{
  "version": 1,
  "topic": "TH10",
  "title": "Same feed two equations of state a reproducible comparison",
  "createdAt": "2026-10-24",
  "case": {
    "title": "PR and SRK on an identical six-component feed",
    "premise": "p = 2 MPa(a); methane/ethane/propane/n-butane/n-pentane/n-hexane mole fractions 0.50/0.15/0.15/0.10/0.05/0.05. CoolProp 8, kij = 0; only T changes.",
    "formula": "zi = (1 − β)xi + βyi; fi,liquid = fi,vapor",
    "variables": "β is vapor mole fraction. Both models use the same pure-component constants and numerical state inputs.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Temperature (K) = 280",
        "explanation": "p = 2 MPa(a); methane/ethane/propane/n-butane/n-pentane/n-hexane mole fractions 0.50/0.15/0.15/0.10/0.05/0.05. CoolProp 8, kij = 0; only T changes."
      },
      {
        "label": "Select the relation",
        "calculation": "zi = (1 − β)xi + βyi; fi,liquid = fi,vapor",
        "explanation": "β is vapor mole fraction. Both models use the same pure-component constants and numerical state inputs."
      },
      {
        "label": "Substitute the values",
        "calculation": "At 280 K and 2 MPa: PR β = 0.657564116; SRK β = 0.658742945; the complete component balances and fugacity diagnostics are saved with each solve.",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "PR vapor mole fraction = 0.657564116; SRK vapor mole fraction = 0.658742945",
        "explanation": "These are model differences, not measured errors or an accuracy ranking."
      }
    ],
    "result": "PR vapor mole fraction = 0.657564116; SRK vapor mole fraction = 0.658742945",
    "interpretation": "These are model differences, not measured errors or an accuracy ranking.",
    "control": "Temperature (K)",
    "columns": [
      "Temperature (K)",
      "PR vapor mole fraction",
      "SRK vapor mole fraction"
    ],
    "rows": [
      [
        240,
        0.4828540173491232,
        0.4870871456213228
      ],
      [
        260,
        0.5691657772688676,
        0.5715310688829293
      ],
      [
        280,
        0.6575641159651632,
        0.6587429448464391
      ],
      [
        300,
        0.749652889145806,
        0.7499510106460565
      ],
      [
        320,
        0.8434580755405012,
        0.8429686910594324
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Temperature (K) = 240. PR vapor mole fraction: 0.482854017; SRK vapor mole fraction: 0.487087146.",
      "Temperature (K) = 260. PR vapor mole fraction: 0.569165777; SRK vapor mole fraction: 0.571531069.",
      "Temperature (K) = 280. PR vapor mole fraction: 0.657564116; SRK vapor mole fraction: 0.658742945.",
      "Temperature (K) = 300. PR vapor mole fraction: 0.749652889; SRK vapor mole fraction: 0.749951011.",
      "Temperature (K) = 320. PR vapor mole fraction: 0.843458076; SRK vapor mole fraction: 0.842968691."
    ],
    "provenance": "Recorded using both supported compositional flash engines. Independent thermo reference fixtures are separately checked by the repository's compositional regression suite.",
    "questions": [
      {
        "question": "Reproduce the baseline PR vapor mole fraction without rounding intermediate values.",
        "answer": "At 280 K and 2 MPa: PR β = 0.657564116; SRK β = 0.658742945; the complete component balances and fugacity diagnostics are saved with each solve.. PR vapor mole fraction = 0.657564116. These are model differences, not measured errors or an accuracy ranking."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Temperature (K) changes from 240 to 320. Other controls remain as stated in the premise. PR vapor mole fraction changes from 0.482854017 to 0.843458076."
      },
      {
        "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. β is vapor mole fraction. Both models use the same pure-component constants and numerical state inputs. These are model differences, not measured errors or an accuracy ranking."
      }
    ]
  },
  "recorded": {
    "kind": "EOS comparison",
    "PR": [
      {
        "inputs": {
          "p": 2,
          "T": 240,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "warnings": [
            "C1-C6 compositional equilibrium screening with zero binary interaction parameters (kij=0). No measured-fluid calibration, heavy-end characterization or energy/flow coupling is included.",
            "Two-phase equilibrium: beta is vapor moles per feed mole, not vapor mass fraction or in-situ gas holdup. Component allocations in the table are moles per feed mole."
