This article covers all formulas that are used while well control situations on the drilling rig ( Check also: **Drilling rigs Types**).

## Pressures Formulas

#### HYDROSTATIC PRESSURE (all depths TVD):

Constants:

- PPG x FT x .052 = PSI,
- SG x FT x .433 = PSI,
- SG x MT x 1.42 = PSI,
- PPG x MT x .171 = PSI,
- SG x MT x .098 = BARS,
- PCF x FT x .0069 = PSI,
- SG x MT x .1 = kg/cm2
- SG x MT x 9.8 = kPa,
- Kg/m3 x MT ÷ 102 = kPa,
- PPG x MT x 1.176 = kPa,
- PPG x FT x .358 = kPa,

**PRESSURE, psi = Mud Weight x Constant x Depth, (TVD)**

#### PRESSURE GRADIENT, psi/ft

= **Mud Weight** x Constant

OR

= Pressure, psi ÷TVD, ft

#### MUD WEIGHT

= Pressure, psi ÷ TVD, ft ÷ Constant

OR

= Pressure Gradient, psi/ft ÷ Constant

#### FORCE

= Pressure x Area

#### LENGTH TO CREATE A PRESSURE, ft

= Pressure, psi ÷ Gradient psi/ft

OR

= Pressure, psi ÷ Mud Weight ppg ÷ *.052*

#### FORMATION PRESSURE, psi

= (Mud Wt, ppg x .052 x Bit TVD, ft) + SIDPP, psi

#### BUOYANCY FACTORS AND MUD WEIGHT EQUIVALENTS

PPG | BUOYANCY FACTOR | PSI/FT | SG | Kg/M3 | PCF |

8.34 | .873 | .433 | 1.0 | 1000 | 62.4 |

8.4 | .872 | .436 | 1.01 | 1008 | 62.8 |

8.6 | .868 | .447 | 1.03 | 1032 | 64.3 |

8.8 | .865 | .457 | 1.06 | 1056 | 65.8 |

9.0 | .862 | .468 | 1.08 | 1080 | 67.3 |

9.2 | .860 | .478 | 1.10 | 1104 | 68.8 |

9.4 | .856 | .488 | 1.13 | 1128 | 70.3 |

9.6 | .853 | .499 | 1.15 | 1152 | 71.3 |

9.8 | .850 | .509 | 1.18 | 1176 | 73.3 |

10.0 | .847 | .519 | 1.20 | 1200 | 74.8 |

10.2 | .844 | .530 | 1.22 | 1224 | 76.3 |

10.4 | .841 | .540 | 1.25 | 1248 | 77.8 |

10.6 | .839 | .551 | 1.27 | 1272 | 79.3 |

10.8 | .836 | .561 | 1.29 | 1296 | 80.8 |

11.0 | .833 | .571 | 1.32 | 1320 | 82.3 |

11.2 | .829 | .582 | 1.34 | 1344 | 83.8 |

11.4 | .826 | .594 | 1.37 | 1368 | 85.3 |

11.6 | .823 | .603 | 1.39 | 1392 | 86.8 |

11.8 | .820 | .613 | 1.41 | 1416 | 88.3 |

12.0 | .817 | .623 | 1.44 | 1440 | 89.8 |

12.2 | .814 | .634 | 1.46 | 1464 | 91.3 |

12.4 | .810 | .644 | 1.49 | 1488 | 92.8 |

12.6 | .808 | .655 | 1.51 | 1512 | 94.3 |

12.8 | .804 | .665 | 1.53 | 1536 | 95.8 |

13.0 | .801 | .675 | 1.56 | 1560 | 97.3 |

13.2 | .798 | .686 | 1.58 | 1584 | 98.7 |

13.4 | .795 | .696 | 1.61 | 1608 | 100.3 |

13.6 | .792 | .706 | 1.63 | 1632 | 101.8 |

13.8 | .789 | .717 | 1.65 | 1656 | 103.3 |

14.0 | .786 | .727 | 1.68 | 1680 | 104.8 |

14.2 | .783 | .738 | 1.70 | 1704 | 106.3 |

14.4 | .780 | .748 | 1.73 | 1728 | 107.8 |

14.6 | .777 | .758 | 1.75 | 1752 | 109.3 |

14.8 | .774 | .769 | 1.77 | 1776 | 110.8 |

15.0 | .771 | .779 | 1.80 | 1800 | 112.3 |

15.2 | .768 | .790 | 1.82 | 1824 | 113.8 |

15.4 | .765 | .800 | 1.85 | 1848 | 115.3 |

