baker hughes inteq drilling fluids reference manual

Drilling Fluids Reference Manual


Chapter 1 – Fundamentals of Drilling Fluids
Chapter 2 – Formation Mechanics
Chapter 3 – Water-Base Drilling Fluids
Chapter 4 – Contamination of Water-Base Muds
Chapter 5 – Oil/Synthetic Drilling Fluids
Chapter 6 – Reservoir Application Fluids
Chapter 7 – Borehole Problems
Chapter 8 – Corrosion
Chapter 9 – Hydraulics
Chapter 10 – Mechanical Solids Control
Chapter 11 – Horizontal & Extended Reach Drilling
Chapter 12 – Pressure Prediction and Control
Chapter 13 – Deepwater Drilling Fluids
Chapter 14 – Fluids Environmental Services
Chapter 15 – Glossary of Terms
Fundamentals of Drilling Fluids
Fundamentals of Drilling FluidsChapter
One


BAKER HUGHES DRILLING FLUIDS REFERENCE MANUAL
REVISED 2006 I
Chapter 1
Table of Contents
Fundamentals of Drilling Fluids 1-1
Functions of Fluids 1-1

Promote Borehole Stability 1-1
Remove Drilled Cuttings from Borehole 1-2
Cool and Lubricate Bit and Drillstring 1-2
Suspend Cuttings / Weight Material When Circulation Ceases 1-3
Support Partial Weight of Drillstring or Casing 1-3
Minimize Adverse Effects on Productive Formations 1-3
Transmit Hydraulic HP to Clean Bit and Bottom of Borehole 1-4
Release Undesirable Cuttings at the Surface 1-4
Ensure Maximum Information from Well 1-4
Limit Corrosion of Drillstring, Casing, and Tubular Goods 1-4
Minimize Environmental Impact 1-4
Physical and Chemical Properties of Fluids 1-5
API Recommended Practices 1-5
Density 1-5
Rheology, Viscosity and Gel Strength Relationships 1-5
Newtonian and Non-Newtonian Fluids 1-7
Viscosity 1-7
Flow Regimes 1-7
Determination of Flow Regime 1-10
Continuity of Flow 1-11
Mathematical Fluid Models 1-11
Newtonian Fluid Model 1-12
Bingham Plastic Model 1-12
Determination of PV and YP 1-14
Power Law Model 1-16
Determination of n and K 1-18
Other Models 1-20
Casson 1-20
Robertson-Stiff 1-20
Herschel-Bulkley 1-20

Table of Content
Reference Manual Baker Hughes Drilling Fluids
ii Revised 2006
Gel Strengths 1-21
Filtration 1-22
Testing Equipment 1-22
Permeability of Filter Cake 1-23
Pressure 1-23
Temperature 1-23
Viscosity 1-24
Time 1-25
Summary 1-25
Solids 1-25
Cation Exchange Capacity (CEC) 1-26
Low-Gravity Solids Analysis 1-29
Summary 1-30
Drilling Fluids pH and Alkalinity 1-30
Example Calculations 1-33
Parameters 1-33
Exercise 1-33
Drill-In Fluids 1-34
Function 1-34
Development 1-34
Attributes 1-34
Screening and Selection 1-34
The Proposed Drill-In and Completion Program 1-35
Leak-Off Control Tests 1-36
Return Permeability Tests 1-36
Drill-In Fluid Properties 1-37
Static Filtration 1-37

Lubricity Testing 1-37
Particle Size Distribution 1-37
Shale Inhibition (Wafer Test) 1-38
Density (API Standard Practice 13B-1, June 1990) 1-38
Fluid Viscosity 1-38
Water, Oil and Solids 1-38
MBT (Methylene Blue Titration) 1-39
Filter Cake Formation and Dispersability 1-39
Baker Hughes Drilling Fluids
Baker Hughes Drilling Fluids Reference Manual
Revised 2006 iii
Return Permeability vs. Breakout Pressure 1-42
Completion Fluids 1-44
Definition 1-44
Function 1-44
Attributes 1-44
Mechanisms for Formation Damage 1-44
Primary Factors Causing Formation Damage 1-45
Nomenclature 1-47
References 1-48

List of Figures
Figure 1-1 Deformation of a Fluid by Simple Shear 1-6
Figure 1-2 Three Dimension View of Laminar Flow in a Pipe for a Newtonian Fluid 1-8
Figure 1-3 Two/Three Dimensional Velocity Profile of Laminar Flow in a Pipe for a
Newtonian Fluid 1-8

Figure 1-4 Two Dimensional Velocity Profiles of Laminar Flow for a Non-Newtonian Fluid 1-9
Figure 1-5 Two-Dimensional Velocity Profile of Turbulent Flow in a Pipe for a Newtonian
Fluid 1-9

Figure 1-6 Fluid Velocity is inversely Proportional to the Cross-Sectional Area of the Fluid
Conductor 1-11

