E-Modul

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Rheology
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Topic overview
Definition
Types of Fluids
Rheological Flow Models
Rheology
Measurements
Instruments
Introduction to Rheology
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1 Introduction

• 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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?- shear stress ?- viscosity ?- shear rate ?- ?-

• Newtons Law for liquids ? ???
• Hookes Law for solid ? ???

Newtons model dashpot, purely viscous response,
permanent deformation.Hookes model spring,
purely elastic response, when stress on spring is
removed it recovers.
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Difficult Subject

• Rheology is a difficult subject.
• For example, rheology is interdisciplinary and
  most scientists and engineers have to move from a
  possibly restricted expertise and develop a
  broader scientific approach.
• 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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2 Definition

• Rheology is the science of flow and deformation
  of matter.

A given material can behave like a solid or a
liquid depending on the time scale of the
deformation process.
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3 Types of Fluids

• There are basically two types of fluids, defined
  by the relationship between shear stress and
  shear rate.
• These are
• Newtonian
• Non-Newtonian

Go to http//web.mit.edu/nnf/ for more
information and videos about non-Newtonian Fluid
phenomena.
Click here to watch video
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• A Newtonian fluid is a fluid or dispersion whose
  rheological behaviour is described by Newtons
  law of viscosity.
• 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
Sett inn tekst
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Newtonian Fluid

• Newtonian behaviour Viscosity remains constant
  no matter what the shear rate.
• 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

• Shear-thinning The reduction of viscosity with
  increasing rate of shear in a steady shear flow.
• Paint and toothpaste is shear-thinning fluids.

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Shear-thickening non-Newtonian Liquid

• Shear-thickening The increase of viscosity with
  increasing rate of shear in a steady shear flow.
• Cream is a shear-thickening fluid.

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Viscoelastic Fluid

• Descriptive term for a liquid having both viscous
  and elastic properties.
• 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
  load-deformation relationship is time dependant.

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Viscoelastic Fluid

• Viscoelasticity everything flows, you just have
  to wait long enough (think of the earths crust
  or glass).

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4 Rheological Flow Models

• 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

• 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.

? viscosity, Pas ? shear stress, Pa ?
shear rate, sec-1
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The Bingham Plastic Model

• The Bingham Plastic model establishes a distinct
  relationship between shear stress, yield point,
  plastic viscosity and shear rate.

? - dial reading rpm rotation per minute
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.
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The Power Law Model

• 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.

? 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 n1 The
fluid is Newtonian n?1 The fluid is
non-Newtonian n?1 The fluid is Dilatent
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5 Measurements

• Rheology Flow property measurements.
• 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

• Shear stress The force required to overcome a
  fluids resistance to flow, divided by the area
  that force is acting upon.

? 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

• Shear rate The relative velocity of the fluid
  layers divided by their normal separation
  distance.

? shear rate, sec-1 U velocity, m/sec d
plate distance, m
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Viscosity

• Viscosity is the resistance a material has to
  change in form. This property can be thought of
  as an internal friction.

• ? viscosity, Pas
• ? shear stress, Pa
• ? shear rate, sec-1

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6 Instruments
Capillaryrheometer
Direct-reading rotating viscometer.
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Developers
Topic expert and coordinator Skule
Strand Petroleum Technology Dept. Stavanger
University College NORWAY Module made
by Student Hege Anita Handeland Petroleum
Technology Dept. Stavanger University
College NORWAY
skule.strand_at_tn.his.no
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References

• An Introduction to Rheology
• H.A. Barnes
• J.F. Hutton
• K. Walters F.R.S.
• Elsevier Science Publishers B.V. 1989
• IDF
• International Drilling Fluids Limited 1982
• Technical Manual
• http//iprod.auc.dk/forsk/poly/student/c6-TK2/sld0
  19.htm
• http//search.eb.com/
• http//www.glossary.oilfield.slb.com/DisplayImage.
  cfm?ID397
• http//www.glossary.oilfield.slb.com/DisplayImage.
  cfm?ID374
• http//www.glossary.oilfield.slb.com/DisplayImage.
  cfm?ID379

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Summary

• In this module we have given you an introduction
  to the subject rheology !