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Dowell Introduction to Rheology

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Dowell

Introduction to Rheology

16/05/2002 Page 2

Introduction

Rheologyis the science of the

deformation and flow of matter

16/05/2002 Page 3

Rheology? Rheology as known in the oilfield, deals with

the relationship between flow rate & flowpressure & their Influence on flowcharacteristics of the fluid.

? Two different flow regimes? Laminar Flow? Turbulent Flow

? Mathematical Models (most common)? Newtonian? Bingham Plastic? Power Law

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Rheology

? The data aquired from these models providesvaluable information about:

? Hole Cleaning Efficiency? Displacement? Hydrostatic Pressures? Surge/Swab Pressures

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Rheology? Used as a basis for determination of several important

aspects of Drilling Fluid performance:

? Calculate the system pressure losses

? Calculate surge and swab pressures

? Optimise nozzle hydraulics

? Optimise hole cleaning efficiency

? Calculate ECD's

? Reduce hole erosion

Proper understanding and application of rheological principalsare valuable aids in establishing the most effective propertiesfor efficient drilling fluid performance

16/05/2002 Page 6

Viscosity of Fluids

FF

Viscosity (µ) Shear StressShear Rate (Poise or Centipoise)

Shear Rate(dvdr) = V2 - V1

r (sec-1)

Shear Stress = FA (Newtons / m2)

AA

AA

VV11

VV22

rr

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Measurement Using A RotationalViscometer

Torsion Spring

Inner Cylinder

Bearing Shaft

Rotor

Bob

Cup

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Fann VG Viscometers•Most have 6 or 8 rotational speeds.•3, 6, 30, 60, 100, 200, 300 and 600 rpm.•Rotational speed is proportional to shear rate.•Bob deflection is proportional to shear stress

Engineers in the lab and atthe rig site now havevariable speed viscometersso that they can measure thedirect shear stress related tothe shear rate available atthe rig site using the fluidsin question.

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Newtonian Fluids

• Newtonian fluids are the simplest of fluids and contain noparticles larger than a molecule.

• Examples of Newtonian fluids are water, oils and brines

• The shear rate is directly proportional to the shear stress.

• A graphical plot is shown as a straight line and can becompared to the other flow models shown here

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Newtonian Model

? Fluid flows as soon as force is applied

? Shear stress is proportional to shear rate

? Viscosity is constant

Viscosity (µ) = Constant

Shear Stress

Shear Rate

? = µ . dvdr

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Non-Newtonian Fluids• Non-Newtonian fluids are basically fluids that don’t act as

Newtonian fluids.• Most drilling fluids are non-Newtonian.• Non-Newtonian fluids require a finite amount of shear

stress to initiate flow.• A graphical plot shows an inital curve which becomes

linear once flow has been achieved.• Typical Non-Newtonian fluids are paint, cream and drilling

fluids.• Drilling fluids contain enough drill solids to form a structure

between the particles, this can result in a resistance to flow.This is known as Structural Viscosity. As shear is appliedthis resistance is gradually overcome until the fluid beginsto flow. This point is known as the Yield Point of the drillingfluid.

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Bingham Plastic Fluids

• Bingham Plastic Fluids are shear rate dependent fluidswhose shear rate/shear stress relationship becomes linearonce the yield point has been reached.

• Bingham Plastic Fluids generally show a decrease inviscosity from the initial value at zero shear rates reachingsome constant at higher shear rates.

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Bingham Plastic Model

• AV = Apparent Viscosity = 600 /2

• YP = Bingham Yield = 300 - PV

• PV = Plastic Viscosity = 600 - 300

? = YP + PV dvdr

Shear Stress

Shear Rate

PV

AVYP

511 sec-1

300 ?1022 sec-1

600 ?

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Newtonian vs. Binghams Models

• Bingham Plastic Fluids therefore approach Newtonianfluids at higher shear rates. This behaviour is known asShear Thinning.

• The Yield Point is the shear stress required to initiate flow.