Figure 1-7 Flow Curve for a Newtonian Fluid 1-12
Figure 1-8 Flow Curve for a Bingham Plastic Fluid 1-13
Figure 1-9 Fann Model 35A 6 Speed V-G Meter 1-14
Figure 1-10 Flow Curve for a Power Law Fluid 1-16
Figure 1-11 Flow Behavior for Power Law Fluids 1-17
Figure 1-12 Drilling Fluid vs. Newtonian, Bingham, and Power Law Fluids 1-17
Figure 1-13 Determination of n and K 1-18
Figure 1-14 Gel Strength Characteristics vs. Time 1-22
Figure 1-15 SEM Photomicrograph X 150 – 2% PERFFLOW
®
Filter Cake on AF-6 1-40
Figure 1-16 SEM Photomicrograph 2% KCl PERFFLOW
®
– Pore Bridging 1-40
Figure 1-17 SEM Photomicrograph – 17 lb/gal PERFFLOW 1-41
Figure 1-18 SEM Photomicrograph - Sized Salt System 1-42
Figure 1-19 A Plot of Net Breakout Pressure vs. Return Permeability 1-42
Figure 1-20 The Effects of PERFFLOW
®
on Return Permeability and Breakout Pressure 1-43
Figure 1-21 Effects of TBC Salt System on Return Permeability and Breakout Pressure 1-43
Table of Content
Reference Manual Baker Hughes Drilling Fluids
iv Revised 2006

List of Tables

Table 1-1 V-G Meter Speed and Corresponding Shear Rate 1-19
Table 1-2 Viscosity of Water vs. Temperature 1-24
Table 1-3 Typical CEC Values 1-28
Table 1-4 Fluid System pH Ranges 1-31
Table 1-5 Typical pH Levels of Some Common Drilling Fluid Additives 1-32
Table 1-6 Fluid Parameters for Exercise Problem 1-33


BAKER HUGHES DRILLING FLUIDS REFERENCE MANUAL
REVISED 2006 1-1
Chapter 1
Fundamentals of Drilling Fluids
A major component in drilling operation success is drilling fluid performance. The cost of searching
for hydrocarbon reserves becomes more expensive when drilling occurs offshore, in deep water, and
in hostile environments. These drilling environments require fluids that excel in performance.
Measuring fluid performance requires the evaluation of all key drilling parameters and their
associated cost. Simply stated, the effectiveness of a fluid is judged by its influence on overall well
cost. This chapter discusses the various fundamentals of drilling fluids and their performance in
assuring a safe and expeditious drilling operation at minimum overall cost.
Functions of Fluids
Promote Borehole Stability
A fluid helps establish borehole stability by maintaining a chemical and/or mechanical balance.
Mechanical Stability
The hydrostatic pressure exerted by the drilling fluid is normally designed to exceed the existing
formation pressures. The desired result is the control of formation pressures and a mechanically
stable borehole. In many cases, these factors must also be considered:
• Behavior of rocks under stress and their related deformation characteristics
• Steeply dipping formations
• High tectonic activity
• Formations with no cohesive (lack of proper grain cementation) strength

• High fluid velocity
• Pipe tripping speeds and corresponding transient pressures
• Hole angle and azimuth
Any of these factors may contribute to borehole instability. In these situations, a protective casing
string may be required, or hydrostatic pressure may need to be increased to values greater than the
anticipated formation pressure.
Chemical Stability
Chemical interactions between the exposed formations of the borehole and the drilling fluid are a
major factor in borehole stability. Borehole formation hydration can be the primary cause of hole
instability, or a contributing factor.
Hydraulics
Reference Manual Baker Hughes Drilling Fluids
1-2 Revised 2006

Aqueous drilling fluids normally use a combination of:
• A coating mechanism (encapsulation)
• A charge satisfaction mechanism
• A mechanical or chemical method of preventing pore pressure transmission
The present use of low solids/non/dispersed fluids incorporates these principles. They rely on
polymers and soluble salts to inhibit swelling and dispersion. Commonly used polymers include:
• Polysaccharide derivatives for filtration control
• Partially hydrolyzed polyacrylamides for encapsulation
• Xanthan gum for viscosity
Isolating the fluid from the formation minimizes the potentially detrimental interaction between the
filtrate and the formation. This is accomplished by controlling mud filtrate invasion of the formation.
Filtrate invasion may be controlled by the type and quantity of colloidal material and by filtration
control materials and special additives like cloud point glycols and products containing complexed
aluminum.
Non-aqueous drilling fluids minimize wellbore instability problems by having all-oil filtrates and by
the osmotic pressure generated by the dissolved salt.

Remove Drilled Cuttings from Borehole
Drilling fluids transport cuttings from the well bore as drilling progresses. Many factors influence the
removal of cuttings from the hole.
The
velocity at which fluid travels up the annulus is the most important hole cleaning factor. The
annular velocity must be greater than the slip velocity of the cuttings for the cuttings to move up the
well bore.

The size, shape, and weight of a cutting determine the viscosity necessary to control its settling rate
through a moving fluid. Low shear rate viscosity strongly influences the carrying capacity of the fluid
and reflects the conditions most like those in the well bore. The drilling fluid must have sufficient
carrying capacity to remove cuttings from the hole.

