Well Control Equations

WELL CONTROL

EquationsCharts & Tables

WELL CONTROL EQUATIONS

1. Pressure (psi)

2. Pressure Gradient (psi/ft)

P.G.(psi

ft) 0.052 Mud Weight (ppg)

3. Hydrostatic Pressure (psi)

a. H.P.(psi) = 0.052 Mud Weight (ppg) True Vertical Depth, TVD (ft)

b. Mud Weight (ppg) = Hydrostatic Pressure (psi)

0.052 True Vertical Depth, TVD (ft)

c. True Vertical Depth, TVD (ft) = Hydrostatic Pressure (psi)

0.052 Mud Weight (ppg)

4. Equivalent Density (ppg)

Eq. Density (ppg) =Pressure (psi)

0.052 TVD (ft)

5. Formation Pressure (psi)

Formation Pressure (psi) = Hydrostatic Pressure in Drill Pipe (psi) + SIDPP (psi)

assuming shut-in well with BHP equalized with formation pressure

6. Density to Balance Formation (ppg)

Kill Mud Weight, KMW (ppg) =

SIDPP (psi)

0.052 TVD (ft) + Original Mud Weight (ppg)

apps\worddocs\wcequatn.doc PAGE 2 OF 12 Revised 4/7/23


7. Equivalent Mud Weight, EMW (ppg)

EMW(ppg) = Leak - Off Pressure (psi)

0.052 Casing Shoe TVD (ft) + Leak - Off Mud Wt (ppg)

8. Maximum Allowable Surface Pressure, MASP (psi) Based on Casing Burst.

MASP(psi) = Casing Internal Yield (psi) .80 (safety factor)

9. Maximum Initial Shut-In Casing Pressure, MISICP (psi) Upon initial closure only--Based onformation breakdown @ shoe. ForIWCF, written as initial MAASP.

MISICP(psi) = EMW (ppg) - Present Mud Wt (ppg) 0.052 Shoe TVD (ft)

10. Initial Circulating Pressure (psi) ENGINEER'S & DRILLER'S METHODS.

ICP (psi) = SIDPP(psi) + Slow Pump Rate Pressure, SPRP (psi)

11. Final Circulating Pressure (psi) ENGINEER'S METHOD.

FCP(psi) = SPRP (psi) Kill Mud Wt (ppg)

Original Mud Wt (ppg)

12. Equivalent Circulating Density, ECD (ppg)

ECD(psi) = Annular Pressure Loss (psi)

0.052 TVD Bit (ft) + Mud Wt (ppg)

13. Gas Pressure and Volume Relationship -- Boyle's Law

P V = P V1 1 2 2 The Pressure (psi) of a gas bubble times its Volume (bbl) in onepart of the hole equals its Pressure times its Volume in another.Disregards effects of Temperature (T) and gas compressibility (z)

P = P V

V2

1 1

2or V =

P V

P2

1 1

2

14. Pump Output (bbl/min)



Pump Output(bbl / min) = bbl

stroke

strokes

min

15. 100% Triplex Pump Output (bbl/stroke)

Pump Output(bbl / stk) =

Liner ID (in)

1029

Stroke Length (in)

12 3

2

16. Surface To Bit Strokes (strokes)

Strokes =Drill String Internal Volume (bbl)

bbl / stroke

17. Circulating Time (min)

Min = Volume (bbl)

Pump Output (bbl / min)

18. Open Hole Capacity Factor (bbl/ft)

Capacity(bbl / ft) =

Open Hole Diameter (in)

1029

2

19. Pipe Capacity Factor (bbl/ft)

Capacity(bbl / ft) =

Pipe Inside Diameter 2

( )in

1029



20. Annulus Capacity Factor, ACF (bbl/ft)

Capacity(bbl / ft) = Open Hole Diameter (in) - Pipe Outside Diameter (in)

Capacity(bbl / ft) = Casing Inside Diameter (in) - Pipe Outside Diameter (in)

2 2

2 2

1029

1029

or

21. Pipe Displacement (bbl/ft) Disregarding tool joints.

Displacement(bbl / ft) =

Pipe Outside Diameter (in) - Pipe Inside Diameter (in)2 2

1029

22. Total Pipe Displacement Including Capacity (bbl/ft) Disregarding tool joints.

Displacement(bbl / ft) =

Pipe Outside Diameter (in)

