Bab_05 Drilling Fluid Rheolgy.pdf

drilling �uid rheology

rheology

section 5

section 5a - rheology of drilling �uids

section 5b - rheology and hydraulics

of drilling �uids

section 5a

rheology of drilling !uids

theory of rheology 2

rheology background 2

shear rate 3

shear stress 3

viscosity 4

!uid models 4

Herschel-Bulkley (modi"ed power law) model 6

measurement of shear stress - shear rate

relationship 9

“n” and “K” constants 10

laminar and turbulent !ow regimes 12

rheology – "eld application 13

plastic viscosity (pv) 13

yield point (yp) 13

gel strength 14

funnel viscosity 15

low shear rheology 16

shear rates in the drilling !uid circulating system 16

cuttings transportation theory 16

cuttings transport ratio 16

general transport ratio (gtr) 17

annular cutting concentration and optimum rop 17

section 5a Scomi Oiltools

2

Section

5a rheology of drilling !uids

theory of rheology

rheology backgroundRheology is derived from the Greek words rheo, meaning flow and logi, meaning science. It can

be defined as the science of the deformation and/or flow of solids, liquids and gases under applied stress.

In essence, the science deals with the stress-strain-time relationships of any matter.

The rheological characteristics of materials form a continuous spectrum of behaviour ranging from

that of the perfectly elastic solid at one extreme to that of the purely viscous Newtonian fluid at the

other. Between these extremes lies the behaviour of fluids which possess varying degrees of the

character of both extreme materials, such materials are termed visco-elastic.

Relatively little theoretical or experimental work was done in the field of rheology until the early

twentieth century. The science is in fact still in it’s infancy in terms of the ability to provide accurate

predictions of the behaviour of real systems. This is particularly true with regard to both the polymer

and invert oil emulsion muds being used in drilling operations today, which have far more complex

behaviour than true fluids.

Despite this it is still common practice to express flow characteristics in terms of simple viscosity

terms such as the constants used in the Bingham Plastic and Power Law models. It is also recognized

that surface measurements do not truly represent the fluid behaviour under downhole conditions

at temperature and pressure, but extensive field studies have resulted in a high degree of success

in predicting a fluids performance from this data.

Certain basic concepts of rheology require to be understood to make optimum use of collected

data. Of these concepts the relationship between shear stress and shear rate is most important in

predicting drilling fluid behaviour.

Knowledge of the flow characteristics of circulating fluids is of advantage in almost all phases of

down hole operations. Some of the more important applications relate to selection and design of

fluids to obtain optimum rates of circulation to transport and suspend drill cuttings, increase drilling

rates and reduce hole erosion.

In the drilling situation the application of rheological concepts for drilling fluids are primarily directed

towards:

a) Suspension.

b) Hydraulic calculations.

c) Hole cleaning and hole erosion.

d) Filtrate migration.

e) Solids Control.

Although these applications may be of equal importance, drilling requirements vary with time and

location so that one may take precedence over another at a particular time.

In all applications, whether or not a fluid performs a specific function can be attributed to the absence

or presence of viscosity at the shear rate of interest.

rheology of drilling !uids

3

shear rateIn a moving fluid shear rate can be defined as the rate at which one layer of fluid is moving by another

layer divided by the distance between the layers. It is the velocity gradient i.e. the ratio of velocity to

distance between layers.

Consider a fluid between two flat plates one centimetre apart. If the bottom plate is fixed while the

top plate slides parallel to it at a constant velocity of 1 cm per sec, a velocity profile will be found

within the fluid. The fluid layer in contact with the bottom plate is static while the layer in contact with

the top plate is moving at 1 cm per sec. Halfway between the plates the fluid velocity is the average

0.5 per sec.

If a moving layer of fluid has a velocity 1cm/sec relative to a static layer at separation distance of 1cm

then the shear rate between these layers will be:

The reciprocal second is the standard unit of shear.

In a drilling fluid circulating system the shear rate is determined by the flow rate through a particular

geometrical configuration. Since the relative velocity between fluid layers is greatest adjacent to the

pipe or hole wall the shear rate is highest at this point. An average shear rate may be used, but the

shear itself is not constant everywhere in the flow.

shear stressShear Stress is defined as the force required to move a given area of the fluid. In this case one Newton

is required for each square meter of area. The units of shear stress are Newtons per square metre,

also known as Pascals. Alternative units for shear stress are dynes per square centimetre and pounds

force per square inch. Shear stress is related to the force required to sustain fluid flow. In a drilling

fluid circulating system this is analogous to the pump pressure.

1 cm/sec

1cm = 1 sec –1

This diagram shows the forces acting on a theoretical liquid. The liquid is contained between the

two 1 square metre plates which are separated by one metre. The bottom plate is stationary and

the top plate is moved at a rate of 1 metre per second. The amount of force required to maintain

this movement is measured in Newtons.

