{
  "version": 1,
  "topic": "FA06",
  "title": "Hydrate onset versus wax appearance in a flow assurance model",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Mixed-Gas Hydrate Onset and Cage Occupancy Calculator",
    "premise": "Fixed controls: Operating temperature = 290 K; Supplied liquid-water activity = 1 dimensionless; Methane guest-gas mole fraction = 0.9 mol/mol; Ethane guest-gas mole fraction = 0.05 mol/mol; Propane guest-gas mole fraction = 0.02 mol/mol; Carbon dioxide guest-gas mole fraction = 0.02 mol/mol; Nitrogen guest-gas mole fraction = 0.01 mol/mol.",
    "formula": "C_ic=A_ic/T exp(B_ic/T), in 1/bar; fi=zi*phi_i*p in bar. A/B are the five-guest NeqSim 3.26.0 COMP.csv subset, not Kihara-integral coefficients. Gas fugacity is calculated with classical PR and explicitly assumed zero binary interactions.; Use the pinned NeqSim PVTsim empty-lattice Gibbs/enthalpy/Cp/volume expression relative to liquid water. nu=(1/23,3/23) for sI and (2/17,1/17) for sII. Solve each bracketed 273.15-303.15 K onset; choose the higher temperature as the first structure to become stable on cooling.",
    "variables": "Absolute gas pressure is varied within the supported input range. 273.15-303.15 K, 3-10 MPa(a), water activity 0.8-1; fixed CH4-rich gas only. Condensation, failed gas stability and unbracketed onset fail explicitly.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Absolute gas pressure (MPa(a)) = 5",
        "explanation": "Fixed controls: Operating temperature = 290 K; Supplied liquid-water activity = 1 dimensionless; Methane guest-gas mole fraction = 0.9 mol/mol; Ethane guest-gas mole fraction = 0.05 mol/mol; Propane guest-gas mole fraction = 0.02 mol/mol; Carbon dioxide guest-gas mole fraction = 0.02 mol/mol; Nitrogen guest-gas mole fraction = 0.01 mol/mol."
      },
      {
        "label": "Select the relation",
        "calculation": "C_ic=A_ic/T exp(B_ic/T), in 1/bar; fi=zi*phi_i*p in bar. A/B are the five-guest NeqSim 3.26.0 COMP.csv subset, not Kihara-integral coefficients. Gas fugacity is calculated with classical PR and explicitly assumed zero binary interactions.; Use the pinned NeqSim PVTsim empty-lattice Gibbs/enthalpy/Cp/volume expression relative to liquid water. nu=(1/23,3/23) for sI and (2/17,1/17) for sII. Solve each bracketed 273.15-303.15 K onset; choose the higher temperature as the first structure to become stable on cooling.",
        "explanation": "Absolute gas pressure is varied within the supported input range. 273.15-303.15 K, 3-10 MPa(a), water activity 0.8-1; fixed CH4-rich gas only. Condensation, failed gas stability and unbracketed onset fail explicitly."
      },
      {
        "label": "Substitute the values",
        "calculation": "p = 5 MPa(a); with the fixed controls above, the workflow evaluates Hydrate onset temperature = 287.264214 K; Temperature minus hydrate onset = 2.73578582 K difference",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Hydrate onset temperature (K) = 287.264214; Temperature minus hydrate onset (K difference) = 2.73578582",
        "explanation": "Water activity is supplied, not derived from salinity, glycols, methanol, dissolved gas or reactive aqueous chemistry. The PR gas and empirical hydrate parameter combination needs measured validation for a particular feed. No ice competition, sH, hydrate quantity, kinetics, multiple simultaneous hydrate phases, condensate or joint VLLS equilibrium. This is a bounded onset screen, not the full NeqSim process simulator."
