{
  "version": 1,
  "topic": "GM06",
  "title": "Leakoff spurt loss and fracture efficiency",
  "createdAt": "2026-10-24",
  "case": {
    "title": "A simplified injected-fluid ledger",
    "premise": "Injected volume fixed at 3,000 ft³; AL = 20,000 ft², CL = 0.003 ft/√min and Sp = 0.02 ft. Other storage terms are excluded.",
    "formula": "Vretained = Vinjected − Vleakoff; efficiency = Vretained/Vinjected",
    "variables": "Fixed simultaneous area exposure is assumed. This does not solve fracture propagation or pressure-dependent leakoff.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Exposure (min) = 60",
        "explanation": "Injected volume fixed at 3,000 ft³; AL = 20,000 ft², CL = 0.003 ft/√min and Sp = 0.02 ft. Other storage terms are excluded."
      },
      {
        "label": "Select the relation",
        "calculation": "Vretained = Vinjected − Vleakoff; efficiency = Vretained/Vinjected",
        "explanation": "Fixed simultaneous area exposure is assumed. This does not solve fracture propagation or pressure-dependent leakoff."
      },
      {
        "label": "Substitute the values",
        "calculation": "At 60 min: leakoff = 1,329.516003 ft³; retained = 3,000 − 1,329.516003; efficiency = retained/3,000",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Leakoff volume (ft³) = 1329.516; Retained volume (ft³) = 1670.484; Efficiency (fraction) = 0.556827999",
        "explanation": "Efficiency is conditional on this complete stated volume ledger, not CL alone."
      }
    ],
    "result": "Leakoff volume (ft³) = 1329.516; Retained volume (ft³) = 1670.484; Efficiency (fraction) = 0.556827999",
    "interpretation": "Efficiency is conditional on this complete stated volume ledger, not CL alone.",
    "control": "Exposure (min)",
    "columns": [
      "Exposure (min)",
      "Leakoff volume (ft³)",
      "Retained volume (ft³)",
      "Efficiency (fraction)"
    ],
    "rows": [
      [
        15,
        864.75800154489,
        2135.2419984551098,
        0.71174733281837
      ],
      [
        30,
        1057.2670690061993,
        1942.7329309938007,
        0.6475776436646002
      ],
      [
        60,
        1329.51600308978,
        1670.48399691022,
        0.5568279989700733
      ],
      [
        120,
        1714.534138012399,
        1285.465861987601,
        0.4284886206625337
      ],
      [
        240,
        2259.03200617956,
        740.9679938204399,
        0.24698933127348
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Exposure (min) = 15. Leakoff volume (ft³): 864.758002; Retained volume (ft³): 2135.242; Efficiency (fraction): 0.711747333.",
      "Exposure (min) = 30. Leakoff volume (ft³): 1057.26707; Retained volume (ft³): 1942.73293; Efficiency (fraction): 0.647577644.",
      "Exposure (min) = 60. Leakoff volume (ft³): 1329.516; Retained volume (ft³): 1670.484; Efficiency (fraction): 0.556827999.",
      "Exposure (min) = 120. Leakoff volume (ft³): 1714.53414; Retained volume (ft³): 1285.46586; Efficiency (fraction): 0.428488621.",
      "Exposure (min) = 240. Leakoff volume (ft³): 2259.03201; Retained volume (ft³): 740.967994; Efficiency (fraction): 0.246989331."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Leakoff volume (ft³) without rounding intermediate values.",
        "answer": "At 60 min: leakoff = 1,329.516003 ft³; retained = 3,000 − 1,329.516003; efficiency = retained/3,000. Leakoff volume (ft³) = 1329.516. Efficiency is conditional on this complete stated volume ledger, not CL alone."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Exposure (min) changes from 15 to 240. Other controls remain as stated in the premise. Leakoff volume (ft³) changes from 864.758002 to 2259.03201."
      },
      {
        "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. Fixed simultaneous area exposure is assumed. This does not solve fracture propagation or pressure-dependent leakoff. Efficiency is conditional on this complete stated volume ledger, not CL alone."
      }
    ]
  },
  "recorded": null
}