Basic Equation of Drilling

Basic Drilling Engineering Equations - p.1

Q=

Triplex Pump :

3 π 2 LEN d 4 231

( )

(

Q=

Hydraulic Horsepower :

HHP =

Annular Area :

A ANN =

Pipe Capacity :

(

π 2 2 d 2 − d1 4

VPIPE =

Pipe Capacity :

Gas in Mud :

Gelled Mud :

)

VPIPE =

⎛ bbl ⎞ ⎜ ⎟ ⎝ ft ⎠

VANN =

d 2 − d1 1,029.4

2

⎛ CPS Z A TA ∆PRED = ⎜⎜ ⎝ (100 − C) Z S TS

⎛ bbl ⎞ ⎜ ⎟ ⎝ ft ⎠

Circulatin g Pr essure :

⎞ ⎟⎟ ⎠

⎛ 1 ⎞ ∆PPARASITIC = ⎜ ⎟ ∆PPUMP ⎝ m + 1⎠

Max Im pact Force :

⎛ 2 ⎞ ∆PPARASITIC = ⎜ ⎟ ∆PPUMP ⎝m+ 2⎠

A NOZ _ TOT =

Nozzle Area :

(

)

π 2 2 2 d1 + d2 + d3 + ... 4

∆PNOZ =

d NOZ =

10,859 A NOZ _ TOT

2

ρMUD ∆PNOZ _ OPT

4 A TOT 3π

⎛ ⎜ log R 60N dC = ⎜ ⎜ 12W ⎜ log 6 10 D B ⎝

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

⎛ ρ MUD _ NORMAL ⎞ ⎜ ⎟ ⎜ρ ⎟ ⎝ MUD _ ACTUAL ⎠

E = en

⎡ dC _ OBSERVED ⎢ ⎢⎣ dC _ NORMAL

⎤ ⎥ ⎥⎦

1.2

⎛ E 1⎞ Lowering Pipe : L = W ⎜1 + + ⎟ n n⎠ ⎝

P S ⎡S ⎛ P ⎞ ⎤ = − ⎢ −⎜ ⎟ ⎥ D D ⎣D ⎝ D ⎠N ⎦

⎛n+ 4⎞ ⎟⎟ Load on Dead _ Line _ Leg : L D = W ⎜⎜ ⎝ 4n ⎠

P S ⎡ S ⎛ P ⎞ ⎤ ⎡ R OBSERVED ⎤ = −⎢ −⎜ ⎟ ⎥ ⎢ ⎥ D D ⎣ D ⎝ D ⎠ N ⎦ ⎣ R NORMAL ⎦

lbf : p = 0.004 V 2 ft 2

ρ MUD Q 2

2

1 1⎞ ⎛ Lifting Pipe : L = W ⎜1 + + ⎟ ⎝ En n ⎠

Wind Load,

∆PNOZ ρ MUD

⎛Q ⎞ A NOZ _ TOT _ OPT = ⎜ OPT ⎟ 104 2 . ⎝ ⎠

With 3 Nozzles :

⎞ ⎟⎟ ⎠

VNOZ = 33.43

Nozzle Pr essure Drop :

ρ MUD ρ STEEL

⎛ SPM 2 P2 = P1 ⎜⎜ ⎝ SPM1

For Max Hyd. HP :

Nozzle Area :

C = Gas Volume as % of Total Volume

Buoyancy Factor for steel : BF = 1 −

τ GEL dP = dL 300 (d 2 − d1 )

Nozzle Velocity :

⎞ ⎛ P + PS ⎟⎟ ln ⎜⎜ B ⎠ ⎝ PS

929 ρ V d µ

Im pact Force : FJ = 0.01732 Q ρ ∆PNOZ

d2 ⎛ bbl ⎞ ⎜ ⎟ 1,029.4 ⎝ ft ⎠ 2

Annular Capacity :

Q ∆P 1,714

π 2 ⎛ 12 ⎞ d ⎜ ⎟ 4 ⎝ 231 * 42 ⎠

N Re =

Re ynolds Number :

π 2 di 4

A PIPE =

Pipe Internal Area :

)

π 2 2 L E N 2d L − d R 2 231

Double − Acting Duplex :

P = 0.052 * Density * Depth

Hydrostati c Pr essure :

P S ⎡ S ⎛ P ⎞ ⎤ ⎡ C NORMAL ⎤ = −⎢ −⎜ ⎟ ⎥ ⎢ ⎥ D D ⎣ D ⎝ D ⎠ N ⎦ ⎣ C OBSERVED ⎦

(V in mph)

