discrete phase modeling of oil droplets in the gas

1 Copyright © 2014 by ASME

DISCRETE PHASE MODELING OF OIL DROPLETS IN THE GAS COMPARTMENT OF A PRODUCTION SEPARATOR

ABSTRACT Computational Fluid Dynamics (CFD) is a powerful

engineering tool that has different applications in the Petroleum

Industry. In recent years, CFD has been used to analyze the

complex 3D multiphase flow inside production separators. Due

to changing reservoir conditions oil companies replace old

internals with upgraded ones. In this study, a numerical

simulation of the turbulent multiphase flow using the Discrete

Phase Model (DPM) is used to assess the effects of the oil

droplet size distribution on the oil carry-over in a production

separator. Liquid droplet size distributions, meant to represent

fine and coarse populations of oil droplets, were generated at

the inlet of the separator within the range of sizes recommended

in the literature for design purposes. The DPM model accounts

for the key phenomena of droplets coalescence and breakup.

Although the real case includes three phases, the present DPM

simulations do not account for the water phase due to its

negligible volume fraction and its prevailing gravitational

settling compared to the carry-over effect. The new internals

included; an inlet device known as Schoepentoeter,

agglomerator, parallel-plates coalescer, and cyclonic mist

extractor. Unlike many of the CFD studies reported in the

literature, usually representing the internals by numerical

models for simplicity, the internals of the separator were

replicated with the maximum of geometrical details in this

study. The present work was compared with field tests and

previous numerical simulations using the Population Balance

Model PBM. The PBM simulations considered the whole

separator volume and the presence of three phases (gas, oil,

water). The mean residence time obtained from the simulations

agreed reasonably with some of the results published in the

literature using semi-empirical formulas and experiments. The

new internals were seen to promote droplet coalescence with

minimal breakup. The new inlet device (Schoepentoeter), in

particular, was found to contribute considerably to the

coalescence of droplets and, hence, to separation.

INTRODUCTION

The Separation of produced oil mixture into its gas, water

and oil components is an important upstream operation in

surface facilities of the petroleum industry. This conversion

from a mixture of substances into two or more distinct products

is usually based on gravity settling using several types of

separators. These separators are considered one of the main

tools in the upstream petroleum industry that have a significant

economic impact on the quality of the produced oil.

In the oil and gas industry, the produced wellhead fluids

consist of a complex mixture of different compounds of

hydrogen and carbon that have various densities, viscosities,

surface tensions, vapor pressures and other physical properties.

Y. F. Qaroot Mechanical Engineering Department,

Petroleum Institute Abu Dhabi, United Arab Emirates

N. Kharoua Mechanical Engineering Department,


L. Khezzar Mechanical Engineering Department,


Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014

November 14-20, 2014, Montreal, Quebec, Canada

IMECE2014-37999


As the well stream exits from a pressurized oil reservoir, it

undergoes massive pressure reduction. Therefore, most of

gases evolve from the liquid mixture entraining some liquid

droplets whilst some gas bubbles are entrained by the liquid

phase as well. This leads to enormous changes in the properties

of the well stream mixtures [1]. The mechanical separation of

liquid-gas phases is considered one of the main operations in

the production, processing and treatment of oil and gas.

With the increase in water cut and gas to oil ratio, several

operating problems are experienced with first stage production

separators. These problems include the carry-over of liquids

with the gas; out of specifications crude oil and produced water.

To address these problems, debottlenecking operations are

conducted where old internals are replaced by new high

efficiency ones [2].

A literature survey on CFD studies related to gravity

separators was conducted by [3] summarizing the main findings

of the most important contributions where more details can be

found.

As most of the investigations were conducted for industrial

purposes, only the overall steps of CFD modeling have

been provided while the details of developed CFD models

were, usually, omitted.

Many of the previous CFD studies, on horizontal

separators, used only two phases in transient time mode

which showed acceptable results when compared to

experimental observations. On the other hand, three-phase

(oil, gas and water) simulations are scant due to their

complexity in addition to the considerable time and

computational resources required.

