1. Drilling Hydraulics

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Drilling Fluids

Hydraulics

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COURSE OBJECTIVES

During this course you will get the necessary knowledge about the following :

 What are Hydraulics.

 Basics for static and non static well conditions.  Basic Rheology.

 Rheological Models for Newtonian and Non Newtonian fluids.

 Calculations of System Pressure Drop.

 Hydraulics Applications in Bit Nozzle Selection.  Hole Cleaning and cutting Transportation.

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COURSE OUTLINES

 Hydrostatic Pressure Liquid & Gas.  Annular Pressure during well control.  Buoyancy

 Rheological Models ( Newtonian & non Newtonian) Fluids  Laminar & Turbulent flow in Pipes and Annulus

 Pressure Drop Calculations  Jet Bit Selection

 Surge and Swab Pressures.

 Particle Slip Velocity.

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Basic Concepts

 What is the meaning of Hydraulics?

Hydraulics are the principles governing the power generated by the movement and force of liquid.

Viscosity : is the Resistance of fluid To flow.

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Basic Concepts

 Hydraulics concepts are primarily an

application of

Pascal’s Law



“

If a fluid has a constant density and

the fluid is at rest, all points at the

same depth below the liquid’s surface

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Basic Concepts

 Force = Pressure x Area

1000 lb/4 in2 = 250 psi

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Basic Concepts

 To Calculate the force exerted by the

cylinder.

 Piston Area = π x r2

3.14 x (1.75)2 = 9.62 in2

 Force = Pressure x Area

3000 psi X 9.62 in2 ₌

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Hydrostatic Pressure in Liquid

 Definition of Hydrostatic Pressure in Liquid  “ The pressure created by a column of fluid.”  Given  MW = 15.0 ppg  TVD = 8000 ft HP = 0.052 (MW) (TVD) HP = 0.052 (15.0) (8000) HP = 6240 psi

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Hydrostatic Pressure in Gas

 Hydrostatic Pressure of the gas column is given

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Annular Pressures During Well Control

 One of the important application of hydrostatic

pressure is the determination of annular pressures during well control operations

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Buoyancy & Calculating Pipe Weight

in

 Weight of open-ended steel pipe

suspended in fluid can be calculated with: Pipe weight in liquid = Buoyancy factor

x Pipe weight in air

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Buoyancy & Calculating Pipe Weight in

 WL = (WA) x [1 - (0.01528 x MW)]

 where:

 WL = weight of pipe suspended in

liquid (lb/ft)

 WA = weight of pipe in air (lb/ft)

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Buoyancy & Calculating Pipe Weight

in

When pipe rams are closed around tubing, the casing becomes a large hydraulic cylinder, and the tubing acts as a piston. Applying pump

pressure to the system can move the piston (tubing) upward.

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Buoyancy & Calculating Pipe Weight

in

Since pressure acts equally in all directions, any surface pressure acts at the bottom of the tubing, across the area from tubing OD to tubing ID.

Pressure also acts at the top of the tubing across the tubing ID. The effective area is equal to the tubing OD.

The upward force caused by the surface pressure that acts on open-ended pipe is measured on the weight indicator.

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Buoyancy & Calculating Weight in

Example : Ten thousand feet of 19.5 Ibm /ft drill pipe and 600 ft of 147 lbm / ft drill collars are suspended off bottom in 15 lbm / gal

mud. Calculate the effective hook load that must be supported by the derrick

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Buoyancy & Calculating Weight in

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18 NSA DEC

P_Stdpipe=P_Surf.Eq.+P_{Drill String}+P_MWD/Motor+P_Bit+P_Annulus

Pressure Losses

• Surface Equipment – Standpipe – Kelly Hose – Swivel – Kelly • Drill String – Pipe – Collars – BHA • Motor/Turbine/MWD/LWD • Bit Nozzles • Annulus • Drill String – Pipe – Collars – BHA • Surface Equipment – Standpipe – Kelly Hose – Swivel – Kelly • Motor/Turbine/MWD/LWD • Bit Nozzles • Annulus

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System Pressure Loss

Pressure is required to push fluid through the pipe

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Hydraulics & Pressure Losses

 We have to describe viscosity.

 Lets Run an experiment.

