4_Optimization

Slide 1Prepared by: Tan Nguyen
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
Optimization of Hydraulic Parameters
: 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
Maximum and Minimum Values - Review
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
Maximum Nozzle Velocity
Prepared by: Tan Nguyen
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.
Maximum Nozzle Velocity
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.
Maximum Bit Hydraulic Horsepower
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:
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
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
The bit horsepower reaches maximum when:
Or
Since
Or:
Jet impact force is a function of Dpbit = Dppump – Dpf . Note that Dpf is the total pressure loss in pipes and annuli.
Maximum Jet Impact Force
Solve the above equation yields,
or
Maximum Jet Impact Force
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.
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.
Nozzle Size Selection – Graphical Analysis
Calculate
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.
Example
Pressure drop through the bit:
Total frictional pressure loss inside the drillstring and in the annulus at different flow rate:
Example
Interval 1:
Interval 2:
Interval 3:
The proper total nozzle area is:
The nozzle size
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.
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.
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.
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.
Run Cycle Speed
Optimization of Economics
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.
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.
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
Remarks
ttotal = tt + te
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
Remarks
0
0
New
30
2
50
4
65
6
77
8
87
10
96
12
104
14
111
16
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.
Drilling Engineering

Date post:	30-Sep-2015
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4_Optimization

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