In a drilling fluid circulating system the shear rate is determined by the flow rate through a particular

geometrical configuration. Since the relative velocity between fluid layers is greatest adjacent to the

pipe or hole wall the shear rate is highest at this point. An average shear rate may be used, but the

shear itself is not constant everywhere in the flow.

If, in the parallel plate example used to describe shear rate, a force of 1.0 dyne was applied to each

square centimetre of the top plate to keep it moving. Then the shear stress would be 1.0 dyne per cm2.

The same force in the opposite direction would be needed on the bottom plate to keep it from moving.

The same shear stress would be found at any level in the fluid. Shear stress is constant only as long as

the flow system geometry is constant. It is more common to find the shear stress varying from one part

of a flow system to another.

4

Section


The units of shear stress are the same as for pressure, but whereas pressure defines the applied force

per unit area, shear stress is the internal resistance to an applied stress.

Shear stress can be expressed:

shear stress = F/A

Where F = force

A = area of surface subject to stress.

The standard unit of shear stress is dynes/cm2

Shear rate and shear stress are the two basic quantities involved in the sliding (shearing) flow of a

fluid. Then shear rate is related to the velocity of motion and the shear stress to the forces being

transmitted both to the fluid and from one part of a fluid to another.

viscosity Viscosity can be described as the resistance to flow and is defined as the ratio of shear stress to

shear rate

Viscosity = shear stress dynes / cm2 = Poise

Shear rate sec–1

The units of Poise are too large for drilling fluid studies and viscosity is reported in centipoises or

millipascal.second (1cP = 1 mPa.s).

Since viscosity is dependent on both shear rate and shear stress, one or the other must be specified

when a viscosity measurement is stated. Shear rate is the usual variable defined, either as an actual

shear rate in reciprocal seconds or as speed in rpm from a concentric cylinder viscometer.

!uid modelsFluids can be separated into different classes according to the relationships which exists in a fluid

between shear rate and shear stress. The most simple class of fluids are called Newtonian. Water and

light oils are examples of Newtonian fluids.

shear stress.dynes/cm2

shear ratesec–1 Viscosity= = Poise

5

In these fluids the shear stress is directly proportional to the shear rate. When the shear rate is doubled

the shear stress is doubled i.e. when the circulation rate is doubled the pressure required to pump the

fluid is doubled. Such fluids have a constant viscosity.

For most fluids, viscosity is not a constant, but varies with the shear rate. Such non Newtonian fluids

are called rate dependent. Almost all drilling fluid viscosifiers provide rate dependent fluids.

To illustrate rate dependent effects a fluid is tested for shear stress or viscosity at a number of shear

rates. When these data are plotted on a log-log scale a viscosity profile of the fluid is obtained.

Examples of types of flow are:

The shear rate / shear stress ratio of non Newtonian fluids is not constant, which is true of most

drilling fluids. The two most popular mathematical models for describing non-Newtonian drilling fluids

are called the Bingham Plastic model and Power Law model.

Non Newtonian Fluid Behaviour

SHEAR RATE ,

SH

EA

R S

TR

ES

S,

6

Section


Some fluids have a critical yield stress which must be exceeded before flow is initiated. If the

fluid has essentially Newtonian flow after the yield stress is exceeded it is termed a Bingham Plastic

fluid. The major shortcoming of the application of this model to drilling fluids is that it only

describes fluid flow over a short shear rate range of 511 - 1022 sec-1. Consequently the Bingham model

may not accurately describe fluid rheological characteristics in all drilling situations.

Most drilling fluids are Pseudoplastic. In this case increased shear rate produces a progressive

decrease in viscosity. In polymer solutions this is due to the alignment of the long polymer chains

along the flow lines. If the application of any shear stress above zero produces fluid flow, i.e. no critical

yield stress, the fluid is termed a Power Law fluid. This model more accurately describes flow

characteristics of drilling fluids over the shear rate ranges experienced in the annulus of a well bore.

Polymeric drilling fluids can be shown to follow the Power Law model very closely. Some other fluids

show a profile which falls between Power Law and Bingham Plastic.

Although the API has selected the Power Law model as the standard model, the Power Law

model, however, does not fully describe drilling fluids because it does not have a yield stress and

underestimates low shear rate viscosity. The modified Power Law or Herschel-Bulkley model can be

used to account for the stress required to initiate fluid movement (yield stress).

The diagram shows the differences between the modified Power Law, the Power Law and Bingham

Plastic models. The modified Power Law falls between the Bingham Plastic model, which is highest,

and the Power Law, which is lowest and consequently more closely resembles the flow profile of a

typical drilling mud.