The density of the suspending fluid has an associated buoyancy effect on the cuttings. An increase in
density increases the capacity of the fluid to carry cuttings.

Hole cleaning is such a complex issue that the best analysis method is to use a simulator, such as the
one contained in ADVANTAGE
®
.
Cool and Lubricate Bit and Drillstring
Considerable heat is generated by rotation of the bit and drillstring. The drilling fluid acts as a
conductor to carry this heat away from the bit and to the surface. Current trends toward deeper and
hotter holes make this a more important function.
The drilling fluid also provides lubrication for the cutting surfaces of the bit thereby extending their
useful life and enhancing bit performance.
Filter cake deposited by the drilling fluid provides lubricity to the drill string, as do various specialty
products. Oil and synthetic base fluids are lubricious by nature.
Baker Hughes Drilling Fluids
Baker Hughes Drilling Fluids Reference Manual

Revised 2006 1-3
Control Subsurface Pressure
As drilling progresses, oil, water, or gas may be encountered. Sufficient hydrostatic pressure must be
exerted by the drilling fluid column to prevent influx of these fluids into the borehole. The amount of
hydrostatic pressure depends on the density of the fluid and the height of the fluid column, i.e., well
depth. Typical materials used to maintain drilling fluid density include barite (MIL-BAR
®
), hematite
(DENSIMIX
®
), ilmenite and calcium carbonate (MIL-CARB
®
). The following formulae can be used
to calculate the total hydrostatic pressure at any given depth or fluid density:
Hydrostatic Pressure (psi) = 0.052 × Depth (ft) × Fluid Density (lb
m
/ gal)
or
Hydrostatic Pressure (psi) = 0.00695 × Depth (ft) × Fluid Density (lb
m
/ ft
3
)
or
Hydrostatic Pressure (kg / cm
2
) = 0.1 Depth (m) × Fluid Density (g / cm
3
)
While static pressures are important in controlling an influx of formation fluids, dynamic fluid

conditions must also be considered. Circulation of the drilling fluid and movement of the drillstring
in and out of the hole create positive and negative pressure differentials. These differentials are
directly related to flow properties, circulation rate, and speed of drillpipe movement. These pressures
may be calculated using the engineering software contained within ADVANTAGE.
Suspend Cuttings / Weight Material When Circulation Ceases
When circulation is stopped, drilling fluids must suspend the drilled cuttings and weight material.
Several factors affect suspension ability.
• Density of the drilling fluid
• Viscosity of the drilling fluid
• Gelation, or thixotropic properties of the drilling fluid
• Size, shape and density of the cuttings and weight material
Circulation of the suspended material continues when drilling resumes. The drilling fluid should also
exhibit properties which promote efficient removal of solids by surface equipment.
Support Partial Weight of Drillstring or Casing
The buoyancy effect of drilling fluids becomes increasingly important as drilling progresses to greater
depths. Surface rig equipment would be overtaxed if it had to support the entire weight of the drill
string and casing in deeper holes. Since the drilling fluid will support a weight equal to the weight of
the volume of fluid displaced, a greater buoyancy effect occurs as drilling fluid density increases.
Minimize Adverse Effects on Productive Formations
It is extremely important to evaluate how drilling fluids will react when potentially productive
formations are penetrated. Whenever permeable formations are drilled, a filter cake is deposited on
the wall of the borehole. The properties of this cake can be altered to minimize fluid invasion into
permeable zones. Also, the chemical characteristics of the filtrate of the drilling fluid can be
controlled to reduce formation damage. Fluid–fluid interactions can be as important as fluid-
formation interactions. In many cases, specially prepared drill-in fluids are used to drill through
particularly sensitive horizons.
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Reference Manual Baker Hughes Drilling Fluids
1-4 Revised 2006
Transmit Hydraulic HP to Clean Bit and Bottom of Borehole

Once the bit has created a drill cutting, this cutting must be removed from under the bit. If the cutting
remains, it will be “re-drilled” into smaller particles which adversely affect penetration rate of the bit
and fluid properties.
The drilling fluid serves as the medium to remove these drilled cuttings. One measure of cuttings
removal force is hydraulic horsepower available at the bit. These are the factors that affect bit
hydraulic horsepower:

• Fluid density
• Fluid viscosity
• Jet nozzle size
• Flow rate
Bit hydraulic horsepower can be improved by decreasing jet nozzle size or increasing the flow rate.
The two most critical factors are flow rate and nozzle size. The total nozzle cross sectional area is a
factor in increasing flow rate and hydraulic horsepower.
Release Undesirable Cuttings at the Surface
When drilled cuttings reach the surface, as many of the drilled solids as possible should be removed to
prevent their recirculation. Mechanical equipment such as shale shakers, desanders, centrifuges, and
desilters remove large amounts of cuttings from the drilling fluid. Flow properties of the fluid,
however, influence the efficiency of the removal equipment. Settling pits also function well in
removing undesirable cuttings, especially when fluid viscosity and gel strengths are low.
Ensure Maximum Information from Well
Obtaining maximum information on the formation being penetrated is imperative. A fluid which
promotes cutting integrity is highly desirable for evaluation purposes. The use of electronic devices
incorporated within the drill string has made logging and drilling simultaneous activities.
Consequently, optimum drilling fluid properties should be maintained at all times during drilling,
logging, and completion phases.
Limit Corrosion of Drillstring, Casing, and Tubular Goods
Corrosion in drilling fluids is usually the result of contamination by carbon dioxide, hydrogen sulfide,
oxygen or, in the case of static fluids, bacterial action. Low pH, salt-contaminated, and non-dispersed
drilling fluids are inherently more corrosive than organically treated freshwater systems. Oil or

synthetic-based fluids are considered non-corrosive. A proper drilling fluid corrosion control program
should minimize contamination and render the contaminating source non-corrosive.
Minimize Environmental Impact
Drilling creates significant volumes of used fluid, drill cuttings and associated waste. Increased
environmental awareness has resulted in legislation that restricts the use, handling and disposal of the
by-products generated during drilling and after the well is finished. Careful attention to the
composition of the fluid and the handling of the residual materials reduces the potential environmental
impact of the drilling operation.
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Baker Hughes Drilling Fluids Reference Manual
Revised 2006 1-5
Physical and Chemical Properties of Fluids
The physical and chemical properties of a drilling fluid play an important role in the success of a
drilling operation.
The properties of drilling fluid are perhaps the only variables of the entire drilling process that can be
altered rapidly for improved drilling efficiency. These properties usually receive the greatest
attention.
API Recommended Practices
The American Petroleum Institute (API) has set forth numerous recommended practices designed to
standardize various procedures associated with the petroleum industry. The practices are subject to
revision from time-to-time to keep pace with current accepted technology. One such standard is API
Bulletin RP 13B-1, “Recommended Practice Standard Procedure for Field Testing Water-Based
Drilling Fluids”. This Bulletin described the following drilling fluid measurements as necessary to
describe the primary characteristics of a drilling fluid:
• Density – for the control of formation pressures
• Viscosity and Gel Strength – measurements that relate to a mud’s flow properties
• Filtration – a measurement of the mud’s loss of liquid phase to exposed, permeable formations
• Sand – the concentration of sand (solid particles < 74µ) being carried in the mud
• Methylene Blue Capacity – an indication of the amount of reactive clays present in the mud
• pH – a measurement of the alkaline / acid relationship in the mud

• Chemical Analysis – qualitative and quantitative measurement of the reactive chemical
components of the mud
Chemical properties, such as chloride content, total hardness, etc., are important. They are discussed
in Chapter 4 of this manual, “Contamination of Water-Base Fluids”.

Density
The density of any fluid is directly related to the amount and average specific gravity of the solids in
the system. The control of density is critical since the hydrostatic pressure exerted by the column of
fluid is required to contain formation pressures and to aid in keeping the borehole open. Fluid density
in English units is commonly expressed in lb
m
/gal (lb
m
/ft
3
in some locations) and in specific gravity or
g/cm
3
in countries utilizing the metric system.
The density of any fluid should be dictated by formation pressures. The density must be sufficient to
promote wellbore stability. The pressure exerted by the fluid column should ideally be only slightly
higher than that of the formation to insure maximum penetration rate with minimal danger from
formation fluids entering the well bore.
The common method for checking the density of any drilling fluid is the mud balance. The mud
balance consists of a supporting base, a cup, a lid, and a graduated beam carrying a sliding weight. A
knife edge on the arm rests on the supporting base. It has become common in many locations to use
pressurized mud balances as these are considered to be more accurate.
Rheology, Viscosity and Gel Strength Relationships
The rheolgical properties, viscosity and gel strength of drilling fluids describe the ability of the fluid
to transport cuttings while drilling and suspend them when circulation is interrupted. Frequently, the

Hydraulics
Reference Manual Baker Hughes Drilling Fluids
1-6 Revised 2006
term “viscosity” is confused with the term “rheology”. A more detailed analysis of the term
“rheology” follows.
Rheology
Rheology is defined as physics of the flow and the deformation of matter. Rheology and the
associated annular hydraulics (Chapter 9) relate directly to borehole stability and how effectively the
borehole is cleaned. An understanding of rheology is essential if wellsite engineering of the drilling
fluid is to cost effectively complement the objective of drilling the well. Rheology and hydraulics of
drilling fluids are not exact sciences, but are based upon mathematical models that closely describe
the rheology and hydraulics of the fluid and do not conform exactly to any of the models.
Consequently, different methods are used to calculate rheology and hydraulic parameters.

Fluid Deformation
Rheology is the study of the deformation of all forms of matter. The deformation of a fluid can
simply be described by two parallel plates separated by some distance as shown in Figure 1-1.


