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University of Stavangeruis.no
University of StavangerNorway
Milad KhatibiPh.D Candidate - IPT
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Experimental Analysis of Cuttings Transportation in non-Newtonian Turbulent Well Flow
(Advance Wellbore Transport Modeling)
Supervisor:Professor Rune Wiggo Time
Co-Supervisor:Senior Engineer Herimonja Andrianifaliana Rabenjafimanantsoa
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Outline
- Background
- Experiments
- Experimental setup for study of cuttings transport in liquid phase- Experimental setup for studies of particle settling
- Theory and Challenges in Simulation of Liquid-Particle Pipe Flow
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Cuttings Transport in Deviated Wells
#: Avila R. et al. (2008) – SPE Drilling and Completion
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Cuttings Transport in Deviated Wells
#: Mohammadsalehi M. et al. (2011) – SPE Pacific Oil and Gas Conference
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Flow patterns
From top to bottom themean flow rate is
decreasing
#: Peysson (2004) – Oil & Gas Science and Technology𝐶𝐶𝑠𝑠 =Particle Concentration
𝐶𝐶𝑠𝑠
𝐶𝐶𝑠𝑠
𝐶𝐶𝑠𝑠
𝐶𝐶𝑠𝑠
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#: Doron and Barnea (1995) – Journal of Multiphase Flow
𝑈𝑈𝑠𝑠 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑣𝑣𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣𝑀𝑀𝑀𝑀𝑣𝑣 = 𝑈𝑈𝐿𝐿𝐿𝐿 + 𝑈𝑈𝐿𝐿𝐿𝐿𝐶𝐶𝑠𝑠 = 𝑃𝑃𝑃𝑃𝑀𝑀𝑀𝑀𝑀𝑀𝑣𝑣𝑣𝑣𝑀𝑀 𝐶𝐶𝑣𝑣𝐶𝐶𝑣𝑣𝑀𝑀𝐶𝐶𝑀𝑀𝑀𝑀𝑀𝑀𝑃𝑃𝑀𝑀𝑀𝑀𝑣𝑣𝐶𝐶𝜌𝜌𝑠𝑠 = 1240 𝑘𝑘𝑘𝑘/𝑚𝑚3
𝐷𝐷 = 50 𝑚𝑚𝑚𝑚𝑑𝑑𝑝𝑝 = 3𝑚𝑚𝑚𝑚
Three layer modelTurian et al. (1987) correlationTurian & Yuan (1977) correlation
o Doron & Barnea (1995) – Experimental data
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Effect of particle density 1240 – 2000 𝑘𝑘𝑘𝑘/𝑚𝑚3 Effect of Pipe Diameter 50 – 200mm
𝜌𝜌𝑠𝑠 =1240 three layer model𝜌𝜌𝑠𝑠 =1500 three layer model𝜌𝜌𝑠𝑠 = 2000 three layer model𝜌𝜌𝑠𝑠 =1240 Turian coreelation𝜌𝜌𝑠𝑠 =1500 Turian coreelation𝜌𝜌𝑠𝑠 =1240 Turian coreelation
D = 50 mm three layer modelD = 100 mm three layer modelD = 200 mm three layer modelD = 50 mm Turian coreelationD = 100 mm Turian coreelationD = 200 mm Turian coreelation
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Effect of particle size 0.5 – 3.0 mm
Homogeneous flowHetrogeneous flowMoving bedStationary bed
Rabenjafimanantsoa (2007) – experimental data
𝜌𝜌𝑝𝑝 = 2520 𝑘𝑘𝑘𝑘/𝑚𝑚3 and 𝑑𝑑𝑝𝑝 = 250~300 𝜇𝜇𝑚𝑚
𝑑𝑑𝑝𝑝 =0.5 mm three layer model𝑑𝑑𝑝𝑝 = 1.0 mm three layer model𝑑𝑑𝑝𝑝 = 3.0 mm three layer model𝑑𝑑𝑝𝑝 =0.5 mm Turian coreelation𝑑𝑑𝑝𝑝 = 1.0 mm Turian coreelation𝑑𝑑𝑝𝑝 = 3.0 mm Turian coreelation
