Practice and answer pack
Multi interval cement volume worksheet with worked answers
Use this worksheet to build a multi-interval volume ledger, assign excess by interval, convert to sacks and calculate water from the prepared batch.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Prepare the interval sheet
Record top and bottom MD, outer boundary ID or hole diameter, inner string OD and the slurry design assigned to each interval. Add internal volumes such as a shoe track as separate rows.
Check that intervals neither overlap nor leave an unintended gap. The geometry sketch should make it possible to identify each volume without reading the arithmetic.
Work in one volume unit before combining
Calculate each entry in barrels, apply only its intended excess and then sum compatible slurry demand. Convert the combined demand to the laboratory yield unit before calculating sacks.
For independently mixed designs, repeat the conversion and rounding by batch. The answer should include both theoretical and whole-sack demand rather than just a final integer.
Audit conservation and recipe consistency
Reverse-check the rounded batch by multiplying sacks by yield. Prepared volume should cover the stated demand. Calculate ingredient water from the same whole sacks and matched recipe.
The printable exercises use synthetic geometry. They test arithmetic and bookkeeping; they do not simulate displacement, cement placement, losses or the pressure schedule.
Explore the example
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Shoe-track length (ft) = 40. Track volume (bbl): 0.710469177; Total geometry volume (bbl): 80.6711835.
- Track volume (bbl)
- Total geometry volume (bbl)
Worked example
Two annuli and one internal shoe track
Annulus A: 8.5/5 in × 1,000 ft; B: 7.75/5 in × 1,000 ft. Shoe-track ID 4.276 in. No excess is added in this geometry-only ledger.
Relation and unit basis
Vtotal = VA + VB + π ID² Ltrack/(4 × 808.5)
Annular entries use the library's rounded 0.7854 coefficient; the internal track uses π/4. All lengths are measured feet.
1. Define the baseline
Shoe-track length (ft) = 40
Annulus A: 8.5/5 in × 1,000 ft; B: 7.75/5 in × 1,000 ft. Shoe-track ID 4.276 in. No excess is added in this geometry-only ledger.
2. Select the relation
Vtotal = VA + VB + π ID² Ltrack/(4 × 808.5)
Annular entries use the library's rounded 0.7854 coefficient; the internal track uses π/4. All lengths are measured feet.
3. Substitute the values
VA = 45.9; VB = 34.0607143; track = π/4 × 4.276² × 40/808.5 bbl; add the three nonoverlapping entries
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Track volume (bbl) = 0.710469177; Total geometry volume (bbl) = 80.6711835
The internal track requires ID, while each annulus uses outer-boundary ID and inner-string OD.
Result and interpretation
Track volume (bbl) = 0.710469177; Total geometry volume (bbl) = 80.6711835
The internal track requires ID, while each annulus uses outer-boundary ID and inner-string OD.
Start with the three-entry worked ledger, then solve the additional questions and reveal answers individually.
Exact scenario data
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Shoe-track length (ft) | Track volume (bbl) | Total geometry volume (bbl) |
|---|---|---|
| 0 | 0 | 79.96071 |
| 20 | 0.3552346 | 80.31595 |
| 40 | 0.7104692 | 80.67118 |
| 60 | 1.065704 | 81.02642 |
| 100 | 1.776173 | 81.73689 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Practice problems and answer key
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. What is the fastest dimensional check before dividing slurry volume by yield?
Show the worked answer
The volume numerator and the volume part of yield must match, such as ft³ divided by ft³/sk, leaving sacks.
2. Reproduce the baseline Track volume (bbl) without rounding intermediate values.
Show the worked answer
VA = 45.9; VB = 34.0607143; track = π/4 × 4.276² × 40/808.5 bbl; add the three nonoverlapping entries. Track volume (bbl) = 0.710469177. The internal track requires ID, while each annulus uses outer-boundary ID and inner-string OD.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Shoe-track length (ft) changes from 0 to 100. Other controls remain as stated in the premise. Track volume (bbl) changes from 0 to 1.77617294.
4. What would be needed to apply this example to a different physical system?
Show the worked answer
Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. Annular entries use the library's rounded 0.7854 coefficient; the internal track uses π/4. All lengths are measured feet. The internal track requires ID, while each annulus uses outer-boundary ID and inner-string OD.
5. Convert 55.08 bbl slurry to ft³ and theoretical sacks at 1.32 ft³/sk.
Show the worked answer
55.08 × 42 × 231/1728 = 309.25125 ft³; /1.32 = 234.28125 sk, rounded upward to 235 for one batch.
6. How much mixing water does that 235-sack batch need at 6.3 US gal/sk?
Show the worked answer
235 × 6.3 = 1,480.5 US gal. The water uses whole prepared sacks.
Before using the result
- Use one nonoverlapping geometry ledger.
- Assign excess and slurry design by interval.
- Reverse-check prepared volume and mixing water.
The internal track requires ID, while each annulus uses outer-boundary ID and inner-string OD.
Continue learning
Start with the broader workflow guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.