15.6 | .763 | .810 | 1.87 | 1872 | 116.8 |

15.8 | .759 | .821 | 1.89 | 1896 | 118.3 |

16.0 | .755 | .831 | 1.92 | 1920 | 119.8 |

16.3 | .751 | .848 | 1.96 | 1956 | 122 |

16.6 | .746 | .862 | 1.99 | 1992 | 124 |

17.0 | .740 | .883 | 2.04 | 2040 | 127 |

17.3 | .735 | .900 | 2.08 | 2076 | 130 |

17.6 | .731 | .914 | 2.11 | 2112 | 132 |

18.0 | .725 | .935 | 2.16 | 2160 | 135 |

18.3 | .720 | .952 | 2.20 | 2196 | 137 |

18.6 | .716 | .966 | 2.23 | 2232 | 139 |

19.0 | .710 | .987 | 2.28 | 2280 | 142 |

## Killing Formulas For Well Control

These formulas are used in **kill sheet** calculations. Assume the following values to help you more understand such calculations

Bit TVD | = | 10,000 ft |

Mud Weight | = | 10.6 ppg |

SIDPP | = | 800 psi |

Slow Circulating Rate Pressure @ 40 SPM | = | 900 psi |

#### KILL MUD WEIGHT, ppg

= (SIDPP, psi ÷ *.052 *÷ TVD, ft) + Mud Wt, ppg

= (800 ÷ *.05**2 *÷ 10,000) + 10.6

= 1.54 + 10.6

= 12.14 ppg

#### ICP (Initial Circulating Pressure)

= Slow Circulating Rate Pressure, psi + SIDPP, psi

= 900 + 800

= 1,700 psi

#### FCP (Final Circulating Pressure)

= **Slow Circulating Rate** Pressure, psi x Kill Mud Wt ÷ Old Mud Wt

= 900 x 12.14 ÷ 10.6

= 900 x 1.1453

= 1,031 psi

Note: After a correct Start-Up the actual SCR pressure = Actual ICP – SIDPP

If using units other than PPG, Feet, and PSI then refer to page 4.1 for constants.

#### STEP DOWN CHART

Used to calculate pressure drop versus strokes as KILL MUD is pumped to the **DRILLING BIT**. There are 2 ways this can be done:-

#### FIXED STROKE INTERVAL OR FIXED PRESSURE INTERVAL

FIXED STROKE INTERVAL

(This number should be replaced if you use a different stroke interval e.g. 50, 200, 300, etc)

#### FIXED PRESSURE INTERVAL

Strokes/50 PSI Drop = Surface to Bit Strokes x 50 psi ÷ (ICP – FCP)

** (This number should be replaced if you use a different pressure interval e.g. 40, 60, etc)

EXAMPLE: ICP = 1600, FCP = 900 – Surface to Bit Strokes = 1084

Fixed Strokes :

= 65 psi approx

STROKES | PSI | |

0 | 1600 | (ICP) |

100 | 1535 | |

200 | 1470 | |

300 | 1405 | |

400 | 1340 | |

500 | 1275 | |

600 | 1210 | |

700 | 1145 | |

800 | 1080 | |

900 | 1015 | |

1000 | 950 | |

1084 | 900 | (FCP) |

Fixed Pressure:

= 77 strokes approx.

STROKES | PSI | |

0 | 1600 | (ICP) |

77 | 1550 | |

154 | 1500 | |

231 | 1450 | |

308 | 1400 | |

385 | 1350 | |

462 | 1300 | |

539 | 1250 | |

616 | 1200 | |

693 | 1150 | |

770 | 1100 | |

847 | 1050 | |

924 | 1000 | |

1001 | 950 | |

1084 | 900 | (FCP) |

With Kill Mud at the drilling bit, the pressure is then held constant for the remainder of Kill. Used for **WAIT and WEIGHT Method**.

