3 - Rheology and Hydraulics_PTM_Handout

8/22/2019 3 - Rheology and Hydraulics_PTM_Handout

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SCOMI OILTOOLS

Global Research & Technology Centre/ GRTC

Training Department

RHEOLOGY andRHEOLOGY andHYDRAULICSHYDRAULICS

RHEOLOGY andRHEOLOGY andHYDRAULICSHYDRAULICS

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Fluids Rheology

Fluid Rheology affects carrying capacity, slipvelocity, and annular hydraulics.

Fluid Rheology also affects the suspendingcharacteristics of the Drilling Fluid.


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What are Hydraulics

An operation where the drilling fluid is used totransfer pressure from the surface to the bit, usingthe pressure drop across the bit to enhance therate of penetration!

Part of this energy is used to clean the face of thebit!

The pressures exerted in circulating a well can becalculated, using Rheological Models!

We need to know the TYPE of fluid!

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Rheological Term


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Rheological Term

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Rheological Term


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What is Rheology

Rheology is the science of the deformation andflow of matter.

When applied to Drilling Fluids, rheology deals withthe relationship between Flow Rate and FlowPressure and their combined effects on the FlowCharacteristics of the fluid.

Each of these three items is inter-related to theother.

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The Type of Fluids

We are primarily concerned with just two TYPES offluids:

Newtonian Fluids

Non-Newtonian Fluids


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Newtonian Fluids

Named after Issac Newton, the Newtonian fluidexhibits constant ratio for the Shear Stress (theforce required to move the fluid) and the Shearrate (the rate at which the fluid moves).

For a NEWTONIAN fluid, the ratio of Shear Stressto Shear Rate is a constant, called the viscosity (m)

Calculated with the formula: m = t / g

Where:

Shear Stress: (t)

Shear Rate: (g)

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Newtonian Model GraphicallyIllustrated

600 RPM Reading = 40

300 RPM Reading = 20

PV = 20; YP = 0

0 200 400 600 800 1,000 1,2000

10

20

30

40

50

Shear Rate, 1/sec

Shear Stress, lb/100 ft


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Any fluid that does not conform to Newtonianbehaviour.

For a NON-NEWTONIAN fluid, the ratio of ShearStress to Shear Rate is NOT a constant!

MOST drilling fluids are NON-NEWTONIAN fluids.

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They contain solid particles of various sizes thatform a structure resistant to flow.

When sufficient force is applied the structureyields and begins to move. We call this the YieldPoint.

We call this type of fluid a BINGHAM fluid.


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Most drilling fluids do not conform perfectly to theBingham Plastic Model.

Most are Shear Thinning, that is, the more shearor velocity applied, the lower their effectiveviscosity becomes.

The lower the shear rate, the thicker theybehave.

Bingham assumes a proportional straight-lineincrease after the yield point is passed.

Bingham points assume a higher shear rate thanis found in most parts of the annulus.

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What is SHEAR STRESS?

Shear Stress is defined as the force required toovercome a fluids resistance to flow, divided by thearea that force is working on.

Shear Stress, lbs/100 ft = Dial Reading X 1.0678

Basic formula is: Shear Stress = F / AWhere: F = Force applied (dynes)

A = Surface area under stress (cm2)


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What is SHEAR RATE?

Shear rate is defined as the relative velocity of thefluid layers, divided by their normal separationdistance.

Shear rate is expressed in reciprocal seconds (sec-1).

Basic formula is: Shear Rate = V / HWhere: V = Velocity (cm/sec)

H = Distance (cm)

Shear Rate = rpm X 1.7033.

600 rpms = 1022 sec-1

. 300 rpms = 511 sec-1.

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Measurement : MARSH FUNNEL

Determination of fluidsViscous properties.

Relies on gravity andpredetermined orifice size.

SS/SR = Funnel Viscosity

Measurement Reported asSeconds / QuartPredicts Trends


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What is Viscosity?

Viscosity relates to the resistance to deformationexhibited by a fluid.

In our world, we can think of it as a relationship thatexists between the Shear Stress and the Shear Rate.

We must not think in terms of thick and thin.

Viscosity is calculated with the following formula:Viscosity = Shear Stress / Shear Rate

The Marsh funnel is NOT a measure of viscosity.


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The Importance of Viscosity

Hole Cleaning

Barite Suspension

Drilling Rate

Circulating Pressures - E.C.D.

Pipe Movement Pressures - Swab & Surge

Erosion - Flow Regimes

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The Rheological Models

A RHEOLOGICAL MODEL is a description of therelationship between:

Shear Stress: (t)

Shear Rate: (g)

Most commonly RHEOLOGICAL MODEL used in thedrilling fluids industry:

Bingham Plastic Model Power Law Model


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The BINGHAM PLASCTIC Model

The simplest model, and one of the mostcommonly used, is the BINGHAM PLASTIC model.

