Transcript TUSTP
TUSTP 2003 Mechanistic Modeling and CFD Simulations of Oil-Water Dispersions in Separation Components
by Carlos F. Torres May 20, 2003
Topics
Background
Objectives
Particle Tracking Model
Preliminary Results
Universal Dispersion Model
Background
Knowledge of particle motion and phase distribution enhance performance evaluation of separation equipment will
TUSTP has used the Eulerian-Lagrangian technique to design and analyze performance of separation devices such as GLCC, LLCC and LLHC
Existing models carry out simulations considering mainly the following forces acting on a particle: drag and buoyancy
Additionally, these models assume particle local equilibrium
Objectives
The general objectives of this study are to develop models capable of characterizing hydrodynamics of multiphase dispersion flow in separations and piping components
Initially, study focuses on dilute and dense dispersed flow
Develop a mechanistic model for calculating droplet motion, considering the different acting forces
Determine dispersed phase void fraction
Validate and extend the three way coupling approach proposed by Gomez 2001
Particle Tracking Model
General approach
Simplified approach
Future improvements
Particle Tracking: General Approach
Gomez 2001 presented a new Eulerian – Lagrangian mechanistic model:
Local equilibrium assumed for dispersed phase
Forces used: drag, lift, body force, added mass and pressure gradient
Model is one way coupling between continuous and dispersed phase, considering variation of interfacial area
Lagrangian Equation
Forces on particle
m p d V
dt
F d
F l
F b
F m
F p
F other
0
Effects of continuous phase turbulence on particle:
Behzadi et al (2001) presented an averaging approach for the effects of fluid turbulence on particles
Iliopoulos et al. (2003) presented a stochastic model for the effects of turbulence in dispersed flow
Particle Tracking: Simplified Approach
Modifications of Gomez model (2001):
Forces considered: drag, lift and body force
Main goal is calculation of particle trajectory
Parametric technique (function of time) allows determination of particle’s residence time (integration 2 nd order accuracy)
Particles are spherical and non-deformable, particle to particle interaction not considered (dilute dispersion)
One way coupling
3D solution developed for Cartesian and Cylindrical coordinate systems
Modified Gomez Model
Forces on Particle
0
F d
F l
F b
Particle Position
x i
1
x i
ti
ti 1 V x dt y i
1
y i
ti ti
1 V y dt z i
1
z i
ti ti
1 V z dt
Particle Tracking: 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 Results
Particle Tracking in Pipe Flow
Particle Tracking in Stratified Flow
Particle Tracking in Conventional Separators
Particle Tracking: Pipe Flow
Dimensionless Velocity Profile 1 0.9
0.8
0.7
y
Re 0.6
0.5
0.4
0.3
0.2
0.1
0 0 0.2
0.4
U
U
max Laufer, J. 1951, (Re = 40000) U+ Inner Layer U+ Outher Layer 0.8
Mixing Length Velocity Profile
1
0.06
0.04
0.02
0 -0.02
-0.04
-0.06
0
Particle Tracking: Pipe Flow
= 0 o , d = 5in, V cont = 0.01 m/s.
Water Continuous (1000 kg/m 3 , 1cp).
Dispersed phase Oil (850 kg/m 3 ), dp = 100 microns
0.5
With lift force.
Residence time = 161.53 s Without lift force. Residence time = 99.35 s 1
Pipe length [m]
1.5
2 2.5
Particle Tracking: Stratified Flow
0.04
0.02
0
= 0 o , d = 3in, Uls = 0.1 m/s, Ugs = 1.0 m/s Air Water system at 25
C and 1 atm.