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Effect of pipe angle
@Ut = 3ft/s 𝑑𝑑𝑝𝑝 = 0.25 𝑀𝑀𝐶𝐶 𝐷𝐷 = 5 𝑀𝑀𝐶𝐶𝜌𝜌𝑝𝑝 = 2620 𝑘𝑘𝑘𝑘/𝑚𝑚3 𝜌𝜌𝑙𝑙 = 8,41 𝑣𝑣𝑙𝑙/𝑘𝑘𝑃𝑃𝑣𝑣
#: Cho (2000) – SPE/Petroleum Society of CIM 65488
Experimental data: Tomren P.H (1979) – “The Transport of Drilled Cutting Slip Velocity – Univerity of Tulsa
Frac
tion
% o
f ann
ulus
Frac
tion
% o
f ann
ulus
Ut = 3ft/s Ut = 3ft/s
Annulus Area10
Effect of pipe angle
@Ut = 3ft/s 𝑑𝑑𝑝𝑝 = 0.25 𝑀𝑀𝐶𝐶 𝐷𝐷 = 5 𝑀𝑀𝐶𝐶𝜌𝜌𝑝𝑝 = 2620 𝑘𝑘𝑘𝑘/𝑚𝑚3 𝜌𝜌𝑙𝑙 = 8,41 𝑣𝑣𝑙𝑙/𝑘𝑘𝑃𝑃𝑣𝑣
#: Cho (2000) – SPE/Petroleum Society of CIM 65488
Experimental data: Tomren P.H (1979) – “The Transport of Drilled Cutting Slip Velocity – Univerity of Tulsa
Frac
tion
% o
f ann
ulus
Frac
tion
% o
f ann
ulus
Ut = 3ft/s Ut = 3ft/s
Annulus Area
Effect of fluid properties?Effect of drill string rotation?
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Two/Three layers – Hydraulic modelScientist Date
Doron and Barnea 1993
Nguyen D. 1998
Zou L. 2000
Kelessidis V. C. 2003
Ramadan A. 2003
Cho H. 2004
Duan M. 2008
Huai W. 2009
.... ....
Yan T. 2014
Lift Force Gravity Force
Drag Force
Buoyancy Force12
Experimental study in Multiphase Laboratory
Experimental 1: A medium-scale flow loop
Experimental 2: Single point particle injection in a Flow Cell
Inclined (fixed) and horizontal Dunes formation Velocity profiles (PIV, UVP) Pressure gradients Particle concenteration at injection point
Experimental setup for studies of particle settling High speed camera (2 or 3) – Optical Measurement
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Experiment 1: Medium-scale flow loop
Source: Doctoral Thesis by Rabenja (2007) 14
Flow meters
Magneticflow meter
CoriolisFlow meter
Screw Pump
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Hydrocyclone
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Hydrocyclone
Particle inejction
Flow direction
DifferentialPressure Cells
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(Particle Imaging Velocimetry) PIV - principle
CCD Camera(1024 x 1280 pixels)
Dantecdynamics (http://www.dantecdynamics.com/PIV/Princip/Index.html)
2D cross correlationof consecutive images
Local spatial shift vector
r∆
Local , instantaneousvelocity vector
rut
∆∆ =
∆
∆t = Time between images( 250 µs )
Fifth ISUD conference – Zurich, Switzerland, 12 - 14 September 20068
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UVP - principle
From Met-Flow User Guide (Release 2, Nov 2000)
Fifth ISUD conference – Zurich, Switzerland, 12 - 14 September 2006
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- UVP- PIVs
Ux
Possible to compare UVP and PIV profiles?