• Plastic Viscosity is the shear stress in excess of the yieldpoint that will induce a unit rate of shear.

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PV and YP Calculation

Shear Stress

Shear Rate

PV

YP

511 sec-1

300 ?1022 sec-1

600 ?

PV = slope of line = tangentof angle

= x/y = (?600 - ?300)511 1022 - 511

PV = ?600 - ?300

YP = ?300 - z

z = ?600 - ?300 = PV

YP = ???????PV

?600

??00

x

y

z

511 is the conversion from lb/100ft2 to centipoises

16/05/2002 Page 16

Power Law Flow Models• Power Law models can also be known as Pseudoplastic

fluids.

• They begin to flow as soon as pressure is applied so theyhave no yield point.

• Pseudoplastic fluids exhibit linearity at higher shear rates.

• Suspensions of long chain polymers are typicallypseudoplastic fluids. This is due to entanglement of thelong chain polymers which cause resistance to flow. Thesegradually align themselves with the flow and the viscositydecreases. These fluids are therefore shear thinning.

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Power Law Model

?? Fluid characterised by :? Behaviour Index, n? Consistency Index, K

n - 3.32 log ?600?300

Shear Stress

Shear Rate

? = K (dvdr

)n

Shear Stress

Shear Rate

K

nLog ? = log K + n log dv

dr

K = (5.11) ( ?300)511 n dynes secn cm-2

K = (0.511) ( ?300)511 n Pa. sec.

K = ?6001022 n lbs/100ft 2

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Power Law Flow Models• These types of fluids are highly desirable to support

cuttings and prevent barite settlement in the low shear rateregimes in the annulus, but also exhibit low viscosities inthe high shear rate areas of the bit.

• ‘n’ is the Flow Behaviour Index and indicates the degree ofshear thinning.

• ‘k’ is the viscosity at a shear rate of 1 sec-1.

• Power Law models also cover Newtonian Fluids where n=1and Dilatant fluids where n>1.

• If plotted on a log log paper the graph becomes linear forpseudoplastic fluids.

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Laminar Flow Profile• Laminar flow tends to occur in the low flow regimes in the

annulus so most drilling fluids exhibit laminar flow.

• The flow at the wall is zero, while flow increases as distancefrom the wall increases to a maximum in the centre of theflow. Can sometimes be considered as a series of concentriccylinders forming a parabolic shape.

• This flow pattern indicates an ideal Bingham Plastic Fluid.The velocity profile for a Power Law model would have aflatter profile.

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Cross-Section View of LaminarFlow

Sliding motion.? Velocity at the wall approaches zero, therefore erosion at the

wellbore tends to decrease.

? Velocity is maximum at the center, therefore bypassing fluidcloser to the wellbore wall (channeling) .

? Vmax = 2V where V = Average Particle Velocity

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Transition from Laminar toTurbulent Flow

• As flow rates increase the profile becomes more elongateduntil breakup occurs and the flow enters a transitionalstage between laminar and turbulent flow.

• Most drilling fluids lie between ideal Bingham Plastic andPower Law models.

• Turbulent flow occurs at high flow rates and ischaracterised by random movements of the particles.

• The velocity profile is flat but the swirling motion can beused to remove a cuttings bed in highly deviated holes.

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Cross-Section View of TurbulentFlow

? Swirling motion of particles with flat interface

? Average particle velocity is uniform throughout thepipe

? The swirling motion while being beneficial, canerode the well bore

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S.P.M.(S.P.M. is proportional to shear rate)

S.P.M.(S.P.M. is

proportional toshear stress)

Turbulent Flow

Transition period

Critical Velocity

Laminar Flow

Critical Velocity = Transition PointRe = <2000 laminar flowRe = 2000 - 3000 transitionalRe = >3000 turbulent

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Typical Flow Curves

Laminar Flow Turbulent Flow

Shear Rate

Shear Stress

Shear Rate

Shear Stress

Transition Zone

Transition Zone

BinghamPlastic

PowerLaw

Newtonian Newtonian Non-NewtonianNon-Newtonian

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? The point at which turbulence occurs is defined bya Reynolds Number (NRe).