#### DEVIATED STEP-DOWN CALCULATION – Well control Formulas

The following can be used to calculate step-down pressure on a deviated well (**directional drilling**).

- SIDP = 300 psi
- ICP = 800 psi
- FCP = 550 psi
- SCR = 500 psi

MD 0 | 1000’ | 2000’ | 3000’ | 4000’ | 5000’ |

TVD 0 | 1000’ | 2000’ | 2500’ | 3000’ | 3400’ |

**P circ (x)** = Pressure to circulate at depth of interest

For **x = 3000 ft TVD (4000 ft MD)**

= [500 + (50 x .8)] + [300 – (300 x .8823)]

= (500 + 40 ) + (300 – 265 )

= 540 + 35

= 575 psi

The equivalent using Vertical Step Down calculation = 600 psi

#### TRIP MARGIN

Approximate Mud Wt. value to be added after killing a kick.

Yield Point of Mud = 14

Hole Diameter (Dh) = 12¼”

Pipe Outside Diameter (dp) = 5”

**TRIP MARGIN**, ppg

= 0.164 ppg

**PSI/BARREL**

In well control formulas, A factor represents the pressure exerted by 1 barrel of mud in the annulus. (Can be used for inside Pipe by using **Pipe Capacity** instead of Annular Volume).

Mud Weight = 11 ppg

Annular Volume = .1215 bbls/ft

PSI/BARREL

= 4.7 psi/barrel

#### MUD TO BLEED DUE TO BUBBLE RISE (VOLUMETRIC)

Method of bringing gas to surface without SIDPP reading and unable to circulate. (Check **Volumetric Method**).

Pressure rise allowed while well is shut in (check **shut-in procedure**) = 100 psi

Current psi/barrel factor = 14 psi (see above **drilling formulas**) VOLUME TO BLEED, bbls

= 7 barrels

- If SICP = 800 psi, Allow 50 to 100 psi for Safety.
- Let SICP rise with well shut-in due to gas migration to 800 + Safety, e.g. 875 psi.
- Allow SICP to continue to rise to 875 + 100 = 975 psi.
- At 975 psi carefully manipulate choke to maintain 975 psi while bleeding off 7 barrels of mud (see above answer). Once 7 bbls have been bled, shut-in and allow SICP to rise to 975 + 100 = 1075. Again continue to hold at 1075 psi while bleeding 7 bbls.
- The process is repeated until gas arrives at the choke. Shut-in and remove gas by Lubricating Method.

#### COMBINED STRIPPING AND VOLUMETRIC WELL CONTROL FORMULA

The following calculations are used for stripping pipe in the hole when influx migration is a potential problem.

Vk | = | Kick Volume, bbls |

A1 | = | Open Hole Capacity, bbls/ft |

A2 | = | Drill Collar to Open Hole Capacity, bbls/ft |

V1 | = | Closed-End Displacement of 1 stand of drill pipe, bbls |

V2 | = | Volume to Bleed, bbls |

Mg | = = | Mud Gradient, psi/ft |

Ig | = | Influx Gradient, psi/ft |

SICP | = | Shut-in Casing Pressure, psi |

Pw | = | Chosen Working Pressure, psi |

Ps | = | Safety Pressure for Hydrostatic Pressure lost when BHA penetrates kick, psi |

Pchoke | = | Choke Pressure Reading, psi |

Step 1 Calculate Ps, psi

Step 2 Choose Pw – Between 50 and 200 psi

Step 3 Calculate V2 bbls

Step 4 Strip into the hole without bleeding mud, until SICP increases to Pchoke1.

**P _{choke1} = SICP + Ps + Pw**

Step 5 Continue stripping in the hole holding casing pressure constant at Pchoke1. This will require mud to be bled from the well. Fill pipe regularly.

