Mechanistic Modeling and CFD Simulations of Oil-Water Dispersions

in Separation Components

Mechanistic Modeling and CFD Simulations of Oil-Water Dispersions

in Separation Components

TUSTP 2003TUSTP 2003TUSTP 2003TUSTP 2003

by

Carlos F. Torres

May 20, 2003

by

Carlos F. Torres

May 20, 2003

BackgroundBackground

Objectives Objectives

Particle Tracking ModelParticle Tracking Model

Preliminary Results Preliminary Results

Universal Dispersion ModelUniversal Dispersion Model

TopicsTopicsTopicsTopics

Knowledge of particle motion and phase distribution will Knowledge of particle motion and phase distribution will

enhance performance evaluation of separation equipmentenhance performance evaluation of separation equipment

TUSTP has used the Eulerian-Lagrangian technique to design TUSTP has used the Eulerian-Lagrangian technique to design

and analyze performance of separation devices such as and analyze performance of separation devices such as

GLCC, LLCC and LLHCGLCC, LLCC and LLHC

Existing models carry out simulations considering mainly the Existing models carry out simulations considering mainly the

following forces acting on a particle: drag and buoyancyfollowing forces acting on a particle: drag and buoyancy

Additionally, these models assume particle local equilibriumAdditionally, these models assume particle local equilibrium

BackgroundBackgroundBackgroundBackground

The general objectives of this study are to develop models The general objectives of this study are to develop models

capable of characterizing hydrodynamics of multiphase capable of characterizing hydrodynamics of multiphase

dispersion flow in separations and piping componentsdispersion flow in separations and piping components

Initially, study focuses on dilute and dense dispersed flow

Develop a mechanistic model for calculating droplet motion, Develop a mechanistic model for calculating droplet motion,

considering the different acting forcesconsidering the different acting forces

Determine dispersed phase void fraction

Validate and extend the three way coupling approach Validate and extend the three way coupling approach

proposed by Gomez 2001proposed by Gomez 2001

ObjectivesObjectivesObjectivesObjectives

General approachGeneral approach

Simplified approachSimplified approach

Future improvementsFuture improvements

Particle Tracking ModelParticle Tracking ModelParticle Tracking ModelParticle Tracking Model

Particle Tracking:Particle Tracking:General ApproachGeneral ApproachParticle Tracking:Particle Tracking:General ApproachGeneral Approach

Gomez 2001 presented a new Eulerian – Lagrangian Gomez 2001 presented a new Eulerian – Lagrangian

mechanistic model:mechanistic model:

Local equilibrium assumed for dispersed phaseLocal equilibrium assumed for dispersed phase

Forces used: drag, lift, body force, added mass and pressure Forces used: drag, lift, body force, added mass and pressure gradientgradient

Model is one way coupling between continuous and dispersed Model is one way coupling between continuous and dispersed phase, considering variation of interfacial areaphase, considering variation of interfacial area

Lagrangian EquationLagrangian EquationLagrangian EquationLagrangian Equation

0

otherpmbldp FFFFFF

dt

Vdm

Forces on particleForces on particle

Effects of continuous phase turbulence on particle:Effects of continuous phase turbulence on particle:

Behzadi et al (2001) presented an averaging approach for the Behzadi et al (2001) presented an averaging approach for the effects of fluid turbulence on particleseffects of fluid turbulence on particles

Iliopoulos et al. (2003) presented a stochastic model for the Iliopoulos et al. (2003) presented a stochastic model for the effects of turbulence in dispersed floweffects of turbulence in dispersed flow

Particle Tracking:Particle Tracking:Simplified ApproachSimplified ApproachParticle Tracking:Particle Tracking:

Simplified ApproachSimplified Approach Modifications of Gomez model (2001):Modifications of Gomez model (2001):

Forces considered: drag, lift and body forceForces considered: drag, lift and body force

Main goal is calculation of particle trajectoryMain goal is calculation of particle trajectory

Parametric technique (function of time) allows determination of Parametric technique (function of time) allows determination of particle’s residence time (integration 2particle’s residence time (integration 2ndnd order accuracy) order accuracy)

Particles are spherical and non-deformable, particle to particle Particles are spherical and non-deformable, particle to particle interaction not considered (dilute dispersion)interaction not considered (dilute dispersion)

One way couplingOne way coupling

3D solution developed for Cartesian and Cylindrical coordinate 3D solution developed for Cartesian and Cylindrical coordinate systemssystems

Modified Gomez Model Modified Gomez Model Modified Gomez Model Modified Gomez Model

Particle PositionParticle Position

bld FFF

0

1ti

ti

zii

1ti

ti

yii

1ti

ti

xii dtVzzdtVyydtVxx 111

Forces on ParticleForces on Particle

Particle Tracking:Particle Tracking:Future Improvements Future Improvements

Extend model capability to include:

Added mass force

Pressure gradient force (hydrodynamic)

Fluid turbulent effects

Particle transients effect

Develop mechanistic model for estimation of void fraction using stochastic approach

Explore limits of dilute flow assumption, and extend to dense flow

Preliminary ResultsPreliminary ResultsPreliminary ResultsPreliminary Results

Particle Tracking in Pipe FlowParticle Tracking in Pipe Flow

Particle Tracking in Stratified FlowParticle Tracking in Stratified Flow

Particle Tracking in Conventional SeparatorsParticle Tracking in Conventional Separators

Particle Tracking: Particle Tracking: Pipe FlowPipe Flow

Particle Tracking: Particle Tracking: Pipe FlowPipe Flow

Mixing Length Velocity ProfileMixing Length Velocity Profile

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Laufer, J. 1951, (Re = 40000)U+ Inner LayerU+ Outher Layer

Dimensionless Velocity Profile

U+/Umax+

y+/R

et

Re

y

maxUU

= 0= 0oo, d = 5in, V, d = 5in, Vcontcont = 0.01 m/s. = 0.01 m/s.

Water Continuous (1000 kg/mWater Continuous (1000 kg/m33, 1cp). , 1cp).

Dispersed phase Oil (850 kg/mDispersed phase Oil (850 kg/m33), dp = 100 microns), dp = 100 microns

Particle Tracking:Particle Tracking:Pipe FlowPipe Flow

Particle Tracking:Particle Tracking:Pipe FlowPipe Flow

Pipe length [m]

Pip

eh

eig

ht

[m]

0 0.5 1 1.5 2 2.5

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

With lift force. Residence time = 161.53 s

Without lift force. Residence time = 99.35 s

Shoham and Taitel (1984)Shoham and Taitel (1984)

= 0= 0oo, d = 3in, Uls = 0.1 m/s, Ugs = 1.0 m/s, d = 3in, Uls = 0.1 m/s, Ugs = 1.0 m/s

Air Water system at 25 Air Water system at 25 C and 1 atm. C and 1 atm.

Particle Tracking: Particle Tracking: Stratified FlowStratified Flow

Particle Tracking: Particle Tracking: Stratified FlowStratified Flow

X [m]

Y[m

]

-0.04 -0.02 0 0.02 0.04-0.04

-0.02

0

0.02

0.04 Vl [m/s]0.3500.3250.3000.2750.2500.2250.2000.1750.1500.1250.1000.0750.0500.0250.000

h/d = 0.5816

hl = 0.6035

Pipe length [m]

Pip

eh

eig

ht

[m]

0 1 2 3 4 5 6 7 8 9-0.04

-0.02

0

0.02

0.04

dp = 25 micros

dp = 50 micros

liquid level

1.2 kg/m3 1000 kg/m3

X [m]

Y[m

]

-1 -0.5 0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

Velocity Magnitude2.600E+00

2.463E+00

2.326E+00

2.189E+00

2.053E+00

1.916E+00

1.779E+00

1.642E+00

1.505E+00

1.368E+00

1.232E+00

1.095E+00

9.579E-01

8.211E-01

6.842E-01

5.474E-01

4.105E-01

2.737E-01

1.368E-01

0.000E+00

Fluent 6.0

Oildensity = 850 kg/m3

viscosity = 30 cp

Velocityat the inlet = 2 m/sat the interphase = 0.2 m/s

Diameterat the inlet = 0.1 mat the outlet = 0.1 m

Vesselliquid level = 1 m

Reynolds Numberat the inlet = 5666.7in the vessel = 5666.7

Fluent 12 Mar 2003 title

x [m]

Y[m

]

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

Vel2.600E+00

2.463E+00

2.326E+00

2.189E+00

2.053E+00

1.916E+00

1.779E+00

1.642E+00

1.505E+00

1.368E+00

1.232E+00

1.095E+00

9.579E-01

8.211E-01

6.842E-01

5.474E-01

4.105E-01

2.737E-01

1.368E-01

0.000E+00

Vessel 2D v1.0

Oildensity = 850 kg/m3

viscosity = 30 cp

Velocityat the inlet = 2 m/sat the interphase = 0.2 m/s

Diameterat the inlet = 0.1 mat the outlet = 0.1 m

Vesselliquid level = 1 m

Reynolds Numberat the inlet = 5666.7in the vessel = 5666.7

Vessel 2D 12 Mar 2003 Vessel

Particle Tracking:Particle Tracking:Conventional SeparatorsConventional Separators

Particle Tracking:Particle Tracking:Conventional SeparatorsConventional Separators

x [m]

Y[m

]