Fifth ISUD conference – Zurich, Switzerland, 12 - 14 September 2006
Method:• Pick out PIV velocities (Ux)along the ultrasonic beam.• Plot together with corresponding UVP data. 20
Experiment 2– Flow Cell
Particle injection
PIV
Fluid Flow𝑈𝑈∞𝑚𝑚/𝑠𝑠
Vx
Vy
‘hit position’ of particles
L=0L =Settling Length = X position
Vy = Vs= Settling velocity=H/tVx = L (Settling Length)/t
t= effective settling time
H=D
Outflow
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Particle collector
Ut= 0.6 m/s
Ansys Fluent:Turbulent dispersion of particle in continuousliquid phase using Stochasting trackingscheme in order to approve the design of theparticle collector
4 cm
Flow direction
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Theory and Challengesin Simulation of Liquid-Particle Pipe Flow
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Forces acting on a particle
#:Wei Yan 2010 – Sand Transport in Multiphase Pipelines
3 ( )D p l pF F F d u vτ πµ= + = −
3
6p
p
dFg mg gρ= =
3
6p
B p l p l
dF pV gV gρ ρ= −∇ = =
Hydrostatic pressure
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For non-uniform free stream velocity around a sphere, the drag force could be extended by an addition of the Faxen force
(Happel and Brenner, 1973)
323 ( )
8p
D l p l
dF d u v uπµ µ π= − − ∇
𝑀𝑀 = 𝐶𝐶𝑣𝑣𝐶𝐶 − 𝑀𝑀𝐶𝐶𝑀𝑀𝑢𝑢𝑣𝑣𝑀𝑀𝑚𝑚 𝑢𝑢𝑀𝑀𝑀𝑀𝑀𝑀 𝑠𝑠𝑀𝑀𝑀𝑀𝑃𝑃𝑚𝑚 𝑣𝑣𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣𝑀𝑀𝑀𝑀𝑣𝑣𝑣𝑣 = 𝑝𝑝𝑃𝑃𝑀𝑀𝑀𝑀𝑀𝑀𝑣𝑣𝑣𝑣𝑀𝑀 𝑣𝑣𝑀𝑀𝑣𝑣𝑣𝑣𝑣𝑣𝑀𝑀𝑀𝑀𝑣𝑣𝜇𝜇𝑙𝑙 = 𝑣𝑣𝑀𝑀𝑙𝑙𝑀𝑀𝑀𝑀𝑑𝑑 𝑑𝑑𝑣𝑣𝐶𝐶𝑃𝑃𝑚𝑚𝑀𝑀𝑣𝑣 𝑣𝑣𝑀𝑀𝑠𝑠𝑣𝑣𝑣𝑣𝑠𝑠𝑀𝑀𝑀𝑀𝑣𝑣𝑑𝑑𝑝𝑝 = 𝑝𝑝𝑃𝑃𝑀𝑀𝑀𝑀𝑀𝑀𝑣𝑣𝑣𝑣𝑀𝑀 𝑠𝑠𝑀𝑀𝑠𝑠𝑀𝑀𝐹𝐹𝐷𝐷 = 𝑑𝑑𝑀𝑀𝑃𝑃𝑘𝑘 𝑢𝑢𝑣𝑣𝑀𝑀𝑣𝑣𝑀𝑀
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Saffman Force
Magnus Force
Velocity gradient around a particle develops a pressure gradient on a particle
The rotation of particle (interaction with particles or walls) causes a velocity differential between both sides of the
particle. This velocity differential develops a pressure gradient on top and bottom of the particle
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Basset history force
The virtual mass effect is happened when a particle is accelerated through a fluid, so there is a corresponding acceleration of the fluid that is related to the virtual
mass effect.
Unsteady Forces?
Virtual mass effect
( )2l p
vm
V Du DvFDt Dt
ρ= −
The Basset history force happens due to the lagging boundary layer development (viscous effect) with changing in relative velocity at low Reynolds number
Reeks and McKee (1984) 2 00
( )3 [ ]2
t
B p l l
Du Dvu vDt DtF d dt
t t tπρ µ
− −′= +′−∫
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𝜑𝜑 =𝐴𝐴𝑠𝑠𝐴𝐴
Particles has a degree of non-sphericity. This is quantified by a shape factor
Non-Spherical Particle?