Most of the CFD studies on three-phase separators

considered only one half of the symmetric domain in order

to reduce the computational time. However, this

assumption might not be realistic for plug flow.

Several multiphase flow models have been used such as:

interface capturing techniques like the Volume of Fluid

(VOF) [4] and those based on two-fluid approaches with

inter-penetrating media such as the Eulerian-Eulerian

model [5-7], the Eulerian-Lagrangian Discrete Phase

Model (DPM) [8], the Drift Flux Model (Advance Mixture

Model) [9] and a combined DPM-VOF model [10-11].

Although the two-equation standard k-ε turbulence model

remains the only model used because of its simplicity,

modest resource requirements and robustness, the

turbulence model was not always clearly described in

several articles.

The combined DPM-VOF model showed the most realistic

simulation when compared to the experimental

observations [10-11].

The DPM can be used effectively for modeling variable

droplet diameters.

The PBM showed a clear improvement on the separation

efficiency when compared to the results of mono-dispersed

size distributions [7].

Using indirect factors for evaluating the oil-water

separation efficiency such as: volumetric utilization [12-13]

and the standard deviation of time-averaged velocity was

not always an accurate measurement of the separation

efficiency.

The computational grids used were of modest sizes,

ranging from 100,000 to 300,000 mesh cells, for

conventional sizes of horizontal separators (10-25m long

and 1-5m diameter), except for the studies of [6] who used

105 million cells for 45.5 m long separator with 4.26m

diameter and [2,14] who used 8 million mesh cells for 14 m

long separator with 3.4m diameter.

The quality of the computational grid system used was not

always validated and grid independence tests were not

performed, presumably because of the limited resources

available and the time required for conducting such tests.

The main aim of this study is to assess the performance of a

three-phase horizontal separator, in terms of oil carry-over,

using the Discrete Phase Model DPM compared to the

Population Balance Model PBM, both, implemented in the

ANSYS FLUENT 14.0 code. The k-ε turbulence model, known

to be the appropriate approach in terms of compromising

numerical accuracy and computational cost, is combined with

the DPM model to simulate the liquid carry-over phenomenon

in the gas compartment of the separator. The liquid

compartments are not considered due to the limitation of the

DPM model. In fact, DPM, as implemented in ANSYS

FLUENT, should be combined with an Eulerian model which

provides the background phases for the DPM droplets. All the

Eulerian models in ANSYS FLUENT assume a primary phase

and one, or more, secondary phases while DPM droplets cannot

interact with the secondary phases of the Eulerian models.

Thus, no Eulerian model is used which limits the study to the

gas-liquid separation in the upper part (gas compartment) of the

separator.

The present work intends to study the effect of coalescence

and breakup of oil droplets on the separation efficiency and to

analyze the multiphase flow behavior inside the separator, the

effectiveness of the internals, residence time and the effect of

drop size distributions on the separator performance.

SIMULATION METHODOLOGY The geometry of the separator is, first, presented followed

by a brief description of the Discrete Phase Model used, details

about the boundary conditions imposed and the simulation

approach adopted. Details about the previous studies, using the

PBM model, can be found in [15].

Geometry and Computational Mesh Figure 1 illustrates the positions of the new internals inside

the 3.4m diameter separator having a length equal to 14m. The

Schoepentoeter is an inlet device which dampens the inlet


velocity considerably in a smooth way between curved sheets

acting as diffusers. Two perforated plates (baffles) are added to

stabilize the oil-water mixture by forcing the flow towards

quiescent conditions so that to enhance the settling separation

mechanism. The coalescer consists of inclined parallel plates

fixed in the lower part of the separator and occupying more than

half of its cross-section. This device is omitted since the study

is limited to the upper gas compartment. At the same location

in the upper part, an agglomerator, formed by corrugated

parallel plates, is used for mist extraction. At the gas outlet, a

battery of cyclones, called Spiraflow, is used as mist extrator.

However, contrary to the previous study [15], the small

cyclones were replicated by a fan numerical model to test this

option of reduced geometrical complexity.

