Drilling Formulas and Drilling Calculations

You may have heard about gas show, connection gas and trip gas. What are differences of those term?

Gas show: It is gas that appears in drilling mud and it indicates the presence of gas zones or soluble gas in oil.

Connection gas: It is relatively small amount of gas that enters well when mud pump is stopped because ECD (equivalent circulating density) decreases when stop pumping. Connection gas indicates that mud weight in hole is less than formation pressure.

The difference of gas show and connection gas: If there is connection gas, gas shown in a mud logger screen increases and decreases sharply like small gas peak; however, gas show demonstrates the smoother curve than connection gas. Lag stroke, lag time are used to  find where the location of connection gas or gas show comes from. Especially, when the connection gas presents, lag time of gas peak will be relative to the time when pumps are off.

Trip gas: It is gas entering to well bore when tripping out of hole. There are several factors as balled-up bit,  fast pulling out rate, bigger diameter BHA, etc can create swab effect that can reduce hydrostatic pressure while tripping out of hole. If too much reduction in hydrostatic pressure is present, formation gas can influx into the well bore, called “Trip gas”.

Ref book: Well Control Book

Positive kick (wellbore influx) indications mean indications showing almost 100% kick (wellbore influx) into wellbore.

Positive Kick Indicators While drilling

1. Increase in flow show – Without any increasing in flow rate in, increase in return flow indicates something coming into wellbore while drilling. Therefore, flow show instrument provided by the rigs or service companies must be checked and calibrated frequently.

2. Increase of active pit system (Pit gain) - Because drilling fluid system on the rig is a closed system, increasing in flow show without adjusting flow rate in will cause pit gain in a pit system. Nowadays, with high technology sensors, detecting change in pit level is easily accomplished at the rig site. However, visually check the pit level is importance as well for double checking figure from the sensors. Sometimes, change in pit level may be detected after the increase in flow show because it takes more time to accumulate volume enough to be able to detect by pit sensors.

3. Continue flowing while the pumps are off – When pumps are turned off, bottom hole pressure will decrease due to loss of equivalent circulating density (ECD). If there is any flow coming after pumps off, it indicates formation influx into wellbore.

Positive Kick Indicators While Tripping

There are 2 positive kick indicators while tripping as listed below;

1. Trip log deviation such as short fill up while tripping out and excess pit gain while tripping in. For tripping operation, it is very important to have a filling system via trip tank that provides continuous hole fill all time. With utilizing that system, we can compare fluid that is filled in or returned from wellbore with steel volume of tubular (drill pipe, drill collar, BHA, tubing, casing, etc). If drilling fluid volume is less than theoretical pipe displacement while tripping out or more return fluid while running in, you need to flow check and monitor the well.

o If flow check indicates wellbore influx, crew must quickly shut the well in.

o If flow check does not show any influx, drill string must be run back to bottom in order to circulate at least bottom up to ensure hole condition.

2. Positive flow when pipe is static. Every time that pipe in static condition. Trip tank with correct filling system must be monitored all time by both rig personnel and mud logger. If volume in trip tank increases, personnel must confirm flow check and prepare to shut the well in.

Ref book: Well Control Book

The ton-miles of work performed in short trip operation is also in term of round trips.

The ton-miles of work done in making a short trip is equal to the difference between round ton-miles of end depth and starting depth. The formula for short trip ton-miles is listed below;

Tst = T6 – T5

Where; Tst = ton-miles for short trip
T6 = ton-miles for one round trip at the deeper depth
T5 = ton-miles for one round trip at the shallower depth

Example;

Please determine short trip ton-miles from 8000 ft to 8050 ft
Ton-miles @ 8050 ft = 200
Ton-miles @ 8000 ft = 190
Tst = (200 – 190)
Tst = 10 ton-miles

Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition

For the setting casing operation, the ton-miles calculation of this operation is similar to round trip ton-miles calculation. Nevertheless, buoyed weight of the casing will be used into calculation instead of buoyed weight of drill pipe and with the result will be multiplied by 0.5, because setting casing is just only one-way operation (1/2 round trip).

Ton-miles for setting casing can be determined from the following formula:

Tc = {Wp x D x (Lcs + D) + D x Wb} x 0.5 ÷ (5280 x 2000)

Where; Tc = ton-miles setting casing
Wp = buoyed weight of casing in lb/ft
Lcs = length of one joint of casing in ft
Wb = weight of travelling block assembly in lb
D = depth of casing in ft
2000 = number of pounds in one ton
5280 = number of feet in one mile

Example: Ton-Miles for Setting Casing

Mud weight = 10.0 ppg
Casing weight = 25.0 lb/ft
Depth of casing = 5200 ft
Travelling block assembly = 95,000 lb
Length of one joint of casing = 42 ft

Solution:

a) Buoyancy factor:
BF = (65.5 – 10.0) ÷ 65.5
BF = 0.8473

b) Buoyed weight of casing in mud, lb/ft (Wp):
Wp = 25.0 lb/ft x 0.8473
Wp = 21.18 lb/ft

c) Casing ton-miles
Tc = {21.18 x 5,200 x (42 + 5,200) + 5,200 x 95,000} x 0.5 ÷ (5280 x 2000)
Tc = 50.73 tone-miles

Ton-Mile (TM) for Setting Casing Calculation Sheet

Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition

For coring operation, the ton-miles calculation is also expressed in terms of work in round trip ton-miles. In order to determine the coring ton-miles, you need to figure out ton-miles for one round trip at the depth where coring stopped minus ton-miles for one round trip at the depth where coring began and the multiplied that value by 2.

