Transcript Modeling of Drill Bits

Drilling Engineering
Drilling Engineering - PE 311
Modeling of Drilling Drill Bits
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of Roller Cone Bit
Rollercone bits have been used extensively in the drilling industry and among its
various types; the three-cone rolling cutter bit is by far the most widely used all
over the two
Cunningham (1960) showed that the drilling rate of a roller-cone bit is proportional
to the rotary speed of the bit at the atmospheric pressure for a wide range of RPM
and WOB as expressed below:
R = K*Wa*N
where R = drilling rate, ft/hr ; W = weight on bit, klbf ; N = rotary speed ; and K, a =
constants of proportionality
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of Roller Cone Bit
Cunningham’s model did not integrate the effect of other drilling parameters: bit
diameter, rock strength, etc.
Maurer (1962) proposed his model for the perfect hole cleaning condition
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of Roller Cone Bit
Bingham (1965) suggested the correlation based on limited laboratory data
K is the constant accounting for the rock strength
a is the WOB exponent
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of Roller Cone Bit
Bourgoyne and Young (1973) suggested a drilling rate model considering the
effect of several drilling variables on rate of penetration. In this model, the effect of
the parameters such as WOB, RPM, bit tooth wear and others were assumed to
be independent of one another.
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of Roller Cone Bit
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of Roller Cone Bit
Warren (1981) introduced an equation to calculate the ROP for roller cone bits that
integrated the effects of the mechanical conditions such as RPM, WOB, rock
strength, bit type and size through the verification with full-scale experimental data.
He developed his model using dimensional analysis and generalized response
curves for the best fit using laboratory data. The results have revealed that the
generated rock volume by a single tooth is proportional to tooth force squared and
inversely proportional to rock strength squared.
His model was later modified by Hareland (1994) for taking into account the bit
wear and chip hold down effects as presented below:
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of Roller Cone Bit
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of Roller Cone Bit
In the above model, the chip hold down function characterizes the resultant force
on the cuttings after they are generated by the bit and its integrated effect on
ROP. Also, the wear function shows the effect of the bit wear on rate of
penetration as presented below:
ΔBG represents the bit wear as a function of WOB, RPM, confined rock strength
and formation abrasiveness. The constant Cc which is called “bit wear coefficient”
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of PDC
Warren and Sinor (1986) proposed a single PDC cutter model to predict some
parameters such as cutter forces, cutter temperature and cutter wear. Their model
was developed based on a thorough geometrical relationships which was tested
and verified using different sets of 30 laboratory data.
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of PDC
Another model was developed by Kuru and Wojtanowsicz (1988) for assessing the
PDC bits’ performance using single cutter force analysis. The effect of the friction
between the PDC cutters and the rock was considered in their study which made it
different than the previous approaches and capable of predicting ROP, bit torque
as well as the bit life.
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of PDC
Hareland and Rampersad (1994) developed a model for predicting formation
drillability of drag bits. It was derived based on the conservation of mass where the
rate of cutting removal in front of the cutters is equivalent to the rate of
penetration. The effect of the operational parameters was integrated on rate of
penetration with proper consideration of geometrical relationship and rock failure
criteria as shown below.
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of PDC
Finally, the most recent ROP model for the PDC bits was developed by Motahari
et al. (2008) which claimed to be working accurately in drilling performance
Prepared by: Tan Nguyen
Drilling Engineering
Modeling of Drill Bits
Modeling of PDC
Prepared by: Tan Nguyen