Herschel-Bulkley (modi"ed power law) modelIn reality, most drilling fluids have a yield stress. The Herschel-Bulkley or the modified power law is

the best model to precisely describe the rheological behaviour of drilling fluids compared to any

other models. It is a three parameter model that reproduces the results of the previous models (Bingham

Power Law, Newtonian) when the appropriate parameters have been measured. The Herschel-Bukley

model uses the following equation to describe fluid behaviour:

+ (K x n)

7

Newtonian

Bingham-Plastic

Power-Law

Herschel-Bulkley ✓

0

13.1257

0

10.9075

Rheology Model YP (Ibf/100ft2)

Vis., PV or K (cp)

n StandardDeviation

DrawCurve

46.8023868

37.2818854

2842.1364294

97.1097869

1

1

0.3578

0.8627

3.9039

0.7181

3.6169

0.1644

Figure 1: Calculated rheology model in “HyPR-CALC”

0

0 100 200 300

Measurement

Newtonian

Herschel-Bulkley

Speed (rpm)

Vis

com

ete

r R

ea

din

g

400 500 600

10

20

30

40

50

60

70

80

90

100

Figure 2: Rheology models available in Scomi Oiltools hydraulic program “HyPR-CALC”

Herschel-Bulkley graph usually reflects a yield stress where the shear stress is greater than zero where as

a Newtonian graph is usually a straight line that originates from shear stress equal to zero.

Where

= shear stress in lb/100 ft2

= fluids yield stress (shear stress at zero shear rate) in lb/100 ft2

K = fluids consistency index in cP - secn or lb - secn/100 ft2

n = fluids flow index

= shear rate in sec-1

In Herschel-Bulkley model, the K and n values are worked out differently than their counterparts in

the power law model. The Herschel-Bulkley reflects more to Bingham model when n = 1 and it

reflects to the power law model when 0 = 0. [One obvious advantage the Herschel-Bulkley model has

over the power law model is that, from a set of data input, only one value for n and K are calculated.]

Hydraulics calculations for Herschel-Bulkley (modified power law) fluids cannot be solved by simple

equations. For quick solutions, consult the Scomi Oiltools hydraulics programs using HyPR-CALC.

Calculated Results

8

Section


Invert emulsion muds are suspensions of both solids and emulsions and there is no accepted

rheological model that can be applied to both emulsions and suspensions, in addition these fluids

show pronounced pressure and temperature effects. A Casson Model is sometimes used to describe

invert fluids though some oil muds can be shown to follow the Bingham Plastic model between

shear rates of 127- 340 sec–1 (75-250 rpm). Below 127–1 the characteristics lie between Power Law and

Bingham Plastic.

The Newtonian, Bingham Plastic, and Power Law models are specific cases of the Robertson-Stiff

model. It is a three parameter model that includes the 3 rpm rheometer dial reading and is written in its

general form as:

= K( 0 + )n

To use common rheometer data for the analysis of a fluid conforming to the Robertson-Stiff model,

the general equation becomes

Where:

N3, N2, and N1 are rpm speeds and N3 > N2 > N1,

3, 2, and 1 are rheometer sheer stress readings at N3, N2, and N1, respectively.

This equation must be solved iteratively to find n. 0 and k can then be calculated by solving the

following equations.

where

b = the ratio of the rheometer sleeve radius to the bob radius.

The Robertson-Stiff equation will generally provide the best approximation for pressure losses in

the circulating system in most drilling situations. It will not, however, emulate a fluid that follows

the Casson equation.

If a fluid profile shows a critical yield stress and then flows like the pseudoplastic model it is referred

to as an Ellis fluid. This model has been used to describe Xanthan Gum solutions. The yield stress is

equivalent to the elastic modulus of the solution.

Some rare fluids show Dilatant or reverse pseudoplastic behaviour. These are characteristically

suspensions having a high solids loading e.g. high concentration gypsum suspensions. These

fluids increase in viscosity with increasing shear rate and can show a negative calculation of yield

point, the true figure is zero.

1

2

nN3 N2

N3 – N1

3

2

nN2 N1

N3 – N1

30 ln(b)

ln(b)

9

Besides shear rate dependent effects some fluids can also exhibit time dependent effects. In these

cases the viscosity changes with continued shear at constant rate.

Fluids which are thixotropic in nature decrease in viscosity with time. This type of fluid shows a

memory effect or hysteresis when subjected to varying rates of shear. There is a time lag in

establishing an equilibrium viscosity when the shear rate is changed, the fluid will initially tend

towards to the viscosity associated with the previous shear rate.

Some highly concentrated suspensions can display herpetic flow. In this case the viscosity of the fluid

will increase with time at a constant shear rate.

measurement of shear stress - shear rate relationship.The most commonly used instrument for the rheology evaluation of a drilling fluid is the concentric

cylinder or cup and bob viscometer. This is typically a Fann 35A six speed model.

