Drilling Engineering

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• Drilling Engineering PE 311
• Drill Bit Optimization

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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

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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

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Optimization of Hydraulic Parameters
Maximum Nozzle Velocity

• Flow velocity through bit nozzle
• 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

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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.

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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.

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Optimization of Hydraulic Parameters
Maximum Bit Hydraulic Horsepower

• The Pump Pressure is expended by
• Frictional pressure losses in the surface
  equipment, ?ps
• Frictional pressure losses in the drillpipe,
  ?pdp, and drill collars, ?pdc
• Pressure losses caused by accelerating the
  drilling fluid through the nozzle
• Frictional pressure losses in the drill collar
  annulus, ?pdca, and drillpipe annulus, ?pdpa
• Let

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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
• It is well know that the frictional pressure loss
  is a function of flow rate and can be expressed
  as

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Optimization of Hydraulic Parameters
Maximum Bit Hydraulic Horsepower

• Hence, Dpd can be expressed as
• 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
• The bit Hydraulic horsepower

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Optimization of Hydraulic Parameters
Maximum Bit Hydraulic Horsepower

• Bit horsepower is a function of flow rate
• The bit horsepower reaches maximum when
• Or

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Optimization of Hydraulic Parameters
Maximum Bit Hydraulic Horsepower

• Bit hydraulic horsepower is a maximum when
• Since
• The hydraulic horsepower will be maximum at
• Or

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Optimization of Hydraulic Parameters
Maximum Jet Impact Force

• Jet impact force is a function of Dpbit Dppump
  Dpf . Note that Dpf is the total pressure loss
  in pipes and annuli.

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Optimization of Hydraulic Parameters
Maximum Jet Impact Force

• The impact force is maximized when,
• Solve the above equation yields,
• or
• Since , the jet impact force will be
  maximum at

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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
• 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 Dpd/Dpp at the optimum
  value. Then the flow rate will be reduced to the
  minimum value which it can still lift the
  cuttings.

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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.

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Optimization of Hydraulic Parameters
Nozzle Size Selection Graphical Analysis
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Optimization of Hydraulic Parameters
Nozzle Size Selection Graphical Analysis

• Show opt. hydraulic path
• Plot Dpf vs q
• From Plot, determine optimum q and Dpf
• Calculate
• Calculate total nozzle area
• Calculate Nozzle Diameter

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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.

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Optimization of Hydraulic Parameters
Example

• Pressure drop through the bit
• Total frictional pressure loss inside the
  drillstring and in the annulus at different flow
  rate

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Optimization of Hydraulic Parameters
Example

• m 1.2, for optimum hydraulics
• Interval 1
• Interval 2
• Interval 3

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Optimization of Hydraulic Parameters
Example
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Optimization of Hydraulic Parameters
Example

• From graph, the optimum point
• The proper total nozzle area is
• The nozzle size

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Optimization of Hydraulic Parameters
Example
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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 DD is the total depth as a given
  total time, ft.

 
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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.

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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 rateft/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
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Optimization of Economics
Cost-per-foot Calculation

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Bit Bit cost Rotating time hours Connection time hours Mean ROPft/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
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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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Optimization of Economics
Break-even Analysis

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Optimization of Economics
Break-even Analysis

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Optimization of Economics
Break-even Analysis
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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 bearing-wear 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.

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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.

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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.

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Optimization of Economics
Termination of a Bit Run

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footage, DD 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 Torque Increased 982.0
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Optimization of Economics
Termination of a Bit Run
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Optimization of Economics
Termination of a Bit Run
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Optimization of Economics
Termination of a Bit Run
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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.
Footage, DD 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
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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.
 
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Optimization of Economics
Termination of a Bit Run