      }
    ],
    "result": "Hydrate onset temperature (K) = 287.264214; Temperature minus hydrate onset (K difference) = 2.73578582",
    "interpretation": "Water activity is supplied, not derived from salinity, glycols, methanol, dissolved gas or reactive aqueous chemistry. The PR gas and empirical hydrate parameter combination needs measured validation for a particular feed. No ice competition, sH, hydrate quantity, kinetics, multiple simultaneous hydrate phases, condensate or joint VLLS equilibrium. This is a bounded onset screen, not the full NeqSim process simulator.",
    "control": "Absolute gas pressure (MPa(a))",
    "columns": [
      "Absolute gas pressure (MPa(a))",
      "Hydrate onset temperature (K)",
      "Temperature minus hydrate onset (K difference)"
    ],
    "rows": [
      [
        3,
        283.35153177594924,
        6.6484682240507595
      ],
      [
        4,
        285.60496079749845,
        4.39503920250155
      ],
      [
        5,
        287.2642141790668,
        2.735785820933188
      ],
      [
        7,
        289.56271368573425,
        0.43728631426574793
      ],
      [
        10,
        291.66843690914925,
        -1.66843690914925
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Absolute gas pressure (MPa(a)) = 3. Hydrate onset temperature (K): 283.351532; Temperature minus hydrate onset (K difference): 6.64846822.",
      "Absolute gas pressure (MPa(a)) = 4. Hydrate onset temperature (K): 285.604961; Temperature minus hydrate onset (K difference): 4.3950392.",
      "Absolute gas pressure (MPa(a)) = 5. Hydrate onset temperature (K): 287.264214; Temperature minus hydrate onset (K difference): 2.73578582.",
      "Absolute gas pressure (MPa(a)) = 7. Hydrate onset temperature (K): 289.562714; Temperature minus hydrate onset (K difference): 0.437286314.",
      "Absolute gas pressure (MPa(a)) = 10. Hydrate onset temperature (K): 291.668437; Temperature minus hydrate onset (K difference): -1.66843691."
    ],
    "provenance": "Original recorded synthetic cases solved with the site's mixed-gas-hydrate-onset engine. The full inputs, outputs and diagnostic rows are in the downloadable JSON. These are discrete solved states; the lesson does not interpolate a new solve.",
    "questions": [
      {
        "question": "Reproduce the baseline Hydrate onset temperature (K) without rounding intermediate values.",
        "answer": "p = 5 MPa(a); with the fixed controls above, the workflow evaluates Hydrate onset temperature = 287.264214 K; Temperature minus hydrate onset = 2.73578582 K difference. Hydrate onset temperature (K) = 287.264214. Water activity is supplied, not derived from salinity, glycols, methanol, dissolved gas or reactive aqueous chemistry. The PR gas and empirical hydrate parameter combination needs measured validation for a particular feed. No ice competition, sH, hydrate quantity, kinetics, multiple simultaneous hydrate phases, condensate or joint VLLS equilibrium. This is a bounded onset screen, not the full NeqSim process simulator."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Absolute gas pressure (MPa(a)) changes from 3 to 10. Other controls remain as stated in the premise. Hydrate onset temperature (K) changes from 283.351532 to 291.668437."
      },
      {
        "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. Absolute gas pressure is varied within the supported input range. 273.15-303.15 K, 3-10 MPa(a), water activity 0.8-1; fixed CH4-rich gas only. Condensation, failed gas stability and unbracketed onset fail explicitly. Water activity is supplied, not derived from salinity, glycols, methanol, dissolved gas or reactive aqueous chemistry. The PR gas and empirical hydrate parameter combination needs measured validation for a particular feed. No ice competition, sH, hydrate quantity, kinetics, multiple simultaneous hydrate phases, condensate or joint VLLS equilibrium. This is a bounded onset screen, not the full NeqSim process simulator."
      }
    ]
  },
  "recorded": {
    "kind": "workflow",
    "workflow": "mixed-gas-hydrate-onset",
    "parameter": "p",
    "runs": [
      {
        "inputs": {
          "p": 3,
          "T": 290,
          "aw": 1,
          "z1": 0.9,
          "z2": 0.05,
          "z3": 0.02,
          "z4": 0.02,
          "z5": 0.01
        },
        "result": {
          "outputs": [
            {
              "label": "Hydrate onset temperature",
              "value": 283.35153177594924,
              "unit": "K"
            },
            {
              "label": "Temperature minus hydrate onset",
              "value": 6.6484682240507595,
              "unit": "K difference"
            },
            {
              "label": "Selected structure (1=sI, 2=sII)",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Hydration number (water / guest)",
              "value": 6.608376801594754,
              "unit": "dimensionless"
            },
            {
              "label": "Water chemical-potential residual / RT",
              "value": 4.275468867831478e-13,
              "unit": "dimensionless"
            }
          ],
          "columns": [
            "Guest index",
            "Gas mole fraction",
            "Gas fugacity (bar)",
            "Small cage occupancy",
            "Large cage occupancy",
            "Hydrate guest mole fraction"
          ],
          "rows": [
            [
              1,
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            [
              2,
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            [
              3,
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              0.00017942864550553835,
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            ]
          ],
          "rowLabels": [
            "Methane",
            "Ethane",
            "Propane",
            "Carbon dioxide",
            "Nitrogen"
          ],
          "chart": {
            "xLabel": "Guest",
            "yLabel": "Cage occupancy",
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "CO2",
                "N2"
              ]
            },
            "series": [
              {
                "name": "Small cage",
                "x": [
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                  3,
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                "y": [
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                "mode": "lines+markers"
              },
              {
                "name": "Large cage",
                "x": [
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                  2,
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                  4,
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                ],
                "y": [
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                ],
                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Selected sII; higher onset of the bracketed structures. Methane-rich, fixed-composition guest gas with supplied water activity. Positive temperature margin favors fluid water relative to the first hydrate onset, not operational safety. No hydrate amount, nucleation time, aqueous composition, inhibitor dose, ice, sH, condensate or joint VLLS flash. Zero PR interaction parameters are explicit uncalibrated assumptions; gas dissolution is absorbed only through the supplied activity, not calculated."