D = Pipe I.D. (m)V = Average flow velocity (ms-1) r = Fluid density (kg/m3)n = Power Law indexK = Consistency index

? If Re < 2000, the flow is Laminar? If Re between 2000 - 3000 flow is transitional? If Re > 3000 flow is Turbulent

Reynolds Number

NRE = ?V2-n Dn

8n-1 [(3n + 1) / 4n] n x K

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Gel Strengths•Gels are measured as the maximum deflection of

the dial at 3 RPM after 10 seconds and 10 minutesrespectively.

•The units of gel strength are: lb/100ft2•Gels can be described as Flat or Progressive.

This is a measure of the difference between the 2values:• Gels 3/3: Low and flat, will not suspend solids• Gels 4/6: Slightly progressive (fragile). Minimum

for barite suspension in an agitated tank.• Initial gel: 8 minimum required to prevent barite

sag under static conditions• Gels 9/20: Typical water base mud• Gels 15/25: Typical oil base muds• Gels 3/40: Strongly progressive, can lead to severe

problems

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Thixotropic Fluids

? Thixotropy

? Time dependent rheological behaviour of fluids.

? Gel Strength (lbs/100ft2)

? Yield Point (lbs/100 ft2)

Shear Stress

Gel Strength

Yield Point

DecreasingShear Rate

IncreasingShear Rate

Shear Rate

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PV and YP Related to Mud Chemistry

? Plastic Viscosity (PV) is the portion of theresistance to flow (viscosity) that is caused byinterparticle friction.

? PV increases as the following increase :

? The size and shape of the solids.? The solids concentration.? The viscosity of the liquid phase without any

solids.? Note: For OBM, water droplets behave as inert

solids. Low oil water ratio's have high P.V's.

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PV and YP Related to Mud Chemistry

? The Yield Point (YP) is due to the attractiveforces between the particles. The YP isinfluenced by:

? Cross linking (eg. xc polymer).? Doubly charged cations causing flocculation

(eg. Ca2+ and Mg2+).? Polymers with anionic or cationic groups.? Reactive clays and bentonite.? Flocculated systems show high YP's and low

PV's

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PV and YP Related to Mud Chemistry

? The YP measured using the Bingham modelis generally higher than the true YP

? due to the inaccuracy of the Bingham modelat low shear rates.

? The Bingham model is fairly realistic forflocculated mud or high solids muds.

? The Power Law model gives greater accuracyat low shear rates.

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Effect of Temperature & Pressure

? Temperature reduces

viscosity

? Pressure increases

viscosity

? High temperature

? Breakdown of polymers

? Gelation of solids

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Variables in Hole Cleaning

? Annular Velocity

? Rate of penetration (ROP)

? Viscosity

? Hole Angle

? Mud Weight

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Recommended Values (Yp & PV)

36”/26”36”/26” 17 1/2”17 1/2” 12 1/4”12 1/4” 8 1/2”8 1/2”

Yield PointYield Point 40+40+ 2525 2020 1515

Plastic ViscosityPlastic Viscosity ALAPALAP ALAPALAP ALAPALAP ALAPALAP

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Recommended Mud PropertiesPrior to Cementing

• For top hole the ideal viscosity is ‘thick’ A Marsh Funnelviscosity of 150 seconds or more is ideal. Make sure thefluid is pumpable though.

• The 17 1/2” hole values are a minimum, most operators nowwish values of 25 - 30 or even 30 - 35 lb/100ft2

• Similarly with the 12 1/4” values, here systems are regularlyrun with YP’s of 25 - 30.

• Remember that during the drilling operations , at casingpoints it is desirable to reduce the viscosity for the cemenetjob, a recommended figure is 20 lb/100ft2 or less. Be carefulas it may be necessary to raise the YP after completion ofthe cement job. This can result in expensive treatments.

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