Drilling Engineering
Drilling Engineering – PE 311
Drill Bit Optimization
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Introduction
Significant increases in ROP can be achieved through the proper choice of bit
nozzle.
Most commonly used hydraulic design parameters are:
Bit nozzle velocity
Bit hydraulic horsepower
Jet impact force
Current field practice involves the selection of the bit nozzle sizes that will cause
one of these parameters to be a Maximum
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum and Minimum Values - Review
y = f(x)
: The tangent to the curve
is horizontal.
Solve this equation we can get the critical
values (either max or min): x = a or x = b.
Second derivative:
The function has a minimum value at x = b if
f/(b) = 0 and f//(b) is a positive number
The function has a maximum value at x = a if
f/(a) = 0 and f//(a) is a negative number
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum Nozzle Velocity
Flow velocity through bit nozzle
vn 
pbit
8.074104 
vn  pb
So velocity is directly proportional to the square root of the pressure drop across the bit
The nozzle velocity is a maximum when the pressure drop available at the bit is a maximum. This
can be achieved when the pump pressure is a maximum and the frictional pressure loss in the
drillstring and annulus is a minimum; the frictional pressure loss is a minimum when the flow rate
is a minimum
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum Nozzle Velocity
Nozzle velocity may be maximized consistent with the following two constraints:
The annular fluid velocity needs to be high enough to lift the drill cuttings out of the hole. This
requirement sets the minimum fluid circulation rate.
The surface pump pressure must stay within the maximum allowable pressure rating of the pump
and the surface equipment.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum Bit Hydraulic Horsepower
Effectiveness of jet bits could be improved by increasing the hydraulic power of the pump.
Penetration rate would increase with hydraulic horsepower until the cuttings were removed as fast
as they were generated. After this level, there should be no further increase in the penetration
rate. Note that the hydraulic horsepower developed by the pump is different from the hydraulic
horsepower at the bottom of the hole. This is due to the friction losses in the drillstring and in the
annulus. Therefore, the bit horsepower was not necessarily maximized by operating the pump at
the maximum possible horsepower.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum Bit Hydraulic Horsepower
The Pump Pressure is expended by:
1.
Frictional pressure losses in the surface equipment, ps
2.
Frictional pressure losses in the drillpipe, pdp, and drill collars, pdc
3.
Pressure losses caused by accelerating the drilling fluid through the nozzle
4.
Frictional pressure losses in the drill collar annulus, pdca, and drillpipe annulus, pdpa
Ppump  ps  pdp  pdc  pdca  pdpa  pbit
Let:
Pf  ps  pdp  pdc  pdca  pdpa
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum Bit Hydraulic Horsepower
Hence, the pressure loss at the pump will be sum of pressure loss at the bit and total frictional
pressure loss to and from the bit:
Ppump  pbit  p f
It is well know that the frictional pressure loss is a function of flow rate and can be expressed as
1.75
dp  0.75 v  0.25  0.75 q1.75  0.25


0.25
dL
1800d
8624d 4.75
p f  q1.75
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum Bit Hydraulic Horsepower
Hence, pd can be expressed as
p f  cqm
m is a constant has a value near 1.75, c is a constant that depends on the mud properties and
wellbore geometry
Pressure drop across the bit
pbit  p pump  cqm
The bit Hydraulic horsepower
m 1
pbit q p pump q  cq
PHb 

1714
1714
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum Bit Hydraulic Horsepower
Bit horsepower is a function of flow rate
m 1
pbit q p pump q  cq
PHb 

1714
1714
The bit horsepower reaches maximum when:
 p q 
d  bit 
m
dPHb
1714  p pump  (m  1)cq



0
dq
dq
1714
Or
p pump  (m 1)cqm  (m 1)p f
p f 
p pump
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m 1
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum Bit Hydraulic Horsepower
Bit hydraulic horsepower is a maximum when
p f 
p pump
m 1
Since
The hydraulic horsepower will be maximum at
Or:
p f
p pump
Prepared by: Tan Nguyen

1
m 1
p f 
p pump
m 1
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum Jet Impact Force
Jet impact force is a function of pbit = ppump – pf . Note that pf is the total pressure loss in
pipes and annuli.
F j  0.01823 cd q  pbit  0.01823 c d q  (p pump  p f )
With p f  cq m then
F j  0.01823 cd
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 p pump q 2   cd q m  2
Drilling Engineering
Optimization of Hydraulic Parameters
Maximum Jet Impact Force
The impact force is maximized when,
dFj
dq
0
Solve the above equation yields,
p f 
2
p pump
m2
Since
Prepared by: Tan Nguyen
or
p f
p pump

