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

2.1 Volumes and Strokes

Drill string volume, barrels

$\mathrm{Barrels}=\frac{{\mathrm{ID,\; in.}}^2}{1029.4}\times \mathrm{pipe\; length}$

Annular volume, barrels

$\mathrm{Barrels}=\frac{{\mathrm{Dh,\; in.}}^2-{\mathrm{Dp,\; in.}}^2}{1029.4}\times \mathrm{pipe\; length}$

Strokes to displace: drill string, Kelly to shale shaker and Strokes annulus, and total circulation from Kelly to shale shaker.

Strokes = barrels ÷ pump output, bbl/stk

Example: Determine volumes and strokes for the following:
Drill pipe — 5.0 in. — 19.5 lb/f, Inside diameter = 4.276 in., Length = 9400 ft
Drill collars — 8.0 in., OD Inside diameter = 3.0 in., Length = 600 ft
Casing — 13-3/8 in. — 54.5 lb/f, Inside diameter = 12.615 in., Setting depth = 4500 ft
Pump data — 7 in. by 12 in. triplex, Efficiency = 95%, Pump output = 0.136 @ 95%, Hole size = 12-1/4 in.

Drill string volume

$\mathrm{Drill\; pipe\; volume,\; bbl}=\frac{{\mathrm{4.276\; in.}}^2}{1029.4}\times \mathrm{9400\; ft}$
Drill pipe volume = 166.94 bbl
$\mathrm{Drill\; collar\; volume,\; bbl}=\frac{{\mathrm{3.0\; in.}}^2}{1029.4}\times \mathrm{600\; ft}$
Drill collar volume = 5.24 bbl
Total drill string vol., bbl = 166.94 bbl + 5.24 bbl
Total drill string vol. = 172.18 bbl

Annular volume

$\mathrm{Drill\; collar\; /\; open\; hole,\; bbl}=\frac{{\mathrm{12.25\; in.}}^2-{\mathrm{8.0\; in.}}^2}{1029.4}\times \mathrm{600\; ft}$
Drill collar / open hole = 50.16 bbl
$\mathrm{Drill\; pipe\; /\; open\; hole,\; bbl}=\frac{{\mathrm{12.25\; in.}}^2-{\mathrm{5.0\; in.}}^2}{1029.4}\times \mathrm{4900\; ft}$
Drill pipe / open hole = 595.3 bbl
$\mathrm{Drill\; pipe\; /\; cased\; hole,\; bbl}=\frac{{\mathrm{12.615\; in.}}^2-{\mathrm{5.0\; in.}}^2}{1029.4}\times \mathrm{4500\; ft}$
Drill pipe / cased hole = 586.38 bbl
Total annular vol. = 50.16 + 595.3 + 586.38
Total annular vol. = 1231.84 bbl

Strokes

Surface to bit strokes: Strokes = drill string volume, bbl ÷ pump output, bbl/stk
Surface to bit strokes = 172.16 bbl ÷ 0.136 bbl/stk
Surface to bit strokes = 1266
Bit to surface (or bottoms-up strokes): Strokes = annular volume, bbl ÷ pump output, bbl/stk
Bit to surface strokes = 1231.84 bbl ÷ 0.136 bbl/stk
Bit to surface strokes = 9058
Total strokes required to pump from the Kelly to the shale shaker: Strokes = (drill string vol., bbl + annular vol., bbl) ÷ pump output, bbl/stk
Total strokes = (172.16 + 1231.84) ÷ 0.136
Total strokes = 1404 ÷ 0.136
Total strokes = 10,324

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