{
  "version": 1,
  "topic": "RF08",
  "title": "Explore the permeability viscosity and pressure tradeoff",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Darcy's Law for Linear Single-Phase Flow",
    "premise": "Fixed controls: A = 500 ft²; DeltaP = 100 psi; mu = 2 cP; L = 1000 ft. k is varied as shown.",
    "formula": "q = 0.001127 k A DeltaP / (mu L)",
    "variables": "k: Permeability (mD). A: Cross-Sectional Flow Area (ft²). DeltaP: Pressure Drop (psi). mu: Fluid Viscosity (cP). L: Flow Length (ft).",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Permeability (mD) = 100",
        "explanation": "Fixed controls: A = 500 ft²; DeltaP = 100 psi; mu = 2 cP; L = 1000 ft. k is varied as shown."
      },
      {
        "label": "Select the relation",
        "calculation": "q = 0.001127 k A DeltaP / (mu L)",
        "explanation": "k: Permeability (mD). A: Cross-Sectional Flow Area (ft²). DeltaP: Pressure Drop (psi). mu: Fluid Viscosity (cP). L: Flow Length (ft)."
      },
      {
        "label": "Substitute the values",
        "calculation": "k = 100; A = 500; DeltaP = 100; mu = 2; L = 1000 → q = 2.8175 bbl/day",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "q (bbl/day) = 2.8175",
        "explanation": "The local fluid-volume rate is proportional to permeability at fixed linear geometry, viscosity and gradient."
      }
    ],
    "result": "q (bbl/day) = 2.8175",
    "interpretation": "The local fluid-volume rate is proportional to permeability at fixed linear geometry, viscosity and gradient.",
    "control": "Permeability (mD)",
    "columns": [
      "Permeability (mD)",
      "q (bbl/day)"
    ],
    "rows": [
      [
        25,
        0.7043749999999999
      ],
      [
        50,
        1.4087499999999997
      ],
      [
        100,
        2.8174999999999994
      ],
      [
        200,
        5.634999999999999
      ],
      [
        400,
        11.269999999999998
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Permeability (mD) = 25. q (bbl/day): 0.704375.",
      "Permeability (mD) = 50. q (bbl/day): 1.40875.",
      "Permeability (mD) = 100. q (bbl/day): 2.8175.",
      "Permeability (mD) = 200. q (bbl/day): 5.635.",
      "Permeability (mD) = 400. q (bbl/day): 11.27."
    ],
    "provenance": "Replayed with the same equation record and calculation engine as /calculators/darcy-s-law-for-linear-single-phase-flow. Original synthetic inputs; engine outputs are saved in the downloadable record.",
    "questions": [
      {
        "question": "Reproduce the baseline q (bbl/day) without rounding intermediate values.",
        "answer": "k = 100; A = 500; DeltaP = 100; mu = 2; L = 1000 → q = 2.8175 bbl/day. q (bbl/day) = 2.8175. The local fluid-volume rate is proportional to permeability at fixed linear geometry, viscosity and gradient."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Permeability (mD) changes from 25 to 400. Other controls remain as stated in the premise. q (bbl/day) changes from 0.704375 to 11.27."
      },
      {
        "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. k: Permeability (mD). A: Cross-Sectional Flow Area (ft²). DeltaP: Pressure Drop (psi). mu: Fluid Viscosity (cP). L: Flow Length (ft). The local fluid-volume rate is proportional to permeability at fixed linear geometry, viscosity and gradient."
      }
    ]
  },
  "recorded": {
    "kind": "scalar",
    "equation": "darcy-s-law-for-linear-single-phase-flow",
    "parameter": "k",
    "inputs": {
      "k": "100",
      "A": "500",
      "DeltaP": "100",
      "mu": "2",
      "L": "1000"
    },
    "values": [
      25,
      50,
      100,
      200,
      400
    ],
    "outputs": [
      {
        "expression": "(0.001127 * k * A * DeltaP) / (mu * L)",
        "intermediates": {},
        "inputs": {
          "k": 25,
          "A": 500,
          "DeltaP": 100,
          "mu": 2,
          "L": 1000
        },
        "target": "q",
        "unit": "bbl/day",
        "value": 0.7043749999999999
      },
      {
        "expression": "(0.001127 * k * A * DeltaP) / (mu * L)",
        "intermediates": {},
        "inputs": {
          "k": 50,
          "A": 500,
          "DeltaP": 100,
          "mu": 2,
          "L": 1000
        },
        "target": "q",
        "unit": "bbl/day",
        "value": 1.4087499999999997
      },
      {
        "expression": "(0.001127 * k * A * DeltaP) / (mu * L)",
        "intermediates": {},
        "inputs": {
          "k": 100,
          "A": 500,
          "DeltaP": 100,
          "mu": 2,
          "L": 1000
        },
        "target": "q",
        "unit": "bbl/day",
        "value": 2.8174999999999994
      },
      {
        "expression": "(0.001127 * k * A * DeltaP) / (mu * L)",
        "intermediates": {},
        "inputs": {
          "k": 200,
          "A": 500,
          "DeltaP": 100,
          "mu": 2,
          "L": 1000
        },
        "target": "q",
        "unit": "bbl/day",
        "value": 5.634999999999999
      },
      {
        "expression": "(0.001127 * k * A * DeltaP) / (mu * L)",
        "intermediates": {},
        "inputs": {
          "k": 400,
          "A": 500,
          "DeltaP": 100,
          "mu": 2,
          "L": 1000
        },
        "target": "q",
        "unit": "bbl/day",
        "value": 11.269999999999998
      }
    ]
  }
}