05 Downhole Motors

7/24/2019 05 Downhole Motors

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O W N H O L E M O T O R S

ling w as the limited num ber of blows possible, the slow rate of pene-

Gradually, turbine downhole motors came into use. The use of downhole

M any turbines were used in the former Soviet Un ion and 80 of the

Because of the drawbacks of turbines, positive displacement motors

s) came w idely into use. The first commercial PDM was introduced in

or kick-off operations. The design capability of the PDM s to

Even though the PDM has inherent disadvantages, the economics and

lexibility in operating cond itions outweigh the disadvantages.


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7 4 C H A P T E RS

This chapter describes percussion hammers, positive displaceme

motors (PDMs), turbines, electric downhole motors (EDM), and miscell

neous downhole m otors (MD M ).

D W N H O L E P E R C U S S I O N H A M M E R S

The word perc ussio n here means impact or collision or vibratory shoc

The principle of using the energy generated by impact loads to cut roc

caught the eyes ofthe researchers for drilling early in the 1950s. This prin

ple is used in percussion drills, ' ' ' ' which are also called by several oth

names, such as downhole hammer, percussion hammer, percussive dri

down-the-hole hammer, etc. Numerous patents have been obtained throug

out the world, ranging from small modifications to major changes to the re

ular hammer drill. Bit bearings and bit tooth should be designed to

compatible with the hamm er to withstand the blows ofth e repeated hamm

ing action. The cutting action of the bit connected to the hammer is entire

different from that in conventional rotary drilling. The cutter should

designed to efficiently transmit the energy into the rock formation so that

breaks as the bit advances.

T yp es o f P er cu ss i ve D r i l l i n g

Broadly the percussive method can be classified under three categories bas

on the impact types used:

*' '**

1. Chum drilling

2 . Dow nhole hamm er drilling

3 .

Ham mer drilling

hurn Drilling

In this method of drilling, the drillbit is fixed to a connecting rod acting a

piston elem ent, which causes the drillbit to reciprocate within the hole lik


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ownhole Motors 2 7 5

ess wave traveling through the bit assembly. This allow s m aintaining a

bination of higher WO B and variable rotary RPM in conjunction with

s as it requires a long connecting rod which is not very effective in

to the bit.

ener l Operating Principle

simple percussive ham mer consists of

Top sub compatible for drillcollar connection

Outer hammer casethe housing

Drive sub

The drive sub carries the anvil to which the bit can be connected. The

ton moves up and down inside the hammer ca se. The drilling fluid enters

dow nward force due to the larger bottom face area the pis-

uid pressure at the top of the piston which forces the piston to move dow n

il. The anvil passes the blow to the bit and further


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2 7 6 CHAPTER 5

The operating principle of the downhole hammer is physically explain

by Figure 5 .1. The operating fluid enters the top of the cylinder and push

the piston downward. The two operational parts of the drill that determi

the output of the tool are the cylinder and piston. The output depends on t

working face area of the piston, piston stroke length, and the weight

the piston.

The w ork done by a percussion hammer can be derived from basic pr

ciples as follows:

Force acting on the piston = Ap x plb

Work done = Force x Distance

= Ap X

ft-lb

Work per minute

Woik B lows

Blow min

Number of blows per minute = n ,

Work per minute = Ap x

x i x

5

From this simple equation, it can be inferred that the work done p

minute is directly proportional to the pressure acting on the piston, Ap, ar

of the piston,Ap,stroke length,

f

and the num ber of blows of the piston, n

W- Weight orthephtton

- Areao f the workingTaceof the pistwn

L - Stroke ofthepblon

P - Pressu re acting on the piston fare

P


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In some hard formations, where normal drilling rate slows down, per-

cussion drilling was able to achieve higher rate of penetration because

of the high dynamic axial load.

Due to low static weight on bit, com plex bottom hole assem blies are

not required to control deviation for straight hole drilling.

Equipm ent and the com m ercially-available bits are most of the time

compatible for percussion drilling.

Due to ham mering action, large cuttings may be generated, allowing a

better geological study.

Proved to be effective in air/gas drilling.

On account of the high-impact energy, the hole deviation was less than

in conventional rotary drilling.

The transfer of stress wave energy to the formation results in severe

vibration transmitted to the drill string. The vibration is more pro-

nounced when the tool is drilling at shallow depth.

When drilling through the shale section, the percussive hammering

action d isturbs the shale resulting in a wellbore stability problem .

The hole becomes tapered resulting in additional reaming of the hole.

The reaming w ith ham mering may result in collapse of wellbore.

No extensive modeling or rigorous simulation studies are available for

percussive drilling.

nergy

iciency of the bit or the drilling tool unde r use. Specific energy ( E J is a


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7 8

CHAPTER 5

where E| = power input

_ = rate of volume removal

Specific energy is also defined as the energy required to create a n

surface area. The creation of a new surface area or new volume depends

the type of breaking m echanism used. Application of different mechan i

results in different specific energy for the same bit and same type of for

tion. Experiments showed that hammering and slow compression show

two different numerical values of specific energy for the same rock ty

This gives a clear insight into the relationship between the mode of r

breakage and new surface area formed.

Specific energy varies with the type of drilling mechanism used

the method applied. Methods of drilling can be classified as percuss

(churn, hammer, downhole hammer) and rotary (rotary, downhole mot

turbines, etc.).

The work done in breaking the rock and disintegrating a length of L

force F applied is given by W = JQFdR.

In rotary drilling work is done both by the thrust and the torque.

The work done by the axial thrust force = FdR

where R = ROP, rate of penetration, in./niin

The work done by torque = 27iNT

where N = rotary speed , in rev/min i

T = torque, ft-lbf

Volume of rock removed V = ^

4

where D,, = diameter of the bit

4(Fdu

2JCNT

Specific energy E, =


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Downhole Motors

2 7 9

ere A = area drilled =

4

E a = Specific energy due to axial thrust com ponent

E,r = specific energy due to rotary com ponent

The following is the empirical equation*'^* for predicting rate of penetra-

CP

ROP =

r

(5.4)

(H N SHN)

C = constant

P = operating pressure

HN = rock impact hardness number

SHN = shore hardness

a, b = empirical indices

peration Sequence

5.2 shows the schematic of a simple percussive hammer,'' ' which con-

a

top sub compatible for drillcollar connection, an outer hamm er case,

dadrivesub.The drive sub carries the anvil to which the bit can be attached.

Figure 5.3a shows the hanging position and the fluid is bypassed through

Upw ard m ovem ent of the piston results in the closure of the upper finger


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28 CHAPTER 5

housing

valve

hammcr

Spring mandrel

hammer

return spring

hammer

anvil

FIGURE 5.2 Percussion hammer operating parts.

2 01


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8

FIGURE 5.3 Percussion ham mer operating po sition.

20


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8 CHAPTER 5

EXPONENTIAL-TYPE STRESS

WAVEFORM.

To obtain a realistic incident str

waveform, the equation is defined

as:*^^

a

=

a

(5

where O| = incident stress

On, = maximum stress

t = time

n = index

The incident stress waveforms shown in Figure 5.4 are plotted for v

ous values of and = 1/t. From the figure it can be inferred that for n =

the stress rise is very fast reac hing m axim um instantaneo usly at t = 0

slowly decaying thereafter, which can be considered an extreme case. Wh

n

= 1,

the rise time is faster than the decay tim e; and when n = 2, the rise ti

is slower than the decay time. As the value of is further increased, the

time to reach maximum stress is further delayed and at a certain stage

1.20 t

8

4


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Downhole Motors 2 8 3

ess waveform assumes a bell shap e, which can be considered as another

case. In reality, when the ham mer strikes the anvil, the stress reaches

approximates

The instantaneous force between the rock and the bit is

F = A ( G - 1 - O I + r W'OJ

G^

= refiected stress

Fo = 0 because at t = 0, F = 0

th bit into the formation is

J 6 / I . / c ^ \

l ^ i ~ ^ r I ^^ o { - > )

dt pc

Vo= 0 because at t = 0, dy/dt = 0

g = acceleration due to gravity

p = density of the material

^y - ^ - I ' I . - (5.8)

dt pc

A = cross-sectional area

Using Eq. 5.5 and defining = l/x, the index of fiow time, the govern -

equa tion '' is derived:

H v O y0 I in I / t\

+ Ky

o, e p.y;

dt Ape pc yn

To obtain a general solution Eq. 5.9 is normalized by defining the fol-

ariables:

imensionless time, t , is


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2 8 4 C H A P T E R 5

The normalized equation is

The solution of this normalized dimensionless equation is

n (n +

The solution for the exponential waveform is shown in Figure 5.5.

