University of Stavangeruis.no

University of StavangerNorway

Milad KhatibiPh.D Candidate - IPT

1

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

2

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

3

Cuttings Transport in Deviated Wells

#: Avila R. et al. (2008) – SPE Drilling and Completion

4

Cuttings Transport in Deviated Wells

#: Mohammadsalehi M. et al. (2011) – SPE Pacific Oil and Gas Conference

5

Flow patterns

From top to bottom themean flow rate is

decreasing

#: Peysson (2004) – Oil & Gas Science and Technology𝐶𝐶𝑠𝑠 =Particle Concentration

𝐶𝐶𝑠𝑠

𝐶𝐶𝑠𝑠

𝐶𝐶𝑠𝑠

𝐶𝐶𝑠𝑠

6

#: 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

7

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

8

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

9

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?

11

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

15

Hydrocyclone

16

17

Hydrocyclone

Particle inejction

Flow direction

DifferentialPressure Cells

17

(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

22

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

− −′= +′−∫

27

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

30

Discrete Phase Modeling (DPM)

Trajectory is calculated by integratingthe particle force balance equation

31

Particulated phase influences the continuous fluid phase via source terms of mass, momentum and energy

32

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

33

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.

34

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

36

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

37

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

39

Y

Y

𝑅𝑅𝑀𝑀𝑝𝑝 =𝜌𝜌𝑙𝑙𝑑𝑑𝑝𝑝(𝑀𝑀 − 𝑣𝑣)

𝜇𝜇𝑙𝑙

40

Particle tracking in turbulent flow

41

Y

Y

Higher frequency ofvelocity fluctuation

Lower relative velocity

Lower frequency ofvelicty fluctuation

Higher relative velocity

42

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”

43

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

44

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

45

Question and Comment!?

46