Vl [m/s] 0.350
0.325
0.300
0.275
0.250
0.225
0.200
0.175
0.150
0.125
0.100
0.075
0.050
0.025
0.000
0.04
0.02
0 dp = 25 micros dp = 50 micros liquid level 1000 kg/m 3 1.2
kg/m 3 -0.02
-0.04
-0.04
-0.02
0
X [m]
0.02
-0.02
h/d = 0.5816
hl = 0.6035
0.04
-0.04
0 1 2 3 4 5
Pipe length [m]
6
Shoham and Taitel (1984)
7 8 9
Fluent
12 Mar 2003
title
2.5
2 1.5
1
Fluent 6.0
Oil density = 850 kg/m 3 viscosity = 30 cp Velocity at the inlet = 2 m/s at the interphase = 0.2 m/s Diameter at the inlet = 0.1 m at the outlet = 0.1 m Vessel liquid level = 1 m Reynolds Number at the inlet = 5666.7
in the vessel = 5666.7
0.5
Velocity Magnitude 2.600E+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 0 -1 -0.5
0 1 1.5
2 2.5
3
Conventional Separators
12 Mar 2003 title Vessel Oil density = 850 kg/m 3 Velocity at the inlet = 2 m/s at the interphase = 0.2 m/s Diameter at the inlet = 0.1 m at the outlet = 0.1 m Vessel liquid level = 1 m Reynolds Number at the inlet = 5666.7
in the vessel = 5666.7
Velocity Magnitude 2.600E+00
Vessel 2D
12 Mar 2003
Vessel
2.5
2 1.5
1
Vessel 2D v1.0
Oil density = 850 kg/m 3 viscosity = 30 cp Velocity at the inlet = 2 m/s at the interphase = 0.2 m/s Diameter at the inlet = 0.1 m at the outlet = 0.1 m Vessel liquid level = 1 m Reynolds Number at the inlet = 5666.7
in the vessel = 5666.7
0.5
0 0 0.5
1 1.5
2
x [m]
2.5
3 3.5
Vel 2.600E+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 4
Fluent
12 Mar 2003
title
2.5
2 1.5
1
Fluent 6.0
Oil density = 850 kg/m 3 viscosity = 30 cp Velocity at the inlet = 2 m/s at the interphase = 0.2 m/s Diameter at the inlet = 0.1 m at the outlet = 0.1 m Vessel liquid level = 1 m Reynolds Number at the inlet = 5666.7
in the vessel = 5666.7
0.5
0 -1 Velocity Magnitude 2.600E+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 -0.5
0 1 1.5
2 2.5
3
Conventional Separators
Vessel Oil density = 850 kg/m viscosity = 30 cp 3 Velocity at the inlet = 2 m/s at the interphase = 0.2 m/s Diameter at the inlet = 0.1 m at the outlet = 0.1 m Vessel liquid level = 1 m Reynolds Number at the inlet = 5666.7
in the vessel = 5666.7
Vel 2.600E+00
Vessel 2D
12 Mar 2003
Vessel
2.5
2 1.5
1
Vessel 2D v1.0
Oil density = 850 kg/m 3 viscosity = 30 cp Velocity at the inlet = 2 m/s at the interphase = 0.2 m/s Diameter at the inlet = 0.1 m at the outlet = 0.1 m Vessel liquid level = 1 m Reynolds Number at the inlet = 5666.7
in the vessel = 5666.7
0.5
0 0 0.5
1 1.5
2
x [m]
2.5
3 3.5
Vel 2.600E+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 4
Particle Tracking: Conventional Separators
Particle Residence Time = 2.63 s Particle Density = 2500 kg/m 3 Particle Diameter = 500 micron
Particle Tracking: Conventional Separators
Frame 001
12 Mar 2003
Particle Tracking
2.5
Particle Residence Time = 2.362 s Particle Density = 2500 kg/m 3 Particle Diameter = 500 micron 2 1.5
1 0.5
0 0 1 2
X
3 4
Frame 002
12 Mar 2003
Contour Plot
2.5
2 1.5
1 0.5
0 0 1 2
X
3 Velocity Magnitud 2.6000E+00 2.4632E+00 2.3263E+00 2.1895E+00 2.0526E+00 1.9158E+00 1.7789E+00 1.6421E+00 1.5053E+00 1.3684E+00 1.2316E+00 1.0947E+00 9.5789E-01 8.2105E-01 6.8421E-01 5.4737E-01 4.1053E-01 2.7368E-01 1.3684E-01 0.0000E+00 4
Universal Dispersion Model
Gomez Model (2001)
The Eulerian field is known (average velocities, turbulent kinetic energy and energy dissipation)
Solve Lagrangian field using the proposed equation, to calculate slip velocity within flow field
Solve diffusion equation using slip velocity information, to predict void fraction distribution
Calculate bubble or droplet diameter using Eulerian turbulent quantities and void fraction distribution
Repeat non-linear process until convergence is reached
Phase Coupling Model
Definition of Phase Coupling
One-way Coupling: reverse effect.
Fluid flow affects particle while there is no
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 Coupling
Phase Coupling Model
Continuous phase momentum equation (N- S Equation)
u i
t
j u i
x j
1
P
x i
x j
u i
x j
u j
x i
u i
MP
so i
T
si i
Dispersed phase momentum equation (average)
m p d V
p dt
F d
F l
F b
F m
F p
F turbulence
F other
Particle Source Term, MPso is estimated by coupling mass and momentum balances over control volume.
Two-way Coupling: Solution Scheme
PSI – Cell technique, Crowe et al. (1977) Huber & Sommerfelt (1997).
Air continuous Phase.
= 0 o , d = 80 mm, V = 24 m/s, Dispersed phase
d = 2500 kg/m 3 d p = 40 micron
Model Potential
LLCC Dispersion of Oil in Water with Water Layer at the Bottom V m = 0.6 m/s W.C = 67%