(5.

(5.

EFFICIENCYOF TH SYSTEM. T he e fficiency is defined as the ra tio of ene

output to the energy input. The energy input is in the form of the stress wa

and is given by :' ' '

dt

5.

aeo

2


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This equation gives

lo

2n e

n

E -

(5.15)

The energy output is the energy used in breaking the rock and is the area

nder the force-displacement graph, and is

io = JKydy = ^

ence, the efficiency is

Substituting E qs. 5.15 and 5.16 in Eq. 5.17 yields

This equation can be written

I ll

n +l , 2 ' " ' ' '

where

4kg

pAc

(5.16)

(5.17)

(5.18)

(5 .19)

RECTANGULAR INCIDENT STRESSWAVES. C o n s i d e r a simple case o f rectangular

pulse with a maximum amplitude of

CT^,

for a duration of nt where n = 0, 1,

2 . . . Mathematically it can be represented


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2 8 6 C H A P T E R 5

1.20

^ 0.80

g

e

0.40

aoo

-

0 - 0

- 1

n 1

n=2

=3

- 4

1

0.00 1.00 2.00 3.00

t

Incident Stress Waveform square -tau=0.5)

FIGURE 5.6 Incid enta l wav eform ( rectan gu lar typ e).

4

Using the rectangular w ave condition as shown in Figure 5.6 , E q. 5.5

written

as'^' ^^*;

^ + Ky

dt A pe pc

< n

dt A pe

0 < t

(5.21

E quation 5.2 0 is normalized using the dimensionless variables as befor


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Down hole Motors 287

The general solution for Eq. 5.21 is

y , - 1 O < t, < n

y , = O O < td

5.23)

Substituting the respective energy input and output values and simplify-

ing, the efficiency is

^ o < td < n

O 0 Rolnr

F I G U R E 5 1 0

housing.

Vertical cross sectionofa rotor stator and

ublicr lcmcni

ine of Housing

< nitre line ofsh ft

5 11

Horizontal cross section ofarotor stator and housing.


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9 CHAPTER 5

Bearing A^embty gap

Hanging Position

Resting on Rotary Table

FIGURE 5.12 Bearing assembly check .

Rotor atching Mechanism and ssembly

Some m otors such as Navi-Drill are equipped with a rotor holding mech

nism to secure the rotor rotor assemb ly and hous ing assembly in case

failure during back-off or

twist off.

The assembly consists ofarotor equipp

with a retaining rod and retaining disc fitted at the top and a stop ring fitt

in the hou sing as shown in Figure 5.13 . In case of failure the assem bly

held at the top of the stop ring. Th e diam eter of the rod and inside diam e


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ownhol Motors 293

power Mx ii

o

Nu/Jtle

Retaining disk

Rolor Cmching stop plaic

FIGURE 5.13 Roto r ca tching

mechanism.

Several prominent manufacturers w ith several options.

Rugged design.

Air/gas may be used as a power fluid.

Uniform d ischarge . Neg ligible fluid pulsation to interfere with MW D

instrumentation.

Output torque and rotational speed are directly proportional to pum p

pressure and fiowrate respectively.

Eigure 5.14 shows the performance characteristic curves of a PDM.

Experience has shown that mud density has little effect on the performance

of the motor. Rather torque and horsepower are directly proportional to the

pressure drop across the motor. As shown in the figure speed is directly pro-

portional to flowrate and rem ains constant as torque inc reases. The effi-

ciency increases with pressure differential until it reaches a maximum value

at the design operation conditions and then starts decreasing .


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94 CHAPTER 5

X

u

LU

/

Efficiency^ /

/ / /

Hofsepower

/

^ .^^ Torque

RPM

Pressure Drop

FIGURE 5.14 PDM performanc

characteristic curve s.

Bypass valve clogging:

After running in to the bottom, the bypass valv

fails to operate, resulting in diversion of fluid power to the weep slot

To correct the defect the string has to be pulled up resulting in loss o

rig time.

Reaming:Whenever the hole needs reaming, the use of PDM is diff

cult. The string gets stalled and stuck in an undergaged hole.

Lubrication:Drilling fluid must have lubricating properties to preve

accelerated stator wear. Stator wear is a function of fluid clean lines

and lubricity. When air/gas is used as the pumping fluid, lubricatin

fluid added to prevent stator damage may cause undesirable materia

to stick to the walls of the borehole, resulting in fonnation dam age .

Downhole motors still have short life expectancies and make the system

less efficient.'^*'' Improved power capability and greater reliability of PDM

is necessary to make the whole system cost effective.


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ownhole Motors

2 9 5

To proceed further it is necessary to derive a general formula for the

cross section of the m ultilobe m otor. Because these cross sections are formed

by a family of curves , it is easy to generalize by considering the pitch circles

or diameters of the housing and shaft as shown in Figures 5.15 and 5.16.

The cross-sectional area between the housing and shaft can be approxi-

mated as:

A , -

- r,)

5.26)

where r = radius of the housing pitch circle

r, = radiusof the shaft pitch circle

Because

-t-e

) = ^ d , - e )

5.27

. , ^ , d, .

On usmg the fact that ^ = l =

d

A, =

n - M

5.28)

Outer Casing thickness h


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9 6 C H A P T E R

5

eisstomerc minor thickness ti

Sha

jter Casing thickness

IGUR 5.16 Cross section of three-lobe power section.

To have a general expression for a multilobe motor, the eccentricity ca

be replaced with either shait pitch circle or housing pitch circle.

e = d,

1 0

Volume of the cavity is

5.2

5.3

For practical use, it will be worthwhile to express the cross-section

area in terms of either the housing diameter or the shaft diam eter instead

tbe respective pitch circles.


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But diameter of tbe shaft is

D

= d, -H 2e

D = 2ne + 2e = 2e(n -i- I). (5.32)

S o diameter of the housing is

Dh = 2ne -i- 2e + 2e = 2e(n 2) (5.33)

Substituting the value of e from Eq. 5.32 into Eq. 5.28 yields

A,

=

0 .7 9 | i ^ D j (5.34)

2-0

Defining outside diameter of the motor as:

D . = D , + t, (5.35)

wbere t, = 2(t| + t,)

t, = thickness of the elastomer of the housing

ti = metal thickness of the housing casing

In terms of diameter of the motor the cross-sectional area is

/ . _ . 2 \

A . = 0 . 7 9 ) ^ ( D , , - t , ) (5.36)

( 2 - i )

where

D

= D, + t,

E X A M P L E 5 1

Calculate the eccentricity and diam eter of motor for the following motor

configuration:

Configuration = 1:2

Diameter of shaft = 3 in.

S O L U T O N


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9 CH PTER

Diameterof the housing = 5.5 in.

Outside diameter of the motor can be approximated using the followin

relation:

= Du + 2e

^

~ 6 in.

V O L U M E G E N ER A T ED B E T W E E N H O U S IN G

A N D S H A F T W i t h

t h e

a b o v e d e v e l o p m e

of generalized cross-sectional area of the multilobe motor, the volume gen

erated by the cavities of the multilobe motor can be derived for an ideal leak

free motor. For a leak-free motor, the volume generated by the geometric

features of the motor is

V = A, X p, 5.37

where p = pitch of the housing

n = number of windings of the shaft

Using Eq. 5.36, volume for the multilobe motor is

V = 0.79- ^ r P h D - t , f 5 38

1 2

where i = winding ratio of the motor, i = ~, - , . . .

SE LING AND SE LING

LINES

The sealing is one of the important character

tics of any positive displacement motor. To ensure ideal operation of th

motor without any leakage, sealing and the seal lines formed need to b

known and understood fully.

The leakage loss is a loss of capacity through the running clearance

between the shaft element and the housing element. Figure 5.17 shows th

elevation and lateral view of the power section at four different position

when the shaft is not rotating.


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ownhole Motors

2 9 9

IGUR 5.17 Horizontal cross section of two-lobe power section.

Rotation of the shaft resu lts in virtual deformation of the surface decreasing

the cavity on one side and increasing the cavity on the other side resulting in

a motoring action. This can be considered as a positive displacement mo tor

of infinite stroke length as explained earlier in the volume traced by the cav-

ities.

