{
  "version": 1,
  "topic": "FA11",
  "title": "Equilibrium wax onset is not a wax deposition forecast",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Recorded equilibrium solid amounts",
    "premise": "Supported three-component synthetic regular-solution model at its documented default feed and solid properties; temperature spans 275–320 K. Full inputs are in JSON.",
    "formula": "Solid–liquid equilibrium satisfies the selected component chemical-potential conditions",
    "variables": "The plotted solid amount is an equilibrium fraction, not a deposition rate or thickness.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Temperature (K) = 297.5",
        "explanation": "Supported three-component synthetic regular-solution model at its documented default feed and solid properties; temperature spans 275–320 K. Full inputs are in JSON."
      },
      {
        "label": "Select the relation",
        "calculation": "Solid–liquid equilibrium satisfies the selected component chemical-potential conditions",
        "explanation": "The plotted solid amount is an equilibrium fraction, not a deposition rate or thickness."
      },
      {
        "label": "Substitute the values",
        "calculation": "Total solid at lower temperature = 0.313892178 mol/mol feed; C18 solid at lower temperature = 0.136655479 mol/mol feed; C20 solid at lower temperature = 0.177236698 mol/mol feed",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Total solid (mol/mol feed) = 0; C18 solid (mol/mol feed) = 0",
        "explanation": "Equilibrium appearance does not determine wall transport, deposition kinetics or blockage time."
      }
    ],
    "result": "Total solid (mol/mol feed) = 0; C18 solid (mol/mol feed) = 0",
    "interpretation": "Equilibrium appearance does not determine wall transport, deposition kinetics or blockage time.",
    "control": "Temperature (K)",
    "columns": [
      "Temperature (K)",
      "Total solid (mol/mol feed)",
      "C18 solid (mol/mol feed)"
    ],
    "rows": [
      [
        275,
        0.3138921777574645,
        0.13665547948705964
      ],
      [
        276.5,
        0.29722779702186314,
        0.12477186503199279
      ],
      [
        278,
        0.27698404920859004,
        0.11040348029626372
      ],
      [
        279.5,
        0.2521941249661011,
        0.09288898499806593
      ],
      [
        281,
        0.22153079506152265,
        0.07132117556031758
      ],
      [
        282.5,
        0.18311943683271703,
        0.04441932410820558
      ],
      [
        284,
        0.13422028985862403,
        0.010312202638200402
      ],
      [
        285.5,
        0.108517439945384,
        0
      ],
      [
        287,
        0.09134743629145547,
        5.503459214038881e-17
      ],
      [
        288.5,
        0.070715366644766,
        1.024148868339959e-16
      ],
      [
        290,
        0.04577643538232362,
        2.2251597418657106e-16
      ],
      [
        291.5,
        0.015408883392852643,
        0
      ],
      [
        293,
        0,
        0
      ],
      [
        294.5,
        0,
        0
      ],
      [
        296,
        0,
        0
      ],
      [
        297.5,
        0,
        0
      ],
      [
        299,
        0,
        0
      ],
      [
        300.5,
        0,
        0
      ],
      [
        302,
        0,
        0
      ],
      [
        303.5,
        0,
        0
      ],
      [
        305,
        0,
        0
      ],
      [
        306.5,
        0,
        0
      ],
      [
        308,
        0,
        0
      ],
      [
        309.5,
        0,
        0
      ],
      [
        311,
        0,
        0
      ],
      [
        312.5,
        0,
        0
      ],
      [
        314,
        0,
        0
      ],
      [
        315.5,
        0,
        0
      ],
      [
        317,
        0,
        0
      ],
      [
        318.5,
        0,
        0
      ],
      [
        320,
        0,
        0
      ]
    ],
    "baseline": 15,
    "rowNotes": [
      "Temperature (K) = 275. Total solid (mol/mol feed): 0.313892178; C18 solid (mol/mol feed): 0.136655479.",
      "Temperature (K) = 276.5. Total solid (mol/mol feed): 0.297227797; C18 solid (mol/mol feed): 0.124771865.",
      "Temperature (K) = 278. Total solid (mol/mol feed): 0.276984049; C18 solid (mol/mol feed): 0.11040348.",
      "Temperature (K) = 279.5. Total solid (mol/mol feed): 0.252194125; C18 solid (mol/mol feed): 0.092888985.",