In operation the rotor and bob is immersed in the fluid sample and the rotor is turned at a

constant speed. The fluid’s resistance to flow imparts a torque on the bob which deflects the dial

proportionally to the viscous properties of the fluid.

The geometry of rotor and bob determines the shear rates obtainable with this viscometer.

The standard rotor – bob combination has a 0.117cm gap and the conversion of rpm to shear rate

in sec–1 is given by the formula

Shear rate (sec–1) = rpm x 1.703

The shear stress from this instrument is taken from the dial reading R.

Shear Stress (lb/100ft2) = R x 1.067

Shear Stress (dynes/cm2) = R x 5.1

RHEOPECTIC

THIXOTROPIC

VIS

CO

SIT

Y

TIME

Time Dependent Effects

10

Section


The six speeds of the Fann 35A and the corresponding shear rates are:-

600 rpm - 1022.0 sec–1

300 rpm - 511.0 sec–1

200 rpm - 340.7 sec–1

100 rpm - 170.3 sec–1

6 rpm - 10.22 sec–1

3 rpm - 5.11 sec–1

In order to obtain accurate correlations, it is important that viscometer readings are taken at the same

temperature, normally 120 ˚F (49 °C).

Using the Bingham Plastic model for data interpretation, the following values are reported.

PV = R600 reading – R300 reading

YP = R300 reading – PV

or

(R300 reading – PV) x 0.48 in Pa

Bingham Plastic Model Parameters

Sh

ea

r S

tre

ss,

Shear Rate (RPM),

300 600

PV

YP

The Bingham values PV and YP give a poor definition of the flow characteristics of the fluid over

a wide shear range, but shear stress values at all six speeds can be converted to viscosity values

for the six shear rates and plotted on a log/log viscograph. This gives a good viscosity profile in a

form readily correlated with the various shear ranges experienced in the circulating system and solids

control equipment.

Measurement of initial gel strength is indicative of the elastic modulus and hence suspension

characteristics of the fluid and the relationship of initial and 10 minute gel strength illustrates the

degree of thixotropy present.

The R6 value is directly relevant to annular viscosity of some hole diameters and this value is

increasingly being used as a control parameter in ensuring good hole cleaning properties.

“n” and “K” constantsAlthough the Bingham Model constants, PV and YP are the most widely used properties for

evaluating drilling fluid rheology, it has to be recognised that this model does not always

accurately predict drilling fluid performance. This applies in particular to annular rheological

calculations.

11

The Power Law Model more closely approximates to the actual drilling fluid, in particular to low

solids polymer based systems. This model can be calculated over the annular region (normally less

than 100 rpm or 150 sec–1 shear rate), it will more accurately predict a drilling fluids performance.

Power Law Model = K n

Where = shear stress dynes / cm2

K = Consistency index dynes secn/ cm2

= Shear rate sec–1

n = Power Law Index

The “n” constant indicates the degree of non-Newtonian character that a fluid exhibits over a

defined shear rate range. Newtonian Fluids have an “n” value of equal to one. As “n” decreases

from one the fluid becomes more pseudoplastic or shear thinning with increase in shear rate.

Lowering the “n” value improves hole cleaning performance by increasing the effective annular

viscosity and flattening the annular velocity profile. This reduces any turning effect on cuttings,

helping to prevent particle breakage and moves the solids more directly up the hole.

The “n” constant is dependant upon the type of viscosifier used. Every material has an inherent

“n” constant, but it may vary with concentration and shear rate. Xanthan Gum provides the lowest

“n” constant, the only material providing a similar value being extended bentonite.

Shear Stress v Shear Rate

12

Section


“K” the consistency index is the shear stress or viscosity of the fluid at a shear rate of one sec–1 . It

relates directly to the system viscosity at low shear rates. An increase in “K” raises the effective

annular viscosity and therefore the hole cleaning capacity. It can also increase, however, the bit

viscosity and circulating pressure loss. The “K” constant is controlled by both the type of viscosifier

and the total solids content of the fluid. It will increase with decrease in the “n” constant or by

increase in solids concentration. “K” can be reported as dynes/cm2 secn or lbs/100ft2 secn. An

increase in “K” value should if possible be obtained via a decrease in “n” value to avoid increasing the

circulating system viscosity.

The “n” and “K” values can be calculated from any two viscometer dial readings. For Hydraulic

calculations determining “n” and “K” in the range of interest (i.e. 5 -150 sec–1 for annular calculations)

will provide more accurate results.

where:

R1 = Dial reading at rpm1

R2 = Dial reading at rpm2

laminar and turbulent !ow regimesSingle phase flow can be either laminar or turbulent. In a drilling situation it is usually important

to know which of these two flow regimes are present in a hole interval.

In laminar flow, motion is parallel to the walls of the flow channel. The particles of fluid move in

straight lines or in long smooth curves. Flow tends to be laminar when it is slow or the fluid is viscous.

