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Rheology
1: Introduction
Definition
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
Types of Fluids
Rheological
Flow Models
Measurements
Instruments
5: Measurements
6: Instruments
Introduction
to Rheology
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From www.iopro.auc.dk
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1: Introduction
Rheology
1: Introduction
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments
The term ”Rheology” was invented by Professor Bingham of
Lafayette College, Easton, PA, on the advice of a colleague, the
Professor of Classics. The definition of rheology (see section 2) was
accepted when the American Society of Rheology was founded in
1929.
Robert Hooke (1635-1703):
 in 1678 he developed his ”True Theory of Elasticy”:
”the power of any spring is the same proportion with the tension thereof”.
Isaac Newton (1643-1727):
 in 1687 he published the scientific book ”Principia”:
”the resistance which arises from the lack of slipperiness is proportional to the
velocity with which the parts of the liquid are separated from one another”.
In the 19th century scientists discovered solids with liquid-like
responses and liquids with solid-like responses.
Today, rheology is an integral part of industry. It is used by scientists
working with plastics, paint, inks, detergent, oils, drilling fluids, and
in quality and process control.
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Rheology
1: Introduction
2: Definition
Newton’s Law for liquids:
Hooke’s Law for solid:
 = 
 = 
3: Types of Fluids
4: Rheological
Flow Models
- shear stress
- viscosity
- shear rate
-
Newton’s model: dashpot, purely viscous response,
permanent deformation.
5: Measurements
6: Instruments

Hooke’s model: spring, purely elastic response, when
stress on spring is removed it ”recovers”.
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Difficult Subject
Rheology
1: Introduction
Rheology is a difficult subject.
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
For example, rheology is interdisciplinary and most scientists
and engineers have to move from a possibly restricted
expertise and develop a broader scientific approach.
6: Instruments
A cursory glance at most text books on rheology would soon
convince the non-mathematicians of the need to come to
terms with at least some aspects of non-trivial mathematics.
In this module we will give you an introduction to rheology
and explain mathematical complication to the nonspecialist.
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Rheology
1: Introduction
2: Definition
Rheology is the science of flow and deformation of matter.
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
A given material can behave like a solid or a liquid
depending on the time scale of the deformation process.
6: Instruments
From IDF 1982
The increase in force compared to
fluid velocity.
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From IDF 1982
The telescoping concentric
cylinder of a fluid in laminar flow.
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From IDF 1982
The relationship between pressure
and velocity on the flow regime.
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3: Types of Fluids
Rheology
1: Introduction
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
There are basically two types of fluids, defined by the
relationship between shear stress and shear rate.
These are:
 Newtonian
 Non-Newtonian
6: Instruments
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here
to
watch
video
From IDF 1982
Consistency curve for a
Newtonian fluid.
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From IDF 1982
Consistency curve for a
typical non-Newtonian fluid.
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From www.glossary.oilfield.slb.com
Go to http://web.mit.edu/nnf/ for more information and
videos about non-Newtonian Fluid phenomena.
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Rheology
1: Introduction
2: Definition
A Newtonian fluid is a fluid or dispersion whose rheological
behaviour is described by Newton’s law of viscosity.
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments
There are different types of non-Newtonian fluids:
 Pseudoplastic, a shear-tinning fluid.
 Dilatant, a shear-thickening fluid.
 Thixotropic: pseudoplastic flow that is time-dependent. At
constant applied shear rate, viscosity gradually decreases.
 Viscoelastic, a liquid (or solid) with both viscous and elastic
properties.
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Video
Rheology
1: Introduction
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments
Sett inn tekst
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Newtonian Fluid
Rheology
1: Introduction
2: Definition
Newtonian behaviour: Viscosity remains constant no matter
what the shear rate.
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments
From IDF 1982
Consistency curve for a
Newtonian fluid.
Newtonian fluids are the simplest type of fluid and contain no
particles larger than a molecule. In an Newtonian fluid, such
as water or oil, the shear stress is directly proportional to the
shear rate, while the fluid is in laminar flow.
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Shear-thinning non-Newtonian Liquid
Rheology
1: Introduction
2: Definition
Shear-thinning: The reduction of viscosity with increasing
rate of shear in a steady shear flow.
3: Types of Fluids
4: Rheological
Flow Models
Paint and toothpaste is shear-thinning fluids.
5: Measurements
6: Instruments
From IDF 1982
The consistency curve for a
Bingham Plastic fluid and the
apparent viscosity.
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Shear-thickening non-Newtonian Liquid
Rheology
1: Introduction
2: Definition
Shear-thickening: The increase of viscosity with increasing
rate of shear in a steady shear flow.
3: Types of Fluids
4: Rheological
Flow Models
Cream is a shear-thickening fluid.
5: Measurements
6: Instruments
From IDF 1982
The consistency curve for a
Pseudoplastic fluid.
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Viscoelastic Fluid
Rheology
1: Introduction
2: Definition
Descriptive term for a liquid having both viscous and elastic
properties.
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments
A viscoelastic liquid will deform and flow under the influence
of an applied shear stress, but when the stress is removed
the liquid will slowly recover from some of the deformation.
Viscoelastic fluids have molecules in which the loaddeformation relationship is time dependant.
From www.iopro.auc.dk
From www.iopro.auc.dk
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Viscoelastic Fluid
Rheology
1: Introduction
2: Definition
Viscoelasticity: everything flows, you just have to wait long
enough (think of the earth’s crust or glass).
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments
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4: Rheological Flow Models
Rheology
1: Introduction
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments
The models are an idealized relationship of rheological
behaviour expressible in mathematical, mechanical or
electrical terms.
Mathematical flow models of greatest interest to the Drilling
Fluids Engineer are the Newtonian, Bingham Plastic and
Power Law models.
Each of these models relate flow rate (shear rate) to flow
pressure (shear stress) while the fluid is in laminar flow.
No mathematical model is capable of providing a truly complete
rheological analysis.
The Bingham Plastic model has limitations in both the low and high
shear rate ranges, while the Power Law model provides more
realistic data that can predict fluid behaviour at low rates with
greater accuracy.
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The Newtonian Model
Rheology
1: Introduction
2: Definition
3: Types of Fluids
The Newtonian model has no value in predicting the
behaviour of a drilling fluid, as the majority of drilling fluids
do not conform to the govering Newtonian fluids.
4: Rheological
Flow Models
5: Measurements
6: Instruments
  