As is the smallest area per unit volume:1/ 3 2 / 3(6 )sA Vπ=
Where is the particle volumeV
surface area of the equivalent
sphere
actual surface area
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Equation of motion of a particle in a continuous liquid phase
xpp
ypp
dUm
dtdU
mdt
D R BA VM
g B R L
F F F F
F F F F Fτ
= + + +
= + + + +
Drag force :𝐹𝐹𝑝𝑝 + 𝐹𝐹𝜏𝜏
Force due to domain rotation
Basset force & Virtual added mass force
Gravity Force Buoyancy Force Shear Force Lift Forces
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Discrete Phase Modeling (DPM)
Continuous phasecontrol volume 𝐶𝐶𝑣𝑣
Particle as discrete phase
Particle trajectory – Lagrangian frame
𝑣𝑣 𝑋𝑋 𝑃𝑃, 𝑀𝑀 , 𝑀𝑀 𝑃𝑃 is a time-independent vector field at the center of particle mass
Continuous liquid phase flow – Eulerian frame
𝑀𝑀 𝑀𝑀, 𝑀𝑀
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Discrete Phase Modeling (DPM)
Trajectory is calculated by integratingthe particle force balance equation
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Particulated phase influences the continuous fluid phase via source terms of mass, momentum and energy
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Based on the model of Gosman and Ioannides (1981), the eddy is characterized by;
3/ 23/ 4( )e
kL Cµ ε=
ee
i
lu
τ =′
Velocity (fluctuating)A time scale (life time)A length scale (size)
eU𝑘𝑘 𝑀𝑀𝑠𝑠 𝑀𝑀𝑀𝑀𝑀𝑀𝑙𝑙𝑀𝑀𝑣𝑣𝑀𝑀𝐶𝐶𝑀𝑀 𝑘𝑘𝑀𝑀𝐶𝐶𝑀𝑀𝑀𝑀𝑀𝑀𝑣𝑣 𝑀𝑀𝐶𝐶𝑀𝑀𝑀𝑀𝑘𝑘𝑣𝑣𝜀𝜀 𝑀𝑀𝑠𝑠 𝑀𝑀𝑃𝑃𝑀𝑀𝑀𝑀 𝑣𝑣𝑢𝑢 𝑑𝑑𝑀𝑀𝑠𝑠𝑠𝑠𝑀𝑀𝑝𝑝𝑃𝑃𝑀𝑀𝑀𝑀𝑣𝑣𝐶𝐶
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Turbulent dispersion of particles
Turbulent dispersion is important because:
o Physically more realistic
o Enhances stability by smoothing souce terms and eliminating local spikes in coupling to the continuous liquid phase
Using Stochastic tracking (discrete random walk) scheme.
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Turbulent fluctuations in the flow
𝑀𝑀𝑖𝑖 = �𝑀𝑀𝑖𝑖 + �́�𝑀𝑖𝑖
�́�𝑀𝑖𝑖 = 𝜁𝜁2𝑘𝑘3
−1 < 𝜁𝜁 < 1
�́�𝑀𝑖𝑖 is derived from local turbulence parameters
𝑘𝑘 is the turbulent kinetic energy and 𝜁𝜁 is normally distributed random number
By computing the trajectory in this manner for a sufficient number of representative particles (termed as “number of tries”), the random effects of turbulence on the
particle dispersion can be included35
Particle is assumed to interact with the fluid phase eddy over
𝑀𝑀 = min(𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑠𝑠𝑠𝑠 , 𝜏𝜏𝑒𝑒)
Particle eddy crossing time 𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑠𝑠𝑠𝑠= −𝜏𝜏 ln[1 − 𝐿𝐿𝑒𝑒𝜏𝜏 𝑢𝑢−𝑢𝑢𝑝𝑝
] 𝜏𝜏 = 𝑀𝑀𝑀𝑀𝑣𝑣𝑃𝑃𝑀𝑀𝑃𝑃𝑀𝑀𝑀𝑀𝑣𝑣𝐶𝐶 𝑀𝑀𝑀𝑀𝑚𝑚𝑀𝑀
