{
  "version": 1,
  "topic": "TH04",
  "title": "Bubble dew and critical regions on a phase envelope",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Recorded fixed-feed bubble and dew band",
    "premise": "Six-component feed 0.50/0.15/0.15/0.10/0.05/0.05, PR-based supported boundary workflow, 280–290 K. The complete branch record is downloadable.",
    "formula": "Incipient-phase boundary: phase fugacities equal, with the new phase amount approaching zero",
    "variables": "Boundary pressure is not an interior phase fraction. The selected band does not claim to locate the critical point.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Temperature (K) = 285",
        "explanation": "Six-component feed 0.50/0.15/0.15/0.10/0.05/0.05, PR-based supported boundary workflow, 280–290 K. The complete branch record is downloadable."
      },
      {
        "label": "Select the relation",
        "calculation": "Incipient-phase boundary: phase fugacities equal, with the new phase amount approaching zero",
        "explanation": "Boundary pressure is not an interior phase fraction. The selected band does not claim to locate the critical point."
      },
      {
        "label": "Substitute the values",
        "calculation": "Supply the stated overall composition and temperature band; solve the two incipient-phase branches with the documented engine. Read each pressure with its bubble or dew label.",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Bubble pressure (MPa(a)) = 9.58148139; Dew pressure (MPa(a)) = 0.159044815",
        "explanation": "Bubble and dew are different onset branches. This limited temperature band is not a full critical-region envelope."
      }
    ],
    "result": "Bubble pressure (MPa(a)) = 9.58148139; Dew pressure (MPa(a)) = 0.159044815",
    "interpretation": "Bubble and dew are different onset branches. This limited temperature band is not a full critical-region envelope.",
    "control": "Temperature (K)",
    "columns": [
      "Temperature (K)",
      "Bubble pressure (MPa(a))",
      "Dew pressure (MPa(a))"
    ],
    "rows": [
      [
        280,
        9.242807141059279,
        0.1260187460735812
      ],
      [
        280.7142857142857,
        9.292320697538,
        0.13035252789592797
      ],
      [
        281.42857142857144,
        9.341466051961262,
        0.13480966760443142
      ],
      [
        282.14285714285717,
        9.390237806234735,
        0.13939294675656574
      ],
      [
        282.85714285714283,
        9.438630578451212,
        0.14410519571487174
      ],
      [
        283.57142857142856,
        9.48663900110796,
        0.1489492945082729
      ],
      [
        284.2857142857143,
        9.53425771929205,
        0.15392817372212692
      ],
      [
        285,
        9.581481388833039,
        0.15904481541827592
      ],
      [
        285.7142857142857,
        9.62830467442359,
        0.1643022540864395
      ],
      [
        286.42857142857144,
        9.674722247706356,
        0.16970357762835311
      ],
      [
        287.14285714285717,
        9.720728785327028,
        0.17525192837608644
      ],
      [
        287.85714285714283,
        9.766318966953218,
        0.18095050414611116
      ],
      [
        288.57142857142856,
        9.811487473257605,
        0.1868025593306666
      ],
      [
        289.2857142857143,
        9.85622898386473,
        0.19281140602814303
      ],
      [
        290,
        9.900538175260724,
        0.1989804152142
      ]
    ],
    "baseline": 7,
    "rowNotes": [
      "Temperature (K) = 280. Bubble pressure (MPa(a)): 9.24280714; Dew pressure (MPa(a)): 0.126018746.",
      "Temperature (K) = 280.714286. Bubble pressure (MPa(a)): 9.2923207; Dew pressure (MPa(a)): 0.130352528.",
      "Temperature (K) = 281.428571. Bubble pressure (MPa(a)): 9.34146605; Dew pressure (MPa(a)): 0.134809668.",
      "Temperature (K) = 282.142857. Bubble pressure (MPa(a)): 9.39023781; Dew pressure (MPa(a)): 0.139392947.",
      "Temperature (K) = 282.857143. Bubble pressure (MPa(a)): 9.43863058; Dew pressure (MPa(a)): 0.144105196.",
      "Temperature (K) = 283.571429. Bubble pressure (MPa(a)): 9.486639; Dew pressure (MPa(a)): 0.148949295.",
      "Temperature (K) = 284.285714. Bubble pressure (MPa(a)): 9.53425772; Dew pressure (MPa(a)): 0.153928174.",
      "Temperature (K) = 285. Bubble pressure (MPa(a)): 9.58148139; Dew pressure (MPa(a)): 0.159044815.",
      "Temperature (K) = 285.714286. Bubble pressure (MPa(a)): 9.62830467; Dew pressure (MPa(a)): 0.164302254.",
      "Temperature (K) = 286.428571. Bubble pressure (MPa(a)): 9.67472225; Dew pressure (MPa(a)): 0.169703578.",
      "Temperature (K) = 287.142857. Bubble pressure (MPa(a)): 9.72072879; Dew pressure (MPa(a)): 0.175251928.",
      "Temperature (K) = 287.857143. Bubble pressure (MPa(a)): 9.76631897; Dew pressure (MPa(a)): 0.180950504.",
      "Temperature (K) = 288.571429. Bubble pressure (MPa(a)): 9.81148747; Dew pressure (MPa(a)): 0.186802559.",
      "Temperature (K) = 289.285714. Bubble pressure (MPa(a)): 9.85622898; Dew pressure (MPa(a)): 0.192811406.",
      "Temperature (K) = 290. Bubble pressure (MPa(a)): 9.90053818; Dew pressure (MPa(a)): 0.198980415."