1.2

2 ⎞ ⎛ Dp ⎟V Vae = ⎜ 0.45 + PIPE 2 2 ⎟ ⎜ D D − H p ⎠ ⎝

P S ⎡ S ⎛ P ⎞ ⎤ ⎡ ∆t NORMAL ⎤ = −⎢ −⎜ ⎟ ⎥ ⎢ ⎥ D D ⎣ D ⎝ D ⎠ N ⎦ ⎣ ∆t OBSERVED ⎦

2 2 ⎞ ⎛ Dp − D i ⎟V Vae = ⎜ 0.45 + PIPE 2 2 2 ⎟ ⎜ D D D − + H p i ⎠ ⎝

⎛S −P⎞ ⎛ γ ⎞ P F=⎜ ⎟⎟ + ⎟ ⎜⎜ ⎝ D ⎠ ⎝1− γ ⎠ D p.1

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1.2

3.0

HCJ - October 9, 2002

Basic Drilling Engineering Equations - p.2 Stress =

Force Area

Pr essure =

1 ft 3 = 7.48 gal

Force Area

1 bbl = 42 gal

Torque = Force * Arm

1 hp = 33,000 ft − lbf / min

Power = Force * Velocity

1 BTU = 779 ft − lbf

Power = Torque * Angular Velocity ρ FLUID 8.33

Specific Gravity =

⎛ lb / gal ⎞ ⎜⎜ ⎟⎟ ⎝ lb / gal ⎠

Newtonian Model

Bingham Plastic Model

dP µV = dL 1,500 d 2

Laminar

τy µp V dP = + 2 dL 1,500 d 225 d

Laminar

τy µp V dP = + 2 dL 1,000 (d 2 − d1 ) 200 (d 2 − d1 )

dP µV = dL 1,000 (d 2 − d1 )2 dP f ρ V 2 = dL 25 .8 d

Turbulent

PCC =

e.g.,

dP ρ 0.75 V 1.75 µ 0.25 = dL 1,800 d1.25

0.75 1.75 dP ρ V µ p = dL 1,800 d1.25

dP f ρV2 = dL 21.1(d 2 − d1 )

dP f ρV2 = dL 21.1(d 2 − d1 )

dP ρ 0.75 V 1.75 µ 0.25 = dL 1,396 (d 2 − d1 )1.25

ρ 0.75 V 1.75 µ p dP = dL 1,396 (d 2 − d1 )1.25

1 ⎛ 17,571− 15,000 ⎞ ⎟ (3,660 − 3,590) ⎜ 3,660 − 1.125 ⎝ 20,000 − 15,000 ⎠

Pump Pr essure : Mixtures :

0.25

0.25

S − S1 ⎞ 1 ⎛ ⎜⎜ P1 − ⎟ (P1 − P2 ) D.F. ⎝ S 2 − S1 ⎟⎠

PCC =

dP f ρ V 2 = dL 25 .8 d

Turbulent

ρ KILL = ρ OLD +

SIDPP 0.052 D

ρ KICK = ρ OLD −

SICP − SIDPP 0.052 hKICK

PPUMP = ∆PS + ∆PDP + ∆PDC + ∆PNOZ + ∆PDC _ ANN + ∆PDP _ ANN + ∆PHYDROSTATIC

Mass = ρ1 V1 + ρ 2 V2 + ρ 3 V3 + ... + ρ n Vn =

(V1 + V2

p.2

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+ V3 + ... + Vn ) ρMIX HCJ - November 13, 2002

Hydraulics Equations - API RP 13D Pipe Flow ⎛R n p = 3 . 32 log ⎜⎜ 600 ⎝ R 300

Kp = Vp = µ ep

⎞ ⎟⎟ ⎠

0.408 Q D2

N Re p =

np −1

⎛ 3np + 1⎞ ⎜ ⎟ ⎜ 4n ⎟ p ⎝ ⎠

Va =

0.408 Q 2 2 D 2 − D1

µ ea

µ ep

fp =

170 .2 na

⎛ 144 Va ⎞ ⎟⎟ = 100 K a ⎜⎜ ⎝ D 2 − D1 ⎠

na −1

⎛ 2n a + 1 ⎞ ⎟⎟ ⎜⎜ 3 n a ⎠ ⎝

na

928 (D 2 − D 1 ) Va ρ µ ea

Laminar

16 NRep

(NRep < 2,100)

