{
  "version": 1,
  "topic": "MB05",
  "title": "Gas expansion factor versus gas formation volume factor",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Complementary volume factors",
    "premise": "Fixed reservoir gas volume 1,000 ft³; Bg uses reservoir ft³/scf throughout.",
    "formula": "Eg = 1/Bg; standard volume = Vres/Bg = Vres Eg",
    "variables": "The reciprocal units are scf/reservoir ft³. The site's separate field correlations use rounded coefficients and can differ slightly from an exact reciprocal.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Bg (reservoir ft³/scf) = 0.005",
        "explanation": "Fixed reservoir gas volume 1,000 ft³; Bg uses reservoir ft³/scf throughout."
      },
      {
        "label": "Select the relation",
        "calculation": "Eg = 1/Bg; standard volume = Vres/Bg = Vres Eg",
        "explanation": "The reciprocal units are scf/reservoir ft³. The site's separate field correlations use rounded coefficients and can differ slightly from an exact reciprocal."
      },
      {
        "label": "Substitute the values",
        "calculation": "1/0.005 = 200 scf/ft³; 1,000/0.005 = 200,000 scf",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Expansion factor (scf/reservoir ft³) = 200; Standard volume (scf) = 200000",
        "explanation": "Exact reciprocity requires complementary units and the same state definitions."
      }
    ],
    "result": "Expansion factor (scf/reservoir ft³) = 200; Standard volume (scf) = 200000",
    "interpretation": "Exact reciprocity requires complementary units and the same state definitions.",
    "control": "Bg (reservoir ft³/scf)",
    "columns": [
      "Bg (reservoir ft³/scf)",
      "Expansion factor (scf/reservoir ft³)",
      "Standard volume (scf)"
    ],
    "rows": [
      [
        0.002,
        500,
        500000
      ],
      [
        0.004,
        250,
        250000
      ],
      [
        0.005,
        200,
        200000
      ],
      [
        0.008,
        125,
        125000
      ],
      [
        0.01,
        100,
        100000
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Bg (reservoir ft³/scf) = 0.002. Expansion factor (scf/reservoir ft³): 500; Standard volume (scf): 500000.",
      "Bg (reservoir ft³/scf) = 0.004. Expansion factor (scf/reservoir ft³): 250; Standard volume (scf): 250000.",
      "Bg (reservoir ft³/scf) = 0.005. Expansion factor (scf/reservoir ft³): 200; Standard volume (scf): 200000.",
      "Bg (reservoir ft³/scf) = 0.008. Expansion factor (scf/reservoir ft³): 125; Standard volume (scf): 125000.",
      "Bg (reservoir ft³/scf) = 0.01. Expansion factor (scf/reservoir ft³): 100; Standard volume (scf): 100000."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Expansion factor (scf/reservoir ft³) without rounding intermediate values.",
        "answer": "1/0.005 = 200 scf/ft³; 1,000/0.005 = 200,000 scf. Expansion factor (scf/reservoir ft³) = 200. Exact reciprocity requires complementary units and the same state definitions."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Bg (reservoir ft³/scf) changes from 0.002 to 0.01. Other controls remain as stated in the premise. Expansion factor (scf/reservoir ft³) changes from 500 to 100."
      },
      {
        "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. The reciprocal units are scf/reservoir ft³. The site's separate field correlations use rounded coefficients and can differ slightly from an exact reciprocal. Exact reciprocity requires complementary units and the same state definitions."
      }
    ]
  },
  "recorded": null
}