A mutli-block technique was used to mesh the

computational domain. Since the geometry of the model

contains many complicated internals, hybrid grids of hexahedral

and tetrahedral mesh cells were used. Fine-hexahedral meshes

were created in regions of interest such as: inlet,

Schoepentoeter, baffles, Agglomerator and Spiraflow while a

tetrahedral mesh was used in locations with complex

geometrical details. The number of grid cells is around 2.6

million, the minimum cell size is around 2 mm and the

maximum cell size is around 0.3 m. The quality of the

produced mesh was examined using the skewness factor and it

indicated that only a small fraction of cells (< 0.1%) were of

relatively poor quality.

Mathematical model The gas-oil flow, in the three-phase separator, was assumed

to be unsteady and turbulent. Hence, it was solved using the

Lagrangian-Eulerian DPM and turbulence k-ε models. Details

on the well-known set of equations solved can be found in [16].

The DPM is an Eulerian–Lagrangian model that solves the

force balance equation for the discrete phase by tracking their

trajectories through the calculated flow domain. Then, their

effects are injected into the continuous fluid phase through

appropriate source terms. The model includes particle-particle

interactions through breakup, coalescence, and collision sub-

models. The drag between phases was estimated using

spherical drag law. The Saffman lift force was considered as

well.

FIG. 1. GEOMETRY OF THE GAS COMPARTMENT

The turbulent dispersion was included through the Discrete

Random Walk model. The DPM has some restrictions [16]

which are the validity for only low volume fraction of the

dispersed phase typically less than 10% and the limitation of the

coalescence/collision model to injections of the same material

only. Since the lower part of the separator, where an

accumulation of a layer of oil occurs, is omitted, the assumption

of low oil volume fraction remained valid in the gas

compartment.

Since the Weber number We of the injected droplets is

relatively low (< 100 in this study), the Taylor Analogy Breakup

TAB and O’Rourke coalescence model were used [16-17]. The

TAB model is based on the analogy between an oscillating and

distorting droplet and a spring mass-damper system. It assumes

that droplet breakup will occur when the distortion of the

droplet (displacement of the droplet equator from its

equilibrium position) grows to a critical ratio of its radius ≈

0.5r. When a steady state solution is reached, the breakup

condition requires a Weber number We >12.

On the other side, O’Rourke coalescence model is based on

a stochastic estimate of collisions between droplets parcels that

only locate within the same continuous phase cell, this collision

results in coalescence only when droplets collide head-on. The

probability of coalescence within the cell is found from the

offset of the collector (larger) droplet center and the trajectory

of the smaller droplet. The collision is assumed to result in

droplets coalescence when a collision parameter, which is a

function of the relative radii of the collector and the smaller

droplet, is less than a critical collision value that is a function of

the Weber number and the relative radii.

Boundary conditions

According to the inlet flow regime, a turbulence intensity

of 2 % was prescribed. The secondary phase (oil) was injected

as poly-dispersed droplets in the continuous gaseous phase with

the same velocity of the gas equal to 7 m/s. It is worth to

mention that the real separator receives a mixture of 2% water,

6% oil and 92% gas by volume. This justifies the omission of

the water phase in addition to the fact that no water carry-over

was observed during field tests and previous simulation studies

[2, 7]. More details about the physical properties of the phases

can be found in [2, 7]. At the walls, no slip condition, with a

standard wall function [16], was imposed. The droplets are

assumed to be reflected at the walls. At the bottom wall,

however, a constant shear stress was specified with the

following values: τxz = 2.44e-05 Pa, τyz= 2.67e-06 Pa and τxy= 0

Pa. These values were approximated from the simulation work

done by [2,14] where information was extracted from the gas-

liquid interface. The particles escape the computational domain

when they reach the bottom surface. A symmetry boundary

condition was applied on the median plane of the separator in

order to reduce the number of grid cells considering, thus, only

half of the separator geometry. A fan boundary condition was

used inside each tube within the Spiraflow mist extractor, which

consists of 26 tubes. This boundary condition was implemented


on the gas-phase flow of both models. The main aim of the fan

boundary condition is to generate a swirling flow, i.e. tangential

and radial velocities, inside the tube and create pressure drop

across the fan. The values of the pressure drop, tangential

velocity and radial velocity were estimated based on previous

work done by [2,14], and these values were found to be equal to

1545 Pa, 2.5m/s and 0.5m/s for the pressure drop, tangential

velocity and the radial velocity, respectively.

