{
  "version": 1,
  "topic": "CE10",
  "title": "How much a small washout changes a synthetic cement estimate",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Hole diameter propagated to volume and sacks",
    "premise": "5 in casing, 1,000 ft measured length, 20% volume excess, yield 1.32 ft³/sk; hole diameter varies.",
    "formula": "Vplan = Va × 1.20; N = Vplan × (42 × 231/1728)/1.32",
    "variables": "Geometry uses the rounded library field coefficient. The barrel conversion uses 42 US gallons and 231 in³/US gal.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Hole diameter (in) = 8.5",
        "explanation": "5 in casing, 1,000 ft measured length, 20% volume excess, yield 1.32 ft³/sk; hole diameter varies."
      },
      {
        "label": "Select the relation",
        "calculation": "Vplan = Va × 1.20; N = Vplan × (42 × 231/1728)/1.32",
        "explanation": "Geometry uses the rounded library field coefficient. The barrel conversion uses 42 US gallons and 231 in³/US gal."
      },
      {
        "label": "Substitute the values",
        "calculation": "Va = 45.9 bbl; planned = 55.08 bbl; 55.08 × 5.614583333/1.32 = 234.28125 sk; round to 235",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Geometry volume (bbl) = 45.9; Theoretical sacks (sk) = 234.28125; Whole sacks (sk) = 235",
        "explanation": "Diameter-squared geometry and final integer rounding are different sources of the response."
      }
    ],
    "result": "Geometry volume (bbl) = 45.9; Theoretical sacks (sk) = 234.28125; Whole sacks (sk) = 235",
    "interpretation": "Diameter-squared geometry and final integer rounding are different sources of the response.",
    "control": "Hole diameter (in)",
    "columns": [
      "Hole diameter (in)",
      "Geometry volume (bbl)",
      "Theoretical sacks (sk)",
      "Whole sacks (sk)"
    ],
    "rows": [
      [
        8.5,
        45.89999999999999,
        234.28124999999991,
        235
      ],
      [
        8.75,
        50.089285714285715,
        255.66406249999994,
        256
      ],
      [
        9,
        54.4,
        277.66666666666663,
        278
      ],
      [
        9.5,
        63.385714285714286,
        323.53124999999994,
        324
      ],
      [
        10,
        72.85714285714286,
        371.875,
        372
      ]
    ],
    "baseline": 0,
    "rowNotes": [
      "Hole diameter (in) = 8.5. Geometry volume (bbl): 45.9; Theoretical sacks (sk): 234.28125; Whole sacks (sk): 235.",
      "Hole diameter (in) = 8.75. Geometry volume (bbl): 50.0892857; Theoretical sacks (sk): 255.664062; Whole sacks (sk): 256.",
      "Hole diameter (in) = 9. Geometry volume (bbl): 54.4; Theoretical sacks (sk): 277.666667; Whole sacks (sk): 278.",
      "Hole diameter (in) = 9.5. Geometry volume (bbl): 63.3857143; Theoretical sacks (sk): 323.53125; Whole sacks (sk): 324.",
      "Hole diameter (in) = 10. Geometry volume (bbl): 72.8571429; Theoretical sacks (sk): 371.875; Whole sacks (sk): 372."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Geometry volume (bbl) without rounding intermediate values.",
        "answer": "Va = 45.9 bbl; planned = 55.08 bbl; 55.08 × 5.614583333/1.32 = 234.28125 sk; round to 235. Geometry volume (bbl) = 45.9. Diameter-squared geometry and final integer rounding are different sources of the response."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Hole diameter (in) changes from 8.5 to 10. Other controls remain as stated in the premise. Geometry volume (bbl) changes from 45.9 to 72.8571429."
      },
      {
        "question": "What would be needed to apply this example to a different physical system?",
        "answer": "Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. Geometry uses the rounded library field coefficient. The barrel conversion uses 42 US gallons and 231 in³/US gal. Diameter-squared geometry and final integer rounding are different sources of the response."
      }
    ]
  },
  "recorded": null
}