SLIDE 6 Methodology (2/3)
to DWOB, Relative abrasiveness constant calculation
PDC drill bit
Rollercone drill bit
3 p WOB p WOB p WOB constant where, p x constant slide
14, RPM If WOB in correction no 14, RPM If
i i i 4 3 2 − − −
∆ + ∆ + ∆ = ∆ = < >
GR (API) Sand 2.6 1 10-30 Silt 2.67-2.7 0.85 50-70
) ( ). ( . . ) tan( . . ) cos( . . .
1 1 1
1
x b x h W BR D CCS SR RPM WOB K ROP
f B c b a
=
3 3
8 1
b f
BG a W ∆ − =
∑
=
= ∆
n i i i i i
ABR CCS RPM WOB Ca BG
2
. . .
2
) 2 ( ) (
b B
D JSA HSI a x h ⋅ ⋅ ⋅ = ] 1714 / . [
B
P Q HHP HSI = =
) ( . . . . 100 tan . . . . 80
1 2 2 1 1
x h W CCS n WOB D RPM m n K ROP
f b t B a t
Ψ =
3 3
8 1
b f
BG a W ∆ − =
∑
=
= ∆
n i i i i i
ABR CCS RPM WOB Ca BG
2
. . .
6
∆p = differential pressure RPM = surface RPM WOB = weight on bit RPM = top-drive / surface RPM SR = PDC cutter side rake angle CCS = confined compressive strength DB = diameter of bit BR = PDC cutter back rake angle Wf = bit wear function h(x) = hydraulic efficiency function b(x) = Nb effect function Nb = number of blades ∆BG = cumulative bit wear Ca = bit wear coefficient ABR = abrasiveness constant HSI = horsepower per sq. inch JSA = junk slot area HHP = hydraulic horsepower Q = pump flow rate PB = bit pressure drop AB = bit face area nt = avg. no. of inserts contacting rock m = no. of inserts penetrations per revolution Ψ = chip formation angle K1, a1,b1,c1,a2,b2,c2,a3,b3 – empirical constants
Silt 2.67-2.7 0.85 50-70 Conglomite 2.4-2.9 0.71 10-140 Dolomite 2.84-2.86 0.65 <30 Limestone 2.7 0.57 <20 Shale 2.4-2.8 0.11 80-300 Coal, bituminus 1.35 0.1 20
2
2 ) (
2 c B
ROP D a x h ⋅ ⋅ =
( )
] 4 / [
2 B B B
D A HSI π = =
92 . ) 02 . 02 . 1 (
) ( RPM RPM x b
x Nb −
=