{
  "version": 1,
  "topic": "WC10",
  "title": "The error from using measured depth for hydrostatic pressure",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Deliberately wrong depth substitution",
    "premise": "Correct TVD 8,000 ft and uniform mud 10 ppg. Only the incorrectly substituted measured depth varies.",
    "formula": "Pcorrect = 4,160; Pwrong = 0.052 × 10 × MD; error = (MD/8,000 − 1) × 100%",
    "variables": "MD belongs to path geometry, not the hydrostatic vertical height. The wrong result is intentionally labelled.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Substituted MD (ft) = 10000",
        "explanation": "Correct TVD 8,000 ft and uniform mud 10 ppg. Only the incorrectly substituted measured depth varies."
      },
      {
        "label": "Select the relation",
        "calculation": "Pcorrect = 4,160; Pwrong = 0.052 × 10 × MD; error = (MD/8,000 − 1) × 100%",
        "explanation": "MD belongs to path geometry, not the hydrostatic vertical height. The wrong result is intentionally labelled."
      },
      {
        "label": "Substitute the values",
        "calculation": "Wrong = 0.52 × 10,000 = 5,200; error = (5,200 − 4,160)/4,160 = 25%",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Correct head (psi) = 4160; Wrong head (psi) = 5200; Overstatement (%) = 25",
        "explanation": "A vertical-well limiting case can conceal this mistake because MD and TVD coincide there."
      }
    ],
    "result": "Correct head (psi) = 4160; Wrong head (psi) = 5200; Overstatement (%) = 25",
    "interpretation": "A vertical-well limiting case can conceal this mistake because MD and TVD coincide there.",
    "control": "Substituted MD (ft)",
    "columns": [
      "Substituted MD (ft)",
      "Correct head (psi)",
      "Wrong head (psi)",
      "Overstatement (%)"
    ],
    "rows": [
      [
        8000,
        4160,
        4160,
        0
      ],
      [
        9000,
        4160,
        4680,
        12.5
      ],
      [
        10000,
        4160,
        5200,
        25
      ],
      [
        12000,
        4160,
        6240,
        50
      ],
      [
        16000,
        4160,
        8320,
        100
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Substituted MD (ft) = 8000. Correct head (psi): 4160; Wrong head (psi): 4160; Overstatement (%): 0.",
      "Substituted MD (ft) = 9000. Correct head (psi): 4160; Wrong head (psi): 4680; Overstatement (%): 12.5.",
      "Substituted MD (ft) = 10000. Correct head (psi): 4160; Wrong head (psi): 5200; Overstatement (%): 25.",
      "Substituted MD (ft) = 12000. Correct head (psi): 4160; Wrong head (psi): 6240; Overstatement (%): 50.",
      "Substituted MD (ft) = 16000. Correct head (psi): 4160; Wrong head (psi): 8320; Overstatement (%): 100."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Correct head (psi) without rounding intermediate values.",
        "answer": "Wrong = 0.52 × 10,000 = 5,200; error = (5,200 − 4,160)/4,160 = 25%. Correct head (psi) = 4160. A vertical-well limiting case can conceal this mistake because MD and TVD coincide there."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Substituted MD (ft) changes from 8000 to 16000. Other controls remain as stated in the premise. Correct head (psi) changes from 4160 to 4160."
      },
      {
        "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. MD belongs to path geometry, not the hydrostatic vertical height. The wrong result is intentionally labelled. A vertical-well limiting case can conceal this mistake because MD and TVD coincide there."
      }
    ]
  },
  "recorded": null
}