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

Vel2.600E+00

2.463E+00

2.326E+00

2.189E+00

2.053E+00

1.916E+00

1.779E+00

1.642E+00

1.505E+00

1.368E+00

1.232E+00

1.095E+00

9.579E-01

8.211E-01

6.842E-01

5.474E-01

4.105E-01

2.737E-01

1.368E-01

0.000E+00

Vessel 2D v1.0

Oildensity = 850 kg/m3

viscosity = 30 cp

Velocityat the inlet = 2 m/sat the interphase = 0.2 m/s

Diameterat the inlet = 0.1 mat the outlet = 0.1 m

Vesselliquid level = 1 m

Reynolds Numberat the inlet = 5666.7in the vessel = 5666.7

Vessel 2D 12 Mar 2003 Vessel

X [m]

Y[m

]

-1 -0.5 0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

Velocity Magnitude2.600E+00

2.463E+00

2.326E+00

2.189E+00

2.053E+00

1.916E+00

1.779E+00

1.642E+00

1.505E+00

1.368E+00

1.232E+00

1.095E+00

9.579E-01

8.211E-01

6.842E-01

5.474E-01

4.105E-01

2.737E-01

1.368E-01

0.000E+00

Fluent 6.0

Oildensity = 850 kg/m3

viscosity = 30 cp

Velocityat the inlet = 2 m/sat the interphase = 0.2 m/s

Diameterat the inlet = 0.1 mat the outlet = 0.1 m

Vesselliquid level = 1 m

Reynolds Numberat the inlet = 5666.7in the vessel = 5666.7

Fluent 12 Mar 2003 title

Particle Tracking:Particle Tracking:Conventional SeparatorsConventional Separators

Particle Tracking:Particle Tracking:Conventional SeparatorsConventional Separators

Particle Tracking: Particle Tracking: Conventional SeparatorsConventional Separators

Particle Tracking: Particle Tracking: Conventional SeparatorsConventional Separators

Particle Residence Time = 2.63 s

Particle Density = 2500 kg/m3

Particle Diameter = 500 micron

Particle Tracking: Particle Tracking: Conventional SeparatorsConventional Separators

Particle Tracking: Particle Tracking: Conventional SeparatorsConventional Separators

X

Y

0 1 2 3 40

0.5

1

1.5

2

2.5

Frame 001 12 Mar 2003 Particle Tracking

Particle Residence Time = 2.362 s

Particle Density = 2500 kg/m3

Particle Diameter = 500 micron

Universal Dispersion ModelUniversal Dispersion Model

Gomez Model (2001)Gomez Model (2001)

The Eulerian field is known (average velocities, turbulent kinetic The Eulerian field is known (average velocities, turbulent kinetic energy and energy dissipation)energy and energy dissipation)

Solve Lagrangian field using the proposed equation, to calculate Solve Lagrangian field using the proposed equation, to calculate slip velocity within flow fieldslip velocity within flow field

Solve diffusion equation using slip velocity information, to Solve diffusion equation using slip velocity information, to predict void fraction distributionpredict void fraction distribution

Calculate bubble or droplet diameter using Eulerian turbulent Calculate bubble or droplet diameter using Eulerian turbulent quantities and void fraction distributionquantities and void fraction distribution

Repeat non-linear process until convergence is reachedRepeat non-linear process until convergence is reached

Phase Coupling Model Phase Coupling Model

Definition of Phase Coupling

One-way Coupling: Fluid flow affects particle while there is no reverse effect.

Two-way Coupling: fluid flow affects particle and vice versa.

Four-way Coupling: Additionally from above, there are hydrodynamic interactions between particles, and turbulent particle collisions.

Three-way CouplingThree-way Coupling

Phase Coupling ModelPhase Coupling Model

iiiji

j

j

i

jij

iji sisouux

u

x

u

xx

P

x

uu

t

uTMP

1

Dispersed phase momentum equation (average)Dispersed phase momentum equation (average)

Continuous phase momentum equation (N- S Equation) Continuous phase momentum equation (N- S Equation)

otherturbulencepmbldp

p FFFFFFFdt

Vdm

Particle Source Term, MPParticle Source Term, MPsoso is estimated by coupling mass and is estimated by coupling mass and momentum balances over control volume. momentum balances over control volume.

Two-way Coupling: Two-way Coupling: Solution SchemeSolution Scheme

PSI – Cell technique, Crowe et al. (1977) PSI – Cell technique, Crowe et al. (1977)

Huber &Huber &Sommerfelt (1997).Sommerfelt (1997).

Air continuousAir continuousPhase. Phase. = 0= 0oo, d = 80 mm,, d = 80 mm, V = 24 m/s, V = 24 m/s,

Dispersed phaseDispersed phasedd = 2500 kg/m = 2500 kg/m33

ddpp = 40 micron = 40 micron

Model PotentialModel Potential

LLCCDispersion of Oil in Water

with Water Layer at the BottomVm = 0.6 m/s W.C = 67%

QuestionsQuestions

? ? ? ?