Turbulent

fa =

24 NRea

fa =

a

Turbulent

log np + 3.93

}

50 1 . 75 − log n p

fp =

a=

a NRep

b

b=

7

156 ρ Q 2 2

b

⎛ dP ⎞ ∆Pa = ⎜ ⎟ ∆L a ⎝ dL ⎠ a

⎛ dP ⎞ ∆Pdp = ⎜ ⎟ ∆L dp ⎝ dL ⎠ dp

N1

}

1 . 75 − log n a 7

NRea

2

2

(D

log na + 3.93 50

fa Va ρ ⎛ dP ⎞ ⎟ = ⎜ ⎝ dL ⎠ a 25.81(D 2 − D1 )

fp Vp ρ ⎛ dP ⎞ ⎜ ⎟ = ⎝ dL ⎠ dp 25 .81 D

∆ PNozzles =

5.11 R 100

NRea =

(NRep < 2,100)

b =

Ka =

np

928 D Vp ρ

Laminar

a=

⎞ ⎟⎟ ⎠

⎛R n a = 0 . 657 log ⎜⎜ 100 ⎝ R3

np

⎛ 96Vp ⎞ ⎟⎟ = 100 K p ⎜⎜ ⎝ D ⎠

p.3

Annular Flow

5.11 R 600 1,022

-

+ D N2 + D N3 2

)

2 2

Slip Velocity - API RP 13D ⎛R n S = 0 . 657 log ⎜⎜ 100 ⎝ R3

⎞ ⎟⎟ ⎠

KS =

5.11R100 170.2nS

γ& S =

12 VS Dp

2 ⎛ µ es ⎞ ⎛⎜ ⎞⎛ Dp ρ ⎞ ⎛ ρp ⎜ ⎟ 1 + 16,465 Dp ⎜ Vs = 0.01344 ⎜ ρ − 1⎟⎟⎜⎜ µ ⎟⎟ ⎜ D ρ ⎟ ⎜⎜ ⎠⎝ es ⎠ ⎝ ⎝ p ⎠⎝

p.3

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n −1 µ eS = 100 K S γ& S S

⎞ ⎟ − 1⎟ ⎟ ⎠ HCJ May 30, 2002

Directional Survey Equations Tangential

∆East = ∆MD • sin(I2 ) • sin( A 2 )

Method

∆North = ∆MD • sin(I2 ) • cos( A 2 )

-

p.4

∆North = ∆MD • sin(I AVG ) • cos( A AVG )

I1 + I2 2

A AVG =

A1 + A 2 2

∆Vert = ∆MD • cos(IAVG )

Radius of Curvature

Balanced Tangential

Minimum Curvature

RF =

2 β tan β 2

∆East =

∆MD • [cos(I1 ) − cos(I2 )] • [cos( A 1 ) − cos( A 2 )] (I2 − I1 ) • ( A 2 − A 1 )

∆North =

∆MD • [cos(I1 ) − cos(I2 )] • [sin( A 2 ) − sin( A 1 )] (I2 − I1 ) • ( A 2 − A 1 )

∆Vert =

∆MD • [sin(I2 ) − sin(I1 )] (I2 − I1 )

∆East =

∆MD [sin(I1 ) • sin(A1 ) + sin(I2 ) • sin(A 2 )] 2

∆North =

∆MD [sin(I1 ) • cos(A1 ) + sin(I2 ) • cos(A 2 )] 2

∆Vert =

∆MD [cos(I2 ) + cos(I1 )] 2

∆East =

∆MD [sin(I1 ) • sin(A1 ) + sin(I2 ) • sin(A 2 )] • RF 2

∆North =

∆MD [sin(I1 ) • cos(A1 ) + sin(I2 ) • cos(A 2 )] • RF 2

∆Vert =

∆MD [cos(I1 ) + cos(I2 )] • RF 2

β = cos −1 [(cos(I2 − I1 ) − sin I1 sin I2 (1 − cos( A 2 − A 1 ))] β = cos −1 [cos(A 2 − A 1 ) sin I1 sin I2 + cos I1 cos I2 ]

⎛I −I ⎞ ⎛ A − A1 ⎞ 2⎛I + I ⎞ β = 2 sin−1 sin2 ⎜ 2 1 ⎟ + sin2 ⎜ 2 ⎟ sin ⎜ 1 2 ⎟ 2 ⎝ 2 ⎠ ⎝ ⎠ ⎝ 2 ⎠

⎛∆A⎞ ⎛ ∆I⎞ β = 2 sin−1 sin2 ⎜ ⎟ + sin2 ⎜ ⎟ sin I1 sin I2 ⎝ 2 ⎠ ⎝ 2⎠ p.4

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HCJ - June 2, 2002

- Be careful when angles are equal

Angle

IAVG =

- Use angles in RADIANS when appropriate

∆East = ∆MD • sin( IAVG ) • sin( A AVG )

CAUTION: RADIUS OF CURVATURE - Be sure to use the MINIMUM angle for the DIFFERENCE

Average

CAUTION: AVERAGE ANGLE - Be sure to use the MINIMUM angle for the AVERAGE

∆Vert = ∆MD • cos(I2 )