{
  "version": 1,
  "topic": "WC07",
  "title": "Initial versus final circulating pressure on a worksheet",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Initial and final worksheet schedule values",
    "premise": "SIDPP 500 psi, original mud 12 ppg, TVD 10,000 ft. Kill density = 12 + 500/(0.052 × 10,000) = 12.96153846 ppg.",
    "formula": "ICP = SCR + SIDPP; FCP = SCR × KWM/OMW",
    "variables": "SCR must be recorded at the same intended pump rate and path. This example is schedule arithmetic, not an operating procedure.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Slow-rate reference (psi) = 900",
        "explanation": "SIDPP 500 psi, original mud 12 ppg, TVD 10,000 ft. Kill density = 12 + 500/(0.052 × 10,000) = 12.96153846 ppg."
      },
      {
        "label": "Select the relation",
        "calculation": "ICP = SCR + SIDPP; FCP = SCR × KWM/OMW",
        "explanation": "SCR must be recorded at the same intended pump rate and path. This example is schedule arithmetic, not an operating procedure."
      },
      {
        "label": "Substitute the values",
        "calculation": "ICP = 900 + 500 = 1,400; FCP = 900 × 12.96153846/12 = 972.115385 psi",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "ICP (psi) = 1400; FCP (psi) = 972.115385",
        "explanation": "ICP contains an additive pressure imbalance; FCP uses the mud-density ratio."
      }
    ],
    "result": "ICP (psi) = 1400; FCP (psi) = 972.115385",
    "interpretation": "ICP contains an additive pressure imbalance; FCP uses the mud-density ratio.",
    "control": "Slow-rate reference (psi)",
    "columns": [
      "Slow-rate reference (psi)",
      "ICP (psi)",
      "FCP (psi)"
    ],
    "rows": [
      [
        500,
        1000,
        540.0641025641025
      ],
      [
        700,
        1200,
        756.0897435897436
      ],
      [
        900,
        1400,
        972.1153846153846
      ],
      [
        1000,
        1500,
        1080.128205128205
      ],
      [
        1200,
        1700,
        1296.1538461538462
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Slow-rate reference (psi) = 500. ICP (psi): 1000; FCP (psi): 540.064103.",
      "Slow-rate reference (psi) = 700. ICP (psi): 1200; FCP (psi): 756.089744.",
      "Slow-rate reference (psi) = 900. ICP (psi): 1400; FCP (psi): 972.115385.",
      "Slow-rate reference (psi) = 1000. ICP (psi): 1500; FCP (psi): 1080.12821.",
      "Slow-rate reference (psi) = 1200. ICP (psi): 1700; FCP (psi): 1296.15385."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline ICP (psi) without rounding intermediate values.",
        "answer": "ICP = 900 + 500 = 1,400; FCP = 900 × 12.96153846/12 = 972.115385 psi. ICP (psi) = 1400. ICP contains an additive pressure imbalance; FCP uses the mud-density ratio."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Slow-rate reference (psi) changes from 500 to 1200. Other controls remain as stated in the premise. ICP (psi) changes from 1000 to 1700."
      },
      {
        "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. SCR must be recorded at the same intended pump rate and path. This example is schedule arithmetic, not an operating procedure. ICP contains an additive pressure imbalance; FCP uses the mud-density ratio."
      }
    ]
  },
  "recorded": null
}