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Hydraulics Model

•This curve is

Not possible from Practical point of View on the rig Site. •Bingham, Power Law Models Solve this equation 0 300 600 Shear Rate,  (rpm) Shear St res s,  (lb/ 100 ft 2

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Hydraulics Model

 The mathematical equation that

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Hydraulics Model

 Newtonian fluids : Fluids exhibits direct

proportional relation ship between shear stress & shear rate

.

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Hydraulics Model

 Non-Newtonian fluids: exhibits both

proportional and non proportional relation ship between shear stress & shear rate

within the laminar flow regime.

 Viscosity varies as a function of shear

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Bingham Plastic Model

 Proposed to solve the equation with only

2 readings ,Use shear stress values @ 600 rpm & 300 rpm shear rate.

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Bingham Plastic Model

Shear Stress

Shear Rate

This is the Yield Point (YP) according to Bingham 300 RPM 600 RPM T₃₀₀ T₆₀₀ ab = bf and cb = bd… then c b a g f d

ac = df this is Plastic Viscosity ag = df = ac Then; PV = T₆₀₀ – T₃₀₀ YP = T₃₀₀ - PV P V Y P

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Bingham Plastic Model

Over estimates hydraulics,

calculated pressure losses & Hydraulic horse power always higher than actual.

This method works in simple shallow wells.

Not recommended in ER wells or horizontal wells.

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Shear Stress

 Drilling fluid shear stress is a function

of shear rate 0 300 600 Shear Rate,  (rpm) Shear St res s,  (lb /100 ft 2

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Yield Point

 Related to the interparticle forces and

ability of clay solids to associate with several layers of bound water.

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Gel Strength

 Measure of the rigid or semi-rigid gel

structure developed during periods of no flow

 Maximum measured shear stress at three rpm

 Ten second gel

 After remaining static for ten seconds

 Ten minute gel

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Power Law Model

 Is more accurate than Bingham method

Model parameters:

1- Flow behavior index (n) 2- Consistency index (K)

n

k

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Herschel & Buckley Model

Provides Most accurate model that predicts down hole rheology.

Tau zero exponential equation

n

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Which Rheological

Model to Use?

Plot 600 rpm reading, the 300 rpm

reading, and the gel strength on shear stress plot

The position of the gel strength along

the shear stress axis predominantly determines which model is the best fit

If the gel strength is high and near the

yield point, the fluid is best

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Which Rheological

Model to Use?



If the gel strength is very low, the

fluid is better approximated by the

Power Law model



If all six

Fann values are

available, then the

Hershel-Bulkley model is the

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Standpipe Pressure

 Standpipe pressure measures total

friction loss within the circulating system.

This includes :

 Surface Equipment pressure loss +  Drillpipe internal pressure loss +  BHA pressure loss +

 Bit pressure loss +

 Annular pressure loss

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Pressure Losses Surface Equipment

• Case 1

– Smallest land rigs

• Case 2

– Most land rigs • Case 3 – Most Offshore rigs • Case 4 – Deep-water rigs/floaters • User Specified

Case Stand Pipe Hose Swivel Kelly

Length (Ft.) ID (In.) Length (Ft.) ID (In.) Length (Ft.) ID (In.) Length (Ft.) ID (In.) 1 40 3.0 45 2.0 4 2.0 40 2.25 2 40 3.5 55 2.5 5 2.5 40 3.00 3 45 4.0 55 3.0 5 2.5 40 3.25 4 45 4.0 55 3.0 6 3.0 40 4.0

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Surface Equipment Pressure Loss

 Pressure loss in surface

connections Psc depends on pipe geometry, surface drilling fluid

density ρs, and flow rate Q. use the appropriate proportionality constant Csc from below table.

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Drill string and annular frictional

pressure loss

 Flow rate, flow regime, rheological properties,

and conduit geometry are among the key parameters that impact frictional pressure losses in the drill string and annulus. The

process to model these pressures, complex in its own right for Herschel-Bulkley fluids, is further complicated in HTHP and deep water wells by the sensitivity of drilling fluid density and rheological properties to down hole

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Drill string and annular frictional

Pressure Loss

 Fluid Annular velocity =

1029.4 x pump out put (bbl/min)

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Pressure Losses Inside Drill pipe

During Turbulent Flow

P = (7.7 x 10-5 _{x MW}0.8 _{x Q}1.8 _{x PV}0.2 _{x L)/ D}4.8

 where

 P = Pressure losses in the drill pipe, psi  7.7 x 10-5 = Constant

 MW = Mud weight, lb/gal  Q = Flow rate, gal/min

 PV = Plastic viscosity, cp  L = Length of pipe, ft

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Pressure Loss Calculation

 Pressure loss in pipes and annuli is

proportional to the Fanning friction factor f which is a function of

generalized Reynolds number, flow

regime, and fluid rheological properties.

