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

2.10 Calculations for the Number of Feet to Be Cemented

If the number of sacks of cement is known, use the following:

Step 1 Determine the following capacities:

a. Annular capacity, ft³/ft:

${\mathrm{Annular\; capacity,\; ft}}^3\text{/ft}=\frac{{\mathrm{Dh,\; in.}}^2-{\mathrm{Dp,\; in.}}^2}{183.35}$

b. Casing capacity, ft³/ft:

${\mathrm{Casing\; capacity,\; ft}}^3\text{/ft}=\frac{{\mathrm{ID,\; in.}}^2}{183.35}$

Step 2 Determine the slurry volume, ft³

Slurry vol, ft³ = number of sacks of cement to be used × slurry yield, ft³/sk

Step 3 Determine the amount of cement, ft³, to be left in casing:

Cement in casing, ft³ = (feet of casing — setting depth of cementing tool, ft) × (casing capacity, ft³/ft) ÷ excess

Step 4 Determine the height of cement in the annulus — feet of cement:

Feet = (slurry vol, ft³ − cement remaining in casing, ft³) ÷ (annular capacity, ft³/ft) ÷ excess

Step 5 Determine the depth of the top of the cement in the annulus:

Depth, ft = casing setting depth, ft − ft of cement in annulus

Step 6 Determine the number of barrels of mud required to displace the cement:

Barrels = feet drill pipe × drill pipe capacity, bbl/ft

Step 7 Determine the number of strokes required to displace the cement:

Strokes = bbl required to displace cement ÷ pump output, bbl/stk

Example:
From the data listed below, determine the following:
1. Height, ft, of the cement in the annulus
2. Amount, ft3, of the cement in the casing
3. Depth, ft, of the top of the cement in the annulus
4. Number of barrels of mud required to displace the cement
5. Number of strokes required to displace the cement
Data:
Casing setting depth = 3000 ft
Hole size = 17-1/2 in.
Casing — 54.5 lb/ft = 13-3/8 in.
Casing ID = 12.615 in.
Drill pipe (5.0 in. — 19.5 lb/ft) = 0.01776 bbl/ft
Pump (7 in. by 12 in. triplex @ 95% eff.) = 0.136 bbl/stk
Cementing tool (number of feet above shoe) = 100 ft
Cementing program:
NEAT cement = 500 sk
Slurry yield = 1.15 ft3/sk
Excess volume = 50%

Step 1 Determine the following capacities:

a. Annular capacity, ft³/ft:

${\mathrm{Annular\; capacity,\; ft}}^3\text{/ft}=\frac{{17.5}^2-{13.375}^2}{183.35}$
Annular capacity = 0.6946 ft³/ft

b. Casing capacity, ft³/ft:

${\mathrm{Casing\; capacity,\; ft}}^3\text{/ft}=\frac{{12.615}^2}{183.35}$
Casing capacity = 0.8679 ft³/ft

Step 2 Determine the slurry volume, ft³:

Slurry vol, ft³ = 500 sk × 1.15 ft³/sk
Slurry vol, ft³ = 575 ft³

Step 3 Determine the amount of cement, ft³, to be left in casing:

Cement in casing, ft³ = (3000 ft − 2900 ft) × 0.8679 ft³/ft
Cement in casing, ft³ = 86.79 ft³

Step 4 Determine the height, ft, of the cement in the annulus:

Height of cement in annulus, ft = (575 ft³ − 86.79 ft³) ÷ 0.6946 ft³/ft ÷ 1.5
Height of cement in annulus, ft = 468.58 ft

Step 5 Determine the depth, ft, of the top of the cement in the annulus:

Depth, ft = 3000 ft − 468.58 ft
Depth, ft = 2531.42 ft

Step 6 Determine the number of barrels of mud required to displace the cement:

Barrels = 2900 ft × 0.01776 bbl/ft
Barrels = 51.5

Step 7 Determine the number of strokes required to displace the cement:

Strokes = 51.5 bbl ÷ 0.136 bbl/stk
Strokes = 379

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