Figure 1-1 Deformation of a Fluid by Simple Shear
Shear Stress
An applied force (F), acting over an area (A), causes the layers to slide past one another. However,
there is a resistance, or frictional drag, force that opposes the movement of these plates. This
resistance or drag force is called shear stress ( τ ). In equation form,
τ

F
A
=

with shear stress having typical units of lb
f
/100 ft
2
.
Additionally, the fluid layers move past each other easier than between a pipe wall and fluid layer.
Therefore, we can consider a very thin layer of fluid next to the pipe wall as stationary.
Shear Rate
The difference in the velocities between two layers of fluid divided by the distance between the two
layers is called the shear rate ( γ ). In equation form,
γ

velocity difference
dis cetan
=

With typical units of or, reciprocal seconds.

ft/sec
ft

1
sec
s e c
1–
==
Baker Hughes Drilling Fluids
Baker Hughes Drilling Fluids Reference Manual
Revised 2006 1-7
Newtonian and Non-Newtonian Fluids

The relationship between shear stress ( τ ) and shear rate ( γ ) defines the flow behavior of a fluid. for
some fluids, the relationship is linear. If the shear rate is doubled, then the shear stress will also
double. Such fluids are called Newtonian fluids. Examples of Newtonian fluids include water,
alcohols, and light oils. Very few drilling fluids fall into the Newtonian category.
Fluids which have flow characteristics such that the shear stress does not increase in direct proportion
to the shear rate are called non-Newtonian fluids. Most drilling fluids are of this type.
Viscosity
For a Newtonian fluid, the relationship between viscosity, shear stress and shear rate is defined as the
viscosity ( μ ) of the fluid where,
μ

τ
γ
=

where,
τ = shear stress
μ = viscosity
γ = shear rate.
As previously described, the relationship between shear stress and shear rate is directly proportional
for a Newtonian fluid. The viscosity remains constant and is the only parameter needed to
characterize the flow properties. The metric unit typically used for viscosity is the poise, defined as
the force in dynes per square centimeter required to produce a difference in velocity of one centimeter
per second between two layers one centimeter apart. A centipoise is one hundredth (1/
100
) of a poise.
For non-Newtonian fluids, the relationship between shear stress and shear rate is defined as the
effective viscosity. However, the effective viscosity of a non-Newtonian fluid is not constant. For
most drilling fluids, the effective viscosity will be relatively high at low-shear rates, and relatively low
at high-shear rates. In other words, the effective viscosity decreases as the shear rate increases. When

a fluid behaves in this manner, it is said to be shear thinning. Shear thinning is a very desirable
characteristic for drilling fluids. The effective viscosity of the fluid will be relatively lower at the
higher shear rates in areas such as the drill pipe and bit nozzles. Likewise, the effective viscosity of
the fluid will be relatively higher at the lower shear rates in the annulus where the higher effective
viscosity of the fluid aids in hole cleaning.

The relationship between shear stress and shear rate for non-Newtonian fluids is developed later in the
sub-section, Mathematical Fluid Models.
Flow Regimes
In 1883, Osborne Reynolds conducted experiments with various liquids flowing through glass tubes.
He introduced a dye into the flowing stream at various points. He found that when the flow rate was
relatively low, the dye he introduced formed a smooth, thin, straight streak down the glass. There was
essentially no mixing of the dye and liquid. This type of flow in which all the fluid motion is in the
direction of flow is called laminar flow.

Reynolds also found with relatively high flow rates, no matter where he introduced the dye it rapidly
dispersed throughout the pipe. A rapid, chaotic motion in all directions in the fluid caused the
crosswise mixing of the dye. This type of flow is called turbulent flow.

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Reference Manual Baker Hughes Drilling Fluids
1-8 Revised 2006
Reynolds showed further that under some circumstances, the flow can alternate back and forth
between being laminar and turbulent. When that happens, it is called transitional flow.

Therefore, we can describe a fluid's flow as being either laminar, turbulent, or transitional.
Additionally, another term has been used to describe a fluid's flow at extremely low flow rates – plug
flow.

The particular flow regime of a drilling fluid during drilling operations can have a dramatic effect on

parameters such as pressure losses, hole cleaning, and hole stability.
Plug Flow
In plug flow, the fluid moves essentially as a single, undisturbed solid body. Movement of the fluid
occurs due to the slippage of a very thin layer of fluid along the pipe wall or conductor surface. Plug
flow generally occurs only at extremely low flow rates.
Laminar Flow
The laminar flow of a Newtonian liquid in a circular pipe is illustrated in Figure 1-2. Laminar flow of
a Newtonian fluid can be visualized as concentric cylindrical shells which slide past one another like
sections of a telescope. The velocity of the shell at the pipe wall is zero, and the velocity of the shell
at the center of the pipe is the greatest.

Figure 1-2 Three Dimension View of Laminar Flow in a Pipe for a Newtonian Fluid
A two-dimensional velocity profile is illustrated in Figure 1-3. The shear rate, previously defined as
the velocity difference between two layers of fluid divided by the difference between the two layers,
is simply the slope of a line at any point along the velocity profile. The shear rate is greatest at the
wall and zero at the center of the pipe. Since the shear stress and shear rate for a Newtonian fluid are
directly proportional, the shear stress is also greatest at the wall and zero at the center of the pipe.