In laminar flow the force required to move the fluid increases with increase in the velocity and viscosity.

In turbulent flow the fluid is continually swirling and eddying as it moves along the flow channel.

There is an average movement of the fluid in a particular direction but individual particles of the

fluid move along in random loops and circles. In turbulent flow these velocity fluctuations arise

spontaneously and are not caused by wall projections or changes in direction. These factors can

however increase the degree of turbulence. Flow tends to be turbulent when the flow is rapid or when the

fluid has low viscosity. In turbulent flow, the force required to move the fluid increases linearly with

density and as the square of viscosity.

Transition Velocity - The flow of any particular fluid in any particular flow channel can be either

laminar or turbulent. At low velocities, the flow will be laminar. If the velocity of a fluid in laminar

flow is increased, the flow at some point will suddenly become turbulent. If the velocity is reduced

again, the flow will return to it’s laminar character. Thus for any particular system there will be a

transition velocity where the flow shifts between laminar and turbulent.

The transition between laminar and turbulent flow occurs because the inertial forces vary as the

square of the flow rate, while viscous forces vary only as the flow rate. The ratio of inertial forces to

viscous forces is the Reynolds Number.

"n"log R2 R 1( )

"K"5.11R2

1.7 rpm 2( )n

log (rpm2 rpm1)

13

In general laminar flow is the desired regime, but exceptions occur where turbulent flow is

desired for specialized applications e.g. turbulent sweeps to remove cutting beds and clean out

enlarged hole sections. Turbulent flow is often chosen by preference to drill horizontal intervals.

Turbulent flow however, does give larger annular pressure losses, increased wellbore erosion and cause

drill cutting attrition through the tumbling effect in the annulus.

In a turbulent regime the fluid viscosity has no contribution to hole cleaning, but the viscosity of a

fluid determines whether a flow regime is turbulent or laminar for a given velocity and hole diameter.

rheology – "eld application

plastic viscosity (pv)Drilling muds are usually composed of a continuous fluid phase in which solids are dispersed.

Plastic viscosity is that part of the resistance to flow caused by mechanical friction. The friction is caused

by:

ƒ Solids concentration.

ƒ Size and shape of solids.

ƒ Viscosity of the fluid phase.

For practical field applications, plastic viscosity is regarded as a guide to solids control. Plastic

viscosity increases if the volume percent of solids increases or if the volume percent remains

constant, and the size of the particle decreases. Decreasing particle size increases surface area, which

increases frictional drag. Plastic viscosity can be decreased by decreasing solids concentration or

by decreasing surface area. Plastic viscosity is decreased by reducing the solids concentration by

dilution or by mechanical separation. As the viscosity of water decreases with temperature, the

plastic viscosity decreases proportionally. Therefore, controlling PV of a mud in practical terms involves

controlling size, concentration and shape of the solids and minimising the viscosity of the liquid

phase - such as avoiding viscosifying polymers and salts unless absolutely needed.

The value of plastic viscosity is obtained by subtracting the 300 rpm reading from the 600 rpm reading:

PV = 600 rpm reading – 300 rpm reading

PV of a mud is the theoretical minimum viscosity a mud can have because it is the effective viscosity

as shear rate approaches infinity. The highest shear rate occurs as the mud passes through the bit

nozzles; therefore, PV will approximate the mud’s viscosity at the nozzles.

yield point (yp)The yield point is the initial resistance to flow caused by electrochemical forces between the particles.

This electrochemical force is due to charges on the surface of the particles dispersed in the fluid

phase. Yield point is a measure of these forces under flow conditions and is dependent upon:

ƒ The surface properties of the mud solids

ƒ The volume concentration of the solids and

ƒ Ionic environment of the liquid surrounding the solids

14

Section


High viscosity resulting from high yield point is caused by:

ƒ Introduction of soluble contaminant (ions) such as: salt, cement, anhydrite or gypsum, which interact

with the negative charges on the clay particles.

ƒ Breaking of the clay particles through mechanical grinding action creating new surface area of

the particles. These new charged surfaces (positive and negative) pull particles together as a floccs.

ƒ Introduction of inert solids (barite) into the system, increasing the yield point. This is the result of

the particles being forced closer together. Because the distance between the particles is now

decreased, the attraction between particles is greatly increased.

ƒ Drilling hydratable shales or clays which introduces new, active solids into the system, increasing

attractive forces by bringing the particles closer together and by increasing the total number of

charges.

ƒ Insufficient deflocculant treatment.

Yield point can be controlled by proper chemical treatment. As the attractive forces are reduced by

chemical treatment, the yield point will decrease. The yield point can be lowered by the following

methods:

ƒ Charges on the positive edges of particles can be neutralised by adsorption of large negative

ions on the edge of the clay particles. These residual charges are satisfied by chemicals such as:

tannins, lignins, complex phosphates, lignosulphonate, etc. The attractive forces that previously

existed are satisfied by the chemicals, and the negative charge of the clay particles predominates,

so that the solids now repel each other.