Step 6 The amount of mud gained in the Trip Tank over and above the drill pipe closed-end displacement (V1) will be the effect of gas expansion. (Some rigs have a Stripping Tank to allow for bleed-off of V1 every stand).

Step 7 When gain in Trip Tank due to gas expansion equals V2, continue to strip with the choke closed to build casing pressure up to Pchoke2.

**P _{choke2} = P_{choke1} + Pw**

Step 8 Continue stripping in hole holding casing pressure constant at Pchoke2.

Step 9 Repeat Steps 6, 7 and 8 (increasing Pchoke by Pw each time V2 is measured in Trip Tank) until back to bottom.

Step 10 Kill well as per standard well control techniques.

## INFLUX HEIGHT/GRADIENT WELL CONTROL FORMULAS

### INFLUX HEIGHT

SIDPP | = | 800 psi |

SICP | = | 900 psi |

Collar Length | = | 538 ft |

Annular Volume around Collars | = | .0836 bbls/ft |

Annular Volume around Pipe | = | .1215 bbls/ft |

Mud Weight | = | 10.6 ppg |

Total Annular Volume around Collars

= Collar Length, ft x Collar Annular Volume, bbls/ft

= 538 ft x .0836 bbls/ft

= 45 barrels

#### If INFLUX is LESS THAN volume around collars e.g. 20 barrels

INFLUX HEIGHT, ft

= Influx Volume, bbls ÷ Annular Volume around Collar bbls/ft

= 20 ÷ .0836

= 239 ft

#### If INFLUX is GREATER THAN volume around collars e.g. 75 bbls

INFLUX HEIGHT, ft

= (( (75 − 45) ÷ .1215 ))+ 538

= 247 + 538

= 785 feet

Using example on previous page where:

#### INFLUX GRADIENT, psi/ft

Influx Volume = 20 bbls

Influx Height = 239 ft

= (10.6 x .052) – (( (900 – 800) ÷ 239 ))

= 0.1328 psi/ft

Gradient of .2 or less = Gas – Gradient of .4 or more = Water

In between could be oil or a mixture of oil, water, and gas.

## FRACTURE MUD WEIGHT/GRADIENT/PRESSURE FORMULAS

In well-control formulas, the fracture can be calculated using the pressure of **the Leak Off Test**.

**Float Shoe**TVD = 8000 ft- The leak-off test (LOT) was 2000 psi with 10.0 ppg mud in the hole.

#### FRACTURE MUD WEIGHT (MAX. EQUIV. MUD WT), ppg

= (LOT, psi ÷ Shoe TVD, ft ÷ *.0**5**2*) + Mud Wt, ppg

= (2000 ÷ 8000 ÷ .052) + 10.0

= 4.81 + 10.0

= 14.81 ppg

#### FRACTURE GRADIENT, psi/ft

= Fracture Mud Wt, ppg x *.052*

= 14.81 x .052

= .77 psi/ft

#### FRACTURE PRESSURE, psi

= Fracture Mud Wt, ppg x *.052 *x Shoe TVD, ft

= 14.81 x .052 x 8000 ft

= 6161 psi

#### Maximum pressure allowed on casing pressure gauge during operations.

(See above example)

Fracture Mud Wt, ppg | = | 14.81 |

Current Mud Wt, ppg | = | 10.6 ppg |

Shoe TVD, ft | = | 8000 ft |

#### MAASP, psi

**MAASP** is the maximum allowable annular surface pressure

= (Frac. M. Wt, ppg – Current M.Wt, ppg) x *.052 *x Shoe TVD, ft

= (14.81 – 10.6) x .052 x 8000

= 4.21 x .052 x 8000

= 1751 psi

#### MAXIMUM SURFACE CASING PRESSURE

Approximate max. pressure at Casing Pressure gauge during a well kill operation. (Occurs when the **well kick** of gas (check also **gas kick behavior and Migration**) is almost at the surface). Using **Wait and Weight**.