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Pressure Loss Calculation

Example : A 15.6 Ibm / gal cement slurry

having a consistency index of 335 eq cp and flow behavior index of 0.65 being pumped at a rate of 672 gal / min between a 9.625 in

hole and a 7.0 in hole. Determine the

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Bit Hydraulics

 HHP is rate @ which fluids do work in

the circulating system

 By applying horsepower @ the bit, a

specific amount of work (cleaning) is accomplished.

 Energy expended by drilling fluids

clean the bottom hole and prevents regrinding of cuttings & clean the Bit.

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Bit Hydraulics

 Bit hydraulic horsepower (BHHP)

 Hydraulic HP @ Bit =

(Pressure Drop)(GPM) 1714

• Pressure Drop @ Bit =

• (Mud weight) X (GPM)2

10858 X (TFA)2

(TFA) = 0.000767(J2 _{+ J}2 _{+ J}2 _+….)

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Bit Hydraulics

 Impact force: is the force with which

drilling fluids hits the Bottom of the Hole after exiting the Nozzles.

 Jet Impact Force =

 (MW)(GPM)(Jet Velocity)

1932

 Jet Velocity = (0.32)(GPM)

TFA

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Hydraulics Optimization

 HHP Theory

 States that efficiency depends upon the

work (HHP) performed by Fluid.

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Hydraulics Optimization (contd.)

 Jet Impact Theory

 States that efficient removal of cuttings

depends upon force with which the fluid hits the bottom

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Hydraulics Optimization

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Pressure to Break Gel

 When pipe is started back in the hole after

a trip, the fluid will have been at rest for some period of time. The pressure

required to break the down hole gel

strength of the fluid can be significant. especially if the gel strengths are

progressive. The primary reason for

measuring 30-minute gel strength is to

determine the progressive or fragile nature of the gel strengths.

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Swab/surge pressures

 Swab pressure

– When casing or drill string is pulled out of the well, pressure at any given point in the well decreases.

– A pressure decrease due to upward

movement of pipe is called the “SWAB” effect

 Surge pressure

– When casing or drill string is tripped into the well, pressure at any given point in the well increases.

– A pressure increase due to downward movement of pipe is called the “SURGE” effect

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Time 0 Pr es sur e C hange, ps i -300 -200 -100 0 100 200 300 400 500 a b c d

Swab & Surge Hydraulics Review Casing: 95_/

8” 40 lb/ft @

2100ft

Pipe: 7” 23 lb/ft 1812ft -1856ft

a : Lifted pipe from slips

b: Joint 44 at maximum trip-in velocity

c: Deceleration - apply brakes d: Joint 45 on bottom

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Swab & Surge Hydraulics Review

 Cases to consider:

– Bit

 _{large nozzle sizes}

 _{small nozzle sizes}  _{plugged nozzles}

– Closed pipe with float sub

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 Since swab and surge pressures are developed by fluid flow, the

changes in flow velocity profile which causes corresponding pressure gradient changes is expressed as follows:

 Closed ended pipe

Open ended pipe

where, V_a = mean annular velocity d₁ = pipe OD v_P = drillpipe velocity d₂ = casing / openhole ID d = pipe ID

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 Since swab and surge pressures are developed by fluid flow, the

changes in flow velocity profile which causes corresponding pressure gradient changes is expressed for two cases as follows:

 Closed ended pipe

V a d v p d d      12 22 12 Va vp d d d d d d d d d        3 4 4 12 2 1 2 6 4 4 2 1 2 22 12 ( ) ( ) ( )

 Open ended pipe

where, V_a = mean annular velocity d₁ = pipe OD v_P = drillpipe velocity d₂ = casing / openhole ID d = pipe ID

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 The viscous pressure gradient is given by:





_p Va v p d d MD            2 1000 2 1 2 where, = viscocity, cp MD = measured depth

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 Example : Calculate the equivalent density below the

bottom joint of 4,000 ft of 10.75 in casing (having 10.0 in ID) if the casing is being lowered at a rate of 1.0 ft/s in a 12 in hole containing 9.0 lbm/gal brine having a viscosity of 2.0 cp. Perform the calculation for (1) casing that is open and (2) casing with a closed bottom end.

