basic drilling engineering equations
TRANSCRIPT
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Basic Drilling Engineering Equations - p.1
Triplex Pump : Q=3 π4
(d2) LEN231
Double−Acting Duplex : Q=π2 (2d L2−d
R2)L E N231
Hydrostatic Pr essure : P=0 .052∗Density∗Depth
Hydraulic Horsepower : HHP=Q ΔP1,714
Pipe Capacity : V PIPE=d2
1 ,029. 4 (bblft )
Pipe Capacity : V PIPE=π4d2 (12231∗42 ) ( bblft )
Gas in Mud : ΔPRED= ( CPS Z AT A
(100−C ) Z ST S) ln ( PB+PS
PS )
Nozzle Velocity : V NOZ= 33 .43 √ ΔPNOZ
ρMUD
Nozzle Pr essure Drop : ΔPNOZ=ρMUD Q
2
10 ,859 ANOZTOT
2
Re ynolds Number : N Re=929 ρ V d
μ
Gelled Mud :dPdL
=τGEL
300 (d2−d1 )
With 3 Nozzles : dNOZ= √ 4 ATOT
3 π
C=Gas Volume as % of Total Volume
For Max Hyd . HP : ΔPPARASITIC= ( 1m+1 ) ΔPPUMP
Max Im pact Force : ΔPPARASITIC= ( 2m+2 ) ΔPPUMP
Im pact Force : FJ= 0 .01732 Q√ ρ ΔPNOZ
Annular Area : A ANN=π4 (d22−d12)
Nozzle Area : A NOZTOT=
π4 (d12+d22+d32+. ..)
Nozzle Area : A NOZTOTOPT
= ( QOPT
104 .2 ) √ ρMUDΔPNOZOPT
Buoyancy Factor for steel : BF= 1−ρMUDρSTEEL
dC= ( logR
60N
log12W
106DB) ( ρMUDNORMAL
ρMUDACTUAL)
Circulating Pr essure : P2= P1 ( SPM 2
SPM 1)2
PD
= SD
−[ SD−( PD )N ] [ ROBSERVEDRNORMAL ]
1 .2
PD
= SD
−[ SD−( PD )N] [ dCOBSERVED
dCNORMAL]1.2
PD
= SD
−[ SD−( PD )N ] [ CNORMAL
COBSERVED ]1 .2
PD
= SD
−[ SD−( PD )N ] [ Δt NORMALΔtOBSERVED ]
3 .0
F= ( S−PD ) ( γ
1−γ )+ PD
Lifting Pipe : L=W (1+ 1En +1n )
Lowering Pipe : L=W (1+ En +1n )
Load on DeadLineLeg : LD=W ( n+44 n )Wind Load ,
lbf
ft 2: p= 0 .004 V 2 (V in mph)
V ae= (0. 45+ Dp2
DH2
−Dp2
) V PIPE
V ae= (0. 45+ Dp2
−Di2
DH2
−Dp2
+Di2) V PIPE
Pipe Internal Area : A PIPE=π4di2
Annular Capacity : V ANN=d22−d
12
1 ,029 .4 ( bblft )
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p.1 HCJ - May 30, 2002
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Basic Drilling Engineering Equations - p.2
Newtonian Model Bingham Plastic Model
Laminar Laminar
Turbulent Turbulent
Stress=ForceArea
Pressure=ForceArea
Torque=Force∗Arm
Power=Force∗Velocity
Power=Torque∗Angular Velocity
1 bbl=42 gal
1 ft 3=7 .48 gal
1 hp=33 ,000 ft−lbf /min
1 BTU=779 ft−lbf
Specific Gravity=ρFLUID8 .33 ( lb / gallb / gal )
dPdL
=μpV
1 ,500 d2+
τ y225 d
dPdL
=μpV
1 ,000 (d2−d1 )2+
τ y200 (d2−d1 )
dPdL
=μ V
1 ,000 (d2−d1 )2
dPdL
=μV
1 ,500d2
dPdL
= f ρ V 2
25 .8 ddPdL
= f ρ V 2
25 .8 d
dPdL
= ρ0 .75 V 1.75 μ0.25
1 ,800 d1 .25dPdL
=ρ0 .75 V 1.75 μ
p0.25
1 ,800 d1.25
dPdL
= f ρ V 2
21 .1 (d2−d1 )dPdL
= f ρ V 2
21 .1 (d2−d1 )
dPdL
=ρ0 .75 V 1.75 μ
p0.25
1 ,396 (d2−d1 )1.25dPdL
= ρ0.75 V 1 .75 μ0 .25
1 ,396 (d2−d1 )1.25
PCC=1
D . F . (P1− S−S1S2−S1 ) (P1−P2 )
PCC=1
1 .125. (3 ,660− 17 ,571−15 ,00020 ,000−15 ,000 ) (3 ,660−3 ,590 )
ρKILL= ρOLD +SIDPP0.052 D
ρKICK= ρOLD −SICP−SIDPP0 .052 hKICK
Pump Pr essure : PPUMP= ΔPS + ΔPDP+ ΔPDC+ ΔPNOZ+ ΔPDC ANN+ ΔPDPANN
+ ΔPHYDROSTATIC
Mixtures : Mass= ρ1V 1 + ρ2V 2 + ρ3V 3 +. .. +ρnV n = (V 1 + V 2 +V 3 +. . . +V n ) ρMIX
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p.2 HCJ - May 30, 2002
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ACRONYMS
API American Petroleum InstituteAPL annular pressure loss
bbls barrelsBHP bottom hole pressureECD equivalent circulating densityEMW equivalent mud weight
FIT formation integrity testFP formation pressureHP hydrostatic pressurehp horse powerID internal diameter
LOT leak off testLWD logging while drilling
MASP maximum allowable surface pressureMAASP maximum allowable annular surface pressure
MD measured depth (along the wellbore)MWD measurement while drillingOD outer diameterppg pounds per galpsi pounds per square inch
psia psi absolutepsig psi gauge = psia - 14.7 (approx)SICP shut-in casing pressure
SIDPP shut-in drillpipe pressure
TVD true vertical depth
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r = density lbm/galp = absolute pressure psiaM = molecular weightZ = gas deviation factor
T = absolute temperature
p = absolute pressure at depth D psia
= psia
oR
p0 absolute pressure at depth D0
Density of Gas: ρ=p M
80 .3 Z T
Pressure : p=p0 e
M (D−D0 )1,544 Z T