          ],
          "outputs": [
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 71.0177835472898,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 32.874526,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction (beta)",
              "value": 0.4828540173491232,
              "unit": "dimensionless"
            },
            {
              "label": "Vapor mass fraction",
              "value": 0.27391840904671255,
              "unit": "dimensionless"
            },
            {
              "label": "Liquid density",
              "value": 607.8454032166677,
              "unit": "kg/m3"
            },
            {
              "label": "Vapor density",
              "value": 21.256290675615478,
              "unit": "kg/m3"
            },
            {
              "label": "Maximum component balance error",
              "value": 2.949029909160572e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 6.246316797131612e-10,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum relative EOS pressure residual",
              "value": 1.1935785693140133e-11,
              "unit": "dimensionless"
            }
          ],
          "rowLabels": [
            "Methane",
            "Ethane",
            "Propane",
            "n-Butane",
            "n-Pentane",
            "n-Hexane"
          ],
          "columns": [
            "Feed z (mol/mol)",
            "Liquid x (mol/mol)",
            "Vapor y (mol/mol)",
            "Liquid allocation (mol/mol feed)",
            "Vapor allocation (mol/mol feed)"
          ],
          "rows": [
            [
              0.5,
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              0.0867312469329818,
              0.4132687530670182
            ],
            [
              0.15,
              0.1889066978004242,
              0.10833017487114915,
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            [
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            ],
            [
              0.05,
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              0.0005114226450555507,
              0.049753057521271626,
              0.0002469424787283874
            ],
            [
              0.05,
              0.09657443552608362,
              0.00011787960514904036,
              0.049943081359090265,
              0.00005691864090974253
            ]
          ],
          "chart": {
            "xLabel": "Component",
            "yLabel": "Mole fraction",
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5,
                6
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "nC4",
                "nC5",
                "nC6"
              ]
            },
            "series": [
              {
                "name": "Feed",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
                  0.5,
                  0.15,
                  0.15,
                  0.1,
                  0.05,
                  0.05
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Liquid",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
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                ],
                "mode": "lines+markers"
              },
              {
                "name": "Vapor",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
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                  0.0005114226450555507,
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                ],
                "mode": "lines+markers",
                "line": {
                  "dash": "dash"
                }
              }
            ]
          }
        }
      },
      {
        "inputs": {
          "p": 2,
          "T": 260,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "warnings": [
            "C1-C6 compositional equilibrium screening with zero binary interaction parameters (kij=0). No measured-fluid calibration, heavy-end characterization or energy/flow coupling is included.",
            "Two-phase equilibrium: beta is vapor moles per feed mole, not vapor mass fraction or in-situ gas holdup. Component allocations in the table are moles per feed mole."