A pressure boundary condition was adopted at the outlets

of the separator. The pressure at the gas outlet was equal to

17.2 barg to replicate the real working conditions.

In accordance with common practice, the perforated baffles

were modeled as porous media with a porosity of 0.21 and 0.36

according to the baffles-open-area fraction. Resistance

coefficients through perforated plates are usually used in the

source terms of the momentum equations to replicate the baffle

resistance effect. The effect of the source terms is transmitted

to the droplets when the continuous-phase velocity field is

implemented in the equations of the multiphase model.

Size Distribution. The size distribution used is represented

by seven individual bins. Naturally, the accuracy of the

simulations might be improved with a higher number of bins,

but with a penalty on the computational cost that has to be kept

reasonable for any practical application.

The size distribution to be used at the inlet can be assumed

to be normally distributed using the Rosin-Rammler function

[16].

n

)d/d(

deY

(1)

Yd is the mass or volume fraction of the droplets which

diameter is greater than d.

The Rosin-Rammler approach requires two parameters

which are the mean diameter and the spread parameter n.

The maximum stable diameter, at the inlet of the separator,

obtained using different correlations from the literature, related

to droplets in turbulent fluid streams, was in the range 2400-

6000 μm which is not compatible with the values mentioned in

the literature for the design of separators. Three oil droplet size

distributions for the PBM model were generated to be imposed

at the inlet of the separator (Fig. 2). It is worth to mention that

the distribution profiles represents bin volume fraction. The

total area below the curves corresponds to the volume fraction

of the phase taken as unity to adjust the peaks to a comparable

scale for all the distributions. These are meant to represent

arbitrary coarse and fine distributions compared with the cut off

size of 0.1-0.14 mm at the settling compartment since no

indications, about the real distributions, are available. For the

DPM model, four distributions were generated (Fig. 3).

For the spread parameter n (see Equ. 1), Laleh [10] used

an average value of 2.6 extracted from the experiments of [18-

19].

0

0.05

0.1

0.15

0.2

0.25

0.3

0 50 100 150 200 250 300 350

Volu

me

frac

tion

Droplet diameter (μm)

50 microns80 microns140 microns

FIG. 2. DROPLET SIZE DISTRIBUTIONS AT THE INLET OF THE

SEPARATOR FOR DIFFERENT MEAN OIL DIAMETERS FOR

THE PBM SIMULATIONS

0.00

0.10

0.20

0.30

0.40

0 40 80 120 160

Volu

me

frac

tion

Droplet diameter (μm)

10 microns

30 microns

50 microns

80 microns

FIG. 3. DROPLET SIZE DISTRIBUTIONS AT THE INLET OF THE

SEPARATOR FOR DIFFERENT MEAN OIL DIAMETERS FOR

THE DPM SIMULATIONS

Relying on the limited information from the literature, a spread

parameter of 2.6 was used in the present study.

Simulation strategy The PBM simulations, necessitated 720 CPU hours of

continuous run to simulate 20 minutes for the transient period

and additional 10 minutes for the calculation of the mean field

properties of real time on 48 parallel processors of a High

Performance Cluster. The DPM simulations were less

demanding and were run in a powerful workstation. The

computational CPU time was in the range 72-120 hours for the

DPM simulations. The number of droplet parcels tracked

within the computational domain was in the range 3000-90000

depending on the size of particles considered. RESULTS AND DISCUSSION

The gravity separator, considered in the present study, was

simulated using different multiphase models and under different

working conditions previously [2,7,14-15]. The focus in this

work will be on the performance of the DPM and PBM models

for this type of multiphase flows in industry. Results describing

the separation efficiency, the residence time, and the droplet


behavior are presented in this section and compared with

findings from the literature. For all the results presented in this

section, the distributions are represented by their mean

diameters.

