14 Jet Bit Nozzle Size Selection

8/12/2019 14 Jet Bit Nozzle Size Selection

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PETE 411

Well Drilling

Lesson 14

Jet Bit Nozzle Size Selection


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14. Jet Bit Nozzle Size Selection

Nozzle Size Selection

for Optimum Bit Hydraulics:

Max. Nozzle Velocity

Max. Bit Hydraulic Horsepower

Max. Jet Impact Force

Graphical Analysis

Surge Pressure due to Pipe Movement


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Read:Applied Drilling Engineering, to p.162

Quiz AThursday, Oct. 10, 7 - 9 p.m. Rm. 101

Closed Book1 Equation sheet allowed, 8 1/2 x 11 (both sides)

HW #7:On the Web - due 10-09-02

{ Quiz A_2001 is on the web }


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Proper bottom-hole cleaning

will eliminate excessive regrinding of drilled

solids, and

will result in improved penetration rates

Bottom-hole cleaning efficiency

is achieved through proper selection of bit

nozzle sizes


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- Optimization -

Through nozzle size selection,

optimization may be based on

maximizing one of the following:

Bit Nozzle Velocity

Bit Hydraulic Horsepower

Jet impact force

There is no general agreement on which ofthese three parameters should be maximized.


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Maximum Nozzle Velocity

Nozzle velocity may be maximized consistent with

the following two constraints:

1. The annular fluid velocity needs to be high

enough to lift the drill cuttings out of the hole.- This requirement sets the minimum

fluid circulation rate.

2. The surface pump pressure must stay within themaximum allowable pressure rating of the

pump and the surface equipment.


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From Eq. (4.31)

i.e.

so the bit pressure drop should be maximized in

order to obtain the maximum nozzle velocity

4

bdn

10*074.8PCv

=

bn Pv


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This (maximization) will be achieved when

the surface pressure is maximized and thefrictional pressure loss everywhere is

minimized, i.e., when the flow rate is

minimized.

pressure.surfaceallowablemaximumtheand

ratencirculatiominimumtheat

satisfied,areabove2&1whenmaximizedisvn


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Maximum Bit Hydraulic Horsepower

The hydraulic horsepower at the bit is

maximized when is maximized.q)p( bit

dpumpbit ppp =

where may be called the parasiticpressure

loss in the system (friction).dp

bitdpump ppp +=


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.turbulentisflowtheif

cqpppppp 75.1dpadcadcdpsd =++++=

In general, wherem

d cqp = 2m0

The parasitic pressure loss in the system,


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0)1(pwhen0

17141714

pump

1

=+=

=

=

+

mHbit

m

pumpbitHbit

qmcdq

dP

cqqpqpP

dpumpbit ppp =m

d cqp =


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whenmaximumis

1

1

pwhen.,.

)1(pwhen.,.

d

pump

Hbit

pump

d

P

pmei

pmei

+

=

+=

pumpd p

m

p

+

=

1

1

0)1(ppump =+ m

qmc


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- Examples -

In turbulent flow, m = 1.75

pumpbit

pump

pumpd

pof%64p

pof36%

%100*p

175.1

1p

=

=

+=

pdp

1m

1p

+

=


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In laminar flow, for Newtonian fluids, m = 1

pumpb

pump

pumpd

pof%50p

pof50%

%100*p

11

1p

=

=

+=


Examples - contd


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In general, the hydraulic horsepower is not

optimized at all times

It is usually more convenient to select a

pump liner size that will be suitable forthe entire well

Note that at no time should the flow rate beallowed to drop below the minimum

required for proper cuttings removal


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Maximum Jet Impact Force

The jet impact force is given by Eq. 4.37:

)(c0.01823

01823.0

d dpump

bitdj

ppq

pqcF

=

=


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But parasitic pressure drop,

2201823.0

+=

=

m

dpdj

m

d

qcqpcF

cqp

)(c0.01823 d dpumpj ppqF =


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Upon differentiating, setting the first derivative

to zero, and solving the resulting quadraticequation, it may be seen that the impact

force is maximized when,

pdp

2m

2p

+

=


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Maximum Jet

Impact Force

- Examples -

pb

pd

pof%47pand

pof%53p1.75,mif,

=

==Thus

pb

pd

pof33%pandpof%67p1.00mif,=

==Also

pd p2m

2

p +

=


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Nozzle Size Selection

- Graphical Approach -


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1. Show opt. hydraulic path

2. Plot pdvs q3. From Plot, determine

optimum q and pd

4. Calculate

5. CalculateTotal Nozzle Area:

(TFA)

6. Calculate Nozzle Diameter

dpumpbit ppp =

optbd

opt

opttpC

qA

)(

10*311.8)(

2

25

=

With 3 nozzles:3

A4d totN =


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Example 4.31

Determine the proper pump operating

conditions and bit nozzle sizes for max.jet impact force for the next bit run.

