1. Drilling Hydraulics

Drilling FluidsHydraulics

COURSE OBJECTIVESDuring this course you will get the necessary knowledgeabout 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.

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. Hole Cleaning and Cutting Concentration

Basic ConceptsWhat is the meaning of Hydraulics?Hydraulics are the principles governingthe power generated by the movementand force of liquid.

Viscosity : is theResistance of fluidTo flow.

Basic ConceptsHydraulics concepts are primarily anapplication of Pascals Law

If a fluid has a constant density andthe fluid is at rest, all points at thesame depth below the liquids surfaceare under equal pressure

Basic Concepts Force = Pressure x Area

1000 lb/4 in2= 250 psi

Basic Concepts To Calculate the force exerted by thecylinder.

Piston Area = x r23.14 x (1.75)2 = 9.62 in2

Force = Pressure x Area3000 psi X 9.62 in2 =28,863 lb

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

Hydrostatic Pressure in Liquid

Hydrostatic Pressure in Gas Hydrostatic Pressure of the gas column is givenby the following Equation :

Annular Pressures During Well Control One of the important application of hydrostaticpressure is the determination of annularpressures during well control operations

Buoyancy & Calculating Pipe Weight inWeight of open-ended steel pipesuspended in fluid can be calculated with:

Pipe weight in liquid = Buoyancy factorx Pipe weight in air

Buoyancy factors = [1 - (0.01528) x (MW)]

Buoyancy & Calculating Pipe Weight in

WL = (WA) x [1 - (0.01528 x MW)]where:WL = weight of pipe suspended inliquid (lb/ft)

WA = weight of pipe in air (lb/ft)MW = mud weight (lb/gal)

Buoyancy & Calculating Pipe Weight inWhen pipe rams are closed around tubing, thecasing becomes a large hydraulic cylinder, andthe tubing acts as a piston. Applying pumppressure to the system can move the piston(tubing) upward.

Buoyancy & Calculating Pipe Weight inSince pressure acts equally in all directions, anysurface 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 acrossthe tubing ID. The effective area is equal to thetubing OD.The upward force caused by the surface pressurethat acts on open-ended pipe is measured on theweight indicator.

Buoyancy & Calculating Weight inExample : Ten thousand feet of 19.5 Ibm /ftdrill pipe and 600 ft of 147 lbm / ft drill collarsare suspended off bottom in 15 lbm / galmud. Calculate the effective hook load thatmust be supported by the derrick

Buoyancy & Calculating Weight inFluid for Steel Pipe

18 NSA DEC

PStdpipe=PSurf.Eq.+PDrill String+PMWD/Motor+PBit+PAnnulusPressure 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

System Pressure Loss

Pressure is required to pushfluid through the pipe

Hydraulics & Pressure LossesWe have to describe viscosity.

Lets Run an experiment.

Plot the Pressure vs the velocity of flow

Rotational Viscometer

Hydraulics ModelThis curve isNot possible fromPractical point ofView on the rigSite.Bingham, PowerLaw ModelsSolve thisequation 0 300 600

Shear Rate, (rpm)

Shear

Stres

s,(lb

/100f

t2

Hydraulics Model The mathematical equation thatdefines this curve is:

Hydraulics ModelNewtonian fluids : Fluids exhibits directproportional relation ship betweenshear stress & shear rate.

Hydraulics ModelNon-Newtonian fluids: exhibits bothproportional and non proportional relationship between shear stress & shear ratewithin the laminar flow regime.

Viscosity varies as a function of shearstress.

Bingham Plastic ModelProposed to solve the equation with only2 readings ,Use shear stress values @600 rpm & 300 rpm shear rate.

Why?

