Rheology

The study of how matter deforms and flows.

Measurement - Rotational Viscometer

Torsion Spring

Inner Cylinder

Bearing Shaft

Rotor

Bob

Cup

Interpretation of VG Readings

• Plastic Viscosity, centipoise- PV, cp = Rdg600 - Rdg300

• Yield Point, lbs/100 ft2

- YP, lbs/100 ft2 = (Rdg300 - PV)- YP, lbs/100 ft2 = 2(Rdg300) - Rdg600

• Initial Gel, lbs/100 ft2

- Static Rdg3 10 sec after stirring• 10 minute Gel, lbs/100 ft2

- Static Rdg3 10 minutes after stirring

Viscosity

V2, ft/sec

V1, ft/sec

V2 - V1

d, ft

orRateShear

StressShearityVis

RateShearainMatoForceStressShear

ftd

VVRateShear

ftlbs

ftlbs

ftft

1

100

100

sec1sec21

sec,

,cos

int,

,

,sec,

2

2

Fluid Layer #2

Fluid Layer #1

Viscosity, cp

• Shear Rate = 1.703 X VG rpm• Shear Stress = 1.0678 X VG rdg• Metric conversion factor = 478.9• Therefore:

, ..

.

:

cpVG

VG

or

VG

rdg

rpm

rpm

478 910678

1703

,cp = 300.28VGrdg

Viscosity from VG Rdgs(Illustration of Shear Thinning)

• Rdg600 = 50- Viscosity = 300(50/600) = 25 cp

• Rdg300 = 30- Viscosity = 300(30/300) = 30 cp

• Rdg100 = 13- Viscosity = 300(13/100) = 39 cp

• Rdg3 = 5- Viscosity = 300(5/3) = 500 cp

Plastic Viscosity, cp

• Determined by the fluid phase viscosity and the size, shape, and distribution of solids

• The lower limit of shear thinning• Should kept at the lowest value which is

economical• Control with:

- Dilution- Solids control equipment

Yield Point, lbs / ft2

• Determined by interparticle forces• Controlled by:

- Chemical (thinner) additions

Gel Strengths, lbs / 100 ft2

• Determined by interparticle forces• Initial Gel is used as an indicator of the shear

stress at ZERO shear rate• Initial Gel of 5 sec-1 is required for barite

suspension• Control by:

- Chemical (thinner) additions:

Fragile Gel Strengths

• Gel strength increases slightly after 10 min even if the Initial Gel is high

• Desirable, easily broken• Low Swab & Surge Pressures

Progressive Gel Strengths

• Gel strength increases significantly after 10 minutes, even if Initial Gel is low

• Indicates:- Solids crowding- High reactive solids concentration- Flocculation- Carbonate contamination

Rheological Models

• Equations which attempt to define the Shear Stress-Shear Rate relationship of fluids

• Models- Newtonian A - Bingham Plastic - Power Law n - Casson

0.5)2

- Robertson-Stiff n- Herschel-Bulkley n

Bingham Plastic Model

• Straight line when plotted on rectangular coordinates:- Plastic Viscosity is the slope of the line- Yield Point is the intercept on the Y axis

• Yield Point > 3rdg • Yield Point > Yield Strength• Does not identify pseudoplastic fluids

• If YP > 0, the data below 511 sec-1 is best described by a curve

Power Law

• Describes a curve on rectangular coordinates through the two Shear Stress-Shear Rate data points and orgin

• Does not approximate a Yield Strength• Not reliable the SS-SR range used for calculation• Not reliable for fluids which approach Bingham at low

Shear Rates• API recommends at least two equations: One for

calculations in pipe and another for the annulus

Power Law

Power Law Equation n

Shear Stress, lbs / ft2 K, Consistency Index , lbs / ft2

Shear stress at 1.0 sec-1 Shear Rate, sec-1 n, Power Law Index

Indicates fluid’s degree of non-Newtonian behavior n = 1, Fluid is Newtonian n < 1, Fluid is non-Newtonian (shear thinning) n > 1, Fluid is Dilatant, (shear thickening)

API Power Law Equations

• General Equations: n = log(log(

n

• Pipe: np = 3.32log(R600/R300) Kp = 5.11*R600np

• Annular: na = 0.657log(R100/R3) Ka = 5.11*R3np

Low Shear Rate Viscosity

• Viscosity of fluid at 0 to 5.1 sec-1 (3 rpm)• Viscosity at shear rates of barite and cuttings

falling in static fluids• Related to:

- Settling- Barite sag- Cuttings beds

Low Shear Rate Viscosity

• Yield Point• Yield Strength• 3rdg - 6rdg Yield Point = 6rdg - 2(3rdg)• 3rdg

• Brookfield Viscometer

Effect of Flow Rate on Pressure Losses, Impact Force & Hydraulic Horsepower

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

2750

3000

0 50 100 150 200 250 300 350 400 450

Flow rate, gpm

Pre

ssu

re L

oss

, Im

pac

t F

orc

e, &

Hyd

rau

lic

Ho

rsep

ow

er

Drill String & Annular LossesBit Pressure Loss

Hydraulic Impact Force

Hydraulic Horsepower

Maximum Allowable Surface Pressure

Optimized for Hyd. Horsepower

Optimized for Impact Force

Pressure Losses v. Flow Rate

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0 50 100 150 200 250 300 350 400 450

Flow Rate, gpm

Pre

ssu

re L

oss

, p

si

Drill String Pressure Losses

Annular Pressure Losses

Changing PV's in Bingham Plastic Model

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600 700 800 900 1000

Shear Rate, sec-1

Sh

ea

r S

tre

ss

PV = 10, YP = 10

PV = 30, YP = 10

PV = 50, YP = 10

Effects of PV on Bingham Plastic Viscosity, cp

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

0 100 200 300 400 500 600 700 800 900 1000

Shear Rate, sec-1

Vis

co

sit

y, c

p

PV = 10 cp, YP = 10 lbs/100 ft2

PV = 30 cp, YP = 10 lbs/100 ft2

PV = 50 cp, YP = 10 lbs/100 ft2

Shear Thinning Limit, 50 cp

Shear Thinning Limit, 30 cp

Shear Thinning Limit, 10 cp

Changing YP's in Bingham Plastic

0

10

20

30

40

50

60

70

80

0 200 400 600 800 1000 1200

Shear Rate, sec-1

Sh

ea

r S

tre

ss

, lb

s/1

00

ft2

PV = 20,YP = 0

PV = 20, YP = 10

PV = 20, YP = 20

PV = 20, YP = 30

Effects of on YP on Bingham Plastic Viscosity, cp

0

25

50

75

100

125

150

175

200

225

250

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Shear Stress, sec-1

Vis

co

sit

y, c

p

PV = 20 cp, YP = 10 lbs/100 ft2

PV = 20 cp, YP = 20 lbs/100 ft2

PV = 20 cp, YP = 30 lbs/100 ft2

PV = 20 cp, Yp = 0 lbs/100 ft2

Shear Thinning Limit of all 4 Fluids