𝜏𝜏 =𝜌𝜌𝑝𝑝𝑑𝑑𝑝𝑝2
18𝜇𝜇𝜑𝜑(𝑅𝑅𝑀𝑀𝑝𝑝)
#: Oh J. 2010 – American Geophysical Union
𝑝𝑝𝑃𝑃𝑀𝑀𝑀𝑀𝑀𝑀𝑣𝑣𝑣𝑣𝑀𝑀 𝑠𝑠𝑀𝑀𝑠𝑠𝑀𝑀 𝑠𝑠𝑣𝑣𝑃𝑃𝑣𝑣𝑀𝑀 𝜑𝜑 = − log2 𝑑𝑑𝑝𝑝
( )p
v
dU f u vdt τ
= −
From equation of motion:
Re24
D pCf = Friction factor
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Single-point particle injection
‘hit position’ of particles
H=D
Fluid Flow
Vy = Vs= Settling velocity=H/tVx = L (Settling Length)/t
t= effective settling time
𝑈𝑈∞𝑚𝑚/𝑠𝑠 L=0L =Settling Length = X position
Vx
Vy
Outflow
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A relatively small change in settling time/settling velocity
as fluid velocity is changed[Chien, S. F. (1994), Sifferman, T.R. et al (1974),
Sample, K.J and Bourgoyne, A.T. (1977)]
Static fluidLaminar flow
Transient
Turbulent flow
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𝑈𝑈∞ [m/s] 𝑉𝑉𝑇𝑇 [m/s] 𝑀𝑀𝑠𝑠 [s]10^-6 -0.0318951 1.259610^-3 -0.0318970 1.259410^-2 -0.0319660 1.258710^-1 -0.0321440 1.2748
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Y
Y
𝑅𝑅𝑀𝑀𝑝𝑝 =𝜌𝜌𝑙𝑙𝑑𝑑𝑝𝑝(𝑀𝑀 − 𝑣𝑣)
𝜇𝜇𝑙𝑙
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Particle tracking in turbulent flow
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Y
Y
Higher frequency ofvelocity fluctuation
Lower relative velocity
Lower frequency ofvelicty fluctuation
Higher relative velocity
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Friction regimes: Schematic patterns of
flow around a sphere for several values of Reynolds
number ρUD/µ.
http://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-090-introduction-to-fluid-motions-sediment-transport-and-current-generated-sedimentary-structures-fall-2006/course-textbook/ch3.pdf
Cuttings particlesflowing in a wellconstantly alter between these
different friction”regimes”
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Steady State drag Coefficient(Newtonian – ”all friction regimes”)
Morrison, F.A. (2013) ”Data Correlation for Drag Coefficient for Sphere”
𝑅𝑅𝑀𝑀𝑝𝑝 < 0.1 𝐿𝐿𝑃𝑃𝑚𝑚𝑀𝑀𝐶𝐶𝑃𝑃𝑀𝑀𝑅𝑅𝑀𝑀𝑝𝑝 ≫ 1 Turbulent
D24CRe
=
Low Re limit
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Cloud of Particle (Hindering Effect+Particle Interaction+Interval Viscosity?)
ParticleFlow direction
high shearturbulence
Turbulence dissipation
𝑀𝑀 > 𝑀𝑀𝑝𝑝
𝑀𝑀 ≈ 𝑀𝑀𝑝𝑝
𝐼𝐼𝐶𝐶𝑀𝑀𝑀𝑀𝑀𝑀𝑣𝑣𝑃𝑃𝑣𝑣 𝑀𝑀, �́�𝑀?�̇�𝛾, ́̇𝛾𝛾? 𝜏𝜏, 𝜏𝜏?
Non-Newtonian Effect Viscosity
𝜏𝜏 = 𝑢𝑢(�̇�𝛾) �̇�𝛾 =𝑑𝑑𝑀𝑀𝑑𝑑𝑣𝑣
𝑀𝑀(𝑀𝑀, 𝑀𝑀) = �𝑀𝑀 + �́�𝑀(𝑀𝑀, 𝑀𝑀) �̇�𝛾 + ́�̇�𝛾 𝜏𝜏 + �́�𝜏
Local liquid velocity profile around the particle
Fluctuation term
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Question and Comment!?
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