Assumes the shear stress is a linear function ofshear rate, once a specific shear stress has beenexceeded.

Expressed as: t = YP + PV (g)

Where:

YP = yield point, lb/100 ft2

PV = plastic viscosity, cp (centipoise)

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The BINGHAM PLASTIC Model

Best characterises fluids at higher shear rates.

PV and YP are calculated from a conventional concentricviscometer with the data taken at 600 and 300 rpm dial

readings.

PV = q600 - q300

YP = q300 PV

By multiplying the shear rate in rpm by 1.702, you can derivethe shear rate in reciprocal seconds (sec-1).


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Bingham Model GraphicallyIllustrated

600 RPM reading = 50

300 RPM reading = 30

PV = 20; YP = 10

0 200 400 600 800 1,000 1,2000

10

20

30

40

50

60

Shear Rate, 1/sec


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Plastic Viscosity and Yield Point

PLASTIC VISCOSITY= 600 Reading - 300 Reading

Plastic Viscosity is a measurement of the size,shape and concentration of the solids in themud and the viscosity of the fluid phase.

YIELD POINT = 300 Reading - Plastic Viscosity

Yield Point is a measurement of the chemical

and electro-chemical charge attractions ofthe solids.


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PLASTIC VISCOSITY : Definition

PV = 600 RPM reading - 300 RPM reading.

Affected by Solids:

Size Distribution

Shape

Concentration

Affected by Fluid Phase Viscosity.

High Shear (Equivalent to Fluid Shear Rates at Bit)

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YIELD POINT : Definition

Yield Point = 300 RPM Rdg - Plastic Viscosity.

Indicates attraction between solids.

Electro-Chemical in Nature (+/- charges).

A Measure of Flocculation.

Gives some indication of the hole cleaning ability ofthe fluid, when the fluid is in motion.


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Yield Point : Influencing Factor

Cross linking polymers (example: xc polymer)

Doubly charged cations causing flocculation

(example: Ca2+ and Mg2+)

Polymers with anionic or cationic groups

Reactive clays

Bentonite

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Causes YP Increase

Flocculation of solids can be caused by:

Temperature

Chemical degradation, clay movement,dehydration

Chemical contaminants

Salt/salt water, calcium, carbonates, cement,H2S

Solids crowding

Weight up, poor solids control, reactiveformations, dehydration


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Causes YP Increase

Flocculation of solids can be caused by:

pH increase/decrease from cement contami

nation, lime additions, acid gas influx

Commercial additives (Bentonite, Polymers)

Inorganic clays, polymers (viscosifiers,

flocculants, some filtration and shale control

additives)

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The POWER LAW Model

The POWER LAW model describes a fluid in which theshear stress/shear rate relationship is a straight linewhen plotted on log-log graph paper.

It more closely approximates the low shear ratebehaviour of a drilling fluid.

The POWER LAW model is: t = K(gn)

Where:

K = The consistency index, (lb-secn/100 ft2)

n = The power law exponent (dimensionless)


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Using Power Law Numbers

Fluid Velocities (in feet per second) are calculatedfor each hydraulic diameter in the pipe or annulus.

Ks and ns are applied to each section.

Effective Viscosity (me) of the mud is calculated foreach section.

A Critical Reynolds Number (Rec) is calculated forthe mud.

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Viscosity Profiles for Fluid Models

1 3 10 30 100 300 1,000 3,00010

20

50

100

200

500

1,000

2,000

5,000

10,000

Shear Rate, 1/sec

Viscosity, cP

Newtonian

Power Law

Actual

Bingham


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The concept n and K

The units of Power Law Model are:

n, the Power Law Index.

K, the Consistency Factor

Two regimes of flow are usually recognised:

Medium range, found inside the pipe, thejets and around the bit.

Low range, found in the annulus.

The cross-over point between the two is

generally recognised as 170 sec-1.

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What about n and K ?

The rheological parameters n and K can becalculated from any two shear-rate/shear-stressdata points. This is rarely a totally straight line.

Normal procedure is to calculate these values atshear rates in the drillstring and in the annulus!

Drillstring = np and Kp Annulus = na and Ka

We use the 3 rpm and 100 rpm readings for the low

shear rate.

We use the 300 rpm and 600 rpm readings for thehighshear rate.


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n Power Law Exponent Definition

= 3.32 log (600 300) viscometer reading

Describes the shear thinning properties of a fluid,i.e. degree of non-newtonian behavior.

A shear thinning fluid is one that thins in a highshear environment, i.e. in the drill pipe & at the bit,and thickens in a low shear environment, i.e. in theannulus.