2

1029

23. Height of Influx (ft)

Height(ft) = Pit Gain (bbl)

Annulus Capacity Factor (bbl / ft)

24. Pressure Gradient of Influx (psi/ft) Bit on bottom.25.

Influx Gradient(psi / ft) = Pressure Gradient of Mud (psi / ft) - SICP (psi) - SIDPP (psi)

Height of Influx (ft)

26. Rate of Kick Rise (ft/hr) Well Shut-In.

R.O.R.(ft / hr) = Change in SICP (psi)

0.052 Mud Wt (ppg) Elapsed Time for Change in SICP (hr)



27. Weight per Foot of Drill Collars (lb/ft)

lbs / ft = 2.67 OD (in) ID (in) 2 2

28. Force (lb)

Force(lbs) = Pressure (psi) Area (in ) 2

29. Area (in2)

Area(in )

Diameter (in)

4, 3.1422

2

30. Degrees API (@ 60oF)

OAPI = 141.5

Specific Gravity - 131.5

31. Specific Gravity (@ 60oF)

Specific Gravity = 141.5

API + 131.5O

32. Mud Weight from Specific Gravity (ppg)

Mud Weight(ppg) Specific Gravity ppg 8 33. (Fresh Water weighs 8.33 ppg)



33. Hang Off Weight (lb)

Weight of Block+ Kelly Weight+ Weight of Compensator+ Air Weight of Drill Pipe (KB to Hang- Off Ram)+ 10, 000 lbs Weight on Indicator after hangoff (lb)

34. Barite Requirement For Weight-up (100 lb sxs)

Barite (sxs) = Volume to weight up (bbls) Increase in MW

35.0 - KWM

15

35. Cutting Back or Weighting Up One Fluid with Another to Obtain Desired Fluid Density

Volume of Mixing Fluid to Add (bbls)

Vol of Starting Fluid (bbls)Starting Fluid Wt (ppg) Desired Fluid Wt (ppg)

Desired Fluid Wt (ppg) Mixing Fluid Wt (ppg)

36. Final Density of a Mixture of Fluids , (ppg)

Final Fluid Wt (ppg)

Fluid Wt 1 (ppg) Volume Fluid 1 (gals) Fluid Wt 2 (ppg) Volume Fluid 2 (gals)

Volume Fluid 1 (gals) Volume Fluid 2 (gals)

37. Final Density of a Mixture of a Fluid and a Solid, (ppg)

Final Fluid Density (ppg)

Fluid Density (ppg) Volume Fluid (gals) Weight of Solid Added (lb)

Volume Fluid (gals)Weight of Solid Added (lb)

True Density of Solid (ppg)

38. Weight of Solid to Add to a Fluid to Obtain Desired Fluid Weight , (lb)



Weight of Solid to Add (lb)

Volume of Starting Fluid (gals) True Density of Solid (ppg)

Desired Fluid Wt (ppg) Starting Fluid Wt (ppg)

True Density of Solid (ppg) Desired Fluid Wt (ppg)



VOLUMETRIC CONTROL EQUATIONS

39. Pressure Increment, PI (psi)

PI = Safety Factor (psi)

= psi3

40. Fluid Increment, MI (bbl)

MI = PI (psi) Annulus Capacity Factor (bbl / ft)

0.052 Mud Wt (ppg) = bbl

41. Rate of Bubble Rise, ROR (ft/hr) See Equation 25 above.

ROR = Change in Casing Pressure (psi)

0.052 Mud Wt (ppg) Elapsed Time for Change (hr) =

ft

hr

42. Time to Bubble Penetration, BPT (hr)

BPT = Depth of Bubble (ft) - Depth of Bit (ft)

ROR (ft / hr) + Stripping Speed (ft / hr) = hr

LUBRICATE AND BLEED

43. Pressure that can be bled off after lubricating in a given volume of fluid , (psi)

Volume Lubricated (bbl)0.052 Fluid Wt (ppg)

Capacity Factor (bbl / ft) = psi



STRIPPING AND SNUBBING EQUATIONS

STRIPPING

44. Pressure-Area Force, F p (lb) Fp

OD (in)Well Head Pressure (psi)

2

4

45. Buoyed Weight of Tubulars, W (lb) W WAIR

(lb)Mud Wt (ppg)65 4

65 4

.