2
m2
, the jet impact force will be maximum at p f 
2
p pump
m2
Drilling Engineering
Optimization of Hydraulic Parameters
Nozzle Size Selection – Graphical Analysis
In general, the hydraulic horsepower is not optimized at all times . It is usually more convenient to
select a pump liner size that will be suitable for the entire well rather than periodically changing
the liner size as the well depth increases to achieve the theoretical maximum. Thus, in the
shallow part of the well, the flow rate usually is held constant at the maximum rate that can be
achieved with the convenient liner size. Note that at no time should the flow rate be allowed to
drop below the required for proper cuttings removal
For a given pump horsepower rating PHP
q max 
1714PHP E
p max
E is the overall pump efficiency, pmax is the maximum allowable pump pressure set by contractor.
This flow rate will be used until the depth is reached at which pd/pp at the optimum value. Then
the flow rate will be reduced to the minimum value which it can still lift the cuttings.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Nozzle Size Selection – Graphical Analysis
Three intervals
Interval 1: defined by q = qmax .Shallow portion of the well where the pump is operated at
the maximum allowable pressure
Interval 2: defined by constant pf .Intermediate portion of the well where the flow rate is
reduced gradually to maintain pd/pmax at the proper value for maximum bit hydraulic
horsepower or impact force.
Interval 3: defined by q = qmin. Deep portion of the well where the flow rate has been
reduced to the minimum value that efficiently will lift the cuttings to the surface.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
p pump q
Nozzle Size
Graphical
Analysis
PH  Selection –log(
p
)

log(
1714PH )  log(q)
pump
1714
Slope -1
dp  0.75 q1.75  0.25

dL
8624d 4.75
Prepared by: Tan Nguyen
Slope 1.75
Drilling Engineering
Optimization of Hydraulic Parameters
Nozzle Size Selection – Graphical Analysis
1.
Show opt. hydraulic path
2.
Plot pf vs q
3.
From Plot, determine optimum q and pf
4.
Calculate
5.
6.
pbit  p pump  p f
Calculate total nozzle area
Calculate Nozzle Diameter
Prepared by: Tan Nguyen
( At ) opt 
8.311*105  qopt
Cd (pb ) opt
2
2
Drilling Engineering
Optimization of Hydraulic Parameters
Example
Determine the proper pump operating conditions and bit nozzle sizes for maximum jet impact
force for the next bit run. The bit currently in use has three 12/32-in nozzles. The driller has
recorded that when the 9.6lbm/gal mud is pumped at a rate of 485 gal/min, a pump pressure of
2800 psig is observed and when the pump is slowed to a rate of 247 gal/min, a pump pressure of
900 psig is observed. The pump is rated at 1,250 hp and has an efficiency of 0.91. The minimum
flow rate to lift the cuttings is 225 gal/min. The maximum allowable surface pressure is 3000psig.
The mud density will remain unchanged in the next bit run.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Example
Pressure drop through the bit:
8.311*105 q 2 8.311*105 * 9.6 * 4852
pb1 

 1894psig
2
2
2
2
cd At
   12  
2
0.95 * 3 * *   
 4  32  
8.311*105 q 2 8.311*105 * 9.6 * 2472
pb 2 

 491psig
2
2
2 2
cd At
   12  
2
0.95 * 3 * *   
 4  32  
Total frictional pressure loss inside the drillstring and in the annulus at different flow rate:
p f 1  p pump  pbit  28001894 906psig
p f 2  p pump  pbit  900 491 409psig
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Example
m = 1.2, for optimum hydraulics
Interval 1:
Interval 2:
Interval 3:
Prepared by: Tan Nguyen
q max 
1,714 PHp E
Pmax

1,714(1,250)(0.91)
 650gal/min
3,000
 2 
 2 
p f  
P

 max 
(3,000)  1,875psig
m2
 1.2  2 
q min  225gal/min
Drilling Engineering
Optimization of Hydraulic Parameters
Example
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Hydraulic Parameters
Example
From graph, the optimum point:
qopt  650
gal
, p f  1,300 psi  pbit  1,700 psi
min
The proper total nozzle area is:
( At )opt 
8.311*105 qopt
Cd (pbit )opt
2
The nozzle size
d N opt 
Prepared by: Tan Nguyen
4 At 14
 32 in
3
2
8.311*10-5 * 9.6 * (650) 2