Bingham Plastic ModelShearStress

Shear Rate

This is the Yield Point (YP)according to Bingham

300 RPM 600 RPM

T300T600

ab = bf and cb = bd thencba

gf

d

ac = df this is Plastic Viscosityag = df = acThen;

PV = T600 T300YP = T300 - PV

PV

YP

Bingham Plastic ModelOver estimates hydraulics,calculated pressure losses &Hydraulic horse power alwayshigher than actual.This method works in simpleshallow wells.Not recommended in ER wells orhorizontal wells.

Shear Stress

Drilling fluid shear stress is a functionof shear rate

0 300 600Shear Rate, (rpm)

Shear

Stres

s,(lb

/100

ft2

Yield PointRelated to the interparticle forces andability of clay solids to associate withseveral layers of bound water.

YP = 300 - PV

Gel StrengthMeasure of the rigid or semi-rigid gelstructure developed during periods of noflow

Maximum measured shear stress at three rpm Ten second gel

After remaining static for ten seconds Ten minute gel

After remaining static for ten minutes

Power Law Model

Is more accurate than Bingham methodModel parameters:1- Flow behavior index (n)

2- Consistency index (K)

nkPower Law Model

Power Law Model

Herschel & Buckley Model

Provides Most accurate model thatpredicts down hole rheology.Tau zero exponential equation

nk 0

Which RheologicalModel to Use?Plot 600 rpm reading, the 300 rpmreading, and the gel strength on shearstress plotThe position of the gel strength alongthe shear stress axis predominantlydetermines which model is the best fitIf the gel strength is high and near theyield point, the fluid is bestapproximated by a Bingham model

Which RheologicalModel to Use?If the gel strength is very low, thefluid is better approximated by thePower Law modelIf all six Fann values areavailable, then the Hershel-Bulkley model is therecommended option

20 minute break..Tea Time!

Hydraulics Applications

Standpipe Pressure

Standpipe pressure measures totalfriction loss within the circulatingsystem.

This includes : Surface Equipment pressure loss + Drillpipe internal pressure loss + BHA pressure loss + Bit pressure loss + Annular pressure loss

SPP = 4000 psi

Pressure Losses Surface Equipment Case 1

Smallest landrigs Case 2

Most land rigs Case 3

Most Offshorerigs Case 4

Deep-waterrigs/floaters User Specified

Case Stand Pipe Hose Swivel KellyLength(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 2.252 40 3.5 55 2.5 5 2.5 40 3.003 45 4.0 55 3.0 5 2.5 40 3.254 45 4.0 55 3.0 6 3.0 40 4.0

Surface Equipment Pressure LossPressure loss in surfaceconnections Psc depends on pipegeometry, surface drilling fluiddensity s, and flow rate Q. usethe appropriate proportionalityconstant Csc from below table.

Drill string and annular frictionalpressure loss Flow rate, flow regime, rheological properties,and conduit geometry are among the keyparameters that impact frictional pressurelosses in the drill string and annulus. Theprocess to model these pressures, complexin its own right for Herschel-Bulkley fluids, isfurther complicated in HTHP and deep waterwells by the sensitivity of drilling fluid densityand rheological properties to down holetemperatures and pressures.

Drill string and annular frictionalPressure Loss

Fluid Annular velocity =1029.4 x pump out put (bbl/min)Hole ID 2 Pipe OD 2

Annular frictional pressure loss

System Pressure loss

System Pressure loss

Pressure Losses Inside Drill pipeDuring Turbulent FlowP = (7.7 x 10-5 x MW0.8 x Q1.8 x PV0.2 x L)/ D4.8 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 D = Drill pipe ID, in.

Pressure Loss CalculationPressure loss in pipes and annuli isproportional to the Fanning frictionfactor f which is a function ofgeneralized Reynolds number, flowregime, and fluid rheological properties.

Calculation is a complex method

Pressure Loss CalculationExample : A 15.6 Ibm / gal cement slurryhaving a consistency index of 335 eq cp andflow behavior index of 0.65 being pumped ata rate of 672 gal / min between a 9.625 inhole and a 7.0 in hole. Determine thefrictional pressure loss per 100ft of slurry.