Due to hyp ocy cloidal m otion oft he shaft the sealing line is helical


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3 CHAPTER 5

IGUR 5.18 Horizontal view of two-lobe power section.

using asterisks. The sectional views at different cross sections are show

and the corresponding designated cross sections are marked in Figures 5.1

and 5.20.

To visualize and have a solid understanding of the cavity it is necessar

to have different views of the motor. Figure 5.21 shows the progress ion o

the cavities and the procession of the shaft/housing cross section at differen

positions along the axis of the power section of the motor.

IGUR 5.19 Sectional view of vertical cross section sections 1-7).


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Downhole Motors

3

IGUR

5.21

Isometric view of housing and shaft.

Figure 5.22 shows the vertical cutaway view of the cavities in the longi-

The cavities can be seen at two different shaft positions in both

a n d lo w r a te

mechanical horsepow er developed by the motor can be calculated from

e product of torque and angular velocity:


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3 2 C H A P T E R 5

IGUR 5.22 Cutaway view of housing/shaft two-lobe, three-lobe power sectio

Tocarry out the calculations for a multilobe motor it is required to expr

various parameters in terms of either winding number or winding ratio.

The flowrate required to rotate the shaft at N rpm for a multilobe moto

Q =

5.

Using the above relations, the hydraulic horsepower for a multilo

motor can be expressed


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ownhol otors

303

T = 0.01 Api

l + i

2 i f

5.44

E X A M P L E 5 2

The following data pertain to a PDM of configuration 7:8. Diameter of

gpm. Assume an efficiency of 70 .

i = winding ratio of the motor = 0.875

T = 0.01x350x0.875

1.875

X 36x24x0.7 = 2,744 ft-lbf

(2-0.875)'

l speed of the motor can be calculated using the relation

Q

N

0.79

o

N

2 0=

400x230.98x1.125'

0.79x0.875x1.875x24x36

= 104 tpm

PRESSURE.

Stalling is one of the disadvantages of the PDM. This con-


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3 0 4 C H A P T E R

without doing any work. The reactive torque at stall condition is signiflc

and will be at a maximum. Once stalling is noticed, the string should be c

rected immediately by pulling the string off bottom and circulation stopp

to prevent elastomer/shaft damage. Stalling pressure can be calculated us

the approximate relationship:

P,p = (1.70 ~ 2 ) p _ (5.4

where Ap^^ = maximum pressure drop across motor, psi

Figure 5.23 shows the change in pressure that can be observed in

standpipe gage during the off-bottom, on-bottom, and drilling off and s

condition of the motor.

Operating stall efficiency, Ti^ is a useful parameter to estimate the mo

stall condition and is defined as the ratio of the operating torque to

stall torque :

T

n = ; p

(5.

where T^, = actual torque measured at the stall cond ition

E X A M P L E 5 3

Calculate the stall pressure for the following operating and geom etri

conditions of a PDM.

Configuration = 1:2

Diameter of the motor = 8.25 in.

Speed and torque ofthe motor = 340 rpm, 1,900

ft-lbf

respectively

a flowrate of 600 gpm

Assum e an efficiency of 80 .

S O L U T O N

i = winding ratio of the motor = 0.5


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ownhole Motors

5

n ll m

rilled Off

Molor Stall

IGURE 5.23 Standpipe gage pressure chan ges due to motor opera tion .

1,900

0.01x0.5

1.5

= 460 psi

X

64

X

24

X

0.8

( 2 - 0 . 5 )

pproximate stall pressure

is 810 psi.


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306 CHAPTER 5

housing as shown in Figure 5.24. So, the effective speed of the motor is l

than the calculated theoretical value. Also due to the change in configurati

at the motor inlet there will be a loss Q,, called inlet losses. The net flowr

is the sum of the theoretical flow, the leakage due to the pressure different

between the cavities and the inlet losses. So the net flowrate is

Qnet = Q, + Q. + Q 3.4

where Q, = geometrical or theoretical displacement per minute

Q, = leakage between the running clearance between the seals

Qi = inlet losses that can be neglected ,

The volumetric efficiency of the motor is the ratio of the actual flowr

to the theoretical ow rate and is

Q,

Q.

5.4

It is very interesting to study the behavior of the seal lines at vario

positions. The seal lines or leakage lines are helical. The length of the se

lines varies for different w indin g ratios of the motor. The num ber of s

lines has a direct relationship with the motor performance.


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Downhole Motors

3 7

e a r in g T h r u s t

e bearing section of the motor is a critical part in the motor assembly, which

r operating conditions of the motor, but also for the system as a wh ole.' '

The axial thrust on the bearings is composed of the following four

Hydraulic thrust created by the pressure drop acting on the cross-

sectional area (hydraulic thrustF^ yJ.

power wcuo n

Weighiofrod

iranstniMKin section

bearing tedian

pressure d n p acrcsx the motor

T Weigtiiof transmission shaft


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3 8 CHAPTER 5

power tedien

I We^of

pressure drop acrt ss the molor

bearing acclion

f d

gbl of Imtim isiion ihali

prc nu rc d rop acn> i ihc Ni

Puillp iilTl i in i ;

IGUR 5.26 Forces acting on the bearing section with

diamond bits.

Hydraulic thrust created due to the pressure drop across the

(hydraulic thrustF^yd^,).

Thrust due to the radia l force {m echanical thrustFn,^^)-

Self-weight of the shaft and the U-joint (weight thrustF^^,).

The hydraulic thrusts can be approximated by


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ownhol

Motors

309

shaft with the eccentricity ofthe shaft.

This unbalanced force has two components, axial F^ and tangential F^.

The tangential force is given by ^

F, = 47i-A,p,^,n,Nê (5.51)

The axial component can be calculated from tbe following equation con-

(5.52)

Ph

F ,

= 8.9xlO-Â,p,l,n,Nê- (5.53)

Ph

The thrust due to weight of the rotating elements including transmission

F^ = ( A , ^ , n , p , - F W J B F

(5.54)

e BF = I - ^

PrJ

p^ = mud density

p^ = rotor density

4 = length of the rotor

The net axial thrust on the bearing can be given as:

- P . F F


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' ' i

3 1 C H A P T E R

The pressure drop across the bit can be given as:

Substituting Eqs. 5.47 and 5.56 in Eq. 5.55, the net thrust on the bea

is modified to:

9xlO^'AAn,ep,N^

Ph

,l,n,Pr + W ) B F - WOB

KKi

y

2 i f

5

Kb = formation hardness, teeth, bearing, and mud coefficient

In addition, the flowrate can be given by the following equation'^**

terms of the configuration and power section dimensions as:

Q = K,iDp,N (5

where K. = 0.0034-

2-i =

O p t i m i z a t i o n w i t h P D M

Often, downhole motor pressure-loss calculations are not explicitly inclu

in the overall hydraulic optimization and bit nozzle selection with the av

able pum p power. To improve the optimization and m ake the system m


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Downhole Motors

3

en, jet nozzle optimization is carried out assum ing pre s-

wer, bit jet impact force, or rate of penetration.

lling operations, the total pum p pressure needed is equal to the sum of

and the frictional pressure losses in tbe annulus. In the 1950s, it was

out that the effectiveness of the jet bits could be improved by increas-

c pow er of the mud pumps. Shortly after that, several authors

Furthermore, for the true maximization of the bit hydraulic horse-

the motor is a strong ftinction of motor

is directly proportional to the weight app lied to the bit. Th e rela-

^ fwOB-D^,"

Apm Kn; ^ (5.5 9)


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3 2 CHAPTER S

pp r

includes the losses in the drillstring, annu lus, and surface lines.

relationship between the pressure drop, App^^, and flowrate for turbulent f

may be satisfactorily represented by a power law equation as follows:

A p p ^

= K Q ' . (5

Here K is a constant and s is an index representing the degree of tur

lence in the circulating system. The coefficients K and s are found by c

ducting a rig pump test with tbe bit offbottom.A minimum of two circula

flowrates and standpipe pressure are required for the estimation of thec

ficients. For nonsealed bearings a small percentage of circulating fluid

passed through the mechanical seal to act as coolant and lubricant for

bearing assembly. So, the bit flowrate m ay not be the same as the pum p

culation flowrate. To account for other split flows in dow nhole com pone

the generalized equations to calculate the K and s for m ultiple flow paths

given by the following equations:

( P -yP-).