 0.47in 2
2
(0.95) * (1,700)
Drilling Engineering
Optimization of Hydraulic Parameters
Example
qopt  650
Prepared by: Tan Nguyen
gal
, p d  1,300 psi
min
Drilling Engineering
Optimization of Economics
Cost-per-foot Calculation
The goal of bit selection is to obtain the lowest cost per foot. The cost per foot can be
calculated by using the equation:
Where C is the overall cost per foot, $/ft; Cb is the cost of the bit, $; Cr is the cost of
operating the rig $/hr; tb is the rotating time with bit on bottom, hours; tt is the round
trip time, including connection time, hours; to is the other time, which is not rotating
time or trip time, hours; and D is the total depth as a given total time, ft.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Cost-per-foot Calculation
Drilling costs tend to increase exponentially with depth. Thus, when curve fitting
drilling cost data, it is often convenient to assume a relationship between cost, C and
depth, D given by
C = aebD
Where a, $, and b, ft-1, depend primarily on the well location.
The cost per day of the drilling operations can be estimated from considerations of
rig rental costs, other equipment rentals, transportation costs, rig supervision costs,
and others. The time required to drill and complete the well is estimated on the basis
of rig-up time, drilling time, trip time, casing placement time, formation evaluation,
borehole survey time, completion time and trouble time.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Cost-per-foot Calculation
Example: A recommended bit program is being prepared for a new well using bit
performance records from nearby wells. Drilling performance records for three bits
are shown for a thick limestone formation at 9000 ft. Determine which bit gives the
lowest drilling cost if the operating cost of the rig is 400 $/hr, the trip time is 7 hours,
and connection time is 1 minute per connection. Assume that each of the bits was
operated at near the minimum cost per foot attainable for that bit.
Bit
Bit cost
$
Rotating time
hours
Connection time
hours
Mean penetration rate
ft/hr
A
800
14.8
0.1
13.8
B
4900
57.7
0.4
12.6
C
4500
95.8
0.5
10.2
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Cost-per-foot Calculation
Bit
Bit cost
$
Rotating time
hours
Connection time
hours
Mean ROP
ft/hr
Total cost
$/ft
A
800
14.8
0.1
13.8
46.80768
B
4900
57.7
0.4
12.6
42.55729
C
4500
95.8
0.5
10.2
46.89099
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Run Cycle Speed
The performance of a bit can also be determined by using run-cycle speed (RCS).
The RCS is defined as:
Where D is the total footage determined by the particular bit.
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Drilling Engineering
Optimization of Economics
Break-even Analysis
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Drilling Engineering
Optimization of Economics
Break-even Analysis
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Drilling Engineering
Optimization of Economics
Break-even Analysis
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Drilling Engineering
Optimization of Economics
Termination of a Bit Run
There is almost always some uncertainty about the best time to terminate a bit run
and begin tripping operations. The use of the tooth-wear equation and the bearingwear equation will provide, at best, a rough estimate of when the bit will be
completely worn. In addition, it is helpful to monitor the rotary-table torque. In the
case of a roller-cone bit, when the bearings become badly worn, one or more of the
cones frequently will lock and cause a sudden increase or large fluctuation in the
rotary torque needed to rotate the bit. With a PDC or fixed-cutter bit, when cutter
elements are heavily worn or broken, or the bit becomes undergauge, the bit will
exhibit much lower than expected ROP and cyclic or elevated torque values.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Termination of a Bit Run
When the ROP decreases rapidly as bit wear progresses, it may be advisable to pull
the bit before it is completely worn. If the lithology of the formation is homogeneous,
the total drilling cost can be reduced by minimizing the cost of each bit run. In this
case, one way to determine when to terminate the bit run is by keeping a current
running calculation of the cost per foot for the run, assuming that the bit would be
pulled at the current depth. Even if significant bit life remains, the bit should be pulled
when the computed cost per foot begins to increase.
However, if the lithology of the formation is not uniform, this procedure will not always
result in the minimum total cost. In this case, an effective criterion for determining
optimum bit life can be better established after offset wells are drilled in the area,
thus defining the lithological variations, and the contribution of the rock properties
can be studied and understood better.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Termination of a Bit Run
Example: Determine the optimum bit life for the bit run described in the table below.
The lithology of the formation is known to be essentially uniform in this area. The bit
cost is $5000. The rig cost is 4000 $/hr; and the trip time is 10 hours.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Termination of a Bit Run
footage, D
ft
drilling time, tb + to
hrs
Remarks
Drilling Cost, C
$/ft
0
0
New
0.0
30
2
1766.7
50
4
1220.0
65
6
1061.5
77
8
1000.0
87
10
977.0
96
12
968.8
104
14
971.2
111
16
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Torque Increased
982.0
Drilling Engineering
Optimization of Economics
Termination of a Bit Run
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Termination of a Bit Run
ttotal = tt + te
te = Cb/Cr
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Termination of a Bit Run
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Termination of a Bit Run
Example: Determine the optimum bit life for the bit run described in the table
below. The lithology of the formation is known to be essentially uniform in this
area. The bit cost is $5000. The rig cost is 4000 $/hr; and the trip time is 10 hours.
Prepared by: Tan Nguyen
Footage, D ft
drilling time
tb + to, hrs
Remarks
0
0
New
30
2
50
4
65
6
77
8
87
10
96
12
104
14
111
16
Torque Increased
Drilling Engineering
Optimization of Economics
Termination of a Bit Run
Solution:
Cb = 5000 USD
Cr = 4000 $/hr
Cb/Cr = 5000/4000 = 1.25 hrs
Using the equation above with different dD/dt. te = Cb/Cr = 1.25 hrs. The optimal
line corresponds to dD/dt = 4.2. Time to change the drill bit is 12 hours and at the
depth of 96 ft.
Prepared by: Tan Nguyen
Drilling Engineering
Optimization of Economics
Termination of a Bit Run
Prepared by: Tan Nguyen