Bit HydraulicsHHP is rate @ which fluids do work inthe circulating system

By applying horsepower @ the bit, aspecific amount of work (cleaning) isaccomplished.

Energy expended by drilling fluidsclean the bottom hole and preventsregrinding of cuttings & clean the Bit.

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 + J2 + J2 +.)

Bit HHSI = BHHP/area of hole

Bit Hydraulics Impact force: is the force with whichdrilling fluids hits the Bottom of the Holeafter exiting the Nozzles.

Jet Impact Force = (MW)(GPM)(Jet Velocity)

1932 Jet Velocity = (0.32)(GPM)

TFA (TFA) = 0.000767(J2 + J2 + J2 +.)

Hydraulics OptimizationHHP TheoryStates that efficiency depends upon thework (HHP) performed by Fluid.

Maintain 65% pressure Loss @ bit

Hydraulics Optimization (contd.) Jet Impact TheoryStates that efficient removal of cuttingsdepends upon force with which the fluidhits the bottom

Maintain 48% pressure Loss @ bit

Hydraulics Optimization Jet selection

Graphical Method

Pressure to Break GelWhen pipe is started back in the hole aftera trip, the fluid will have been at rest forsome period of time. The pressurerequired to break the down hole gelstrength of the fluid can be significant.especially if the gel strengths areprogressive. The primary reason formeasuring 30-minute gel strength is todetermine the progressive or fragile natureof the gel strengths.

Pressure to Break Gel (contd.)

Swab/surge pressures Swab pressure

When casing or drill string is pulled out ofthe well, pressure at any given point in thewell decreases.

A pressure decrease due to upwardmovement of pipe is called the SWABeffect

Surge pressure When casing or drill string is tripped into

the well, pressure at any given point in thewell increases.

A pressure increase due to downwardmovement of pipe is called the SURGEeffect

Time0

Pressu

re Ch

ange

,psi

-300

-200

-100

0100200300400500

a

b

cd

Swab & Surge Hydraulics ReviewCasing: 95/8 40 lb/ft @2100ftPipe: 7 23 lb/ft 1812ft -1856ft

a : Lifted pipe from slipsb: Joint 44 at maximum trip-invelocityc: Deceleration - apply brakesd: Joint 45 on bottom

Swab & Surge Hydraulics Review

Cases to consider: Bit

large nozzle sizes small nozzle sizes plugged nozzles

Closed pipe with float sub Open- ended pipe

Swab & Surge Hydraulics Review Since swab and surge pressures are developed by fluid flow, thechanges in flow velocity profile which causes correspondingpressure gradient changes is expressed as follows:

Closed ended pipe

Open ended pipewhere,Va = mean annularvelocityd1 = pipe OD

vP = drillpipe velocityd2 = casing / openhole IDd = pipe ID

Swab & Surge Hydraulics Review Since swab and surge pressures are developed by fluid flow, the

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

Closed ended pipe V a d v pd d 12

22 12

Va vpd 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 pipewhere,Va = mean annularvelocityd1 = pipe OD

vP = drillpipe velocityd2 = casing / openhole IDd = pipe ID

Swab & Surge Hydraulics Review

Swab & Surge Hydraulics Review The viscous pressure gradient is given by:

pVa

v p

d dMD

21000 2 1 2

where,= viscocity, cp

MD = measured depth

Swab & Surge Hydraulics Review Example : Calculate the equivalent density below the

bottom joint of 4,000 ft of 10.75 in casing (having 10.0 inID) if the casing is being lowered at a rate of 1.0 ft/s in a12 in hole containing 9.0 lbm/gal brine having a viscosityof 2.0 cp. Perform the calculation for (1) casing that isopen and (2) casing with a closed bottom end.Assume that the flow pattern is laminar

Surge & Swab PressureAverage Pipe SpeedVp = (ft/stand)(60 sec/min)/ (sec/stand)Calculate the average pipe speedwhen 93 ft stand of drill pipe are beingpulled at 30 sec/stand.