Separation Efficiency Figure 4 illustrates the separation efficiency changing with

the representative mean diameter of the distributions

considered. The separation efficiency was estimated by relating

the mass flow rate of oil in the gas outlet to that of oil at the

inlet. Although some distributions were not used for both

models, they are included in Fig. 4 just for indication of the

performance of each model. The overall separation efficiency

is in a good agreement with the existing results from the

literature, e.g., [1], recommending cutoff diameters of 100-140

μm for the oil phase when similar separator configurations are

used.

The DPM simulation results showed that when the effect of

coalescence and breakup was omitted, the overall separation

efficiency increased as the mean droplet size became coarser

(Fig. 4). However, introducing the effects of coalescence and

breakup led to perfect separation efficiencies regardless of the

size distribution used. This is because the coalescence

phenomenon was found to be prevalent and influences the

separator performance significantly by generating coarser

droplets right at the Schoepentoeter.

In general, the DPM showed acceptable separation

efficiencies that were in good agreement with the PBM for

relatively large mean droplet diameters (> 80 microns), and also

lay within the range given by the field performance test (< 0.1

USG/MMSCF) bearing in mind that test results are field results

of which the precision is not known. However, the DPM

coalescence model was found to most probably overestimate the

coalescence rate in the Schoepentoeter region, which resulted in

higher separation efficiencies compared to PBM and the field

performance test, when finer size distributions were used.

0

20

40

60

80

100

120

0 50 100 150

Sep

arat

ion

eff

icie

ncy

(%

)

Mean droplet diameter (μm)

DPM without coal. & breakup

DPM with coal. & breakup

PBM

FIG. 4. SEPARATION EFFICIENCY

The discrepancy of the results (DPM against PBM and

field tests) can be attributed to:

The omission of water phase in the DPM and hence the

omission of liquid-liquid interactions, the assumption that

the oil-gas interface can be represented by a fixed surface,

which in fact does not replicate the free surface behavior

appropriately

The difference in the method used to solve the secondary

phases (DPM is Lagrangian and PBM is Eulerian): DPM

solves the force balance equation for each droplet to obtain

positions and velocities while PBM solves an equation for

the probability density function of the secondary phase in

each computational cell.

The assumption made by the coalescence model of the

PBM which assumes that the largest droplets cannot

undergo coalescence, i.e. new bins with larger sizes than

those chosen as maximum sizes (see Fig. 2) cannot be

created. This last limitation does not exist in the DPM

coalescence model (droplets coalescence without

constraints).

To further analyze the separation efficiency, the available

results from field tests, PBM [7] and DPM (with/without

coalescence and breakup) are plotted, in terms of field units, as

a function of the representative mean droplet diameter in Fig. 5.

The DPM model seems to really over-predict the coalescence

rate since it eliminates any entrainment for the realistic case

with coalescence even for very fine droplets smaller than the

sizes speculated in the literature of separator design guidelines.

Residence Time In addition to the separation efficiency, validated with the

field test results, the mean residence time MRT was compared

with the existing correlation from the literature [1, 20-21].

Danckwerts [22] stated that the MRT can be estimated simply

from:

phase

phase

Q

VMRT

(2)

where V is the volume occupied by the phase and Q is the

volumetric flow rate of the same phase at the inlet of the

separator. Thus, the MRT is calculated by averaging the

volume occupied by the phase inside the separator within a

period of quasi-steady flow regime.

The MRT for the gas-liquid separation (Fig. 6), obtained

using PBM, exhibits a decreasing trend with increasing mean

diameters of the inlet size distributions which is caused by the

rapid settling of the larger droplets. The simulation values are

three times larger than those recommended by [20] and about

40% lower than Arnold and Stewart method.


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 20 40 60 80 100 120 140

Oil

in g

as (

USG

/MM

SCF)

Mean droplet diameter (μm)

DPM Without Coal. & breakup

DPM with coal. & breakup

Field tests

PBM

FIG. 5. AMOUNT OF OIL IN GAS

Machado et al. [21] used the tracer technique to measure

the MRT for gas-liquid separation in a battery of three

separators operating in serial mode. Although the dimensions

of the separators were not mentioned, their values obtained by

experiments and simulations are reported in Fig. 6 and are

comparable to the recommended values in [20]. The two

dashed lines represent two different separators.