The formula for calculating ton-mile for coring operation is shown below;

Tc = 2 x (T4 – T3)

Where;

Tc = ton-miles for coring operation
T4 = ton-miles for one round trip at depth where coring operation stopped before coming out of hole
T3 = ton-miles for one round trip at depth where coring get started

Example – Please determine coring ton-mils from 8000 ft to 8050 ft.

Ton-miles @ 8050 ft (end of coring operation) = 200
Ton-miles for trip @ 8000 ft (start of coring operation) = 190

Tc = 2 x (T4 – T3)
Tc = 2 x (200 – 190)
Tc = 20 ton-miles

Ton-Mile (TM) for Coring Operation Calculation Sheet

Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition

Drilling or Connection ton-miles is  ton-miles of work in drilling operations. These are the actual ton-miles of work in drilling down the length of a section of drill pipe, usually around +/- 31 ft, plus picking up, connecting, and starting to drill again. In order to figure out connection or drilling ton-miles, it takes 3 times of ton-miles for current round trip minus ton-miles for previous round trip. The formula for calculating drilling ton mile is listed below;

Td = 3 x (T2 – T1)
Where;
Td = Ton-miles for drilling
T2 = Ton-miles for one round trip of last depth before coming out of hole.
T1 = Ton-miles for one round trip of first depth that drilling is started.

Example;
Please determine drilling tome-miles from 8000 ft to 9000 ft.
Ton-miles for trip @ 9000 ft = 230
Ton-miles for trip @ 8000 ft = 195
Td = 3 x (T2 – T1)
Td = 3 x (230 – 195)
Td = 3 x 35
Td = 105 ton-miles
Download the Excel sheet for calculating drilling or connection ton-mile.

Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition

All types of ton-mile service should be calculated and recorded in order to obtain a true picture of the total service received from the rotary drilling line. There are several types of ton miles as follows;

1. Round trip ton-miles
2. Drilling or “connection” ton-miles
3. Coring ton-miles
4. Ton-miles setting casing
5. Short-trip ton-miles

For this time, I will show how to calculate round trip ton-mile.

Round Trip Ton-Miles Calculation

The formula for round trip ton-miles is listed below;

RTTM = (Wp x D x (Lp + D) + (2 x D) x (2 x Wb + Wc)) ÷ (5280 x 2000)

where
RTTM = Round Trip Ton-Miles
Wp = buoyed weight of drill pipe in lb/ft
D = hole measured depth in ft
Lp = Average length per stand of drill pipe in ft
Wb = weight of travelling block in lb
Wc = buoyed weight of BHA (drill collar + heavy weight drill pipe + BHA) in mud minus the buoyed weight of the same length of drill pipe in lb
** If you have BHA (mud motor, MWD, etc) and HWDP, you must add those weight into calculation as well not just only drill collar weight. **
2000 = number of pounds in one ton
5280 = number of feet in one mile

Example: Round trip ton-miles

Mud weight = 10.0 ppg
Average length per stand = 94 ft
Drill pipe weight = 13.3 lb/ft
Hole measure depth = 5500 ft
Drill collar length = 120 ft
Drill collar weight = 85 lb/ft
HWDP length = 49 lb/ft
HWDP weight = 450 ft
BHA weight from directional driller = 8,300 lb
BHA length = 94 ft
Travelling block assembly = 95,000 lb

Solution:

a) Buoyancy factor:
BF = (65.5 – 10.0) ÷ 65.5
BF = 0.847

b) Buoyed weight of drill pipe in mud, lb/ft (Wp):
Wp = 13.3 lb/ft x 0.847
Wp = 11.27 lb/ft

c) buoyed weight of BHA (drill collar + heavy weight drill pipe + BHA) in mud minus the buoyed weight of the same length of drill pipe in lb (Wc):

Wc = {[(120x85) + (49x450) + (8300)] x 0.847} – [(120+450+94) x13.3x 0.847]
Wc = 26,866 lb

Round trip ton-miles = [(11.27 x 5500 x (94+ 5500)) + (2 x 5500) x (2 x 95000 + 26,866)] ÷ (5280 x 2000)
RTTM = 258.75 ton-mile

Please find the excel sheet for round trip ton-miles calculation via click this link.
Ref book: Formulas and Calculations for Drilling, Production and Workover, Second Edition