, 5 .

and

K

where ^ ^

bypass flow ratio or the ratio of the diverted flow in the dow

hole tools to the total pum p flow

The flowrate and total flow area of the nozzles are selected to use

available pum p pressure fully (i.e., for the given solution, the sum of the p

asitic losses, pressure drop across the motor, and the pressure drop over

bit equals the maximum pump pressure). This means that after the true op


41/79


impact force is given by

[ 2 A p - A p

K s+2 ) J

5.64

The av erag e rate of pene tration as a function of weight on bit and bit

(5.65)

The power required for drilling can be given by the following empirical

H P , K,WOB^ND^ (5 .66)

Equations 5.64 and 5.65 are based on the assumptions that the formation

ed that will maximize the rate of penetration with the available pump pre s-

E X A M P L E 5 4

The following numerical example illustrates the calculations of the opti-

16-in. casing depth = 1,000 ft Openhole depth = 6 ,450 ft

Bit diameter = 6X in. DrillcoUar length = 400 ft

Mud weight = 9.5 ppg Rheology model = Pow er law

Weight on bi = 6,000 lbf Maximum pum p power = 1,500 hp

a,

1.25 a = 0.75


42/79

3 4 C H A P T E R 5

Diam eter of the housing = 5.5 in.

D iam eterof the shaft = 2.43 in.

Pitch of the motor = 35.75 in.

Efficiency = 70

Maximum horsepower = 40 hp

S O L U T O N

K =

K K

^b

KyKi

where K, = 5,252;

and

= 0 . 0 1

Kb = 4 X 10 '

= 0.333

S o pressure drop coefficient,

Kj = 63.08

Equation 5.59 can be used to calculate the pressure drop across the m o

for various weights on bit. The pressure drop calculated for a weight on

of 6,000 M i s

6.37

Figure 5.27 shows the plot of power per area through the bit for a ran

of flowrates, various total flow areas (TFA ), and w eight on bit for a 1:2 mo

configuration. The following steps can be used to determine the TFA a

pump rate required to maximize bit power per area.


43/79


kips

o

0.6

0.4

O

O 100 200 300 400 500 600 700 800

Flowrate gpm)

IGUR 5.27 Hydraulic horsepower/in.^ (HSI) versus flowrate.

2

1.8

1.6

1.4

1.2

1

Further, in a similar fashion, calcu lations can be repeated for different

of the total system pressure loss. (Essentially, this case results in zero

t increases, the flowrate at which the maximum power per area of the bit

From the foregoing calculations it can be clearly seen that the sizing of

ithout the inclusion of the weight on bit might result in lower

er per area. So an operating window of weight on bit needs to be selected

estimate the total flow area to achieve the maximum power per area.


44/79

3 6 CHAPTER 5

100 200 300 400 500 600 700 800

Flow Rate gpm)

IGUR

5.28 Impact force versus flowrate.

capable of producing this pump rate, use the maximum pump r

that the pumps can produce.

2. De termine the TFA right-side Y axis) that corresponds to the pu

rate determined in Step 1.

The behavior observed in power per area is also observed in the ma

mum impact force calculations. Noninclusion of weight on bit in the ana

sis not only results in lower impact force but also results in improper sizi

of the nozzles.

Figure 5.29 shows the plot of ROP for various weights on bit. Also, t

plot shows the ROP for various configurations of the motor. It can be se

that maximum rate of penetration decreases with the increase in the numb

of lobes of the motor, and the occurrence of the maxim um RO P is achiev


45/79

ownhole Motors 317

O 10 20 30 40 50 60 70 80 90 100

WOB Ibf)

IGUR

5 29

ROP versus WOB.

otor in use. The rate of penetration prediction is restricted

bit

haft by fltting a nozzle at the top of the sbaft which aids running

otor at lower speed at high flowrate. Tbe nozzle can be changed accord-

ng to the amount of the flow to be bypassed or split. If bypass is not required

clean the hole calls for additional flowrate the fluid can be bypassed through


46/79

3 8 C H A P T ER 5

the motor. PDM with rotor nozzle can be run into the hole without dum p valv

and with this option the fluid gets drained automatically thereby preventi

wet trip-out. It also helps to reduce the swab and surge pressures.

otor ozzleSizing

Sizing of the rotor nozzle is important, and the correct nozzle size should

selected to ensure that the desired power is available throughout the run an

at the same time minimum flowrate required to clean the hole is maintaine

The following simple steps'^'' help to size the nozzle effectively:

1. Establish the differential pressure range based on the expected weig

on bit range.

2 .

Calculate the range of operating flowrates,

Qp.

required for the run

3 .

Estimate the minimum flowrate required for hole cleaning , Q.

4.

If the operating flowrate is less than the minimum flowrate for hol

cleaning, calculate the additional flowrate, Q,, that will be bypasse

through the rotor nozzle.

5 . Size the nozzle using the equation:

^2 8 . 3 1 1 x 1 0 ' x Q ; x p ,

A^r = ^2 , ^^ (5.6

C d X

A p ^

where Q, = discharge coefficient

Ap,n = pressure drop across the motor, psi

p^ = density of the circulating fluid, ppg

Qrn = bypass flowrate through the rotor nozzle, gpm

A, = area of the rotor nozzle, in.

The proper nozzle size can be calculated by rearranging Eq. 5.6

Ro tor noz zle is often ex pressed in ^ in. For exam ple, if th

rotor nozz le is specifled as 14 , the rotor nozzle has a diam eter o

% in.

6. Check that the diameter of the nozzle is sufficiently smaller than th


47/79

Downhole Motors

319

Minimum flowrate required for hole cleaning = 475 gpm.

Motor Data: Conflguration = 2:3

Diameterof the motor = 6.75 in.

Pitchof the bousing = 23 in.

S O L U T O N

Diameter of the housing is assumed to be 6 in.

Pressure drop expected across the motor power section is

3

0 .01x0 .66

1.666

i 2

= 8 3 6 p s i

X 23 X 36 X 0.7

(2-0 .666)

Operating flowrate required:

_ 300 X 0.79 X

0.666

x 1.666 x 23 x 36

~ 230 .98x1 .333

530 gpm

Because this flowrate is higher than the minimum required flowrate of

475 gpm, there is no necessity to flt a rotor nozzle.

E X A M P L E 5 6

Compute the rotor nozzle size required to drill a 12J^-in. hole with a bit

torque of 4,000 ft-lbf and 90 rpm. The mud weight required is 10 ppg.

Minimum flowrate required for hole-cleaning is 900 gpm.

Motor Data:

Motor configuration = 6:7

Diameter of the motor = 8 in.

Length of the motor = 16.8 ft

Number of stages = 5.3


48/79

32 CHAPTER 5

Pressure drop expected across the motor power section is

4,000

0 . 0 1 x 0 . 8 5 7 1 4 2

1 857142

252 p

X 38 X49 X0.7

( 2 - 0 . 8 5 7 1 4 2 )

Flowrate required:

_ 90 X0.79 X 0.857142 x

1 857142

x 38 x 49

' ~ 2 3 0 . 9 8 x 1 . 1 4 2 8 6 '

Because the operating flowrate is less than the minimum flowrate, t

additional flowrate that needs to be bypassed is

Qm

Qmm Qop = 900 - 698 = 202 gpm

202 0 _

Bypassed flowrate =

698

Assu m ing a discharg e coefficient of 0.95 , the area of the rotor nozz

can be computed as below:

| 8 . 3 1 1 x l 0 ^ x 2 0 2 x 9 . 5 ^

0.95' X 252

Rotor nozzle diam eter = d^ = V 4 x 0.37637/71 = 0.692 in. Nozzle size

expressed in / in. and the closest rotor nozzle that can be selected

22 (0.49X32 22).

Squa re Mo to r

Square downhole motor design is a variation of the typical PDM with mod

fied body design. However, the operating principle is the same. A squa

motor and a BHA with a square m otor are shown in Figure 5.30. Other attac

ments, such as a dump sub and thruster, can be used with this type of mot


49/79

Downhole Motors

321

Pawfv StKtlini

Hixifing

FkMiSub

Stabrco

Square

Motor

IllHItJllg

3

or

6 Point

SUnl Rpi im

F I M I

Sub

(if rnfuirMt)

Suunrp

Mh>r

Modified

Nt 8il

FIGURE 5.30 Square motor and associated BH As .

Courtesy: NQL-Stabeco.)

ave been widely usedby theRu ssian drilling industry to avoid drill-

string rotation.