 – viscosity, Pas
 – shear stress, Pa
 – shear rate, sec-1
From IDF 1982
Consistency curve for a
Newtonian fluid.
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The Bingham Plastic Model
Rheology
1: Introduction
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
The Bingham Plastic model establishes a distinct relationship
between shear stress, yield point, plastic viscosity and shear
rate.
300  rpm
Apparant Viscosity 
5: Measurements
6: Instruments
RPM
 - dial reading
rpm – rotation per minute
Plastic Viscosity   600   300
Yield Point   300  Plastic Viscosity  2  300   600
PV: the portion of the resistance to flow (viscosity) that
is caused by interparticle friction (relates to solids
concentration, size and shape of the solids, viscosity of
the liquid phase).
YP: the portion of viscosity that is related to the
interparticle attractive force.
From IDF 1982
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The Power Law Model
Rheology
1: Introduction
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
The Power Law model is considerably more complex than the
Bingham Plastic model, but it provides for far greater
accuracy in the determination of shear stress at low shear
rates.
5: Measurements
6: Instruments
  K 
n
 – shear stress, N/m2 = Pa = 10 dynes/cm2
 – shear rate, sec-1
K – consistency index (constant)
n – Power Law index
The Power Law model actually describes
three types of fluids, based on the n value:
n=1: The fluid is Newtonian
n1: The fluid is non-Newtonian
n1: The fluid is Dilatent
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5: Measurements
Rheology
1: Introduction
Rheology: Flow property measurements.
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments
All fluids exhibit a certain resistance to flow, which is loosely
termed viscosity. Viscosity is defined as the relationship
between the shear stress (flow pressure) and the shear rate
(flow rate).
A non-Newtonian fluid is a fluid whose viscosity depends on
the force applied.
Temperature and pressure effects can alter rheological
properties drastically.
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Shear Stress
Rheology
1: Introduction
2: Definition
3: Types of Fluids
Shear stress: The force required to overcome a fluid’s
resistance to flow, divided by the area that force is acting
upon.
4: Rheological
Flow Models
5: Measurements
6: Instruments
F

A
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 – shear stress, N/m2 = Pa = 10 dynes/cm2
F – force applied, N
A – surface area subjected to stress, m2
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Shear Rate
Rheology
1: Introduction
2: Definition
Shear rate: The relative velocity of the fluid layers divided by
their normal separation distance.
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments
U
 
d
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 – shear rate, sec-1
U – velocity, m/sec
d – plate distance, m
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Viscosity
Rheology
1: Introduction
2: Definition
Viscosity is the resistance a material has to change in form.
This property can be thought of as an internal friction.
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments



Developers
 – viscosity, Pas
 – shear stress, Pa
 – shear rate, sec-1
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6: Instruments
Rheology
1: Introduction
2: Definition
3: Types of Fluids
4: Rheological
Flow Models
5: Measurements
6: Instruments
From www.iopro.auc.dk
Capillaryrheometer
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From www.glossary.oilfield.slb.com
Direct-reading rotating viscometer.
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Summary
Rheology
1: Introduction
2: Definition
3: Types of Fluids
In this module we have given you an
introduction to the subject rheology !
4: Rheological
Flow Models
5: Measurements
6: Instruments
Developers
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