The n value defines the velocity profile in theannulus.

Note: PV:YP ratio also defines the velocity profile in

the annulus, i.e. PV equal to or < YP results in a flatvelocity profile PV > YP will sharpen the velocityprofile incrementally.

n power lawexponent

High shear

environment

Low shear

environment

Annulus

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The n Value

n is the Power Law Exponent.

n dictates the logarithmic curve followed in aShear Rate/Shear Stress graphical analysis.

n is a function of the Shear-Thinning properties ofa fluid.

n values are always less than 1.000

n values near 1 indicate fluids that

immediately Shear-Thin. A fluid with n near 1 is easier to force into

turbulent flow


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Calculating n

Using the 600 and 300 rpm dial readings, the equationsimplifies to:

(q600)

n = 3.32log --------------

(q300)

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n Value Relationship

Ifn = 1, the fluid is Newtonian.

Ifn < 1, the fluid is non-Newtonian and moreshear thinning.

Low n values:

Promote laminar flow

Increase carrying capacity

As n decreases flow profile flattens

Most drilling fluids have n values between 0.3 - 0.5


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Fluid velocity diminishes to almost

zero at the face of the borehole and

the drill pipe due to frictional drag .n = 0.7

n = 0.5n = 0.3

drill pipe borehole wall

Maximum velocity

Vertical well bore

Horizontal well bore

Velocity Profile in the annulus

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The K Value

K is a consistency constant that gives a measureof thickness compared to other fluids.

It may be compared to Plastic Viscosity, but therelationship is not precise.

Actual Effective Viscosity must be calculatedusing K and n for each specific Shear Rate.


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Calculating K

Using the 600 and 300 rpm dial readings, theequation simplifies to:

(q300)K = ----------

511n

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K Value Relationship

Kdefines viscosity at a low shear rate

approximately 1 1/sec

Higher Kgenerally improves hole cleaning

Higher Kincreases system pressure loss


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Adjusting n and K

To lower n value:

Add flocculants and electrolytes

Use cross link type polymers

To increase K value:

Add biopolymers or bentonite

Increase solids concentration

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Other Models

HERSCHEL-BUCKLEY (Modified Power Law)Best fit to Drilling Fluids

YP = q3n = (3.32) log [( q600-YP ) / ( q300-YP )]

K = q300 / 511n

CASSON

Very accurate at low shear rates, but complicated and

difficult to use.

ROBERTSON-STIFFThe best model for HPHT Wells

A three parameter model that is also difficult to use.

Very accurate in many cases.


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Graph of Actual Readings vs. Bingham and PowerLaw Models

0 200 400 600 800 1,000 1,2000

10

20

30

40

Shear Rate, 1/sec


Bingham

Model

Actual

Values

Power Law

Pipe

Power Law

Annulus

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Yz Factor

In recent years a trend has developed where the Yzfactor is applied as an indicator of the LOW ENDrheology of a drilling fluid.

It is calculated with the following formula:

Yz Factor = (2 * FANN 3) - FANN 6

The LOW END rheology has only a moderateinfluence on hole cleaning.


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Defining the Flow Regime

What is a Flow Regime?

Essentially the nature of the fluid flow.

AFlow Regime can be classed in several ways:

Plug Flow

Laminar Flow

Transitional Flow

Turbulent Flow

What do these terms mean?

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PLUG Flow

The condition where the fluid moves like a solid.

Generally attributed to very low flow rates, with highviscosities and/or high solids concentrations.

Wellbore Wall Drillpipe Wall


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LAMINAR Flow

Laminar Flow is associated with low flow rates and anorderly pattern of flow.

The flow rate/flow pressure relationship is governed bythe viscous properties of the fluid.

Wellbore WallDrillpipe Wall

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TURBULENT Flow

Characterised by chaotic, random flow patterns.

Associated with high fluid velocities.

The change from Transitional to Turbulent isgoverned by a dimensionless number, called theReynolds Number.

Wellbore WallDrillpipe Wall


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TRANSITIONAL Flow

Transitional Flow is a theoretical state where theFlow Regime is in Transition from Laminar Flow toTurbulent Flow.

This transition occurs at some Critical Velocity.

If the velocity is reduced slightly, the fluid returnsto Laminar flow.

Conversely, if the velocity is increased, turbulenceis achieved.

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Critical Velocity

The Critical Velocity is that velocity when themovement of a fluid changes from:

Laminar to Transitional to Turbulent

It is largely governed by the ratio of the fluidsinternal forces to its viscous forces.

We must know the Reynolds Number to determinethe Critical Velocity.


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Reynold Number (Re)

It is the ratio of the fluids internal forces to itsviscous forces.