    ],
    "provenance": "Recorded supported hydrocarbon-bubble-dew-band workflow; the full PR envelope tool is linked for continuation beyond this band.",
    "questions": [
      {
        "question": "Reproduce the baseline Bubble pressure (MPa(a)) without rounding intermediate values.",
        "answer": "Supply the stated overall composition and temperature band; solve the two incipient-phase branches with the documented engine. Read each pressure with its bubble or dew label.. Bubble pressure (MPa(a)) = 9.58148139. Bubble and dew are different onset branches. This limited temperature band is not a full critical-region envelope."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Temperature (K) changes from 280 to 290. Other controls remain as stated in the premise. Bubble pressure (MPa(a)) changes from 9.24280714 to 9.90053818."
      },
      {
        "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. Boundary pressure is not an interior phase fraction. The selected band does not claim to locate the critical point. Bubble and dew are different onset branches. This limited temperature band is not a full critical-region envelope."
      }
    ]
  },
  "recorded": {
    "inputs": {
      "T_low": 280,
      "T_high": 290,
      "z1": 0.5,
      "z2": 0.15,
      "z3": 0.15,
      "z4": 0.1,
      "z5": 0.05,
      "z6": 0.05
    },
    "result": {
      "outputs": [
        {
          "label": "Lowest sampled bubble pressure",
          "value": 9.242807141059279,
          "unit": "MPa(a)"
        },
        {
          "label": "Highest sampled dew pressure",
          "value": 0.1989804152142,
          "unit": "MPa(a)"
        },
        {
          "label": "Audited endpoint count",
          "value": 30,
          "unit": "dimensionless"
        }
      ],
      "columns": [
        "Temperature (K)",
        "Bubble pressure (MPa(a))",
        "Dew pressure (MPa(a))"
      ],
      "rows": [
        [
          280,
          9.242807141059279,
          0.1260187460735812
        ],
        [
          280.7142857142857,
          9.292320697538,
          0.13035252789592797
        ],
        [
          281.42857142857144,
          9.341466051961262,
          0.13480966760443142
        ],
        [
          282.14285714285717,
          9.390237806234735,
          0.13939294675656574
        ],
        [
          282.85714285714283,
          9.438630578451212,
          0.14410519571487174
        ],
        [
          283.57142857142856,
          9.48663900110796,
          0.1489492945082729
        ],
        [
          284.2857142857143,
          9.53425771929205,
          0.15392817372212692
        ],
        [
          285,
          9.581481388833039,
          0.15904481541827592
        ],
        [
          285.7142857142857,
          9.62830467442359,
          0.1643022540864395
        ],
        [
          286.42857142857144,
          9.674722247706356,
          0.16970357762835311
        ],
        [
          287.14285714285717,
          9.720728785327028,
          0.17525192837608644
        ],
        [
          287.85714285714283,
          9.766318966953218,
          0.18095050414611116
        ],
        [
          288.57142857142856,
          9.811487473257605,
          0.1868025593306666
        ],
        [
          289.2857142857143,
          9.85622898386473,
          0.19281140602814303
        ],
        [
          290,
          9.900538175260724,
          0.1989804152142
        ]
      ],
      "chart": {
        "xLabel": "Temperature (K)",
        "yLabel": "Pressure (MPa(a))",
        "series": [
          {
            "name": "Bubble",
            "x": [
              280,
              280.7142857142857,
              281.42857142857144,
              282.14285714285717,
              282.85714285714283,
              283.57142857142856,
              284.2857142857143,
              285,
              285.7142857142857,
              286.42857142857144,
              287.14285714285717,
              287.85714285714283,
              288.57142857142856,
              289.2857142857143,
              290
            ],
            "y": [
              9.242807141059279,
              9.292320697538,
              9.341466051961262,
              9.390237806234735,
              9.438630578451212,
              9.48663900110796,
              9.53425771929205,
              9.581481388833039,
              9.62830467442359,
              9.674722247706356,
              9.720728785327028,
              9.766318966953218,
              9.811487473257605,
              9.85622898386473,
              9.900538175260724
            ]
          },
          {
            "name": "Dew",
            "x": [
              280,
              280.7142857142857,
              281.42857142857144,
              282.14285714285717,
              282.85714285714283,
              283.57142857142856,
              284.2857142857143,
              285,
              285.7142857142857,
              286.42857142857144,
              287.14285714285717,
              287.85714285714283,
              288.57142857142856,
              289.2857142857143,
              290
            ],
            "y": [
              0.1260187460735812,
              0.13035252789592797,
              0.13480966760443142,
              0.13939294675656574,
              0.14410519571487174,
              0.1489492945082729,
              0.15392817372212692,
              0.15904481541827592,
              0.1643022540864395,
              0.16970357762835311,
              0.17525192837608644,
              0.18095050414611116,
              0.1868025593306666,
              0.19281140602814303,
              0.1989804152142
            ]
          }
        ]
      },
      "warnings": [
        "A 15-temperature low-temperature bubble/dew band, not a full phase-envelope continuation. No critical point, cricondenbar/cricondentherm, retrograde branches or interpolated phase verdict. Every endpoint is checked; failed points stop the entire band rather than leaving hidden gaps. C1-C6 PR, zero kij, no water/heavy ends/solids."
      ]
    }
  }
}