ƒ In the case of contamination from calcium or magnesium, the ions causing the attractive force

are removed as insoluble precipitants, thus decreasing the attractive forces and YP of the mud.

ƒ Water dilution can lower the yield point, but unless the solids concentration is very high, it is

relatively ineffective.

Yield point (YP) is calculated from VG measurements as follows:

YP = 300 rpm reading – (600 rpm reading - 300 rpm reading)

YP = 300 rpm reading – PV

or

YP = (300 rpm reading – PV) x 0.48 in Pa

The limitation of the Bingham plastic model is that most drilling fluids, being pseudoplastic,

exhibit an actual yield stress which is considerably less than calculated Bingham yield point. This

error exists because the Bingham plastic parameters are calculated using a VG meter at 600 rpm

(1022 sec-1) and 300 rpm (511 sec-1); whereas, typical annular shear rates are much less (Table 1).

gel strengthGel strengths, 10-second and 10-minute, measured on the VG meter, indicate strength of attractive

forces (gelation) in a drilling fluid under static conditions. Excessive gelation is caused by high solids

concentration leading to flocculation.

15

Signs of rheological trouble in a mud system often are reflected by a mud’s gel strength

development with time. When there is a wide range between the initial and 10-minute gel readings

they are called “progressive gels”. This is not a desirable situation. If initial and 10-minute gels are

both high, with no appreciable difference in the two, these are “high-flat gels”, also undesirable.

The magnitude of gelation with time is a key factorin the performance of the drilling fluid.

Gelation should not be allowed to become much higher than is necessary to perform the function

of suspension of cuttings and weight material. For suspension “low-flat gels” are desired.

Excessive gel strengths can cause:

ƒ Swabbing, when pipe is pulled.

ƒ Surging, when pipe is lowered.

ƒ Difficulty in getting logging tools to bottom.

ƒ Retaining of entrapped air or gas in the mud.

ƒ Retaining of sand and cuttings while drilling.

Gel strengths and yield point are both a measure of the attractive forces in a mud system. A

decrease in one usually results in a decrease in the other; therefore, similar chemical treatments

are used to modify them both. The 10-second gel reading more closely approximates the

true yield stress in most drilling fluid systems. Water dilution can be effective in lowering

gel strengths, especially when solids are high in the mud.

funnel viscosityThe funnel viscosity is measured with the Marsh funnel and is a timed rate of flow in seconds per

quart. It is basically a quick reference check that is made routinely on a mud system; however,

there is no shear rate/shear stress relationship in the funnel viscosity test. Thus, it cannot be related to

any other viscosity nor can it give a clue as to why the viscosity may be high or low.

Types of Gel Strengths Diagram (to convert to Pa multiply gel strength by 0.48)

16

Section


low shear rheologyWhile many invert emulsions, particularly high o/w ratio formulations, approximate Bingham

plastic behaviour at shear rates most commonly examined (600 & 300 rpm) they do not maintain this

behaviour as shear rates decrease. This is of particular importance when studying hole cleaning

with inverts particularly in large diameter holes where annular shear rates are low. The use of Yield

Point derived from 600 & 300 viscometer readings can be misleading when considering efficient

hole cleaning particularly in large diameter or deviated holes. Both experimental and field data have

shown that it is of great importance to study the viscosity at shear rates nearer to those prevailing at

the wall of the hole. The 6 rpm reading, equivalent to a shear rate of 10.2 sec-1, is the best approximation

of low annular shear rate for fluids in laminar flow available on a standard V-G meter. This shear rate of

10.2 sec-1 is equivalent to a mean annular velocity of 53 ft/min (16.2 m/min) in 17 1/2” hole.

The following rule of thumb for 6 rpm readings for fluids in laminar flow is useful:

Hole deviation 0 - 45° 1.0 x Hole Diameter (inches)

45 - 90° 1.2-1.5 x Hole Diameter (inches)

In water based fluids, increases in low shear viscosities are best achieved with biopolymers e.g.

XCD, Rhodopol.

In invert emulsions the required 6 rpm readings can usually be attained with the normal organophilic

clay viscosifiers. Several rheology modifiers are currently available which claim to boost low

end viscosity without greatly altering overall viscosity. The success of these products appears

to vary greatly with base oil type hence laboratory pilot testing is necessary before inclusion in invert

formulations.

shear rates in the drilling !uid circulating system.Shear rates present in the circulating system of a drilling operation usually fall within the following

ranges.