Figure 1-3 Two/Three Dimensional Velocity Profile of Laminar Flow in a Pipe for a Newtonian
Fluid
The laminar flow of a non-Newtonian fluid is very similar to that of a Newtonian fluid with the
exception that some portion of the cylindrical shells in the center of a pipe may not slide past one
another.

Baker Hughes Drilling Fluids
Baker Hughes Drilling Fluids Reference Manual
Revised 2006 1-9

Figure 1-4 Two Dimensional Velocity Profiles of Laminar Flow for a Non-Newtonian Fluid

The two dimensional velocity profile of a non-Newtonian fluid in laminar flow depends upon the
relationship between the shear stress and shear rate. Several examples of the velocity profile are
shown in Figure 1-4.
Turbulent Flow
Turbulent flow occurs when a fluid is subject to random, chaotic shearing motions that result in local
fluctuations of velocity and direction, while maintaining a mean velocity parallel to the direction of
flow. Only near the walls does a thin layer of orderly shear exist. Thus the velocity profile is very
steep near the walls, but essentially flat elsewhere as shown in Figure 1-5.
Transitional Flow
Transitional flow occurs when the flow of a fluid is neither completely laminar nor completely
turbulent. In other words, there is no abrupt transition from one flow regime to another.


Figure 1-5 Two-Dimensional Velocity Profile of Turbulent Flow in a Pipe for a Newtonian Fluid
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Reference Manual Baker Hughes Drilling Fluids
1-10 Revised 2006
Determination of Flow Regime
The experiments conducted by Reynolds, besides naming the behavior of fluid flow, made the most
celebrated application of dimensional analysis

in the history of fluid mechanics by introducing the
Reynolds Number (Re).

Reynolds number takes into consideration the basic factors of pipe flow – pipe diameter, average fluid
velocity, fluid density, and fluid viscosity. Reynolds number is defined as
where,
V = average fluid velocity

D = pipe diameter
ρ = fluid density
μ= fluid viscosity
Reynolds showed that for smooth, circular pipes, for all Newtonian fluids, and for all pipe, the
transition from laminar to turbulent flow occurs when the Reynolds number has a value of
approximately 2000. However, turbulent flow throughout the fluid occurs when the Reynolds number
is more than 4000.

Therefore, for Newtonian fluids, laminar flow is defined as a Reynolds number of 2000 or less.
Turbulent flow is defined as a Reynolds number of 4000 or greater. Transitional flow is defined when
the Reynolds number is between 2000 and 4000.
As previously shown, the viscosity of non-Newtonian fluids depends upon the relationship between
shear stress and shear rate. Likewise, the value of the Reynolds number at which the transition from
laminar to turbulent flow occurs depends upon the shear stress/shear rate relationship.
The relationship between shear stress and shear rate for non-Newtonian fluids is developed in the
subsection, Mathematical Fluid Models .
μ
=Re
()()()
ρ
DV
Baker Hughes Drilling Fluids
Baker Hughes Drilling Fluids Reference Manual
Revised 2006 1-11

Continuity of Flow
Many hydraulic calculations in this manual require the use of the fluid velocity. It is important to
understand the difference between flow rate and velocity. Consider the flow of a liquid through a
pipe at a constant flow rate, as illustrated in Figure 1-6

Figure 1-6 Fluid Velocity is inversely Proportional to the Cross-Sectional Area of the Fluid
Conductor
An algebraic solution to the above diagram is described as follows:
Q
flow
= V
1
A
1
= V
2
A
2

If A
2
= ½ A
1

V
1
(2A
2
) = V
2
A
2

V
1
= ½ V
2

Because drilling fluids are very nearly incompressible, the volumetric flow rate of fluid entering the
pipe must equal the volumetric flow rate leaving the pipe. This is the principle of continuity of flow.
The important result of this principle is that, at a constant flow rate, the fluid velocity is inversely
proportional to the area through which it flows. In other words, if the area decreases, the fluid
velocity must increase for a constant flow rate.

Mathematical Fluid Models
A mathematical fluid model describes the flow behavior of a fluid by expressing a mathematical
relationship between shear rate and shear stress. As described in the viscosity section, the shear
stress/shear rate relationship is a constant for Newtonian fluids.
For non-Newtonian fluids, however, the relationship between shear stress and shear rate is much more
complex. A generalized relationship for all non-Newtonian fluids has not been found. Instead,
various mathematical models have been proposed. These mathematical models do not describe the
behavior of non-Newtonian fluids exactly, but are merely close approximations.
Discussed below is a Newtonian Fluid Model which can be considered exact for Newtonian fluids,
and two non-Newtonian fluid models – the Bingham Plastic Model and the Power Law Model.
Additional models described are the Casson Model, the Robertson-Stiff Model, and the
Herschel-Bulkley Model.
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Reference Manual Baker Hughes Drilling Fluids
1-12 Revised 2006
Newtonian Fluid Model
The Newtonian Fluid Model is the basis from which other fluid models are developed. The flow
behavior of Newtonian fluids has been discussed and it can be seen from this equation that the shear
stress-shear rate relationship is given by:

τ

μ
()γ)
(
=

where,
τ = shear stress
μ = viscosity
γ = shear rate
At a constant temperature, the shear stress and shear rate are directly proportional. The
proportionality constant is the viscosity (μ).
Figure 1-7 illustrates the flow curve of a Newtonian fluid. Note that the flow curve is a straight line
which passes through the origin (0, 0) and the slope of the line is the viscosity (μ).

