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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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ownhole Motors 2 7 7
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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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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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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ownhole Motors 2 8 5
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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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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Downhole Motors 2 9 7
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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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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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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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
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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,N^e (5.51)
The axial component can be calculated from tbe following equation con-
(5.52)
Ph
F ,
= 8.9xlO-^A,p,l,n,N^e- (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
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Downhole Motors 3 1 3
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
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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.
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ownhole Motors 3 1 5
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.
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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
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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
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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
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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
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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
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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.
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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
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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
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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 .
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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
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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
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Downhole Motors 3 2 7
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
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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
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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
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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
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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.
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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 (
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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
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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
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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 / /
/ /
/ /
\ \ ^
^ \
\ \
\ \
\ \
\ \
\ \
\
\\
\\
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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
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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
^
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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
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ownhole Motors 3 3 9
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.
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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
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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
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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
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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
=
cross-sectional area
of
the cavity
Ar
=
area
of
the rotor nozz le
Ap
=
area
of
the piston
Af
=
cross-sectional area
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
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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
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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
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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.
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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.,
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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
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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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Johnson. P.W., "Testing a Downhole Pneumatic Turbine-Powered
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0.
Angel, R.R., "Volume Requirements for Air and Gas Drilling,"
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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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