2. Basic Calculations

Table of Content

1. Volumes and Strokes
2. Slug Calculations
3. Accumulator Capacity — Usable Volume Per Bottle
4. Bulk Density of Cuttings (Using Mud Balance)
5. Drill String Design (Limitations)
6. Ton-Mile (TM) Calculations
7. Cementing Calculations
8. Weighted Cement Calculations
9. Calculations for the Number of Sacks of Cement Required
10. Calculations for the Number of Feet to Be Cemented
11. Setting a Balanced Cement Plug
12. Differential Hydrostatic Pressure Between Cement in the Annulus and Mud Inside the Casing
13. Hydraulicing Casing
14. Depth of a Washout
15. Lost Returns — Loss of Overbalance
16. Stuck Pipe Calculations
17. Calculations Required for Spotting Pills
18. Pressure Required to Break Circulation

2.6 Ton-Mile (TM) Calculations

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. These include:
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

Round trip ton-miles (RT_TM)

${\mathrm{RT}}_{\mathrm{TM}}=\frac{\mathrm{Wp}\times D\times (\mathrm{Lp}+D)+(2\times D)(2\times \mathrm{Wb}+\mathrm{Wc})}{5280\times 2000}$

where RT_TM = round trip ton-miles
Wp = buoyed weight of drill pipe, lb/ft
D = depth of hole, ft
Lp = length of one stand of drill pipe, (aye), ft
Wb = weight of travelling block assembly, lb
Wc = buoyed weight of drill collars in mud minus the buoyed weight of the same length of drill pipe, lb
2000 = number of pounds in one ton
5280 = number of feet in one mile

Example: Round trip ton-miles
Mud weight = 9.6 ppg
Average length of one stand = 60 ft (double)
Drill pipe weight = 13.3 lb/ft
Measured depth = 4000 ft
Drill collar length = 300 ft
Travelling block assembly = 15,000 lb
Drill collar weight = 83 lb/ft

Solution:
a. Buoyancy factor:
BF = (65.5 − 9.6 ppg.) ÷ 65.5
BF = 0.8534
b. Buoyed weight of drill pipe in mud, lb/ft (Wp):
Wp = 13.3 lb/ft × 0.8534
Wp = 11.35 lb/ft
c. Buoyed weight of drill collars in mud minus the buoyed weight of the same length of drill pipe, lb (Wc):
Wc = (300 × 83 × 0.8534) — (300 × 13.3 × 0.8534)
Wc = 21,250 − 3,405
Wc = 17,845 lb
${\mathrm{RT}}_{\mathrm{TM}}=\frac{11.35\times 4000\times (60+4000)+(2\times 4000)\times (2\times 15000+17845)}{5280\times 2000}$
${\mathrm{RT}}_{\mathrm{TM}}=\frac{11.35\times 4000\times 4060+8000\times (30000+17845)}{5280\times 2000}$
${\mathrm{RT}}_{\mathrm{TM}}=\frac{11.35\times 4000\times 4060+8000\times 47845}{10560000}$
${\mathrm{RT}}_{\mathrm{TM}}=\frac{184324000+382760000}{10560000}$
RT_TM = 53.7

Drilling or “connection” ton-miles

The ton-miles of work performed in drilling operations is expressed in terms of work performed in making round trips. These are the actual ton-miles of work in drilling down the length of a section of drill pipe (usually approximately 30 ft) plus picking up, connecting, and starting to drill with the next section.

To determine connection or drilling ton-miles, take 3 times (ton-miles for current round trip minus ton-miles for previous round trip):

Td = 3 × (T2 − T1)

where Td = drilling or “connection” ton-miles
T2 = ton-miles for one round trip — depth where drilling stopped before coming out of hole.
T1 = ton-miles for one round trip — depth where drilling started.

Example: Ton-miles for trip @ 4600 ft = 64.6
Ton-miles for trip @ 4000 ft = 53.7
Td = 3 × (64.6 − 53.7)
Td = 3 × 10.9
Td = 32.7 ton-miles

Ton-miles during coring operations

The ton-miles of work performed in coring operations, as for drilling operations, is expressed in terms of work performed in making round trips.

To determine ton-miles while coring, take 2 times 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:

Tc = 2 × (T4 − T3)

where Tc = ton-miles while coring
T4 = ton-miles for one round trip — depth where coring stopped before coming out of hole
T3 = ton-miles for one round trip — depth where coring started after going in hole

Ton-miles setting casing

The calculations of the ton-miles for the operation of setting casing should be determined as for drill pipe, but with the buoyed weight of the casing being used, and with the result being multiplied by one-half, because setting casing is a one-way (1/2 round trip) operation. Tonmiles for setting casing can be determined from the following formula:

$\mathrm{Tc}=\frac{\mathrm{Wp}\times D\times (\mathrm{Lcs}+D)+D\times \mathrm{Wb}}{5280\times 2000}\times 0.5$

where Tc = ton-miles setting casing
Wp = buoyed weight of casing, lb/ft
Lcs = length of one joint of casing, ft
Wb = weight of travelling block assembly, lb

Ton-miles while making short trip

The ton-miles of work performed in short trip operations, as for drilling and coring operations, is also expressed in terms of round trips. Analysis shows that the ton-miles of work done in making a short trip is equal to the difference in round trip ton-miles for the two depths in question.

Tst = T6 − T5

where Tst = ton-miles for short trip
T6 = ton-miles for one round trip at the deeper depth, the depth of the bit before starting the short trip.
T5 = ton-miles for one round trip at the shallower depth, the depth that the bit is pulled up to.

⬆ Table of Content