Shear Rate V-G Meter rpm

Mud Pits 1 - 5 sec -1 0 - 3

Annulus 5 - 170 sec -1 3 - 100

Solids Removal Equipment 170 -10,000 sec -1 100 - 600 (+)

Bit 10,000 - 100,000 sec -1 N/A

cuttings transportation theory

cuttings transport ratioCuttings transport ratio is the ratio of the cuttings transport velocity (Vt) and the mean annular velocity (Va).

Cuttings transport velocity is the difference between the mean annular velocity and the cuttings slip

velocity (Vs).

Transport Ratio (Tm) = Vt / Va

= (Va - Vs) / Va

= 1 - Vs/Va

This ratio is a measure of the effectiveness of hole cleaning. Any positive value indicates that

some cuttings will be removed. A value of 100% indicates the removal of all cuttings from the hole.

Any value in excess of 75% is generally considered to indicate efficient hole cleaning.

17

Slip Velocity =

Where Dp = Particle diameter (cm)

Pp = Particle density (kg/m3)

Pf = Fluid density (kg/m3)

u = Fluid viscosity (cps) (Equivalent thickness)

The above equation approximates to slip velocity, in fact the equation varies with Reynold’s number.

Many PC and hand held calculator programmes exist for slip velocity calculations and first

principle calculations for all cases will not be given here. It suffices to say that in all cases slip

velocity can be reduced by increasing viscosity and fluid density, or by reducing particle size (by

bit selection). The most practical approach is to increase fluid viscosity bearing in mind that this will

increase ECD, and oil retention figures and hinder efficient solids removal.

It can be seen from the second equation that the transport ratio can be increased by increasing

annular velocity or by decreasing slip velocity.

general transport ratio (gtr)The application of Cuttings Transport Ratio, in hole cleaning calculations works well in vertical

holes, but its effectiveness is reduced as hole angle increases. To allow for this fact, in calculations of

optimum rates of penetration a constant (the GTR) is required and has been determined by

experimentation to fall within the following range:

Hole Angle 0 20 30 40 50 60

GTR 1.0 0.8 0.5 0.3 0.25 0.2

annular cutting concentration and optimum ropIt is generally accepted that the recommended cuttings concentration in the annulus should not

exceed 4% v/v and that an optimum ROP should be employed to achieve this figure is not exceeded.

The optimum ROP is calculated as follows: -

where

F = cuttings concentration (0.04)

Tm = cuttings transport ratio

GTR = general transport ratio

section 5b

rheology and hydraulics of

drilling !uids

bit hydraulics 2

equivalent circulating density 3

power law inside the drillpipe for each hydraulic

interval 3

power law inside the annulus for each hydraulic

interval 4

bingham-plastic inside the drillpipe for each

hydraulic interval 6

bingham-plastic inside the annulus for each

hydraulic interval 7

section 5b Scomi Oiltools

2

Section

5b rheology and hydraulics of drilling !uids

Bit hydraulics

Nozzle area

Nozzle velocity

Bit pressure drop

Bit hydraulic horsepower

Bit hydraulic horsepower per unit bit area

Percent pressure drop at bit

Jet impact force

rheology and hydraulics of drilling !uids

)( 22 0.000767n

liiN JetinA

N

GPMN

A

POftV

32.0sec/

1120

2N

Bit

VpsiPD

1714

GPMBitBit

POPDhpHHP

Bit

Bit

A

HHPareaHHP /

100Pr Pump

Bit

ess

PD

1932Im mudGPMN

Bit

POVlbfp

Where

mud = Mud density in lb/gal

Presspump = Pump press in psi

POGPM = Pump output in gal/min

Jeti = Nozzle diameter in 32nds of an inch

ABit = Area of the bit

AN = Total nozzle area in in2

VN = Nozzle velocity in ft/sec

PDBit = Bit pressure drop in psi

3

Equivalent circulating densityThe following formulas can be used to calculate pressure drop (PD) and equivalent circulating density

(ECD).

Where

PDa = pressure drop in the annulus in psi

n = number of intervals

Li = length of intervals in feet

LVI = vertical length of the interval in feet

mud = density of mud in lb/gal

The sum of the pressure drops for each annular section (regardless of hole angle) is:

The equivalent circulating density (ECD) for any vertical wellbore is:

In deviated wellbores, the TVD must be taken into account when calculating ECD values. The above

equation then becomes:

Power Law inside the drillpipe for each hydraulic interval

Average velocity inside the drillpipe (Vp)

Where

IDDP = inside diameter of drillpipe or drill collar in in2

POGPM = pump output in gal/min

Vp = average mud velocity inside drillpipe in ft/sec

Reynolds number (NRep)

Where


Kp = consistency index in drillpipe, eq cP

mud = mud density in lb/gal

np = flow index n inside drillpipe


n

liia PDPD

mudn

lii

a

L

PDECD

052.0

mudn

lii

a

LV

PDECD

052.0

2

408.0sec/

DP

GPMp

ID

POftV

ppn

p

DP

p

n

pmud

pn

ID

K

VN

13

0416.0100,892

Re

4

Section


Friction factor (f)