Formation Pressure (Fp) | = | 6000 psi (See page 4.1 for formula) |

Pit Gain | = | 20 bbls |

Kill Mud Weight | = | 11.5 ppg |

Surface Annular Volume | = | .1279 bbls/ft |

#### MAXIMUM CASING PRESSURE, psi

= 200 x 3.2848

= 657 psi

## GAS KICK ASSOCIATED FORMULAS

#### Approximate volume gain at the surface due to gas expansion when circulating out a kick.

Formation Pressure (Fp) | = | 6000 psi (see page 4.1 for formula). |

Pit Gain | = | 20 bbls |

Surface Annular Volume | = | .1279 bbls/ft |

Kill Mud Wt | = | 11.5 ppg |

Volume Increase, BBLs =

**= 4 x 36.5 = 146 bbls**

#### GAS EXPANSION FOR To AND ‘Z’

This formula is based on Boyles Law and Charles Law, incorporating temperature and compressibility effects.

To | = | F Deg + 460 |

Z | = | Variable |

P | = | psi + 14.7 |

#### GAS PERCOLATION RATE, ft/hr

How fast is gas percolating (migrating) up the hole.

SIDPP at time Zero | = | 700 psi |

SIDPP after 15 mins | = | 725 psi |

Mud Weight | = | 10.5 ppg |

GAS PERCOLATION RATE, ft/hr

Increase per 15 minute interval = 25 psi

Increase per hour = 4 x 25 psi = 100 psi

= 183 ft/hr

(SIDPP can be replaced with SICP)

## DRILLING MUD-ASSOCIATED CALCULATIONS IN WELL CONTROL

#### BARITE REQUIRED

Amount added to mud to obtain kill weight.

Original Mud Wt (W1) | = | 10 ppg |

Kill Mud Wt (W2) | = | 11.5 ppg |

Pit Volume | = | 840 barrels |

BARITE REQUIRED, pounds/barrel

= 94 pounds/barrel

TOTAL BARITE, pounds

= Mud Volume in Pits, bbls x Barite Required, lbs/bbl

= 840 x 94

= 78,960 pounds

#### VOLUME INCREASE/100 BARRELS OF MUD (due to adding barite)

= Barite Required, pounds/barrel ÷ 15

*= * 94 / 15

= 6.3 barrels/100 barrels of Mud (each 15 sacks of Barite added increases volume by approx 1 barrel).

#### TOTAL VOLUME after weight up

= (Barrels/ 100 barrels of Mud x Pit Volume ÷ 100 )+ Pit Volume

*= * (6.3 x 840 ÷ 100) + 840

= 5292 ÷ 100 + 840

= 53 + 840= 893 barrels

## WELL CONTROL EQUIPMENT RELATED FORMULAS

#### USABLE FLUID VOLUME

Gallons of usable fluid in a *single *Accumulator Bottle. Multiply by the number of bottles to get the total.

USABLE FLUID VOLUME, gals/bottle

API RP53 gives recommended pressures for various units:-

- Precharge Pressure is normally 1000 psi
- Minimum Operating is normally 1200 psi
- Accumulator Operating Pressure is 3000 psi for most current units
- Check API RP 53 for 500 psi units

#### MINIMUM OPERATING PRESSURE

Minimum Operating Pressure is the pressure required to operate a BOP Ram against full-rated Wellbore Pressure.

Note:- This calculated value of minimum operating pressure is normally applied in the Usable Fluid equation only when the result is greater than the API recommendation of 1200 psi

#### ACCUMULATOR VOLUME REQUIRED

GALLONS OF FLUID REQUIRED,

VR = Volume required to perform chosen functions, (either from API specs, client requirements or local regulations).

#### ACCUMULATOR PRECHARGE PRESSURE

A method of measuring average Accumulator Precharge Pressure by operating the unit with charge pumps switched off.

Accumulator Starting Pressure (Ps) | = | 3000 psi |

Accumulator Final Pressure (Pf) | = | 2200 psi |

Total Accumulator Volume | = | 180 gallons |

Volume of Fluid Removed | = | 20 gallons |

AVERAGE PRECHARGE PRESSURE, psi

= 20 ÷180 X (2200 x 3000) ÷ (3000-2200)

= 917 psi