          ]
        }
      },
      {
        "inputs": {
          "p": 4,
          "T": 290,
          "aw": 1,
          "z1": 0.9,
          "z2": 0.05,
          "z3": 0.02,
          "z4": 0.02,
          "z5": 0.01
        },
        "result": {
          "outputs": [
            {
              "label": "Hydrate onset temperature",
              "value": 285.60496079749845,
              "unit": "K"
            },
            {
              "label": "Temperature minus hydrate onset",
              "value": 4.39503920250155,
              "unit": "K difference"
            },
            {
              "label": "Selected structure (1=sI, 2=sII)",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Hydration number (water / guest)",
              "value": 6.464873770305929,
              "unit": "dimensionless"
            },
            {
              "label": "Water chemical-potential residual / RT",
              "value": 5.793143742494067e-13,
              "unit": "dimensionless"
            }
          ],
          "columns": [
            "Guest index",
            "Gas mole fraction",
            "Gas fugacity (bar)",
            "Small cage occupancy",
            "Large cage occupancy",
            "Hydrate guest mole fraction"
          ],
          "rows": [
            [
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            [
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          ],
          "rowLabels": [
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            "Ethane",
            "Propane",
            "Carbon dioxide",
            "Nitrogen"
          ],
          "chart": {
            "xLabel": "Guest",
            "yLabel": "Cage occupancy",
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "CO2",
                "N2"
              ]
            },
            "series": [
              {
                "name": "Small cage",
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                "mode": "lines+markers"
              },
              {
                "name": "Large cage",
                "x": [
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                  3,
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                  5
                ],
                "y": [
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                ],
                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Selected sII; higher onset of the bracketed structures. Methane-rich, fixed-composition guest gas with supplied water activity. Positive temperature margin favors fluid water relative to the first hydrate onset, not operational safety. No hydrate amount, nucleation time, aqueous composition, inhibitor dose, ice, sH, condensate or joint VLLS flash. Zero PR interaction parameters are explicit uncalibrated assumptions; gas dissolution is absorbed only through the supplied activity, not calculated."
          ]
        }
      },
      {
        "inputs": {
          "p": 5,
          "T": 290,
          "aw": 1,
          "z1": 0.9,
          "z2": 0.05,
          "z3": 0.02,
          "z4": 0.02,
          "z5": 0.01
        },
        "result": {
          "outputs": [
            {
              "label": "Hydrate onset temperature",
              "value": 287.2642141790668,
              "unit": "K"
            },
            {
              "label": "Temperature minus hydrate onset",
              "value": 2.735785820933188,
              "unit": "K difference"
            },
            {
              "label": "Selected structure (1=sI, 2=sII)",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Hydration number (water / guest)",
              "value": 6.3679660841485575,
              "unit": "dimensionless"
            },
            {
              "label": "Water chemical-potential residual / RT",
              "value": 5.763167720829188e-13,
              "unit": "dimensionless"
            }
          ],
          "columns": [
            "Guest index",
            "Gas mole fraction",
            "Gas fugacity (bar)",
            "Small cage occupancy",
            "Large cage occupancy",
            "Hydrate guest mole fraction"
          ],
          "rows": [
            [
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          "rowLabels": [
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            "Nitrogen"
          ],
          "chart": {
            "xLabel": "Guest",
            "yLabel": "Cage occupancy",
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "CO2",
                "N2"
              ]
            },
            "series": [
              {
                "name": "Small cage",
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                "mode": "lines+markers"
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                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Selected sII; higher onset of the bracketed structures. Methane-rich, fixed-composition guest gas with supplied water activity. Positive temperature margin favors fluid water relative to the first hydrate onset, not operational safety. No hydrate amount, nucleation time, aqueous composition, inhibitor dose, ice, sH, condensate or joint VLLS flash. Zero PR interaction parameters are explicit uncalibrated assumptions; gas dissolution is absorbed only through the supplied activity, not calculated."
