{
  "version": 1,
  "topic": "WC03",
  "title": "Gauge versus absolute pressure in petroleum calculations",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Gauge pressure converted to an absolute state",
    "premise": "Atmosphere is assumed 14.7 psia. The table isolates a pressure-reference conversion, not a weather or elevation model.",
    "formula": "Pabs = Pg + Patm; omitted fraction = Patm/Pabs",
    "variables": "Pabs in psia and Pg in psig; the error fraction applies to density only when T, Z and molecular weight are fixed.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Gauge pressure (psig) = 85.3",
        "explanation": "Atmosphere is assumed 14.7 psia. The table isolates a pressure-reference conversion, not a weather or elevation model."
      },
      {
        "label": "Select the relation",
        "calculation": "Pabs = Pg + Patm; omitted fraction = Patm/Pabs",
        "explanation": "Pabs in psia and Pg in psig; the error fraction applies to density only when T, Z and molecular weight are fixed."
      },
      {
        "label": "Substitute the values",
        "calculation": "85.3 + 14.7 = 100 psia; 14.7/100 × 100 = 14.7%",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Absolute pressure (psia) = 100; Density underestimate (%) = 14.7",
        "explanation": "The atmospheric offset matters most as a fraction of a low absolute pressure."
      }
    ],
    "result": "Absolute pressure (psia) = 100; Density underestimate (%) = 14.7",
    "interpretation": "The atmospheric offset matters most as a fraction of a low absolute pressure.",
    "control": "Gauge pressure (psig)",
    "columns": [
      "Gauge pressure (psig)",
      "Absolute pressure (psia)",
      "Density underestimate (%)"
    ],
    "rows": [
      [
        0,
        14.7,
        100
      ],
      [
        10,
        24.7,
        59.51417004048583
      ],
      [
        85.3,
        100,
        14.7
      ],
      [
        500,
        514.7,
        2.8560326403730327
      ],
      [
        1000,
        1014.7,
        1.4487040504582636
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Gauge pressure (psig) = 0. Absolute pressure (psia): 14.7; Density underestimate (%): 100.",
      "Gauge pressure (psig) = 10. Absolute pressure (psia): 24.7; Density underestimate (%): 59.51417.",
      "Gauge pressure (psig) = 85.3. Absolute pressure (psia): 100; Density underestimate (%): 14.7.",
      "Gauge pressure (psig) = 500. Absolute pressure (psia): 514.7; Density underestimate (%): 2.85603264.",
      "Gauge pressure (psig) = 1000. Absolute pressure (psia): 1014.7; Density underestimate (%): 1.44870405."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Absolute pressure (psia) without rounding intermediate values.",
        "answer": "85.3 + 14.7 = 100 psia; 14.7/100 × 100 = 14.7%. Absolute pressure (psia) = 100. The atmospheric offset matters most as a fraction of a low absolute pressure."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Gauge pressure (psig) changes from 0 to 1000. Other controls remain as stated in the premise. Absolute pressure (psia) changes from 14.7 to 1014.7."
      },
      {
        "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. Pabs in psia and Pg in psig; the error fraction applies to density only when T, Z and molecular weight are fixed. The atmospheric offset matters most as a fraction of a low absolute pressure."
      }
    ]
  },
  "recorded": null
}