The MRT obtained from the DPM calculations ranges from

35 to 40 sec, which is in an acceptable agreement with results

from [20] and the typical MRT found by [1] for gas-liquid

separation (30 sec to 3min). It can be seen that the DPM seems

to be insensitive to the size distributions used in this study.

Indeed, similar trends were observed for the separation

efficiency in Figs. 4 and 5. It is probably due to an

overestimation of the coalescence phenomenon as mentioned

previously. Using smaller diameters would be an interesting

test for this insensitivity to droplet sizes.

0

100

200

300

400

500

600

0 50 100 150

Mea

n re

side

nce

time

(s)

Mean diameter (μm)

[1][20][21]PBMDPM: single injectionDPM: without coal. and breakup

FIG. 6. MEAN RESIDENCE TIME VS. MEAN DROPLET

DIAMETER

However, a discrepancy was found against the MRT

calculated using PBM. This was attributed to the different type

of model used for solving the secondary phases, the omission of

the water phase in the DPM and the elimination of the

Coalescer in the present geometrical model.

It is worth to mention that the large scale of the geometry,

its complexity and the scarce source of information, for this

industrial application, do not allow a deep and accurate

comparison such in fundamental research.

Phase Behavior

However, a discrepancy was found against the MRT

calculated using PBM. This was attributed to the different type

of model used for solving the secondary phases, the omission of

the water phase in the DPM and the elimination of the

Coalescer in the present geometrical model.

It is worth to mention that the large scale of the geometry,

its complexity and the scarce source of information, for this

industrial application, do not allow a deep and accurate

comparison such in fundamental research.

Tracking the amount of oil in gas at different locations. The white vertical lines, in Fig. 7, represent the

planes created to quantify the amount of entrained oil at

different positions inside the separator and the plotted values

correspond to the mass flow rate (kg/s) through these planes.

Wherever the entrainment is marginal it was omitted.

It can be seen, from Fig.7, that the entrained oil amount

decreases throughout the separator volume when injecting

coarser distributions. Downstream of the Schoepentoeter, the

entrained oil-in-gas amount, for the fine distribution (50 μm), is

almost equal to that at the inlet while it decreases by 20% each

time the inlet size distribution was made coarser.

FIG. 7. CONTOURS OF THE OIL VOLUME FRACTION IN THE

SYMMETRY PLANE (PBM MODEL).


In the settling compartment, the oil is entrained with the

gas through both the coalescer and the agglomerator for the fine

distribution whereas no entrainment occurs at the level of the

agglomerator for the two other distributions.

Although the coalescer is designed for oil/water separation,

it contributes to the oil/gas separation through its unsubmerged

part and is seen to have a considerable effect on the fine

distribution, by reducing the amount of entrained oil-in-gas by

70 %, contrary to the coarser ones for which no effects are

noticed. It can be concluded that the coalescer is inefficient for

the medium and coarse distributions. In addition, the

agglomerator seems to have a weak contribution by reducing

the amount of entrained oil-in-gas by only 3% for the fine

distribution which explains the high amount seen at the gas

outlet.

In Figs. 8 and 9, the amount of entrained oil at 6 different

locations across the axial-direction of the separator is illustrated

for three cases (10, 50 and 80 microns) using the DPM model

with and without breakup and coalescence.

When the effect of breakup and coalescence is present,

more than 90% of the inlet flow rate was separated by the

Schoepentoeter independently of the droplet diameter.

This is because the Schoepentoeter is designed in such a

way to enhance coalescence of droplets under the effect of

centrifugal acceleration imparted by the curved blade cascades

[14]. Thus, most of the droplet collisions and coalescence

occur within the Schoepentoeter region, and hence are

separated in the mixing compartment.

