{
  "version": 1,
  "topic": "PP07",
  "title": "Capillary pressure versus relative permeability",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Pressure and mobility at shared effective saturation",
    "premise": "Brooks–Corey Pe = 5 psi, λ = 2; separate illustrative wetting kr = Se³. These are synthetic curves, not a jointly fitted rock model.",
    "formula": "Pc = 5 Se^(−1/2); krw = Se³",
    "variables": "Pc has pressure units and kr is dimensionless. Se uses fixed residual-endpoint assumptions.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Effective saturation = 0.5",
        "explanation": "Brooks–Corey Pe = 5 psi, λ = 2; separate illustrative wetting kr = Se³. These are synthetic curves, not a jointly fitted rock model."
      },
      {
        "label": "Select the relation",
        "calculation": "Pc = 5 Se^(−1/2); krw = Se³",
        "explanation": "Pc has pressure units and kr is dimensionless. Se uses fixed residual-endpoint assumptions."
      },
      {
        "label": "Substitute the values",
        "calculation": "At Se = 0.5: Pc = 5/√0.5 = 7.07106781 psi; krw = 0.5³ = 0.125",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Capillary pressure (psi) = 7.07106781; Illustrative relative permeability = 0.125",
        "explanation": "Sharing a saturation coordinate does not make pressure and relative permeability interchangeable."
      }
    ],
    "result": "Capillary pressure (psi) = 7.07106781; Illustrative relative permeability = 0.125",
    "interpretation": "Sharing a saturation coordinate does not make pressure and relative permeability interchangeable.",
    "control": "Effective saturation",
    "columns": [
      "Effective saturation",
      "Capillary pressure (psi)",
      "Illustrative relative permeability"
    ],
    "rows": [
      [
        0.1,
        15.811388300841895,
        0.0010000000000000002
      ],
      [
        0.25,
        10,
        0.015625
      ],
      [
        0.5,
        7.071067811865475,
        0.125
      ],
      [
        0.75,
        5.773502691896257,
        0.421875
      ],
      [
        0.9,
        5.270462766947299,
        0.7290000000000001
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Effective saturation = 0.1. Capillary pressure (psi): 15.8113883; Illustrative relative permeability: 0.001.",
      "Effective saturation = 0.25. Capillary pressure (psi): 10; Illustrative relative permeability: 0.015625.",
      "Effective saturation = 0.5. Capillary pressure (psi): 7.07106781; Illustrative relative permeability: 0.125.",
      "Effective saturation = 0.75. Capillary pressure (psi): 5.77350269; Illustrative relative permeability: 0.421875.",
      "Effective saturation = 0.9. Capillary pressure (psi): 5.27046277; Illustrative relative permeability: 0.729."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Capillary pressure (psi) without rounding intermediate values.",
        "answer": "At Se = 0.5: Pc = 5/√0.5 = 7.07106781 psi; krw = 0.5³ = 0.125. Capillary pressure (psi) = 7.07106781. Sharing a saturation coordinate does not make pressure and relative permeability interchangeable."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Effective saturation changes from 0.1 to 0.9. Other controls remain as stated in the premise. Capillary pressure (psi) changes from 15.8113883 to 5.27046277."
      },
      {
        "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. Pc has pressure units and kr is dimensionless. Se uses fixed residual-endpoint assumptions. Sharing a saturation coordinate does not make pressure and relative permeability interchangeable."
      }
    ]
  },
  "recorded": null
}