If the Reynolds number is greater than 2100 the flow is turbulent and the friction factor is:

Where

a =

b =

If the Reynolds number is less than 2100 the flow is laminar and the friction factor is:

Turbulent !ow pressure drop

Where


fp = friction factor inside drillpipe

L = length of drillpipe in feet



Laminar !ow pressure drop

Where


Kp = consistency index inside drillpipe, eq cP

np = flow index n inside drillpipe



Power Law inside the annulus for each hydraulic interval

Average velocity inside the annulus (Va)

Where

IDHOLE = diameter of borehole or inside diameter of casing in in2

ODDP = outside diameter of drillpipe or drill collar in in2


Va = average mud velocity inside drillpipe in ft/sec

bREN

af

50

93.3log n

7

log75.1 n

RENf

16

LID

VfPD

DP

pmudp

p8.25

2

LID

nVK

PDp

p

p

n

DP

n

pn

pp

p 1000,144

0416.0

13

22

408.0sec/

DPHOLE

GPMa

ODID

POftV

5

Reynolds number (NRea)

Where



Ka = consistency index in annulus, eq cP


na = flow index n inside annulus

Va = average mud velocity inside drillpipe in ft/sec

Friction factor (f)

If the Reynolds number is greater than 2100 the flow is turbulent and the friction factor is:

Where

a =

b =

If the Reynolds number is less than 2100 the flow is laminar and the friction factor is:

Turbulent !ow pressure drop in annulus

Where



fa = friction factor inside annulus

L = length of drillpipe in feet


Va = average mud velocity inside annulus in ft/sec

Laminar !ow pressure drop in annulus

Where



Ka = consistency index inside annulus, eq cP

na = flow index n inside annulus



aa

n

a

DPHOLE

p

namud

an

ODID

K

VN

12

0208.0100,1092

Re

bREN

af

50

93.3log n

7

log75.1 n

RENf

16

LODID

VfPD

DPHOLE

amudaa

1.21

2

LODID

nVK

PDa

p

a

nDPHOLE

n

anaa

a 1000,144

0208.0

12

6

Section


Bingham-plastic inside the drillpipe for each hydraulic interval

Average velocity inside the drillpipe (Vp)

Where




Determine whether the flow is laminar or turbulent.

Calculate the Hedstrom number in the drillpipe (NHep)

Where




YP = yield point in lb/100 ft2

PV = plastic viscosity in Cp

Determine critical Reynolds number (NRec) from figure 1 (page 8) using the calculated Hedstrom number

Calculate the Reynolds number in the drillpipe (NRep)

Where





PV = plastic viscosity in cP

If NRep < NRec, the flow is laminar. If NRep > NRec, the flow is turbulent.

Turbulent !ow pressure drop

= mud density in lb/gal


PV = plastic viscosity in Cp


L = length of the drillpipe in feet

2

408.0sec/

DP

GPMp

ID

POftV

2

2000,37

PV

IDYPN DPmudHep

PV

IDVN

DPpmud

p

928Re

LID

PVVPD

DP

p

P 25.1

25.075.175.0

1800

7

Laminar !ow pressure drop

Where






Bingham-plastic inside the annulus for each hydraulic interval

Average velocity inside the annulus (Va)

Where





Determine whether the flow is laminar or turbulent

Calculate the Hedstrom number in the annulus (NHea)

Where






Determine critical Reynolds number (NREC) from figure1 using the calculated Hedstrom number

Calculate the Reynolds number in the annulus (NRea)

Where






If NRea < NRec, the flow is laminar. If NRea > NRec, the flow is turbulent.

LID

YP

ID

VPVPD

DPDP

p

P2251500

2

2

2700,24

PV

ODIDYPN DPHOLEmudHea

22

408.0sec/

DPHOLE

GPMa

ODID

POftV

PV

ODIDVN DPHOLEamud

a

757Re

8

Section


Turbulent !ow pressure drop in annulus

Where







Laminar !ow pressure drop in annulus

Where







LODID

PVVPD

DPHOLE

amuda 25.1

25.075.175.0

1396

LODID

YP

ODID

VPVPD

DPHOLEDPHOLE

aP

20010002

Figure 1: Critical Reynolds numbers for Bingham-plastic fluids. This graph shows Hedstrom numbers vs

Reynolds numbers for Bingham-plastic fluids.

Critical Reynolds numbers for

Bingham Plastic Fluids

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07

Hedstrom number, NHe

Cri

tical

Reyn

old

s n

um

ber,

NR

ec

Bab_05 Drilling Fluid Rheolgy.pdf

Documents

drilling fluids

drilling rates

drilling operations

low shear rheology

drilling situation

arheology of drilling

behaviour of fluids

shear rates