{
  "version": 1,
  "topic": "PV09",
  "title": "Dead oil versus live oil viscosity in a correlation workflow",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Beggs-Robinson Live Oil Viscosity Correlation",
    "premise": "Fixed controls: mu_od = 2 cP. R_s is varied as shown.",
    "formula": "mu_o = A mu_od^B; A = 10.715 (R_s + 100)^-0.515; B = 5.44 (R_s + 150)^-0.338",
    "variables": "mu_od: Dead Oil Viscosity (cP). R_s: Solution Gas-Oil Ratio (SCF/STB).",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Solution Gas-Oil Ratio (SCF/STB) = 600",
        "explanation": "Fixed controls: mu_od = 2 cP. R_s is varied as shown."
      },
      {
        "label": "Select the relation",
        "calculation": "mu_o = A mu_od^B; A = 10.715 (R_s + 100)^-0.515; B = 5.44 (R_s + 150)^-0.338",
        "explanation": "mu_od: Dead Oil Viscosity (cP). R_s: Solution Gas-Oil Ratio (SCF/STB)."
      },
      {
        "label": "Substitute the values",
        "calculation": "mu_od = 2; R_s = 600 → mu_o = 0.548940213 cP",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "mu_o (cP) = 0.548940213",
        "explanation": "This is the implemented live-oil correlation at a fixed dead-oil viscosity, not a depletion history."
      }
    ],
    "result": "mu_o (cP) = 0.548940213",
    "interpretation": "This is the implemented live-oil correlation at a fixed dead-oil viscosity, not a depletion history.",
    "control": "Solution Gas-Oil Ratio (SCF/STB)",
    "columns": [
      "Solution Gas-Oil Ratio (SCF/STB)",
      "mu_o (cP)"
    ],
    "rows": [
      [
        0,
        2.0002195395533047
      ],
      [
        100,
        1.2540140941044604
      ],
      [
        300,
        0.7899957409100351
      ],
      [
        600,
        0.5489402131353023
      ],
      [
        1000,
        0.4120254511025445
      ]
    ],
    "baseline": 3,
    "rowNotes": [
      "Solution Gas-Oil Ratio (SCF/STB) = 0. mu_o (cP): 2.00021954.",
      "Solution Gas-Oil Ratio (SCF/STB) = 100. mu_o (cP): 1.25401409.",
      "Solution Gas-Oil Ratio (SCF/STB) = 300. mu_o (cP): 0.789995741.",
      "Solution Gas-Oil Ratio (SCF/STB) = 600. mu_o (cP): 0.548940213.",
      "Solution Gas-Oil Ratio (SCF/STB) = 1000. mu_o (cP): 0.412025451."
    ],
    "provenance": "Replayed with the same equation record and calculation engine as /calculators/beggs-robinson-live-oil-viscosity-correlation. Original synthetic inputs; engine outputs are saved in the downloadable record.",
    "questions": [
      {
        "question": "Reproduce the baseline mu_o (cP) without rounding intermediate values.",
        "answer": "mu_od = 2; R_s = 600 → mu_o = 0.548940213 cP. mu_o (cP) = 0.548940213. This is the implemented live-oil correlation at a fixed dead-oil viscosity, not a depletion history."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Solution Gas-Oil Ratio (SCF/STB) changes from 0 to 1000. Other controls remain as stated in the premise. mu_o (cP) changes from 2.00021954 to 0.412025451."
      },
      {
        "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. mu_od: Dead Oil Viscosity (cP). R_s: Solution Gas-Oil Ratio (SCF/STB). This is the implemented live-oil correlation at a fixed dead-oil viscosity, not a depletion history."
      }
    ]
  },
  "recorded": {
    "kind": "scalar",
    "equation": "beggs-robinson-live-oil-viscosity-correlation",
    "parameter": "R_s",
    "inputs": {
      "mu_od": "2",
      "R_s": "600"
    },
    "values": [
      0,
      100,
      300,
      600,
      1000
    ],
    "outputs": [
      {
        "expression": "A_br_live_oil * mu_od^B_br_live_oil",
        "intermediates": {
          "A_br_live_oil": 0.9999819833039758,
          "B_br_live_oil": 1.0001843484534048
        },
        "inputs": {
          "mu_od": 2,
          "R_s": 0
        },
        "target": "mu_o",
        "unit": "cP",
        "value": 2.0002195395533047
      },
      {
        "expression": "A_br_live_oil * mu_od^B_br_live_oil",
        "intermediates": {
          "A_br_live_oil": 0.6997803248410479,
          "B_br_live_oil": 0.8415795557889738
        },
        "inputs": {
          "mu_od": 2,
          "R_s": 100
        },
        "target": "mu_o",
        "unit": "cP",
        "value": 1.2540140941044604
      },
      {
        "expression": "A_br_live_oil * mu_od^B_br_live_oil",
        "intermediates": {
          "A_br_live_oil": 0.48970132583457265,
          "B_br_live_oil": 0.6899427732794315
        },
        "inputs": {
          "mu_od": 2,
          "R_s": 300
        },
        "target": "mu_o",
        "unit": "cP",
        "value": 0.7899957409100351
      },
      {
        "expression": "A_br_live_oil * mu_od^B_br_live_oil",
        "intermediates": {
          "A_br_live_oil": 0.36708503909207024,
          "B_br_live_oil": 0.5805347119800152
        },
        "inputs": {
          "mu_od": 2,
          "R_s": 600
        },
        "target": "mu_o",
        "unit": "cP",
        "value": 0.5489402131353023
      },
      {
        "expression": "A_br_live_oil * mu_od^B_br_live_oil",
        "intermediates": {
          "A_br_live_oil": 0.2908539341439465,
          "B_br_live_oil": 0.5024386379936088
        },
        "inputs": {
          "mu_od": 2,
          "R_s": 1000
        },
        "target": "mu_o",
        "unit": "cP",
        "value": 0.4120254511025445
      }
    ]
  }
}