Well Control Equations

WELL CONTROL

Equations Charts & Tables

WELL CONTROL EQUATIONS 1.

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

2.

Pressure Gradient (psi/ft) P.G.(

3.

psi ) = 0.052 × Mud Weight (ppg) ft

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) = 4.

Equivalent Density (ppg) Eq. Density (ppg) =

5.

Hydrostatic Pressure (psi) 0.052 × Mud Weight (ppg)

Pressure (psi) 0.052 × TVD (ft)

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

apps\worddocs\wcequatn.doc

PAGE 2 OF 12

Revised 5/2/13


Equivalent Mud Weight, EMW (ppg) EMW(ppg) =

8.

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

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 on formation breakdown @ shoe. For IWCF, written as initial MAASP. MISICP(psi) =

10.

[ EMW (ppg)

- Present Mud Wt (ppg)] × 0.052 × Shoe TVD (ft)

Initial Circulating Pressure (psi)

ENGINEER'S & DRILLER'S METHODS.

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

11.

Final Circulating Pressure (psi) FCP(psi) = SPRP (psi) ×

12.

Annular Pressure Loss (psi) + Mud Wt (ppg) 0.052 × TVD Bit (ft)

Gas Pressure and Volume Relationship -- Boyle's Law P1V1 = P 2 V 2

P2 =

14.

Kill Mud Wt (ppg) Original Mud Wt (ppg)

Equivalent Circulating Density, ECD (ppg) ECD(psi) =

13.

ENGINEER'S METHOD.

P1V1 V2

The Pressure (psi) of a gas bubble times its Volume (bbl) in one part of the hole equals its Pressure times its Volume in another. Disregards effects of Temperature (T) and gas compressibility (z) or

V2 =

P1V1 P2

Pump Output (bbl/min)


PAGE 3 OF 12

Revised 5/2/13

WELL CONTROL EQUATIONS

Pump Output(bbl / min) =

15.

100% Triplex Pump Output (bbl/stroke) Pump Output(bbl / stk) =

16.

×

Stroke Length (in) × 3 12

Drill String Internal Volume (bbl) bbl / stroke

Volume (bbl) Pump Output (bbl / min)

Open Hole Capacity Factor (bbl/ft) Capacity(bbl / ft) =

19.

1029

2

Circulating Time (min) Min =

18.

[ Liner ID (in)]

Surface To Bit Strokes (strokes) Strokes =

17.

bbl strokes × stroke min

[ Open Hole Diameter (in)]

2

1029

Pipe Capacity Factor (bbl/ft) Capacity(bbl / ft) =


[ Pipe Inside Diameter ( in )]

2

1029

PAGE 4 OF 12

Revised 5/2/13


Annulus Capacity Factor, ACF (bbl/ft)

Capacity(bbl/ft) =

[Open Hole Diameter (in)]2 - [ Pipe Outside Diameter (in)]2 1029

or

Capacity(bbl/ft) =

21.

[Casing Inside Diameter (in)]2 - [ Pipe Outside Diameter (in)]2 1029

Pipe Displacement (bbl/ft)

Displacement(bbl / ft) =

22.

[ Pipe Outside Diameter (in)]

- [ Pipe Inside Diameter (in)] 1029

[ Pipe Outside Diameter (in)]

2

Disregarding tool joints. 2

1029

Height of Influx (ft) Height(ft) =

24. 25.

2

Total Pipe Displacement Including Capacity (bbl/ft) Displacement(bbl / ft) =

23.

Disregarding tool joints.

Pit Gain (bbl) Annulus Capacity Factor (bbl / ft)

Pressure Gradient of Influx (psi/ft)

Bit on bottom.

 SICP (psi) - SIDPP (psi)  Influx Gradient(psi / ft) = Pressure Gradient of Mud (psi / ft) -    Height of Influx (ft) 

26.

Rate of Kick Rise (ft/hr) R.O. R.(ft / hr) =


Well Shut-In.

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

PAGE 5 OF 12

Revised 5/2/13


Weight per Foot of Drill Collars (lb/ft)

(

lbs / ft = 2.67× [ OD(in)] −[ ID(in)]

28.

2

2

)

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

29.

Area (in2) π × [ Diameter (in)] Area(in ) = , π ≈ 3.142 4 2

2

30.

Degrees API (@ 60oF) O

31.

API =

141. 5 - 131. 5 Specific Gravity

Specific Gravity (@ 60oF) Specific Gravity =

32.

O

141. 5 API + 131. 5

Mud Weight from Specific Gravity (ppg) Mud Weight(ppg) = Specific Gravity × 8.33 ppg


PAGE 6 OF 12

(Fresh Water weighs 8.33 ppg)

Revised 5/2/13


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)  15 × Increase in MW  Barite (sxs) = Volume to weight up (bbls) ×    35.0 - KWM

35.

