{
  "version": 1,
  "topic": "WC02",
  "title": "Convert mud weight to pressure gradient with units shown",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Mud weight, gradient and fluid head",
    "premise": "Uniform mud, 8,000 ft vertical height, no added surface pressure. Mud weight is the only changing input.",
    "formula": "gradient = 0.052 MW; ΔP = gradient × TVD",
    "variables": "MW in ppg, gradient in psi/ft, TVD in ft, ΔP in psi. The rounded field coefficient assumes these units.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Mud weight (ppg) = 10",
        "explanation": "Uniform mud, 8,000 ft vertical height, no added surface pressure. Mud weight is the only changing input."
      },
      {
        "label": "Select the relation",
        "calculation": "gradient = 0.052 MW; ΔP = gradient × TVD",
        "explanation": "MW in ppg, gradient in psi/ft, TVD in ft, ΔP in psi. The rounded field coefficient assumes these units."
      },
      {
        "label": "Substitute the values",
        "calculation": "0.052 × 10 = 0.520 psi/ft; 0.520 × 8,000 = 4,160 psi",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Gradient (psi/ft) = 0.52; Fluid head (psi) = 4160",
        "explanation": "Fluid head is a pressure difference. A top boundary pressure would be added separately."
      }
    ],
    "result": "Gradient (psi/ft) = 0.52; Fluid head (psi) = 4160",
    "interpretation": "Fluid head is a pressure difference. A top boundary pressure would be added separately.",
    "control": "Mud weight (ppg)",
    "columns": [
      "Mud weight (ppg)",
      "Gradient (psi/ft)",
      "Fluid head (psi)"
    ],
    "rows": [
      [
        8,
        0.416,
        3328
      ],
      [
        9,
        0.46799999999999997,
        3744
      ],
      [
        10,
        0.52,
        4160
      ],
      [
        11,
        0.572,
        4576
      ],
      [
        12,
        0.624,
        4992
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Mud weight (ppg) = 8. Gradient (psi/ft): 0.416; Fluid head (psi): 3328.",
      "Mud weight (ppg) = 9. Gradient (psi/ft): 0.468; Fluid head (psi): 3744.",
      "Mud weight (ppg) = 10. Gradient (psi/ft): 0.52; Fluid head (psi): 4160.",
      "Mud weight (ppg) = 11. Gradient (psi/ft): 0.572; Fluid head (psi): 4576.",
      "Mud weight (ppg) = 12. Gradient (psi/ft): 0.624; Fluid head (psi): 4992."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Gradient (psi/ft) without rounding intermediate values.",
        "answer": "0.052 × 10 = 0.520 psi/ft; 0.520 × 8,000 = 4,160 psi. Gradient (psi/ft) = 0.52. Fluid head is a pressure difference. A top boundary pressure would be added separately."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Mud weight (ppg) changes from 8 to 12. Other controls remain as stated in the premise. Gradient (psi/ft) changes from 0.416 to 0.624."
      },
      {
        "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. MW in ppg, gradient in psi/ft, TVD in ft, ΔP in psi. The rounded field coefficient assumes these units. Fluid head is a pressure difference. A top boundary pressure would be added separately."
      }
    ]
  },
  "recorded": null
}