          ],
          "outputs": [
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 56.52672133864306,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 32.874526,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction (beta)",
              "value": 0.5691657772688676,
              "unit": "dimensionless"
            },
            {
              "label": "Vapor mass fraction",
              "value": 0.352030386375362,
              "unit": "dimensionless"
            },
            {
              "label": "Liquid density",
              "value": 600.56145262257,
              "unit": "kg/m3"
            },
            {
              "label": "Vapor density",
              "value": 21.191574942026982,
              "unit": "kg/m3"
            },
            {
              "label": "Maximum component balance error",
              "value": 5.551115123125783e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 1.7344170544220106e-10,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum relative EOS pressure residual",
              "value": 1.0192291455268787e-11,
              "unit": "dimensionless"
            }
          ],
          "rowLabels": [
            "Methane",
            "Ethane",
            "Propane",
            "n-Butane",
            "n-Pentane",
            "n-Hexane"
          ],
          "columns": [
            "Feed z (mol/mol)",
            "Liquid x (mol/mol)",
            "Vapor y (mol/mol)",
            "Liquid allocation (mol/mol feed)",
            "Vapor allocation (mol/mol feed)"
          ],
          "rows": [
            [
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              0.4459664539115297
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              0.0004432965413700792,
              0.04974769077947049,
              0.00025230922052950187
            ]
          ],
          "chart": {
            "xLabel": "Component",
            "yLabel": "Mole fraction",
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5,
                6
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "nC4",
                "nC5",
                "nC6"
              ]
            },
            "series": [
              {
                "name": "Feed",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
                  0.5,
                  0.15,
                  0.15,
                  0.1,
                  0.05,
                  0.05
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Liquid",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
                  0.12541609565262102,
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                "mode": "lines+markers"
              },
              {
                "name": "Vapor",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
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                ],
                "mode": "lines+markers",
                "line": {
                  "dash": "dash"
                }
              }
            ]
          }
        }
      },
      {
        "inputs": {
          "p": 2,
          "T": 280,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "warnings": [
            "C1-C6 compositional equilibrium screening with zero binary interaction parameters (kij=0). No measured-fluid calibration, heavy-end characterization or energy/flow coupling is included.",
            "Two-phase equilibrium: beta is vapor moles per feed mole, not vapor mass fraction or in-situ gas holdup. Component allocations in the table are moles per feed mole."
          ],
          "outputs": [
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 46.134843488332926,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 32.874526,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction (beta)",
              "value": 0.6575641159651632,
              "unit": "dimensionless"
            },
            {
              "label": "Vapor mass fraction",
              "value": 0.4489132959587217,
              "unit": "dimensionless"
            },
            {
              "label": "Liquid density",
              "value": 591.9532946677658,
              "unit": "kg/m3"
            },
            {
              "label": "Vapor density",
              "value": 21.639978235090823,
              "unit": "kg/m3"
            },
            {
              "label": "Maximum component balance error",
              "value": 5.551115123125783e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 1.8632706488830308e-10,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum relative EOS pressure residual",
              "value": 8.761880110341735e-12,
              "unit": "dimensionless"
            }
          ],
          "rowLabels": [
            "Methane",
            "Ethane",
            "Propane",
            "n-Butane",
            "n-Pentane",
            "n-Hexane"
          ],
          "columns": [
            "Feed z (mol/mol)",
            "Liquid x (mol/mol)",
            "Vapor y (mol/mol)",
            "Liquid allocation (mol/mol feed)",
            "Vapor allocation (mol/mol feed)"
          ],
          "rows": [
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          ],
          "chart": {
            "xLabel": "Component",
            "yLabel": "Mole fraction",
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5,
                6
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "nC4",
                "nC5",
                "nC6"
              ]
            },
            "series": [
              {
                "name": "Feed",
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                  3,
                  4,
                  5,
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                ],
                "y": [
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                "mode": "lines+markers"
              },
              {
                "name": "Liquid",
                "x": [
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                  3,
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                ],
                "y": [
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              },
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                "name": "Vapor",
                "x": [
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                "mode": "lines+markers",
                "line": {
                  "dash": "dash"
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          }
        }
      },
      {
        "inputs": {
          "p": 2,
          "T": 300,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "warnings": [
            "C1-C6 compositional equilibrium screening with zero binary interaction parameters (kij=0). No measured-fluid calibration, heavy-end characterization or energy/flow coupling is included.",
            "Two-phase equilibrium: beta is vapor moles per feed mole, not vapor mass fraction or in-situ gas holdup. Component allocations in the table are moles per feed mole."