The Reynolds Number is based on the followingformula:

Nre = ( Dfc * Va * Dm ) / Fv

Where: Dfc = Dimensions of theflow channel

Va = Average flow

velocityDm = Density of the fluid

Fv = Fluid viscosity

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Gel Strength - Definition

Attraction between solids under static conditions.

Closely related to Yield Point.

Types:

Fragile or Flat

Progressive or Elevated


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Gel Strength - Importance

An Indication of Low Shear Rate RheologicalProperties.

Too low may cause:

Settling Barite and/or Cuttings

Cutting Beds Build-up

Too high may cause:

Pressure Surges

Swabbing

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Fragile Gel Strength

A Gel Strength which increases only slightly after10 minutes, even if the ten second gel is high.

Generally Desirable

Lower :

Pump Pressures

Swab/Surge Pressures


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Progressive Gel Strength

A Gel Strength which increases significantly after 10minutes, even if the ten second gel is low.

May be an indication of:

Concentration of Reactive Solids Too High

Solids Crowding

Insufficient Deflocculation

Carbonate Contamination

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Fragile and Progressive GelStrength

0

10

20

30

40

50

0 20 40 60 80 100 120

Time In Minutes

Progressive Gel Fragile Gel

Gel Strength (Lb/100 Sq. Ft.)


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HYDRAULICS Analysis

Scomi Oiltools is starting to use HyPR-CALCsimulation program

The objective of using this program is to assess theeffects of the viscosity of any drilling fluid oncertain critical drilling parameters at any givendepth, formation types, temperature and pressure.

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What does HYDRAULICS mean?

Mechanical and Flow properties of Fluids as applied

to practical Mud Engineering

Otherwise referred to as Fluid Mechanics

Drilling Fluid is the Blood of the Drilling Operation


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Why Effective Hydraulics

Hole Cleaning

Hydrostatic Pressure Optimisation

Wellbore Stability

Wellbore Control

Equivalent Circulating Densities (ECD)

Surge and Swab Control whilst Tripping

Limitation of Pump Capacity

Optimisation of Drilling Operation

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Circulating Pressure Losses

Surface Equipment:

From Mud Pump to Top of Drillpipe

Varies from Rig to Rig - typically 100 psi

Drillstring:

Bottom Hole Assembly (BHA):

MWD tools

Downhole Motors

Drill Bit:

Nozzle number and size

Annulus:

Open hole

Casing


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Circulating System Shear rateRanges

0.01 0.1 1 10 100 1,000 10,000 100,000 1,000,000

SHEAR RATE (1/sec)

Settling Barite Particle

Annulus

Drill Pipe Drill Collars

BitH.C.*

*H.C = Hydroclones

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Primary Design Criteria

Pore Pressure < Hydrostatic Pressure/ECD < Fracture Pressure

Depth

Pressure or Equivalent Mud Weight

Fracture Pressure Gradient

Pore Pressure Gradient

MudWeight

Poor Design will likely lead to;

Wellbore Control Lost Circulation


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Hydraulics Design Criteria

Pump Capacity Tripping Speed

Pore PressureFracture Pressure Maximum ROP

Hole Geometry / Cleaning Bit HydraulicsBHA Design

OptimumDesign

Casing / Completion Operations

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Key Variable in Hydraulics

Pump Rate High

Good Hole Cleaning Too High

Excessive Pump Pressure, High ECD, AnnularTurbulence

Density High

Wellbore Stability and Control

Too high Low ROP, Lost Circulation, Differential

Sticking


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Key Variable in Hydraulics

Rheology

High

Good hole Cleaning, No Barite Sag

Too High

Low ROP, High ECD, High Pump Pressure,Inefficient Solids Removal

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Design

Mud Selection

Environment

Lithology

Cost

Modify Rheology and Hydraulics to meet Drilling

Requirements

Geometry

Modify Drilling Parameters to meet needs of Hydraulics

Tools

Accurate Dynamic Hydraulics Software

Hole Cleaning Software


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Why should calculate the Pressure Losses andRheology

Determine the ECD (Equivalent Circulating Density)of a drilling fluid.

Assess the effects of fluid changes on hydraulicperformance.

Optimise hydraulics for enhanced drillingperformance.

Ensure good hole cleaning.

Preventing erosion.

Prevent borehole instability.

Prevent losses due to surge pressures.

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Steps!

Draw the wellbore geometry.

Calculate the total annular pressure drop.

Calculate the ECD.

Calculate the Critical Flow Velocity and Flow Ratearound the drill collars.

Calculate surge and swab pressures.

Calculate cuttings transport efficiency.

Calculate the pressure drop in the drillstring.

Optimise bit hydraulics.

Date post:	08-Aug-2018
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