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 )

p.1 HCJ - May 30, 2002

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

p.2 HCJ - May 30, 2002

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

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