{
  "version": 1,
  "topic": "MB11",
  "title": "How input rounding propagates into a volumetric estimate",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Porosity rounding propagated through volumetrics",
    "premise": "160 acres, 50 ft net pay, Sw 0.25, Bg 0.005 ft³/scf. Reference porosity 0.1537; rounding precision varies.",
    "formula": "Grounded/Greference = φrounded/0.1537",
    "variables": "Only decimal rounding changes. This is arithmetic error, not a geological uncertainty distribution.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Porosity decimal places = 4",
        "explanation": "160 acres, 50 ft net pay, Sw 0.25, Bg 0.005 ft³/scf. Reference porosity 0.1537; rounding precision varies."
      },
      {
        "label": "Select the relation",
        "calculation": "Grounded/Greference = φrounded/0.1537",
        "explanation": "Only decimal rounding changes. This is arithmetic error, not a geological uncertainty distribution."
      },
      {
        "label": "Substitute the values",
        "calculation": "Reference G = 8034206400 scf at φ = 0.1537; rounded φ at four decimals remains 0.1537, so error = 0%",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Rounded gas in place (scf) = 8034206400; Relative error (%) = 0; Rounded porosity = 0.1537",
        "explanation": "Display precision does not create geological knowledge, but premature rounding can add avoidable arithmetic error."
      }
    ],
    "result": "Rounded gas in place (scf) = 8034206400; Relative error (%) = 0; Rounded porosity = 0.1537",
    "interpretation": "Display precision does not create geological knowledge, but premature rounding can add avoidable arithmetic error.",
    "control": "Porosity decimal places",
    "columns": [
      "Porosity decimal places",
      "Rounded gas in place (scf)",
      "Relative error (%)",
      "Rounded porosity"
    ],
    "rows": [
      [
        1,
        10454400000,
        30.123617436564732,
        0.2
      ],
      [
        2,
        7840800000,
        -2.407286922576457,
        0.15
      ],
      [
        3,
        8049888000,
        0.19518542615484247,
        0.154
      ],
      [
        4,
        8034206400,
        0,
        0.1537
      ],
      [
        5,
        8034206400,
        0,
        0.1537
      ]
    ],
    "baseline": 3,
    "rowNotes": [
      "Porosity decimal places = 1. Rounded gas in place (scf): 10454400000; Relative error (%): 30.1236174; Rounded porosity: 0.2.",
      "Porosity decimal places = 2. Rounded gas in place (scf): 7840800000; Relative error (%): -2.40728692; Rounded porosity: 0.15.",
      "Porosity decimal places = 3. Rounded gas in place (scf): 8049888000; Relative error (%): 0.195185426; Rounded porosity: 0.154.",
      "Porosity decimal places = 4. Rounded gas in place (scf): 8034206400; Relative error (%): 0; Rounded porosity: 0.1537.",
      "Porosity decimal places = 5. Rounded gas in place (scf): 8034206400; Relative error (%): 0; Rounded porosity: 0.1537."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Rounded gas in place (scf) without rounding intermediate values.",
        "answer": "Reference G = 8034206400 scf at φ = 0.1537; rounded φ at four decimals remains 0.1537, so error = 0%. Rounded gas in place (scf) = 8034206400. Display precision does not create geological knowledge, but premature rounding can add avoidable arithmetic error."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Porosity decimal places changes from 1 to 5. Other controls remain as stated in the premise. Rounded gas in place (scf) changes from 10454400000 to 8034206400."
      },
      {
        "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. Only decimal rounding changes. This is arithmetic error, not a geological uncertainty distribution. Display precision does not create geological knowledge, but premature rounding can add avoidable arithmetic error."
      }
    ]
  },
  "recorded": null
}