Figure 1-7 Flow Curve for a Newtonian Fluid
Bingham Plastic Model
In the early 1900s, E.C. Bingham first recognized that some fluids exhibited a plastic behavior,
distinguished from Newtonian fluids, in that they require a yield stress to initiate flow. No bulk
movement of the fluid occurs until the applied force exceeds the yield stress. The yield stress is
commonly referred to as the Yield Point. The shear stress / shear rate relationship for the Bingham
Plastic Model is given by:
τ

τ
o
μ(
∞
)γ)(

+=

where,
τ = shear stress
τ
o
= yield point
μ
∞
= Plastic viscosity
γ = shear rate.


Baker Hughes Drilling Fluids
Baker Hughes Drilling Fluids Reference Manual
Revised 2006 1-13
The flow curve for a Bingham Plastic fluid is illustrated in Figure 1-8. The effective viscosity, defined as
the shear stress divided by the shear rate, varies with shear rate in the Bingham Plastic Model. The
effective viscosity is visually represented by the slope of a line from the origin to the shear stress at some
particular shear rate. The slopes of the dashed lines represent effective viscosity at various shear rates.
As can be seen, the effective viscosity decreases with increased shear rate. As discussed in the Viscosity
section, this is referred to as shear thinning.



Figure 1-8 Flow Curve for a Bingham Plastic Fluid

As shear rates approach infinity, the effective viscosity reaches a limit called the Plastic Viscosity.
The plastic viscosity of a Bingham Plastic fluid represents the lowest possible value that the effective
viscosity can have at an infinitely high shear rate, or simply the slope of the Bingham Plastic line.

The Bingham Plastic Model and the terms plastic viscosity (PV) and yield point (YP) are used
extensively in the drilling fluids industry. Plastic viscosity is used as an indicator of the size, shape,
distribution and quantity of solids, and the viscosity of the liquid phase. The yield point is a measure
of electrical attractive forces in the drilling fluid under flowing conditions. The PV and YP are two
parameters of a drilling fluid that many in the industry still consider to be vitally important in the
overall drilling operation. The YP is now considered an outdated concept that has no real meaning or
application in drilling operations. The following rheological models better describe the behavior of
drilling fluids. This can clearly be seen when the viscometer readings are plotted on a graph and the
resultant line is a curve and not a straight line. The Bingham model uses a straight line relationship.
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Reference Manual Baker Hughes Drilling Fluids
1-14 Revised 2006
Determination of PV and YP
The commonly used V-G (viscosity-gel) meter, or direct indicator viscometer, was specifically
designed to facilitate the use of the Bingham Plastic Model in conjunction with drilling fluids in the
field. The instrument has a torsion spring-loaded bob which gives a dial reading proportional to
torque and analogous to the shear stress. The speed of rotation (rpm) is analogous to the shear rate.
When the V-G meter (with the proper rotor, bob, and spring) is used, the dial reading is determined
as:
θ
= YP + PV
ω
300

⎠
⎞
⎝
⎛

where,

θ = dial reading
YP = yield point
PV = plastic viscosity
ώ = rotation speed (rpm)

Figure 1-9 Fann Model 35A 6 Speed V-G Meter
Baker Hughes Drilling Fluids
Baker Hughes Drilling Fluids Reference Manual
Revised 2006 1-15
As defined in the Fluids Testing Procedures Manual, the determination of PV and YP are obtained
from the dial readings at 600 rpm and 300 rpm. Substitution of the appropriate data into the equation
shows how these terms are derived.
θ
600
= YP + PV
600
300

⎠
⎞
= YP + 2PV
⎝
⎛

θ
300
= YP + PV
300
300

⎠
⎞
= YP + PV
⎝
⎛

By subtracting θ
300
from θ
600
, we obtain,
θ
600
θ
300
–
()
= YP
(
2PV
)
YP PV+
()
= YP YP
)
+ 2PV PV
)
= 0 –PV+
(
–

(
–+

or,
PV
θ
600
θ
300
–
()
=

By re-arranging the earlier equation for θ
300
, we have,
YP
θ
300
PV–
()
=

where,
θ
600
= 600 rpm dial reading
θ
300
= 300 rpm dial reading

Effective viscosity has been previously defined as the shear stress divided by the shear rate or the
slope of the line passing through the origin to the shear stress at some particular shear rate. From the
equations above, we see that PV can represent the effective viscosity if YP = 0, written as,
θ
600
02
μ(
∞
)
+=