50/79

3 C H A P T E R 5

IGUR

5 31

Turbodrill performa

characteristic curves.

Figure 5.31 shows the perfonnance characteristic curves of a turbodri

Unlike the PD M , the turbine s torque is inversely proportional to speed, wi

its maximum value at zero speed (stall point) decreasing to zero at runawa

speed (no WO B). Power is zero at stall point, rises to a max imum at desig

operating speed (half the runaway speed), and decreases back to zero at ru

away speed. The motor speed is independent of mud density and depen

only on the flowrate. The pressure drop remains almost constant at diftere

speeds.

Turbine perating arts

The main parts of a turbine motor, shown in Figure 5.32, are

1.

Bypass or dum p valve

2. Rotor and stator housing

3.

Bearing and rotating assembly


51/79

Downhole Motors

3 2 3

or Dump

Vaive

ypass va lve consists of radial po rts. The ports are closed by pressure

uid circulation is established resulting in actuation of a sliding

. The ports get opened when the pressure is released as a spring forces

ion of the motor while tripping. Also the valve serves to drain the

similar to one shown in Figure 5.9 wh ich shows the valve in open and

Stator Housing

which forces the rotor to tum in the clockwise direction. The continu-

ws a turbine stator and rotor.

earing and Rotating

ssembly

is part is considered to be the most critical part of the turbine m otor and

dvantages of the Turbine

High rotary torque is developed at the bit where actually required. So

no flexible joint is required as in the case of PD M .

Turbine produces high rotational speed with low weight on bit.

Due to the high rotational speed high penetration rates can be achieved

with PDC diamond bits.

Allows fluid circulation regardless of motor hp or torque produced o r


52/79

3 4 C H A P T E R

S

FIGURE

5.33

T u r b i n e s t a t o r

a n d

r o t o r . {Courtesy: Smith Internationa

Inc.)

FIGURE 5.34

T u r b i n e b e a r i n i

a s sem b ly . Courtesy: Smith

International, Inc.)

o c c u r s i n t h e t u r b i n e itself B e c a u s e t h e c l e a r a n c e b e t w e e n t h e s t a t

a n d r o t o r i s v e r y s m a l l , s o l i d p a r t i c l e s i n t h e m u d c l o g t h e t u r b i n e

c a u s i n g s e i z u r e .

Reaming:

T h e u s e o f t u r b i n e s m a ke s ho l e re a m i n g w he n e v e r r e qu i r e

d i ffi cu lt d u e to hi gh r o t a t i o n o f t h e b i t r u n a w a y s p e e d ). T h e s t r in

g e t s s t a lle d a n d s t u ck in u n d e r ga g e d h o l e s .

Bit selection:

H i g h r o t a t i o n a l s p e e d o f t h e t u r b i n e r e s t r i c t s t h e t y p e

b i t s t o b e u s e d . T r i co n e r o lle r b it b e a r i n g life i s d r a s t i ca l ly r e d u ce d b

h i g h r o t a t i ona l s p e e d .


53/79

Downhole Motors 3 25

Efficiency: Efficiency decreases drastically (compared to PDM) when

operating at off-design conditions.

Performance: Difficult to assess the dow nho le perform ance wh ile

drilling.

Hydraulic Turbine

In a hydraulic turbine the working fluid is assumed to be incompressible and

he main performance parameters are torque and rotary speed. The torque

deve loped by a turbodrill can be calculated from the following mo dified

Ruler equation:'^

T = 27rQp^r'n,NTi (5.68)

where

r\

Q = flowrate, gpm

Pm = mud weight, ppg

r = square of mean blade radius, in.

n^

number of turbine stages

N = rotation speed of turbine, rpm

r|i, = hydraulic efficiency

Stall Torque and Runaway Speed

Stall torque is the maximum torque needed to stop the turbine shaft from

rotating and occurs at zero rpm.

Runaway speed or no load speed is the rotational speed of the turbine

when there is no torque or resistance to the fluid flow through the turbine. It

occurs at maximum speed.

Stall torque and runaway speed are related by

T =T -T ~

where 0) = angular velocity


54/79

3 6 C H A P T E R

5

The mechanical horsepower developed by the turbine can be calculate

from the product of torque and angular velocity:

MHP = N (5.70

5501,60 J

which can be further written as:

550

or, in terms of torque:

550 l,60J

Stall torque of a turbine can be given by the following equation:

(5.71

T, =8 6595 10^= ta n ,n ,p ,Q T i ,

27th

where ^ = exit angle,

ri| = mechanical efficiency

h = height of the vane, in.

n^ = number of stages

l io = Hm X Tlvol

Tlo = overall efficiency

T) = volumetric efflciency

Runaway speed of the turbine can be calculated from

N, ^18 .3 8 ^r; (5.73

7chr


55/79


Torque,

= ^ an d T; = T f

X

Cf

T, [Q j

Horsepower,

= ^ l and HP^^HP, xc,

HPa

I Q J

where Cf = mud correction factor defined as the ratio of the new mud w eight

to the reference mud weight

These relationships are helpful to estimate the required performance param-

eters of the turbine for other than the reference flowrate and mud density.

E X A M P L E 5 7

Calculate the flowrate required and the output of a turbine to produce a

torque of 2,000 ft-lbf operating at 500 rpm for a turbine pressure drop of 800

p s i

Assum e an efficiency of 70% .

S O L U T O N

QAp

1,714

MHP = ^ 1 x 5 0 0 = 190 hp

550 l,60j ^

. . MHP

using the equation r\ =

QAp

1,714

^ MHP 190x 1 ,71 4 ^^

Q - -

~

= 509 gpm

* 0 8x800


56/79

3 8 CHAPTER

Number of stages = 200

Flowrate = 300 gpm

Mud weight = 9 ppg and 12 ppg

Performance characteristics of the motor with reference flowrate of 300 gp

and 9 ppg mud are given in Figure 5.35.

SOLUT ON

For mud

we ight

9 ppg:

P re ssu re d rop : F rom the g r a ph the p r e s su re d rop for 300 gpm

755psi.

M a x i m u m h o r s e p o w e r : F r o m

the

g r a p h

it can be

s e en t h a t m a x i m u

horsepower

is 90.

B e c a use theto rque atop t im u m spe e dis onehalfof the s ta ll to rqu e th

stall torqueis - 2 x torqueat 300 gpm.

From

the

chart

it can be

seen that

the

torque

at 300 gpm is 820

ft-lbf.

He nce s tal l torque= 1 640 ft-lbf

For

mud weight

12 ppg:

P r e s s u r e d r o p for new mud d e n s i t y can be c a l c u la t e d u s ing th

re la t ionship.

35oq


57/79

ownhole Motors

3 2 9

So pressure drop for the case of 12 ppg mud is

Ap = 7 5 5 x = 1 006 psi

F ^ f

Maximum horsepower is

HP = 9 0 x = 1 2 0 hp

9

Stall torque is

T = 1 640 x = 2 187 ft-lb

n e u m a t ic T u r b i n e

Turbines consist of stages and each stage is composed of a stator and a rotor.

The stator is an array of chokes used to direct jets of high-speed air into the

rotor. The je ts of air are diverted by the rotor producing a turning force or

torqu e. The max imum torqu e is produ ced w hen the rotor is still and the

torque decreases linearly w ith rotor speed because the velocity of the air jet s

relative to the rotor also decreases with rotor speed. When the rotor tip is

moving at the air speed there is no force and the turbine is said to be at the

no-load speed.

The pneumatic turbine-powered drilling engine is an impulse-type tur-

bine.In ideal impulse-type turbines there is no expansion in the flow through

the stator. The entire p ressure drop occurs in the rotor which acts as a sta-

tionary nozzle. The pressure remains con stant through the blade w hile the

kinetic energy decreases. It is desirable to have subsonic flow at the nozzle

outlet so that pressure surges can be felt at the surface. H ow ever if the

required power implies supersonic velocities then a converging-diverging


58/79

3 3 C H A P T E R

S

motor, and should therefore be determined for each configuration (air an

motor prope rties). ,

The following are the main equations used to model the performance o

the motor:

VN = 109.45V (T| + 460X1 - PR^'^^ ) (5.7

where PR = pressure ratio

(5.7

(5.7

sonic ^ Pthioal

d

5 5

HP

Pos i tive D isp lacem ent M oto rs PD M ) ve rsus Turbodr ills

The critical parameter in the performance of a PDM is the pressure dro

across the motor, while for a turb ine it is the speed. ^^' Th is is due to the fu

damental principle of operation of each motor. PD M s operate on the Moinea

principle, in which torque is produced from the pressure differential. Th

turbodrill works according to a hydrodynamic principle, in which power

produced from the energy transfer between the moving fluid and the van

inside the motor. The flowrate in a PDM must be zero if the bit does n

move . Contrarily, in the turbine tbe fluid can always be circulated.