FIG. 8. OIL MASS FLOW RATES (Kg/s) DISTRIBUTION (DPM

WITH COALESCENCE AND BREAKUP)

FIG. 9. OIL MASS FLOW RATES (Kg/s) DISTRIBUTION (DPM

WITHOUT COALESCENCE AND BREAKUP)

There is a qualitative agreement of the DPM results,

without coalescence and breakup, with the predictions of the

PBM model although important quantitative differences are

generated by the two approaches. In the absence of any evident

experimental results describing the coalescence phenomenon in

different parts of the separator, it could be concluded that CFD

showed the importance of the coalescence phenomenon

although rigorous validations are necessary to quantify its

amplitude and locations. It could be, also, assumed that either

DPM overestimates the coalescence or PBM underestimate it.

Tracking of local size distribution. The size distributions

were tracked in the same planes shown in Figs. 7-9.

Table 1 illustrates that the Schoepentoeter plays an

essential role in coalescing the oil droplets into larger ones (20

times larger than the inlet mean sizes). This is because the

design of the Schoepentoeter enhances coalescing of droplets,

as it consists of several lateral flow passages with guiding vanes

act like diffusers that change the flow direction of the inlet

mixture to gain centrifugal forces, which in turn eject the

droplets towards the outer wall and thereby enhance liquid

droplets collisions, coalescing and separation. Therefore, most

all of the droplets (> 99%) are separated in the Schoeptoeter

and the gravity settling compartment, thus evaluating the other

internals might not be realistic when the coalescence model is

present.


TABLE 1. MEAN DROPLET DIAMETER UPSTREAM AND

DOWNSTREAM THE INTERNALS (WITH COALESCENCE AND

BREAKUP)

Location Mean diameter (μm)

Inlet 10 30 50 80

DPM downstream Schoepentoeter 271 421 738 2021

PBM downstream Schoepentoeter - - 80 150

DPM upstream Agglomerator 43 34 38 51

PBM upstream Agglomerator - - 80 150

DPM downstream Agglomerator

18 32 43 48

PBM downstream Agglomerator - - 80 150

DPM gas outlet 22 15 35 33

PBM gas outlet - - 80 -

The PBM model in turn, shows an increase of the mean

droplet size within the Schoepentoeter being limited as

explained previously. Then, the same size distribution persists

within the whole internal volume of the separator which reflects

a negligible breakup effect. At this stage, reliable experimental

results are required to judge the correct behavior of the droplet

in terms of size distribution through the separator internals.

The local size distributions of the DPM case, with 50

microns with coalescence and breakup, were also investigated

across the internals, and then compared against the results

obtained using PBM. Overall, it was found that the

Schoepentoeter was the most important element affecting the

coalescence of the fine droplets considerably.

The DPM simulation results (Fig. 10) show that the Rosin-

Rammler distribution at the inlet of the separator yields a

distribution with very large sizes downstream the

Schoepentoeter.

This proves the aforementioned fact about the significant

role of the Schoepentoeter in coalescing the small droplets into

larger ones. Similar trend was observed downstream the

Schoepentoeter by the PBM but with no noticeable

perturbations of smaller droplets; however, the diameter of the

mono-dispersed distribution did not exceed the specified

maximum size (92 micron), which is an assumption made only

by the coalescence model of the PBM.

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

Bin

vol

ume

frac

tion

Diameter (μm)

PBM: Inlet

PBM: Downstream Schoep

DPM: Inlet

DPM: Downstream Schoep

FIG. 10. OIL FRACTION DISTRIBUTION OF THE CASE OF 50

MICRONS MEAN DIAMETER AT THE INLET AND

DOWNSTREAM SCHOEPENTOETER

Viteri et al. [23] mentioned that the Schoepentoeter

separates 60-70 % of the incoming liquid but nothing has been

mentioned about the assessment approach and how the

separation efficiency was estimated. Mosca et al. [24]

explained briefly that the Schoepentoeter efficiency was

estimated based on the information upstream (inlet) and

downstream (column diameter of vertical separator) which is

similar to what was done in the present study by creating a

plane crossing the gas phase immediately downstream of the

Schoepentoeter.

