{
  "version": 1,
  "topic": "WC11",
  "title": "One surface pressure two different equivalent mud weights",
  "createdAt": "2026-10-24",
  "case": {
    "title": "One pressure expressed over different depths",
    "premise": "Fixed 500 psi added pressure and 10 ppg base mud. TVD is the only changing quantity.",
    "formula": "ΔMW = 500/(0.052 TVD); total EMW = 10 + ΔMW",
    "variables": "Density increments and total equivalent density are in ppg; the actual fluid remains 10 ppg.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Evaluation TVD (ft) = 8000",
        "explanation": "Fixed 500 psi added pressure and 10 ppg base mud. TVD is the only changing quantity."
      },
      {
        "label": "Select the relation",
        "calculation": "ΔMW = 500/(0.052 TVD); total EMW = 10 + ΔMW",
        "explanation": "Density increments and total equivalent density are in ppg; the actual fluid remains 10 ppg."
      },
      {
        "label": "Substitute the values",
        "calculation": "500/(0.052 × 8,000) = 1.20192308; total = 11.20192308 ppg",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Equivalent increment (ppg) = 1.20192308; Total EMW (ppg) = 11.2019231",
        "explanation": "A fixed pressure has a smaller equivalent density increment at a deeper evaluation point."
      }
    ],
    "result": "Equivalent increment (ppg) = 1.20192308; Total EMW (ppg) = 11.2019231",
    "interpretation": "A fixed pressure has a smaller equivalent density increment at a deeper evaluation point.",
    "control": "Evaluation TVD (ft)",
    "columns": [
      "Evaluation TVD (ft)",
      "Equivalent increment (ppg)",
      "Total EMW (ppg)"
    ],
    "rows": [
      [
        2500,
        3.8461538461538463,
        13.846153846153847
      ],
      [
        5000,
        1.9230769230769231,
        11.923076923076923
      ],
      [
        8000,
        1.2019230769230769,
        11.201923076923077
      ],
      [
        10000,
        0.9615384615384616,
        10.961538461538462
      ],
      [
        15000,
        0.6410256410256411,
        10.64102564102564
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Evaluation TVD (ft) = 2500. Equivalent increment (ppg): 3.84615385; Total EMW (ppg): 13.8461538.",
      "Evaluation TVD (ft) = 5000. Equivalent increment (ppg): 1.92307692; Total EMW (ppg): 11.9230769.",
      "Evaluation TVD (ft) = 8000. Equivalent increment (ppg): 1.20192308; Total EMW (ppg): 11.2019231.",
      "Evaluation TVD (ft) = 10000. Equivalent increment (ppg): 0.961538462; Total EMW (ppg): 10.9615385.",
      "Evaluation TVD (ft) = 15000. Equivalent increment (ppg): 0.641025641; Total EMW (ppg): 10.6410256."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Equivalent increment (ppg) without rounding intermediate values.",
        "answer": "500/(0.052 × 8,000) = 1.20192308; total = 11.20192308 ppg. Equivalent increment (ppg) = 1.20192308. A fixed pressure has a smaller equivalent density increment at a deeper evaluation point."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Evaluation TVD (ft) changes from 2500 to 15000. Other controls remain as stated in the premise. Equivalent increment (ppg) changes from 3.84615385 to 0.641025641."
      },
      {
        "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. Density increments and total equivalent density are in ppg; the actual fluid remains 10 ppg. A fixed pressure has a smaller equivalent density increment at a deeper evaluation point."
      }
    ]
  },
  "recorded": null
}