The main disadvantage that drillers find in turbodrills (compared to PD M

is the bit problem s caused by the high rotational speed at which they operat


59/79

ownhole Motors 331

The operational advantage of a PDM over a turbodrill is that the PD M s

efficiency is less affected when operating at off-design conditions. As seen

in Figures 5.14 and 5 .30, the efficiency curve of a PDM is flatter than that of

the turbine.

Regarding positive displacement m otors, while a lot of varieties are avail-

able in the market, there are still inherent problems associated with tbe per-

formance of the tool with coiled tubing drilling. While some simulation and

performance characteristics studies have been done for turbines, there is no

evidence of simulation studies done or mathematical models available to

address the behavior and performance of the positive displacement motor.

The force of tbe air jets can be quite high, as high velocities are easy to

achieve . At a pressure ratio across tbe stator of about two to one, the air veloc-

ity w ill be sonic (1,100 ft/s). Even higher veloc ities can be reached in super-

sonic nozzles, but such designs are tricky, due to the shocks that may occur

as the pressure and flowrate vary.

The added advan tage of the turbine is that it is open to flow it will pass

air at tbe same rate regardless of rotor speed. This advantage is balanced by

the tendency to run at high speeds. High air speeds are required to get high

torques at small sizes and low flowrates, and as a result, such units naturally

tend to run at high speeds.

Fluid Volume Requirements

Air drilling engines are generally designed to run based on the cleaning vol-

ume,

that is, the fluid volume that is required to remove the drilled cuttings

from the ho le. All techniques* *' for selecting volum e requirem ents in air

and gas drilling require both the specification of a cleaning criterion and a

method for evaluating whether that criterion is met.

Hole-cleaning criteria fall into three categories: gas energy, cuttings ter-

minal velocity, and minimum bottomhole pressure. There is no universally

accepted approach to designing volume requirements either in vertical or

deviated air drilling. What works well in one area may prove a poor choice

in another.


60/79

33 CHAPTER S

the required bit torque at operating conditions and from that estimate the ma

imum required turbine torque. Given the required turbine torque and the tu

bine rotor diameter, it is then possible to estimate the number of turbin

rotor/stator stages that will be required to extract that torque from the airflow

Three methods for estimating the bit torque required for drilling are giv

below. A simple integration indicates that for a flat-faced drag bit the torqu

should be

^ l , 0 0 0 | i x W O B x D b

T =

^ z

^ (5.7

Smith Tool*^* has published a horsepow er model for roller cone bits th

can be converted to a torque m odel:

T = (5,250)F,fWOB' - DJ-^ (5.8

and

Warren* ' * *

has developed the following relationship;

C1 HC2

(5.8

where WOB = weight on bit, 1,000 Ib

Db = bit diam eter, in.

|X = bit to formation friction factor

F r = formation constant (1.4 x 10 ^ for the softest formation an

highest torque)

R = rate of penetration (ft/hr)

f = tooth wear function (


61/79

ownhole Motors

3 3 3

The lock-rotor torque can be calculated from:

^ 2rhvrcos(a)

g

= the weight flowrate of air, lb/s

V = the air velocity, ft/s

r = the rotor radius, ft, in all cases 4 in. less than the tool outer

diameter

a = the attack angle of the air je t (30 in this study)

g = the accelera tion due to gravity, 32.2 ft/s^

e a r in g T h r u s t

basic components of the thrust on the bearing of the turbine are the sam e

he case of the PDM as described below.

The net axial thrust on the bearings due to weight on bit and hydraulic

Hydraulic thrust created by the pressure drop acting on the cross-

sectional area (hydraulic thrustF,,^jJ.

Hydraulic thrust created due to the pressure drop across the bit

(hydraulic thrustFi, , ^,).

Self-weight of the shaft (weight thrustF^^,,).

Weight on bit.

The hydraulic thrust'^*' can be approximately obtained from Eqs. 5.48

r ^ | ? f ) 5 . 8 4 )

^ = rotor diameter

Dj = stator inside diameter

Di = rotor body (hub) diameter

Apn, = pressure drop across the motor


62/79

4 CHAPTER 5

where p = mud density

p,

= rotor density

w^ = weight of the rotor

D3 = hub extended portion diameter (usuallyD3> D2)

The net axial thrust on the bearing is

(5.

The pressure drop across the bit is

E L E C T R O D R I U M O T O R E D M )

The history of the electrodrill dates back to 1891 .**** Russians developed

field-tested three noteworthy electrodrills. The first too called the Arutun

electrodrill carried an electric motor, which was used to drive the bit throu

a gear reduction system. The tool was lowered into the hole with the w

line,

which supplied the povyer. The second tool resembled the above pi

less tool, but had the capability to rotate the upper part of the tool. The th

version was a modified tool, which was attached to the bottom of the p

and run with cables and cable connectors. All these tools had the disadva

tage of high rotational speed com pared to rotary drilling.

The electrodrill downhole motor built and tested by General Electric

1976 is based on standard submersible pum p mo tors. They use a retrieva

power cable and a telemetry system, which makes downhole measureme

of various drilling and safety parameters, and transmits them to the surfa


63/79

ownhole Motors 335

A feasibility study on Electric Drilling M otor for Coiled Tu bing was

e performance param eters of the electric motor are frequency, horsepow er,

According to the conceptual design performed by CTE S, motor systems

K in. and larger outside diameters are technically feasible. These motors

ld run at speeds of 1,200 to 3,600 rpm by varying the frequency from

o 60 Hz. This may c reate a need for a gearbox, similar to the pneum atic

Horsepower

F = Frequency>^.K /

F -->'-^''' 7/

/ /

1 / /

/ /

/ /

\ \ ^

^ \

\ \

\ \

\ \

\ \

\ \

\

\\

\\


64/79

336 CHAPTER 5

turbine. The maximum power output is close to 80 hp with output torque

high as 160

ft-lbf.

Slimmer motors may be possible if the horsepower requ

ments are lowered. A 10-hp motor could be as small as 1.688 in. in diame

and 11.6 ft long.

Recently, XL Techno logy Limited of London developed a drilling s

tem cou pling electric dow nh ole motor'^' with coiled tub ing. The syst

used a submersible electric motor along with near-bit downhole sensors a

drilled 600 m of cem ent. The field tests indicated that signiflcant poten

advantages are possible using EDM. The specifications call for a3%-in.

assembly to enable the use of

3

/:-in. bit. The project is at the initial st

of development.

Listed in the Table 5.1 are the specifications of the electric motors u

in the former Soviet '* '

M IS C E L LA N E O U S D O W N H O LE M O T O R S M O M )

Other types of positive displacement motors such as vane, piston, and g

pumps have been proposed for downhole drilling motors. Researchers ha

also proposed o ther new concepts of dow nho le motors''''^^' to ove rcom e

problems posed by the conventional dow nhole m otors. A dow nhole mo

consisting of

a

double shaft assembled in line was prototyped. The shafts

coupled by a flexible coupling. They can be connected with either elect

motor or fluid turbine. This provides a flexibility of operation in directio

drilling. There is no evidence of field testing of tbis type of motor.

A

patent

was obtained for a fluid pressure, peristaltic dow nhole motor. It cons ists o

shaft, housing, and a few rollers so as to form deformable working cha

bers. The drilling fluid entering the cham bers on the trailing side of the roll

causes the rotor to rotate. In this case too there is no evidence of field test

reports. Figure 5.37 shows a cross section of one such motor.

A combustion type of downhole drillingmotor'* was proposed that c

veys the fuel and oxygen to the bottom through umbilical chor

Combustion, occurring in different chambers of the apparatus, causes


65/79

ownhole Motors

337

o

o

h

e

c

a

{ J

M

O

v:

C

c

c

o

^

S

.2

s cS

e 3

E

13 n

c

3

C

2

1 ^

LH .-^

^

o "t.

_?

p a.

R

e

^

C

J ^

b .

