{
  "version": 1,
  "topic": "GM07",
  "title": "Fracture conductivity versus dimensionless conductivity",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Normalize a fixed fracture conductivity",
    "premise": "Specified kfw = 100 mD·ft and fracture half-length xf = 100 ft. Reservoir k varies.",
    "formula": "Fcd = kfw/(k xf)",
    "variables": "This normalization is separate from the linked bilinear-test estimate of dimensional conductivity.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Reservoir permeability (mD) = 1",
        "explanation": "Specified kfw = 100 mD·ft and fracture half-length xf = 100 ft. Reservoir k varies."
      },
      {
        "label": "Select the relation",
        "calculation": "Fcd = kfw/(k xf)",
        "explanation": "This normalization is separate from the linked bilinear-test estimate of dimensional conductivity."
      },
      {
        "label": "Substitute the values",
        "calculation": "100 mD·ft/(1 mD × 100 ft) = 1",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Dimensionless conductivity = 1; Fracture conductivity (mD·ft) = 100",
        "explanation": "The same dimensional fracture conductivity can have different significance relative to reservoir resistance."
      }
    ],
    "result": "Dimensionless conductivity = 1; Fracture conductivity (mD·ft) = 100",
    "interpretation": "The same dimensional fracture conductivity can have different significance relative to reservoir resistance.",
    "control": "Reservoir permeability (mD)",
    "columns": [
      "Reservoir permeability (mD)",
      "Dimensionless conductivity",
      "Fracture conductivity (mD·ft)"
    ],
    "rows": [
      [
        0.1,
        10,
        100
      ],
      [
        0.5,
        2,
        100
      ],
      [
        1,
        1,
        100
      ],
      [
        5,
        0.2,
        100
      ],
      [
        10,
        0.1,
        100
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Reservoir permeability (mD) = 0.1. Dimensionless conductivity: 10; Fracture conductivity (mD·ft): 100.",
      "Reservoir permeability (mD) = 0.5. Dimensionless conductivity: 2; Fracture conductivity (mD·ft): 100.",
      "Reservoir permeability (mD) = 1. Dimensionless conductivity: 1; Fracture conductivity (mD·ft): 100.",
      "Reservoir permeability (mD) = 5. Dimensionless conductivity: 0.2; Fracture conductivity (mD·ft): 100.",
      "Reservoir permeability (mD) = 10. Dimensionless conductivity: 0.1; Fracture conductivity (mD·ft): 100."
    ],
    "provenance": "Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.",
    "questions": [
      {
        "question": "Reproduce the baseline Dimensionless conductivity without rounding intermediate values.",
        "answer": "100 mD·ft/(1 mD × 100 ft) = 1. Dimensionless conductivity = 1. The same dimensional fracture conductivity can have different significance relative to reservoir resistance."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Reservoir permeability (mD) changes from 0.1 to 10. Other controls remain as stated in the premise. Dimensionless conductivity changes from 10 to 0.1."
      },
      {
        "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. This normalization is separate from the linked bilinear-test estimate of dimensional conductivity. The same dimensional fracture conductivity can have different significance relative to reservoir resistance."
      }
    ]
  },
  "recorded": null
}