The effective viscosity at a shear rate of 600 rpm on the V-G meter is distinguished from the effective
viscosity at other shear stress/shear rate data values by the term apparent viscosity. Therefore,
apparent viscosity is defined at a 600 rpm shear rate by,
μ
∞

θ
600
2
=

Although plastic viscosity (PV) and yield point (YP) are two of the most recognized properties of
drilling fluids, these terms are simply constants in the Bingham Plastic Mathematical Model. Very
few drilling fluids follow this model, but the empirical significance of PV and YP is firmly entrenched
in drilling technology. In fact, drilling fluid systems such as the NEW-DRILL
®
system and many
others deviate significantly from the Bingham Plastic Model and the terms PV and YP must be
interpreted with caution.

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Reference Manual Baker Hughes Drilling Fluids
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Power Law Model
Most drilling fluids exhibit behavior that falls between the behaviors described by the Newtonian
Model and the Bingham Plastic Model. This behavior is classified as pseudo plastic. The
relationship between shear stress and shear rate for pseudo plastic fluids is defined by the power law
mathematical model,
τ
K
γ
(
n
)
=

where,
τ = shear stress
K = consistency factor
γ = shear rate
n = flow behavior index
Figure 1-10 illustrates the flow curve for a pseudo plastic fluid.

Figure 1-10 Flow Curve for a Power Law Fluid
The two terms, K and n, are constants in the Power Law Model. Generally, K is called the consistency
factor and describes the thickness of the fluid and is thus somewhat analogous to effective viscosity.
If the drilling fluid becomes more viscous, then the constant K must increase to adequately describe
the shear stress/shear rate relationship.

Additionally, n is called the flow behavior index and indicates the degree of non-Newtonian behavior.
A special fluid exists when n = 1, when the Power Law Model is identical to the Newtonian Model. If
n is greater than 1, another type of fluid exists classified as dilatant, where the effective viscosity
increases as shear rate increases. For drilling fluids, the pseudo plastic behavior is applicable and is
characterized when n is between zero and one. Pseudo plastic fluids exhibit shear thinning, where the
effective viscosity decreases as the shear rate increases just like the Bingham Plastic Model. Figure
1-11 shows the flow curves for these values of n.
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Revised 2006 1-17


Figure 1-11 Flow Behavior for Power Law Fluids
Similar to the Bingham Plastic Model, the Power Law Model does not describe the behavior of
drilling fluids exactly. However, the Power Law constants n and K are used in hydraulic calculations
(Chapter 9) that provide a reasonable degree of accuracy.

Figure 1–12 compares the flow curve of a typical drilling fluid to the flow curves of Newtonian,
Bingham Plastic, and Power Law Models.

Figure 1-12 Drilling Fluid vs. Newtonian, Bingham, and Power Law Fluids
A typical drilling fluid exhibits a yield stress and is shear thinning. At high rates of shear, all models
represent a typical drilling fluid reasonably well. Differences between the models are most
pronounced at low rates of shear, typically the shear rate range most critical for hole cleaning and the
suspension of weight material.
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Reference Manual Baker Hughes Drilling Fluids
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The Bingham Plastic Model includes a simple yield stress, but does not accurately describe the fluid
behavior at low shear rates. The Power Law Model more accurately describes the behavior at low

shear rates, but does not include a yield stress and therefore can give poor results at extremely low
shear rates. A typical drilling fluid actually exhibits behavior between the Bingham Plastic Model
and the Power Law Model. This sort of behavior approximates the Herschel Bulkley model which is
described below.
Determination of n and K
The Power Law constants n and K can be determined from any two sets of shear stress-shear rate data.
Baker Hughes Drilling Fluids has chosen to follow API Bulletin 13D in developing n and K values
from 300 rpm and three rpm V-G meter readings (initial gel shear rate is approximately equal to three
rpm) for the low shear rate region, and 600 rpm and 300 rpm readings for the high shear rate range.
The low shear rate region corresponds roughly to the shear rate existing in the annulus, while the high
shear rate region corresponds to the shear rate existing in the drill pipe. This may be written in
logarithmic form as,
τ
K + n
γ
lo
g
()
lo
g
=lo
g

A plot of shear stress versus shear rate on log-log paper is linear for a pseudo plastic fluid. As shown
in Figure 1–13, the slope of the curve is equal to n, and the intercept on the shear stress axis at γ = 1 is
equal to K (since log 1 = 0).
LOG DIAL READING, Θ
SHEAR RATE, Ў
1
10 100 1000

Log Θ
300
Log Θ
600
Log Θ
600
–Log Θ
300
n
p
n
a
Log Θ
3
Log Θ
300
–log Θ
3
Log 511 – log 5.11
n
Log K
3 rpm
Log Θ
600
–n
p
log 1022
Log Θ
300
–n

a
log 511
300 rpm
600 rpm
Log 1022 – log 511
n
p
log 1022
n
a
log 511

Figure 1-13 Determination of n and K