drilling hydraulics 3

8/12/2019 Drilling Hydraulics 3

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D

rilling E

ngineering 2

Course (

1

st

Ed.)
http://bit.ly/Q921-DE2http://bit.ly/Q921-DE2mailto:[email protected]://bit.ly/Q921-DE2mailto:[email protected]


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1. drilling hydraulics:

A.

types & criteria of fluid flowB.

fluid Rheology and models

a. Bingham plastic & Power

-

law models


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1. Laminar Flow in Pipes and Annuli

2. Turbulent Flow in Pipes and Annuli

3. Pressure Drop Across Surface Connections

4. Pressure Drop Across Bit

5. Optimization of Bit Hydraulics

6. Particle Slip Velocity


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laminar flowing pattern applicationFor drilling operations

the fluid flow of mud and

cement slurriesare most important.

When laminar flowing pattern occurs,

the following set of equations can be appliedto calculatethe friction pressure drop [psi] p,

the shear rate at the pipe wall andthe circulation bottom hole pressurefor the different flow models:

Fall

13

H. AlamiNia Drilling Engineering

2

Course (

1

st Ed.) 5


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Laminar:Bingham Plastic Fluid ModelFlow through pipe

cp in [ft/sec]

Flow through annulus

can in [ft/sec]:

Fall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 7


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Laminar:Power law Fluid ModelFlow through pipe

cp in [ft/min]:

Flow through annulus

can in [ft/min]:



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friction factor determination for fullydeveloped turbulent flow pattern [in] ... absolute roughness of pipe,

see from following table

(Absolute pipe roughness for several types of circular pipes)

[1] ... relative roughness of pipe

To solve this equation for f, iteration techniques have tobe applied.



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Friction factor for turbulent flowThe friction

factor can alsobe obtainedfrom thefigure.



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Friction factor estimationIn drilling operations,

the relative roughness is oft assumed to beinsignificant (usually less than 0.0004) whichreduces the friction factor equationto the following equation for smooth pipes:

For smooth pipes and turbulent flow(

= 0 and 2,100


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The pressure drop calculation atturbulent flow patternThe pressure drop at turbulent flow pattern is then

computed for the different flow modelswhen replacing diwith the equivalent diameter de = 0.816 (d2 d1).

When the friction factor is computed,the pressure dropsfor the individual flow models can be calculated.

For Newtonian Fluid Model:



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Power law Fluid Model:For fluids that behave according to the power-law

fluid model, an empirical friction factor correlationbased on the flow behaviour index n is used.

This correlation gives for:Flow through pipe:

Flow through annulus:

a [cp] ... apparent Newtonian viscosity



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Friction factor for Power LawReynolds

number is thencompared withthe critical

Reynoldsnumber,which isdepended onthe flowbehaviourindex n andshould beobtained fromthe figure

Friction factor for Power-Law fluid modelFall 13 H. AlamiNia Drilling Engineering 2 Course (1st Ed.) 16


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pressure drop for power lawInstead of using the figure,

following equation can be appliedto determine the friction factor iteratively:

When the friction factor f is calculated, thecorresponding pressure drop can be calculated with

the Newtonian fluid model equation:



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the total pressure lossat the surface equipmentThe pressure drop in surface connections comprise

the pressure drops along the standpipe,the rotary hose, swivel and kelly.

Since different rigs do use different equipment, thetotal pressure loss at the surface equipment canonly be estimated.

(pf )se [psi] ... pressure loss through total surfaceequipment, q [gpm] ... flow rate, E [1] ... constantdepending on the type of surface equipment used


Groups of surface equipment


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Equivalent drillpipe lengthsfor surface equipmentAnother approach is

to determine the equivalent length of drillpipe for eachsurface equipment and

then use the relevant equations

to determine the surface pressure loss.

The Figure gives the equivalent lengths of thedifferent equipment parts.



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pressure drop across the bitThe pressure drop across the bit is mainly due to

the change of fluid velocities in the nozzles.

