{
  "version": 1,
  "topic": "MB12",
  "title": "Reservoir volumetrics and material balance problem set",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Rock volume to standard gas inventory",
    "premise": "160 acres, 50 ft net pay, Sw = 0.25, Bg = 0.005 reservoir ft³/scf. Porosity varies.",
    "formula": "G = 43,560 A h φ(1 − Sw)/Bg",
    "variables": "A in acres, h in ft, φ and Sw as fractions; 43,560 converts acre-ft to ft³.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Porosity (fraction) = 0.15",
        "explanation": "160 acres, 50 ft net pay, Sw = 0.25, Bg = 0.005 reservoir ft³/scf. Porosity varies."
      },
      {
        "label": "Select the relation",
        "calculation": "G = 43,560 A h φ(1 − Sw)/Bg",
        "explanation": "A in acres, h in ft, φ and Sw as fractions; 43,560 converts acre-ft to ft³."
      },
      {
        "label": "Substitute the values",
        "calculation": "43,560 × 160 × 50 = 348,480,000 ft³; × 0.15 × 0.75 = 39,204,000 reservoir ft³; /0.005 = 7,840,800,000 scf",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Gas in place (scf) = 7840800000; Gas-filled pore volume (ft³) = 39204000",
        "explanation": "This is initial gas in place, without a recovery or reserves classification."
      }
    ],
    "result": "Gas in place (scf) = 7840800000; Gas-filled pore volume (ft³) = 39204000",
    "interpretation": "This is initial gas in place, without a recovery or reserves classification.",
    "control": "Porosity (fraction)",
    "columns": [
      "Porosity (fraction)",
      "Gas in place (scf)",
      "Gas-filled pore volume (ft³)"
    ],
    "rows": [
      [
        0.1,
        5227200000,
        26136000
      ],
      [
        0.125,
        6534000000,
        32670000
      ],
      [
        0.15,
        7840800000,
        39204000
      ],
      [
        0.175,
        9147599999.999998,
        45737999.99999999
      ],
      [
        0.2,
        10454400000,
        52272000
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Porosity (fraction) = 0.1. Gas in place (scf): 5227200000; Gas-filled pore volume (ft³): 26136000.",
      "Porosity (fraction) = 0.125. Gas in place (scf): 6534000000; Gas-filled pore volume (ft³): 32670000.",
      "Porosity (fraction) = 0.15. Gas in place (scf): 7840800000; Gas-filled pore volume (ft³): 39204000.",
      "Porosity (fraction) = 0.175. Gas in place (scf): 9147600000; Gas-filled pore volume (ft³): 45738000.",
      "Porosity (fraction) = 0.2. Gas in place (scf): 10454400000; Gas-filled pore volume (ft³): 52272000."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Gas in place (scf) without rounding intermediate values.",
        "answer": "43,560 × 160 × 50 = 348,480,000 ft³; × 0.15 × 0.75 = 39,204,000 reservoir ft³; /0.005 = 7,840,800,000 scf. Gas in place (scf) = 7840800000. This is initial gas in place, without a recovery or reserves classification."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Porosity (fraction) changes from 0.1 to 0.2. Other controls remain as stated in the premise. Gas in place (scf) changes from 5227200000 to 10454400000."
      },
      {
        "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. A in acres, h in ft, φ and Sw as fractions; 43,560 converts acre-ft to ft³. This is initial gas in place, without a recovery or reserves classification."
      }
    ]
  },
  "recorded": null
}