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Surge & Swab Pressure

 Average Pipe Speed

V_p = (ft/stand)(60 sec/min)/ (sec/stand)

Calculate the average pipe speed

when 93 ft stand of drill pipe are being pulled at 30 sec/stand.

V_p = (93 ft/stand)(60 sec/min)/30

sec/stand)

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Surge & Swab Pressure

 Mud velocity maximum

V_m = (0.45 + (d_p2 _{/ (d}

h2 - dp2))) (Vp)(1.5)

 Calculate the mud velocity when tripping 5

inch (127 mm)drill pipe from an 8-1/2 inch (215.9 mm) hole at an average pipe speed of 186 fpm. (56.7 mpm)

V_m = (0.45 + (52 / (8.52 - 52))) (186)(1.5)

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Surge & Swab Pressure

 Equivalent circulating rate

The circulating rate in gallons per

minute to produce the annular velocity caused by movement of the drill string into or out of the borehole

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Surge & Swab Pressure

 Find the equivalent circulating rate for a

273 fpm (83.1)mud velocity inside an 8-1/2 inch (215.9) hole around 5 inch (127) drill pipe.

GPM = 526 gpm

 Fluid Annular velocity =

1029.4 x pump out put (bbl/min)

Hole ID 2 _{– Pipe OD} 2

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Surge & Swab Pressure

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Surge & Swab Pressure

 Find the surge/swab pressure for an

equivalent circulating rate of 520 gpm (1984 lpm) when tripping 9,000 feet (2,743 mt) of 5 inch (127 mm) drill pipe from an 8-1/2 inch (215.9 mm) hole. The mud weight is 13.0 ppg (1558 kpcm).

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Surge & Swab Pressure

 Find the pressure loss gradient for 10.0 ppg

mud weight

Psi/1000 ft = 30 ….Table 7

Calculate the pressure loss psi with 9,000

ft (2,743 mt) of drill pipe

(30 psi/1000 ft) (9,000 ft) = 270 psi

Correct the pressure loss to a mud weight

of 13.0 ppg (1558 kpcm)

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 Cuttings Transport Ratio and Cuttings Concentration (vol %), Newton

Cutting Transportation & hole Cleaning

V_s d_p

Fd Wp Fb 

 Slip Velocity of Cuttings in LAMINAR Flow

F_b F_d W_p F_d = Viscous Drag W_p = Particle Weight F_b= Buoyant Force Vs  ₁₃₈  (    2  p mud ) d p

 Slip Velocity for Cuttings in TURBULENT Flow Vs          189. d p CD p _mudmud   

V_s = Slip Velocity (ft/min)

P= Particle density (lb/gal mud= Fluid density (lb/gal)

dp = Particle diameter (in.)

= equivalent viscosity

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 Moore Correlation for Non Newtonian fluids : the most accurate correlations

Cutting Transportation & hole Cleaning

K = Consistency Index, Power Law

N= Flow Index

s= Particle density (lb/gal f= Fluid density (lb/gal)

dp = Particle diameter (in.)

a= Apparent viscosity

Va = Average Annular Velocity

 Apparent Viscosity

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Cuttings Transport Key Variables

‘High’ Influence on cuttings transport ‘Low’

‘Low’ Ability to control ‘High’

Flow Rate ROP RPM Cuttings size Cuttings density Drillpipe eccentricity Mud weight Hole geometry Mud rheology

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Cutting Transportation & hole Cleaning

 Cutting concentration in excess of five

(5) volume % can lead to a pack-off and Stuck pipe.

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Cutting Transportation & hole Cleaning

 Example : Compute the transportation ration of a 0.25 in cutting having gravity of 2.6 (21.6 lbm/gal) in a 9.0 lbm/gal clay water mud being pumped at an annular velocity of 120 ft/min (2.0 ft/s) in a

10x5 in annulus. Apply the correlation of Moore, Chien and Walkers and Mayes. The following data were obtained for the drilling fluid using a rotational viscometer.

Rotor Speed Dial Reading

RPM Degree 3 2.0 6 3.3 100 13 200 22 300 30 600 50