Il

a s

^5

^ -

m

n

^

o

( N

n

o

o

o

( N

O

o

( N

S

O

( N

O

o

i n

f ^

m

O

OO

i n

r-

m

ON

r o

m

( N

0 0

i n

( N

m

( N

u-,

oo

~~

( N

- H

m

0 0

i n

r-

O

r o

( N

~ ~

u-i

^

o

O

O

o

m

>n

OO

r

( N

n

O

ON

( N

n

i n

0 0

o

r o

( N

Q

O

r- i

oo

o

ro

O

n

O

r o

( N

^


66/79

338 CHAPTER

Rol len

Deformable membrane

FIGURE 5.37

Vertical cross section of the peristaltic motor.

rotor. Although it had several advantages, such as lightweight, short leng

and long operating life, it could not be tested successfully in the fleld.

Equations for flowrate, Q, torque, T, and hydraulic horsepower of t

motor are given by'^'' ^

Q

=

k ,Nr ,w ,L

T = kjjr w^LAp

HHP

=

k3Nr,w,Lp, (5.

where r

=

rad iuso f exposed roller section

w

=

width of the exposed roller section

L

=

tool length

A new concept of downhole motor called McDrill*^''^^^ was lab and fie

tested. It has a stainless steel rotor and stator and is vertical, thereby avo


67/79


LE

5 2 Com parison of Operating and Profile Variables for M DM s

51)

Length

Weight

Rotation

Hydraulic Efficiency

Temperature Resistance

Standpipe Pressure

Maintenance

Additional Rowrate

Handling Capacity

FDM

Medium

Medium

Eccentric

High

No

Medium

Shop

Yes

IXirbine

Long

Heavy

Concentric

Low

Yes

High

Shop

Yes

Roller Vane

Short

Light

Concentric

High

Yes

Low

Rig Site

No

McDrill

Short

Light

Concentric

High

Yes

Medium

Rig Site

No

Comparison of operating and profile variables for different MDMs for

eter are given in Table 5.2.

S U P P L E M E N T R Y PR O B L E M S

1 The following data pertain to a motor of 3:4 configuration:

Diameter of the motor = 8 in.

Rotor diameter = 2.7 in.

Pressure drop across the motor = 500 psi

Assum e a total efficiency of 80 and a volumetric efficiency of 90

and calculate

a. Tbe torque developed by the motor.

b.

Rotational speed for a flowrate of 500 gpm.

c. Power output of the motor.


68/79

34 CHAPTER 5

5.3 Using the data in Problem

5 2

obtain the following:

a. Plot the torque versus pressure drop from 0 to 800 psi with an inc

ment of 100 psi.

b. Plot rotational speed of motor versus flowrate from 0 to 600 g

with an increment of 50 gpm .

c. Repeat a and b for var ious efficiencies from 70 to 100% w ith

increment of 5% .

5.4 W hat is the torque for a 1:2 configuration motor with a rotor diame

of

3

in., eccentricity

in., and a rotor pitch 12 in. opera ting at 450 p

5.5 Com pare the theoretical speed, torque, and horsepow er of a ;2 l

and a 3:4 lobe motor.

5.6 If a 12>i-in. bit requires a torque of 3,500 ft-lbf to drill a sandstone f

mation, what is the required pressure drop across a motor with

dimensions given below?

Diameter = 8 in.

Configuration = 3:4

Shaft pitch = 40 in.

Eccentricity = 1.5 in.

5.7 Pitch and diam eter of the housing are expres sed in terms of the he

angle. Derive the equation and calculate the torque of a m otor usi

the following data:

Diameter of the housing = 6 in.

Configuration = 4:8

Pressure drop across the m otor = 400 psi

Helix angle

AT

Efficiency = 80%

5.8 Select a suitable PDM for the following requirements:

Diam eter of the hole to be drilled = 12 ^ in.

Bit torque = 4,225 ft-lbf

Power output of the motor = 50 to 75 hp


69/79

ownhole Motors

341

delivered by multilobe downhole motors with the constraint of fluid

velocity inside the multilobe motors given by

where D,,, P^, r), i, AP, N, and n deno te the d iam eter, p itch, efficiency,

lobe ratio, pressure drop , rpm, and num ber of shaft lobes, respectively.

Com pute the rotor nozzle size required to drill a 12 -in. hole with a bit

torque of

5 250

ft-lbf and rotating at 120 rpm. The mud weight required

is 10.2 ppg. Minimum flowrate required for hole-cleaning is 850 gpm.

Motor data:

Motor configuration = 5:6

Diam eter of the motor = 8 in.

Length of the motor = 18 ft

Num ber of stages = 6

Assume an efficiency of 80 .

11 The performance curve for a 9X-in. hole motor is shown in Figure 5.38 .

The p erformance curve is based on water at 70F. The m otor details

are as follows: 6:7 lobe, 5.0 stage, length of the power section 20.61 ft,

maximum bit speed range 75 -15 0 rpm, flow range 600-1 ,200 gpm. The

m otor is used to drill a 20-in. hole with the minim um hole-clean ing


70/79


71/79

ownhole Motors

343

Pressure d rop across

the

motor

=

300

psi

Estimate

the

torque

and

speed when

the

flowrate

=

450

gpm

Assume

an

efllciency

of

80 .

A

turbine-generator-bit com bination connected

in

tandem

is

used

as

downhole drive mechanism

to

power

the bit.

Dev elop equations

for

torque, pressure drop ,

and

overall efficiency

of

the system.

the

volumetric efficiency, mechanical efficiency,

and

overall

efficiency

of

a

4

in., 4:5 configuration PDM whose performance curve

is shown

in

Figure

5.39.

Pitch

of the

housing

=

2

in.

Ecce ntricity

=

0.333in.Pressure drop acrossthemotor= 400 psi andflowrate= 200

gpm.Fordrilling certain sectionsofa6-in.hole,the bitrequires200

rpm

and 1,2 X)

ft-lbf torque.

To

maintain proper hole-cleaning,

a

mini-

mum requirement

of

200 gpm

is

desired. Determine w hether the above

motor can

be

used

to

drill.

If

not provide

an

alternate selection.

3


72/79

CHAPTER

N O M E N C L A T U R E

a, b = empirical indices

a, = WOB exponent

S =

speed exponent

A

=

cross-sectional area

A

=

wave velocity

A

=


of

the cavity

Ar

=

area

of

the rotor nozz le

Ap

=

area

of

the piston

Af

=


of

the shaft

Ap

=

effective pump-off area

b

= bit

B F

=

buoyancy factor

C

=

constant

C j

=

discharge coefficient

C =

mud correction factor

Db

=

diameter

of

th e

b it

=

d iameterof the housing

=

rotor diameter

=

diameter

of

the shaft

e

=

eccentricity

of

the motor

E

=

Y oung s modulus

E

=

energy input

E^

=

specific energy

f

=

final condition

F f

=

formation constant

Fhyd

=

hydraulic thrust

F ^ =

axial force

Fy

=

tangential force

F j = side force

g

=

gravitational constant

h

=

he igh t

of

the v ane


73/79

Downhole Motors 34 5

k| = housing/shaft wear coefficient

kj = material property coefficient

kl = housing, shaft, pitch wear coefficient

k^ = coefficient, 9.48

k, = coefficient,

1.8x10

K = constant

Kh = formation hardness, teeth, bearing, mud coefficient

K, = formation drillability factor, ft/hr

K| = winding ratio coefficient

K, = winding ratio coefficient

Kr, = pressure drop coefficient

K, = constant 5,252)

K^ = constant, 0.01

K, = constant, 0.028

I = stroke length

L = tool length

m = maximum

rii = mass flowrate. Ibm/sec

MHP = mechanical horsepower

n^ = num ber of blows per minute

n, = num ber of stages

N = rotary speed, rpm

Nr = runaway speed in rpm

NT = net thrust

ph = pitch of the housing

P,

= pitch of the shaft

P^

= stall pressure

PR = pressure ratio

Q = flowrate

Q = inlet losses that can be neglected

Qn, = bypass flowrate through the rotor nozzle, gpm

Qr = reference flowrate

Q, = the leakage between the running clearance between the seals


74/79

46 CHAPTER 5

S = turbulence coefficient

SHN = shore hardness

t = time

t| = thickness of the elastomer of the housing

tj = metal thickness of the housing casing

T = torque

Tas = actual torque measured at the stall condition

Tf = torque on the cutting face of the bit, ft-lbf

Tj = torque due to side force, ft-lbf

w = width of the exposed roller section

w^ = massof the U-joints in fluid, lb

w, = mass of the rotor in air, lb

Wp = pump-off force, lb

W OB = weight on bit, klb

Wfs = width of the exposed ro ller section

a = flow ratio

= index of flow time

e = exit ang le,

p^ ~ mud weight, lbm/gal

Tl,r|o = overall efficiency

Tlh = hydraulic efficiency

T|n, = mechanical efficiency

Tls = operating stall efficiency

Tl ,

= volumetric efficiency

|l = bit to formation friction factor

p = density, Ibm/ft^

Oj = incident stress

y^

= maximum stress

Or = reflected stress

Aph = pressure drop across the bit, psi

Apm = pressure drop across motor, psi

Apmax - maximum pressu re dro p across motor, psi


75/79

Downhole Motors 347

2. Kayes, A.G., Imp rovem ents in and Relating to Impact-Action Self

Propelled Mechanism for Driving Holes in the Earth, U.K . Patent No .