          ]
        }
      },
      {
        "inputs": {
          "p": 7,
          "T": 290,
          "aw": 1,
          "z1": 0.9,
          "z2": 0.05,
          "z3": 0.02,
          "z4": 0.02,
          "z5": 0.01
        },
        "result": {
          "outputs": [
            {
              "label": "Hydrate onset temperature",
              "value": 289.56271368573425,
              "unit": "K"
            },
            {
              "label": "Temperature minus hydrate onset",
              "value": 0.43728631426574793,
              "unit": "K difference"
            },
            {
              "label": "Selected structure (1=sI, 2=sII)",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Hydration number (water / guest)",
              "value": 6.242521759055514,
              "unit": "dimensionless"
            },
            {
              "label": "Water chemical-potential residual / RT",
              "value": 2.3314683517128287e-14,
              "unit": "dimensionless"
            }
          ],
          "columns": [
            "Guest index",
            "Gas mole fraction",
            "Gas fugacity (bar)",
            "Small cage occupancy",
            "Large cage occupancy",
            "Hydrate guest mole fraction"
          ],
          "rows": [
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          ],
          "chart": {
            "xLabel": "Guest",
            "yLabel": "Cage occupancy",
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "CO2",
                "N2"
              ]
            },
            "series": [
              {
                "name": "Small cage",
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                "mode": "lines+markers"
              },
              {
                "name": "Large cage",
                "x": [
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                "y": [
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                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Selected sII; higher onset of the bracketed structures. Methane-rich, fixed-composition guest gas with supplied water activity. Positive temperature margin favors fluid water relative to the first hydrate onset, not operational safety. No hydrate amount, nucleation time, aqueous composition, inhibitor dose, ice, sH, condensate or joint VLLS flash. Zero PR interaction parameters are explicit uncalibrated assumptions; gas dissolution is absorbed only through the supplied activity, not calculated."
          ]
        }
      },
      {
        "inputs": {
          "p": 10,
          "T": 290,
          "aw": 1,
          "z1": 0.9,
          "z2": 0.05,
          "z3": 0.02,
          "z4": 0.02,
          "z5": 0.01
        },
        "result": {
          "outputs": [
            {
              "label": "Hydrate onset temperature",
              "value": 291.66843690914925,
              "unit": "K"
            },
            {
              "label": "Temperature minus hydrate onset",
              "value": -1.66843690914925,
              "unit": "K difference"
            },
            {
              "label": "Selected structure (1=sI, 2=sII)",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Hydration number (water / guest)",
              "value": 6.132874265700335,
              "unit": "dimensionless"
            },
            {
              "label": "Water chemical-potential residual / RT",
              "value": 7.771561172376096e-15,
              "unit": "dimensionless"
            }
          ],
          "columns": [
            "Guest index",
            "Gas mole fraction",
            "Gas fugacity (bar)",
            "Small cage occupancy",
            "Large cage occupancy",
            "Hydrate guest mole fraction"
          ],
          "rows": [
            [
              1,
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            [
              3,
              0.02,
              0.6355043142070558,
              0,
              0.5306665220797081,
              0.19144182687831413
            ],
            [
              4,
              0.02,
              1.1393214316020772,
              0.008282778531332195,
              0.0259102781256095,
              0.01532346803178198
            ],
            [
              5,
              0.01,
              1.0567494541117786,
              0.0029172777329696583,
              0.0004465077413449947,
              0.0022659394650112446
            ]
          ],
          "rowLabels": [
            "Methane",
            "Ethane",
            "Propane",
            "Carbon dioxide",
            "Nitrogen"
          ],
          "chart": {
            "xLabel": "Guest",
            "yLabel": "Cage occupancy",
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "CO2",
                "N2"
              ]
            },
            "series": [
              {
                "name": "Small cage",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5
                ],
                "y": [
                  0.8775060002514127,
                  0,
                  0,
                  0.008282778531332195,
                  0.0029172777329696583
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Large cage",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5
                ],
                "y": [
                  0.13686375153170816,
                  0.3006474325391316,
                  0.5306665220797081,
                  0.0259102781256095,
                  0.0004465077413449947
                ],
                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Selected sII; higher onset of the bracketed structures. Methane-rich, fixed-composition guest gas with supplied water activity. Positive temperature margin favors fluid water relative to the first hydrate onset, not operational safety. No hydrate amount, nucleation time, aqueous composition, inhibitor dose, ice, sH, condensate or joint VLLS flash. Zero PR interaction parameters are explicit uncalibrated assumptions; gas dissolution is absorbed only through the supplied activity, not calculated."
          ]
        }
      }
    ]
  }
}