.

46. Barrels to Bleed per Stand , (bbls/stand) BBL / Stand

OD (in)

1029Stand Length (ft)

2

47. Volumetric Control Considerations

Pressure Increment, PI (psi) See Equation 37 above.

Fluid Increment, MI (bbl) See Equation 38 above.

Surface Pressure Increase due to Penetration of the Bubble, SP INCR (psi)

L L PG PG psiK DP OH K OH MUD GAS( ) ( )

Open Hole Kick Length, L K(OH) (ft)

LK OH( ) Kick Volume at penetration (bbl)

ACF (bbl / ft)OH

DP by Hole Kick Length, L K(DPOH) (ft)

LK DP OH( )

Kick Volume at penetration (bbl)

ACF (bbl / ft)DP OH

Rate of Bubble Rise, ROR (ft/hr) See Equation 40 above.

Time of Bubble Penetration, BPT (hrs) See Equation 41 above.



SNUBBING

48. Snub Force, SF (lb) SF Fp Friction Force W

49. Neutral Point SF Fp 0; W

50. Effective String Weight, W E (lb/ft) WW (lb)

L (ft)E (lb / ft)

51. Calculating Effective String Weight and Change in Effective String Weight after Filling

a) Effective String Weight with no fluid in the workstring:

WE (Effective String Wt, lb / ft)

Air Wt (lb / ft)OD (in) Fluid Wt (ppg)WELL

2

24 5.

Note that WE and Air Wt both have units of lb/ft. For example, the air weight of 2-7/8” tubing normally would be 6.5 lb/ft.

b) Increase in the Effective String Weight after the pipe is filled with the same Fluid Weight that is in the well:

W

ID inE (lb / ft)

Fluid Wt (ppg)WELL( )

.

2

24 5

c) Increase in the Effective String Weight after the pipe is filled with a different FluidWeight than the Fluid Weight that is in the well:

W

ID inE (lb / ft)

Fluid Wt (ppg)FILL( )

.

2

24 5

d) After filling the pipe, the Effective String Weight will be:



W W WE EE (AFTER FILLING)

WELL FILL

(lb / ft)

Air Wt (lb / ft)OD (in) Fluid Wt (ppg)

24.5

ID (in) Fluid Wt (ppg)

24.5

2 2

In this case, note that Fluid WtFILL in the last term above will be Fluid WtWELL if filled with the same fluid.

NOTE: This the GENERAL EQUATION for the Effective Buoyed Weight of the String. It works regardless of the fluid that is inside or outside the pipe. If the fluid is gas at fairly low pressure, use 0 lbs/gal for the fluid wt.

52. Predicting the Neutral Point

Combining Equations 47 and 48 above gives an equation for the length L (ft) of pipe that must be run into the well to reach the Neutral Point:

FW (lb)

L (ft)

L (ft)F

W

p E

p

E

(lb) W (lb) and W (lb / ft)

(lb)

(lb / ft)

a) The Neutral Point occurs in unfilled pipe when the length of pipe run into the well is:

L

F

OD in lui

p (ft) (lb)

AIR Wt (lb / ft)F d Wt (ppg)WELL

( )

.

2

24 5

b) The Neutral Point occurs in filled pipe when the length of pipe run into the well is:

L

Fp (ft) (lb)

AIR Wt (lb / ft)OD (in) Fluid Wt (ppg)

+ID (in) Fluid Wt (ppg)WELL FILL

2 2

24 5 24 5. .



Accumulator Sizing

52. Bottle Capacity Required (gals)

Bottle Volume (gals)Volume Fluid Required(gals)

Precharge Pressure

Minimum Operating Pressure -

Precharge Pressure

Maximum Operating Pressure

53. Volume Useable Fluid Available (gals)

Volume Useable Fluid (gals)

= Bottle Volume (gals)Precharge Pressure

Minimum Operating Pressure -

Precharge Pressure

Maximum Operating Pressure


Well Control Equations

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