2147035 A, May 1, 1985.

3. Bourgoyn e, Jr., A.T., M lhe im, K.K., Chenvert, M.E., Young Jr., F.S.,

Applied Drilling Engineering.SPE, Richardson, TX, 1986.

4.

W illis, C.A., Axial Return Ham m er, U .S. Patent No. 4,509 ,606,

April 9, 1985.

5.

Cu nningham , R.A, An Em pirical Ap proach for Relating Drilling

Parameters,

7P7:

July 1978.

6. Cline , Jr., W.H., Progress Report on a Fluid Actuated Rotary Percussion

Engine, ASM E PE, September 1953.

7. Dow ns, H.F., Air Ham mer Drilling Permian Ba sin, The Petroleum

Engineer June 1960.

8. Guarian, P.L., and Arnold, H.E ., Rotary Percussion Drilling , Oil Gas

Journal

November 10, 1949.

9. John T.F., 'investigation of Percussion Drills for Geothermal

Applications,

JPT

85.

Liljestrand, W., Percussion Drilling Tool Increases Bit Fo otage, The

PetroleumEngineer July 1960.

Price V., and W ilder L.B ., Fluid Powered Percussion Drilling Too l,

Transact, of Rotary Drilling Conference, 1969.

Brow n, R., The Bassinger Rotary Percussion Drill , The Petroleum

Engineer.

December 1950.

Bassinger, R., Rotary Percussion Drilling: Review and a Prediction,

Oil and Gas Journal

October 12, 1950.

Topanelian Jr. E., Effects of Lo w-F requen cy Percussion in Drilling

Hard Rock, AIME Petroleum Transaction, vol. 2 13 ,19 58 .

W hitely, M .C., and England, W.P., Air Drilling Op erations Improved

by Percussion Bit/Ham merT ool Tandem, SPE/IAD C, No . 13429, 1985.

W anamaker, J.A., Rotary Percussion Drilling in West Tex as, World

Oil September 1951.

Goikhman,

Y.

A .. Ulitsa etal., PercussionR otary Drilling Too l, U .S.

Patent No. 5,004,056, April 2, 1991.


76/79

4 8 CHAPTER 5

2 1 . Lund berg, B. , Energy Transfer in Percussive Rock Destruction I

III, J. Rock Mech.

Min. Sei, Pergamon Press, 1973.

2 2 .

Simon R.. Transfer of Stress

ave

Energy in the Drill Steel of

a

Percus

Drill to the Rock, J

Rock

Mech. Min. Sei, Pergamon Press, 1 964.

2 3. Sam uel, R., Percu ssion Drilling Ts It a Lost Technique? A Rev ie

SPE 35240, prepared for presentation at the Permian Basin Oil & G

Recovery Conference, Midland, TX, March 27-29, 1996.

24. M oineau. Ren e' J.L., Doctoral Thesis, Faculty of Scien ces, Univer

of Paris, 1930.

2 5.

Samuel R., M iska, S., and Volk, L., Analytical Study of the Performa

of Positive Displacement Motor (PDM): Modeling for Incompressi

Fluid, SPE 3902 6, presented at the 5th Latin Am erican C aribbe

Petroleum Conference & Exhibition, Rio de Janeiro, August

September3, 1997.

2 6.

Tiraspoisky, W.,Hydraulic Dow nhole Drilling Motors.Gulf Publishi

Houston, TX, 1985.

27.

Sam uel, R., and M iska, S., Op timization of Drilling Parameters w

the Performance of Multilobe Positive Displacement Motor (PDM

IADC/SPE 47791, 1998 IADC/SPE Asia Pacific Drilling Conferen

Jakarta, Indonesia, September 7-9, 1998.

2 8.

Sam uel, R,, and M cCo lpin, G., Optimizafion of Drilling Param et

with the Performance of Multilobe Positive Displacement Mo

(PDM), IADC/SPE 47791 , 1998 IADC/SPE Asia Pacific Drill

Conference, Jakarta. Indonesia, September 7-9, 1998.

2 9.

Azar, J.J., and Sam uel, G.R.,

D rilling Engineering

Pennwell Pub lishe

Tulsa, OK, 2 007.

30. Report, Smith Tool, Technical Services, Irvine, CA .

31 .

San chez , A., Ro bello, S., and Joh nso n, P., An Ap proach for

Selection and Design of Slim Downhole Motors for Coiled Tubi

D rilling, SPE 37054 , International Conference on Horizontal W

Technology, Calgary, Alberta, Canada, November 1 8-2 0, 1 996.

32 .

Schlumberger Pow erPak,

Steerable Motor Handbook

Sugarland, T

1993.


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Downhole Motors

3 4 9

6.

M iska, S., and Bookw alter, R., "Tu rbine Perform ance at Other than

Design Conditions." Rift Engineering & Drilling, 1985.

7.

John son, P.W., "Sim ulation of the Therm al Tran sients E ncou ntered

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8.

Johnson. P.W., "Testing a Downhole Pneumatic Turbine-Powered

Drilling Motor," New Mexico Institute of Mining and Technology,

Socorro, 1990.

9. D eLu cia, F., and Herbert, R., "PD M vs. Tu rbod rill: A Drilling Co m-

parison ." SPE 13026, 1984.

0.

Angel, R.R., "Volume Requirements for Air and Gas Drilling,"

Petroleum Transactions

.1951) 325-3 30; AIME, 210.

1.

Ikoku, Chi U., Azar, J.J., and W illiams, C.R., "P ractical Ap proach to

Air and G as Volume Requirements for Air and Gas D rilling," SPE 944 5,

Dallas. September 21-24, 1980.

2. Gray, K.E., "The Cutting Carrying Capacity of Air at Pressures Above

Atmospheric,"

Petroleum Transactions

i\95S)

180-185; AIME, 213.

3. Weymouth,

Weymot^th

Engineering DataBook, Gas Processors Sup-

pliers Association, 1972.

4.

Machado, C.J., and

Dcoku,

Chi U., "Experimental Determination of Solids

Fraction and Minimum Volumetric Requirements nAir and Gas Drilling,"

Journal of Petroleum Techno logy November 1982, 264 5-265 5.

45.

W arren. T.M.. "Factors Affecting T orque for a Ro l er-Cone Bit,"

JPT

September 1984.

46.

Zade. S., Mirzadzhanzade, S.A.. Oganov. A.H., Gulatarov, H.G.,

"Drilling of Horizontal Wells with an Electric Downhole Motor,"

Proceedings of the 14th World Petroleum Conference, 1994.

47.

Coiled Tubing Engineering Services, "Electric Drilling Motor for Coiled

Tubing, Phase IFeasibility Study." 1995.

48. Manual for Oiland as IndustryW orkers

Mir Publishers. Moscow, 1989.

49.

Allan. G.K.. "Im provem ents in and Relating to Impact-Action

Self

Propelled Mechanism for Driving Holes in the Earth," U.K. Patent No.

2147035 A, May 1, 1985.


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3 5 C H A P T E R

5

53 . M undell, R.H ., Fluid Pressure Do wn hole Drilling M otor, Gr

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54. Harris, G.L., Dow nhole Motor System, U .S. Patent No 55 183 79, M

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AdHoc Committee Report on Technology of Drilling for Ener

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Fletcher, G.L., Com bustion Operated Drilling Ap paratus, U .S. Pate

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488313 3, November 1989.


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05 Downhole Motors

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