocity have small
value.
The carrier phase of the emulsion passes through the small area
OUT
, located on the
lower wall of the domain, and the dispersed phase is also allowed to pass through the area
OUT
in
figure 1
.
Residen
ce time distribution was modeled by means of numerical tracers injecte
d into
the INLET for short time, assuming that the tracer was soluble in the carrier phase
and
was
not soluble in the dispersed phase.
The way of setting all the boundary conditions desc
ribed above in PHOENICS terms
of sources by setting “coefficient” and “value” is
placed
in input
Q1
file
available
on
request
via e

mail
, which contains all settings for the case presented in the
RESULTS
item here.
Initial values of variables are read from
phi
file, obtained by running
the other
Q1
file
,
which
is also available on re
que
st via e

mail and
corresponds
to one

phase flow with carrier phase
properties, but it is considered to be only a way of generation of proper initial values of
variables for t
he two

phase problem.
RESULTS
A steady state problem was solved first.
The calculated vector field of the carrier
phase velocity on the left and right parts of the device is presented in
figure 2
(X

Z plane
Y=0.1 m) . The flow enters into the apparatus vi
a a tube in the direction opposite to the main
direction of flow in the apparatus, then the flow reflects from the walls and it forms a
complicated picture of flow. However, this way of flow inlet homogenizes the velocity field
(figure 3)
, decreases length
s of circulation zones and, consequently, enhances the efficiency
of gravitational separation of the two

phase flow.
The geometry of the device is mirror symmetric, and the top view in
figure 3
gives a
quite realistic mirror symmetric velocity field with i
nsignificant rejections.
Field of volume fraction of the dispersed phase is given in
figure 4
. The range for
R2
contour plotting was set in Virtual Reality Viewer to obtain the suitable picture in
figure 4
:
Min=0, Max=0.01. There is a yellow

green colore
d transitive boundary between the initial red
colored raw emulsion and the blue colored cleaned emulsion, going out from the device via
the small area in the lower surface of the device in the
picture 4
.
The volume fraction of the dispersed phase along
x

coordinate lines with different
fixed values of
x
and
z

coordinates are presented in
figure 5
.
Having computed
steady
field of velocity, transient problem was solved for scalar
tracer concentration distribution after its impulse injection into the INLET.
The distribution of
concentration of the tracer is a
feature
of residence time distribution, because
an
outlet curve
of
tracer
concentration after normalizing is the residence time distribution function curve as it
described in
(
Yang
et a
l
, 2001)
.
So, tra
nsient
computations
were made,
starting from the
hydrodynamics solution and solving for a single scalar quantity, which enter
ed
in a short
pulse and then
went
out of the domain. Using CGR solver whole field for
the
scalar
and
higher

order scheme appeared t
o be beneficial for numerical accuracy
, while velocity field
was fixed
.
Concentration fields at different time
s
are presented in
figure 6.
Results of these calculations make it possible to choose proper technological regimes
of sedimentation processing and
to optimize geometry of device.
REFERENCES
Atkinson E. (1991)
.
The Vortex Tube Sediment Extractor: A Flow Analysis and its
design Implications, HR Repo
rt OD/TN 51, Hydraulics Research , Wallingford, UK.
Clift R., Grace J.R. and Weber M.E. (1978)
.
Bubbles, Drops and Particles. Academic
Press, New York.
Danckwerts P.V. (1953)
.
Continuous flow systems. Distribution of residence times,
Chemical Engineering S
cience,
2
, p.1.
Fish I.L., Lawrence P., Atkinson E. (1986)
.
Sedimentation in the Chatra Canal,
Nepal, HR Report OD 85, Hydraulics Research, Wallingford, UK.
Kumar S.B., Devanathan N., Moslemian D. and Dubukovik M.P. (1994)
.
Effect of
scale on liquid c
irculation in bubble columns,
Chemical Engineering Science,
49
, p.5637.
Kuo J. T. and Wallis G. B. (1988)
.
Flow of bubbles through nozzles,
International
Journal of Multiphase Flow
,
14
, p.547
Ranade V.V. (1992)
.
Numerical simulation of dispersed gas

liquid flow,
Sadhana,
17,
p.237.
Yang Y., Hartman D.T., Reuter M.A.
(2001).
CFD Simulation of Residence Time
Distribution of a Rotary Kiln Waster Incinerator,
The
PHOENICS Journal
of Computational
Fluid Dynamics and i
ts Applications
,
14
, No.1, p.82.
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