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

Volume of Mixing Fluid to Add (bbls) =  Starting Fluid Wt (ppg) − Desired Fluid Wt (ppg)  Vol of Starting Fluid (bbls) ×    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)  Weight of Solid Added (lb)  Volume Fluid (gals) +    True Density of Solid (ppg)  38.

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


PAGE 7 OF 12

Revised 5/2/13


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) 


PAGE 8 OF 12

Revised 5/2/13

WELL CONTROL EQUATIONS VOLUMETRIC CONTROL EQUATIONS 39.

Pressure Increment, PI (psi)

PI = 40.

Safety Factor (psi) = psi 3

Fluid Increment, MI (bbl) MI =

41.

Rate of Bubble Rise, ROR (ft/hr) ROR =

42.

PI (psi) × Annulus Capacity Factor (bbl / ft) = bbl 0. 052 × Mud Wt (ppg) See Equation 25 above.

Change in Casing Pressure (psi) 0.052 × Mud Wt (ppg) × Elapsed Time for Change (hr)

=

ft hr

Time to Bubble Penetration, BPT (hr) BPT =

Depth of Bubble (ft) - Depth of Bit (ft) = hr ROR (ft / hr) + Stripping Speed (ft / 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) = psi Capacity Factor (bbl / ft)

PAGE 9 OF 12

Revised 5/2/13


STRIPPING AND SNUBBING EQUATIONS STRIPPING π × [ OD (in)]

2

44.

Pressure-Area Force, Fp (lb)

45.

Buoyed Weight of Tubulars, W (lb)

 65 .4 − Mud Wt (ppg)  W = WAIR (lb) ×   65 .4  

46.

Barrels to Bleed per Stand, (bbls/stand)

2 OD (in)] [ BBL / Stand =

47.

Volumetric Control Considerations

Fp =

4

× Well Head Pressure (psi)

1029

× Stand Length (ft)

Pressure Increment, PI (psi)

See Equation 37 above.

Fluid Increment, MI (bbl)


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

( L K ( DP× OH ) − L K ( OH ) ) × ( PG MUD − PG GAS ) = psi Open Hole Kick Length, LK(OH) (ft) L K ( OH ) =

Kick Volume at penetration (bbl) ACFOH (bbl / ft)

DP by Hole Kick Length, LK(DP×OH) (ft) L K ( DP× OH ) =

Kick Volume at penetration (bbl) ACFDP× OH (bbl / ft)

Rate of Bubble Rise, ROR (ft/hr)


Time of Bubble Penetration, BPT (hrs)



PAGE 10 OF 12

Revised 5/2/13

WELL CONTROL EQUATIONS SNUBBING 48.

Snub Force, SF (lb)

SF = Fp + Friction Force − W

49.

Neutral Point

SF = 0;

50.

Effective String Weight, WE (lb/ft)

WE (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:

Fp = W

W (lb) L (ft)

WE (Effective String Wt, lb / ft) =

Air Wt (lb / ft) −

[ OD(in)] 2 ×

Fluid Wt WELL (ppg) 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: ∆WE (lb / ft) =

c)

Fluid Wt WELL (ppg) 24 .5

Increase in the Effective String Weight after the pipe is filled with a different Fluid Weight than the Fluid Weight that is in the well: ∆WE (lb / ft) =

d)

[ ID ( in)] 2 ×

[ ID ( in)] 2 ×

Fluid Wt FILL (ppg) 24 .5

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


PAGE 11 OF 12

Revised 5/2/13

WELL CONTROL EQUATIONS WE (AFTER FILLING) (lb / ft) = WE + ∆WE

= Air Wt (lb / ft) −

[ OD (in)]

2

× Fluid Wt WELL (ppg) [ ID (in)] × Fluid Wt FILL (ppg) + 24.5 24.5 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:

Fp (lb) = W (lb) L (ft) =

a)

WE (lb / ft) =

and

Fp (lb) WE (lb / ft)

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

L (ft) = AIR Wt (lb / ft) −

b)

W (lb) L (ft)

[ OD (in )]

2

× Fluid Wt WELL (ppg) 24.5

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

L (ft) = AIR Wt (lb / ft) −


[ OD (in)] 2 ×

Fp (lb)

Fluid Wt WELL (ppg) [ ID (in)] × Fluid Wt FILL (ppg) + 24.5 24.5 2

PAGE 12 OF 12

Revised 5/2/13

WELL CONTROL EQUATIONS Accumulator Sizing 52.

Bottle Capacity Required (gals) Bottle Volume (gals) =

Volume Fluid Required(gals) Precharge Pressure Precharge Pressure Minimum Operating Pressure Maximum Operating Pressure

53. Volume Useable Fluid Available (gals) Volume Useable Fluid (gals)   Precharge Pressure Precharge Pressure = Bottle Volume (gals) ×   Minimum Operating Pressure Maximum Operating Pressure  


PAGE 13 OF 12

Revised 5/2/13

Well Control Equations

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