To increase the penetration rate,

when the mud flows through the nozzlesits speed is increased drastically which causesa high impact force when the mud hits the bottomof the hole.

This high fluid speed on the other handcauses a relative high pressure loss.

This pressure loss is very sensitive to the nozzle seize.



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Calculation of pressure dropacross the bitThe bit pressure drop

itself can be calculatedwith:

AT [in2] ...total nozzle area

dn [1/32] ...jet nozzle seize

[ft/sec] ...mean nozzle velocity

q [gpm] ... flow rate

m [ppg] ... mud density

Cd [1] ... dischargecoefficient, depending onthe nozzle type and size(commonly Cd = 0.95)



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Initiating Circulationpressure drop calculationThe additional pressure drop can be estimated

applying the gel strength g of the drilling mud as:

For flow through pipes:

For flow through annuli:

g [lbf/100 ft2] ... gel strength of the drilling mud



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hydraulic program designThe penetration rate in many formations is

roughly proportional to

the hydraulic horsepower expended at the bit.

To drill most efficiently hydraulic programs aredesigned

for maximum bottom hole cleaning(how much bottom hole cleaning is necessaryto reach maximum penetration rate)

combined with maximum bottom hole cleaning basedon the surface hydraulic horsepower availability.



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drilling optimization parametersFor this reason,

mud rheology,

hydraulics (individual pressure drops) and

bit nozzle selectionare the parameters to consider for drilling optimization.

To optimize drilling hydraulics,different approaches can be made.The hydraulics can be designed to either

optimize the nozzle velocity,the bit hydraulic horsepower or

to optimize the jet impact force.



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The total pressure dropat the circulation systemThe total pressure drop at the circulation system

is the summation of

the pressure drop at the bit and

the pressure drop throughthe rest of the circulation system.



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Optimum hydraulic horsepower andjet impact forceOptimum hydraulic horsepower andjet impact force are given with:

The optimum nozzle area leads to the respectivenozzle selection.

Nozzles for drilling bits are given 1/32 [in] seizes thus thecalculated nozzle area has to be converted into n/32 [in].

Knowing n (has to be an integer and is commonlyrounded down to ensure the nozzle velocity) andthe amount of nozzles to use,the individual seizes are found.



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The annular flow of the drilling fluidThe annular flow of the drilling fluid

(carrying drilling cuttings anda certain amount of gas to the surface,)is disturbed by frictional and centrifugal forces

caused by the rotation of the drillstring.

In practice, when it is noticed thatinefficient hole cleaning is present,either the mud flow rate is increased or

the effective viscosity of the mud is increased or

both adjustments are performed.To estimate the slip velocity of the cuttings,following correlation methods were developed empirically

and are widely accepted and used in the industry:



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Estimation of the slip velocity;Moores CorrelationMoores Correlation:

for NRp > 300:

for NRp < 3:

for 3 NRp < 300:

a [cp] apparentNewtonian viscosity

ds [in]drilling cuttings diameter

NRp [1]

particle Reynolds number [ft/sec] particle slip

velocity

s [ppg] cuttings density

g [lbf/100 ft2] gel

strength required tosuspend a particle ofdiameter ds



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Estimation of the slip velocity;Chiens CorrelationChiens Correlation:

The correlation equations determined by Chien aresimilar to the ones defined by Moore.

For clay-water muds,

he recommends the usage of the apparent viscosity.

The correlation is performed as:

for NRp < 100:

for NRp > 100:



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transportation velocityThe so called transportation velocity is defined as

the difference between the mean annular velocity and

the slip velocity . The transportation ratio FT given by:

determines whether the cuttings aretransported to the surface (FT is positive) or not and

provides a relative measure ofthe carrying capability of the drilling mud.



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1. Dipl.-Ing. Wolfgang F. Prassl. Drilling

Engineering.

Master of PetroleumEngineering. Curtin University of Technology,

2001. Chapter 4


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drilling hydraulics 3

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