Vp = (93 ft/stand)(60 sec/min)/30sec/stand)Vp = 186 ft/min

Surge & Swab PressureMud velocity maximum

Vm = (0.45 + (dp2 / (dh2 - dp2))) (Vp)(1.5)Calculate the mud velocity when tripping 5inch (127 mm)drill pipe from an 8-1/2 inch(215.9 mm) hole at an average pipe speedof 186 fpm. (56.7 mpm)Vm = (0.45 + (52 / (8.52 - 52))) (186)(1.5)Vm = 273 fpm , Vm = 83.1 mpm

Surge & Swab PressureEquivalent circulating rate

The circulating rate in gallons perminute to produce the annular velocitycaused by movement of the drill stringinto or out of the borehole

Surge & Swab Pressure Find the equivalent circulating rate for a273 fpm (83.1)mud velocity inside an 8-1/2inch (215.9) hole around 5 inch (127) drillpipe.GPM = 526 gpm

Fluid Annular velocity =1029.4 x pump out put (bbl/min)Hole ID 2 Pipe OD 2LPM = 1984 lpm

Surge & Swab Pressure for 10 ppg Mud

Surge & Swab Pressure Find the surge/swab pressure for anequivalent circulating rate of 520 gpm (1984lpm) when tripping 9,000 feet (2,743 mt) of 5inch (127 mm) drill pipe from an 8-1/2 inch(215.9 mm) hole. The mud weight is 13.0ppg (1558 kpcm).

Surge & Swab Pressure Find the pressure loss gradient for 10.0 ppgmud weight

Psi/1000 ft = 30 .Table 7Calculate the pressure loss psi with 9,000ft (2,743 mt) of drill pipe(30 psi/1000 ft) (9,000 ft) = 270 psi

Correct the pressure loss to a mud weightof 13.0 ppg (1558 kpcm) (270 psi)(13.0 ppg/10.0 ppg) = 351 psi

Cuttings Transport Ratio and Cuttings Concentration (vol %), NewtonCutting Transportation & hole Cleaning

Vs

dp

Fd Wp Fb

Slip Velocity of Cuttings in LAMINAR Flow

Fb

Fd

Wp

Fd = Viscous DragWp = Particle WeightFb = Buoyant Force

Vs 138

2(

p mud dp)

Slip Velocity for Cuttings in TURBULENT Flow

Vs 189.

dpCD

p mudmud

Vs = Slip Velocity (ft/min)P = Particle density (lb/galmud = Fluid density (lb/gal)dp = Particle diameter (in.)= equivalent viscosity

CD = Coefficient of Drag or friction factor

Moore Correlation for Non Newtonian fluids : the most accurate correlationsCutting Transportation & hole Cleaning

K = Consistency Index, Power LawN= Flow Indexs = Particle density (lb/galf = Fluid density (lb/gal)dp = Particle diameter (in.)a= Apparent viscosity

Va = Average Annular Velocity

Apparent Viscosity

Slip Velocity

Cuttings Transport Key VariablesHigh

Influenceon cuttingstransport

LowLow Ability to control High

FlowRate

ROP

RPM

Cuttingssize

Cuttingsdensity

Drillpipeeccentricity

Mudweight

Holegeometry

Mudrheology

Cutting Transportation & hole Cleaning

Cutting Transportation & hole CleaningCutting concentration in excess of five(5) volume % can lead to a pack-offand Stuck pipe.

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 mudbeing pumped at an annular velocity of 120 ft/min (2.0 ft/s) in a10x5 in annulus. Apply the correlation of Moore, Chien andWalkers and Mayes. The following data were obtained for thedrilling fluid using a rotational viscometer.

Rotor Speed Dial ReadingRPM Degree

3 2.06 3.3100 13200 22300 30600 50