          ],
          "outputs": [
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 38.32698416519073,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 32.874526,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction (beta)",
              "value": 0.749652889145806,
              "unit": "dimensionless"
            },
            {
              "label": "Vapor mass fraction",
              "value": 0.5681344488463878,
              "unit": "dimensionless"
            },
            {
              "label": "Liquid density",
              "value": 582.9464406447249,
              "unit": "kg/m3"
            },
            {
              "label": "Vapor density",
              "value": 22.411221277692594,
              "unit": "kg/m3"
            },
            {
              "label": "Maximum component balance error",
              "value": 5.551115123125783e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 7.263132317802956e-10,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum relative EOS pressure residual",
              "value": 7.569722626499242e-12,
              "unit": "dimensionless"
            }
          ],
          "rowLabels": [
            "Methane",
            "Ethane",
            "Propane",
            "n-Butane",
            "n-Pentane",
            "n-Hexane"
          ],
          "columns": [
            "Feed z (mol/mol)",
            "Liquid x (mol/mol)",
            "Vapor y (mol/mol)",
            "Liquid allocation (mol/mol feed)",
            "Vapor allocation (mol/mol feed)"
          ],
          "rows": [
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            "C1-C6 compositional equilibrium screening with zero binary interaction parameters (kij=0). No measured-fluid calibration, heavy-end characterization or energy/flow coupling is included.",
            "Two-phase equilibrium: beta is vapor moles per feed mole, not vapor mass fraction or in-situ gas holdup. Component allocations in the table are moles per feed mole."
          ],
          "outputs": [
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 37.61676847743025,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 32.874526,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction (beta)",
              "value": 0.7499510106460565,
              "unit": "dimensionless"
            },
            {
              "label": "Vapor mass fraction",
              "value": 0.5675596502012606,
              "unit": "dimensionless"
            },
            {
              "label": "Liquid density",
              "value": 516.1004556577545,
              "unit": "kg/m3"
            },
            {
              "label": "Vapor density",
              "value": 22.044584863144962,
              "unit": "kg/m3"
            },
            {
              "label": "Maximum component balance error",
              "value": 2.0816681711721685e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 4.615014925768435e-9,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum relative EOS pressure residual",
              "value": 6.513309480649099e-8,
              "unit": "dimensionless"
            }
          ],
          "rowLabels": [
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            "Ethane",
            "Propane",
            "n-Butane",
            "n-Pentane",
            "n-Hexane"
          ],
          "columns": [
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            "Liquid x (mol/mol)",
            "Vapor y (mol/mol)",
            "Liquid allocation (mol/mol feed)",
            "Vapor allocation (mol/mol feed)"
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          "chart": {
            "xLabel": "Component",
            "yLabel": "Mole fraction",
            "xTicks": {
              "values": [
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                2,
                3,
                4,
                5,
                6
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "nC4",
                "nC5",
                "nC6"
              ]
            },
            "series": [
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                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
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                "mode": "lines+markers"
              },
              {
                "name": "Liquid",
                "x": [
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                ],
                "y": [
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              },
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                "x": [
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                  3,
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                "line": {
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      },
      {
        "inputs": {
          "p": 2,
          "T": 320,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "warnings": [
            "C1-C6 compositional equilibrium screening with zero binary interaction parameters (kij=0). No measured-fluid calibration, heavy-end characterization or energy/flow coupling is included.",
            "Two-phase equilibrium: beta is vapor moles per feed mole, not vapor mass fraction or in-situ gas holdup. Component allocations in the table are moles per feed mole."
          ],
          "outputs": [
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 31.838416908610164,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 32.874526,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction (beta)",
              "value": 0.8429686910594324,
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            },
            {
              "label": "Vapor mass fraction",
              "value": 0.7086088259711958,
              "unit": "dimensionless"
            },
            {
              "label": "Liquid density",
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            },
            {
              "label": "Vapor density",
              "value": 22.981022730419852,
              "unit": "kg/m3"
            },
            {
              "label": "Maximum component balance error",
              "value": 5.551115123125783e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 4.41195363576341e-9,
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            },
            {
              "label": "Maximum relative EOS pressure residual",
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              "unit": "dimensionless"
            }
          ],
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            "Propane",
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          ],
          "columns": [
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            "Liquid x (mol/mol)",
            "Vapor y (mol/mol)",
            "Liquid allocation (mol/mol feed)",
            "Vapor allocation (mol/mol feed)"
          ],
          "rows": [
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              0.04026351140663502,
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          "chart": {
            "xLabel": "Component",
            "yLabel": "Mole fraction",
            "xTicks": {
              "values": [
                1,
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                3,
                4,
                5,
                6
              ],
              "text": [
                "C1",
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                "C3",
                "nC4",
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                "nC6"
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            },
            "series": [
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}