To sum up, different distributions were generated by the

two models (PBM and DPM), when the coalescence was

present especially in the settling compartment. This was due to

the excessive amount of coalescences in the DPM simulation

compared to the PBM. Nearly similar behavior was observed

when the coalescence model was neglected, with some

deviations due to the differences in the method used to account

for the secondary phases (DPM is Lagrangian and PBM is

Eulerian). Finally, the breakup phenomenon was less important

especially at small droplet sizes. To prove the absence of

breakup phenomenon from the DPM simulations, seven random

droplets were chosen from the regions characterized by a high

turbulence level (Inlet and Schoepentoeter regions) and thus

higher probability of breakup. The corresponding Weber

number was calculated for each droplet (case of mean diameter

equals 50 μm) as illustrated in Table 2.

From Table 2, it can be seen that none of the droplets had

met the breakup condition (We > 12), which explains fairly the

absence of any noticeable breakup effect under the working

conditions considered. One of the reasons that led to this low

rate of breakup is probably the use of the Porous Media Model

to account for the effect of the perforated baffles where breakup

is more likely to occur as mentioned by [25].


TABLE 2 RELATIVE VELOCITY AND WE NUMBER FOR

SEVEN SELECTED DROPLETS

Droplet Vdroplet (m/s) Vgas (m/s) d (m) We

1 7.78 7.53 4.5e-3 0.1

2 1.36 1.16 4.5e-3 0.01

3 7.65 7.61 1.8e-2 0.01

4 0.76 0.79 4e-4 0.000015

5 0.79 7.53 2.4e-4 0.1

6 0.41 0.26 2.4e-4 0.002

7 4.80 0.6 8.3e-5 2

CONCLUSIONS Series of numerical simulations to study the turbulent

multiphase flow using the Discrete Phase Model (DPM) and the

Population Balance Model (PBM) were conducted. The PBM

results were extracted from previous publications of the same

authors for comparison with the DPM findings. The PBM

model has the limitation of a maximum droplet size fixed a

priori which is not the case of the DPM model. Although the

PBM simulations considered three phases and the whole

separator including all the internals, only those relevant to gas-

oil separation were considered in the present work due to

limitations related to the combination of Eulerian primary phase

with DPM secondary ones. The objective was to study the

effect of the oil droplet size distribution, at the inlet of the

separator, on the liquid carry-over in the gas compartment. The

droplet size distributions were generated based on

recommendations from the literature for usual design size

ranges. The internals were represented by realistic geometrical

models with the maximum of details to minimize the

computational errors due to the approximation of the internals

by numerical models. However, only the gas compartment was

included in the DPM simulations.

The present parametric study could confirm some known

features from the literature and field tests, such as the residence

time, the cut off droplet size, and the separation efficiency

which allows acquiring more confidence that CFD is a good

tool for the study of such large-scale industrial processes. The

mean residence time obtained from the simulations agreed

reasonably with some of the results published in the literature

using semi-empirical formulas and experimental results. The

new internals are well designed for the improvement of droplet

coalescence with negligible shearing effects leading to a

minimal breakup rate confirmed by the small Weber number for

the range of droplet size considered. The new inlet device

(Schoepentoeter), in particular, was found to play a key role in

coalescing droplets and enhancing separation.

ACKNOWLEDGMENTS The authors acknowledge the technical support from Dr.

Hisham Saadawi and the financial support from Abu Dhabi

Company for Onshore Oil Operation (ADCO). They are, also,

thankful to the Petroleum Institute of Abu Dhabi for providing

High Performance Computing facilities.

NOMENCLATURE d Droplet diameter

d Mean droplet diameter

n Spread parameter for the Rosin-Rammler size

distribution

Q Volumetric flow rate

We Weber number

x, y, z Coordinates

Yd Mass or volume fraction of the droplets which

diameter is greater than d

Greek Symbols τxz, τyz, τxy Shear stress components

Abbreviations

API American Petroleum Institute

DPM Discrete Phase Model

MMSCF Million standard cubic feet

MRT Mean residence time

USG United States Gallons

VOF Volume of Fluid

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