Current nozzle sizes: 3 EA 12/32Mud Density = 9.6 lbm.gal

At 485 gal/min, Ppump = 2,800 psi

At 247 gal/min, Ppump = 900 psi


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Example 4.31 - given data:

Max pump HP (Mech.) = 1,250 hp

Pump Efficiency = 0.91

Max pump pressure = 3,000 psig

Minimum flow rate

to lift cuttings = 225 gal/min


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Example 4.31 - 1(a), 485 gpm

Calculate pressure drop through bit nozzles:

22

2510*311.8:)34.4.(

td

bAc

qpEq

=

psi9061,894-2,800losspressureparasitic

psi1,894

32

12

43(0.95)

)485)(6.9)(8.311(10p2

2

2

2-5

b

==

=

=


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Example 4.31 - 1(b), 247 gpm

psip b 491

32

12

43)95.0(

)247)(6.9)(10(311.82

2

2

25

=

=

psi409491-900losspressureparasitic ==

Plot these two

points in Fig. 4.36

(q1, p1) = (485, 906)

(q2, p2) = (247, 409)


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Example 4.31 - contd

2. For optimum hydraulics:

gal/min650000,3

)91.0)(250,1(714,1714,1q

max

max ===P

EPHp

1,Interval)a(

gal/min225q

psi875,1

)000,3(22.1

2

2

2p

min

maxd

=

=

+=

+= P

m2,Interval(b)

3,Interval(c)

3

2

1


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Example 4.31

3. From graph, optimum point is at

)(

10*311.8)(2

25

optbd

opt

opttpC

qA

=

)700,1(*)95.0()650(*6.9*10*8.311

2

2-5

=

( ) indoptN

nds2

opt 3214in0.47A ==

psippsigal

q b 700,1300,1p,min650d ===


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psippsigal

q b 700,1300,1p,

min

650 d ===


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Example 4.32

It is desired to estimate the proper pump

operating conditions and bit nozzle sizes for

maximum bit horsepower at 1,000-ftincrements for an interval of the well

between surface casing at 4,000 ft and

intermediate casing at 9,000 ft. The wellplan calls for the following conditions:

Well Planning


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Example 4.32

Pump: 3,423 psi maximum surface pressure

1,600 hp maximum input0.85 pump efficiency

Drillstring: 4.5-in., 16.6-lbm/ft drillpipe

(3.826-in. I.D.)

600 ft of 7.5-in.-O.D. x 2.75-in.-I.D. drill collars


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Example 4.32

Surface Equipment: Equivalent to 340

ft. of drillpipe

Hole Size: 9.857 in. washed out to 10.05 in.10.05-in.-I.D. casing

Minimum Annular Velocity: 120 ft/min


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Mud Program

Mud Plastic YieldDepth Density Viscosity Point

(ft) (lbm/gal) (cp) (lbf/100 sq ft)

5,000 9.5 15 5

6,000 9.5 15 5

7,000 9.5 15 5

8,000 12.0 25 9

9,000 13.0 30 12


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Solution

The path of optimum hydraulics is as

follows:

Interval 1

gal/min.681

423,3)85.0)(600,1(714,1

pEP714,1q

max

Hp

max

=

==


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Solution

Interval 2

Since measured pump pressure data are notavailable and a simplified solution technique

is desired, a theoretical m value of 1.75 is

used. For maximum bit horsepower,

( )

psia1,245

423,3

175.1

1

1

1max

=

+

=

+

= p

m

pd


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Solution

Interval 3

For a minimum annular velocity of120 ft/min opposite the drillpipe,

( )

gal/min395

60

1205.405.10448.2 22min

=

=q


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Table

The frictional pressure loss in other

sections is computed following aprocedure similar to that outlined above for

the sections of drillpipe. The entire

procedure then can be repeated todetermine the total parasitic losses at

depths of 6,000, 7,000, 8,000 and 9,000 ft.

The results of these computations aresummarized in the following table:


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Table

5,000 38 490 320 20 20 888

6,000 38 601 320 20 25 1,004

7,000 38 713 320 20 29 1,1208,000 51 1,116 433 28 75* 1,703

9,000 57 1,407 482 27* 111* 2,084

* Laminar flow pattern indicated byHedstrom number criteria.

ddpadcadcdps ppppppDepth


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Table

The proper pump operating conditions

and nozzle areas, are as follows:

5,000 600 1,245 2,178 0.380

6,000 570 1,245 2,178 0.361

7,000 533 1,245 2,178 0.3388,000 420 1,245 2,178 0.299

9,000 395 1,370 2,053 0.302

in.)(sq(psi)(psi)(gal/min))ft(

(5)Ap(4)p(3)Rate(2)FlowDepth)l( tbd


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Table

The first three columns were read directly

from Fig. 4.37. (depth, flow rate and

pd)

Col. 4 (pb) was obtained by subtracting

shown in Col.3 from the maximum pumppressure of 3,423 psi.

Col.5 (Atot) was obtained using Eq. 4.85

dp


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When a string of pipe is

being lowered into thewellbore, drilling fluid is

being displaced and forced

out of the wellbore.The pressure required to

force the displaced fluid out

of the wellbore is called thesurge pressure.


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An excessively high surge pressure can

result in breakdown of a formation.When pipe is being withdrawn a similar

reduction is pressure is experienced. This

is called a swab pressure, and may behigh enough to suck fluids into the wellbore,

resulting in a kick.

swabsurge PP ,vfixedFor pipe =

Fi 4 40B


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Figure 4.40B

- Velocity profile for laminar flow pattern when closed

pipe is being run into hole

14 Jet Bit Nozzle Size Selection

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