      "Temperature (K) = 281. Total solid (mol/mol feed): 0.221530795; C18 solid (mol/mol feed): 0.0713211756.",
      "Temperature (K) = 282.5. Total solid (mol/mol feed): 0.183119437; C18 solid (mol/mol feed): 0.0444193241.",
      "Temperature (K) = 284. Total solid (mol/mol feed): 0.13422029; C18 solid (mol/mol feed): 0.0103122026.",
      "Temperature (K) = 285.5. Total solid (mol/mol feed): 0.10851744; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 287. Total solid (mol/mol feed): 0.0913474363; C18 solid (mol/mol feed): 5.50345921e-17.",
      "Temperature (K) = 288.5. Total solid (mol/mol feed): 0.0707153666; C18 solid (mol/mol feed): 1.02414887e-16.",
      "Temperature (K) = 290. Total solid (mol/mol feed): 0.0457764354; C18 solid (mol/mol feed): 2.22515974e-16.",
      "Temperature (K) = 291.5. Total solid (mol/mol feed): 0.0154088834; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 293. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 294.5. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 296. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 297.5. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 299. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 300.5. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 302. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 303.5. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 305. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 306.5. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 308. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 309.5. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 311. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 312.5. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 314. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 315.5. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 317. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 318.5. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0.",
      "Temperature (K) = 320. Total solid (mol/mol feed): 0; C18 solid (mol/mol feed): 0."
    ],
    "provenance": "Recorded nonideal-multisolid-wax-equilibrium workflow. No deposition or field validation is claimed.",
    "questions": [
      {
        "question": "Reproduce the baseline Total solid (mol/mol feed) without rounding intermediate values.",
        "answer": "Total solid at lower temperature = 0.313892178 mol/mol feed; C18 solid at lower temperature = 0.136655479 mol/mol feed; C20 solid at lower temperature = 0.177236698 mol/mol feed. Total solid (mol/mol feed) = 0. Equilibrium appearance does not determine wall transport, deposition kinetics or blockage time."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Temperature (K) changes from 275 to 320. Other controls remain as stated in the premise. Total solid (mol/mol feed) changes from 0.313892178 to 0."
      },
      {
        "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. The plotted solid amount is an equilibrium fraction, not a deposition rate or thickness. Equilibrium appearance does not determine wall transport, deposition kinetics or blockage time."
      }
    ]
  },
  "recorded": {
    "inputs": {
      "T_low": 275,
      "T_high": 320,
      "z1": 0.6,
      "z2": 0.2,
      "z3": 0.2,
      "V1": 131,
      "V2": 329,
      "V3": 365,
      "delta1": 15000,
      "delta2": 15500,
      "delta3": 15600
    },
    "result": {
      "outputs": [
        {
          "label": "Total solid at lower temperature",
          "value": 0.3138921777574645,
          "unit": "mol/mol feed"
        },
        {
          "label": "C18 solid at lower temperature",
          "value": 0.13665547948705964,
          "unit": "mol/mol feed"
        },
        {
          "label": "C20 solid at lower temperature",
          "value": 0.1772366982704048,
          "unit": "mol/mol feed"
        },
        {
          "label": "Maximum solid stability residual / RT",
          "value": 4.440892098500626e-16,
          "unit": "dimensionless"
        }
      ],
      "columns": [
        "Temperature (K)",
        "Total solid (mol/mol feed)",
        "C18 solid (mol/mol feed)",
        "C20 solid (mol/mol feed)",
        "Solvent liquid mole fraction",
        "C18 liquid mole fraction",
        "C20 liquid mole fraction",
        "KKT residual / RT",
        "Convexity bound"
      ],
      "rows": [
        [
          275,
          0.3138921777574645,
          0.13665547948705964,
          0.1772366982704048,
          0.8744981190258214,
          0.09232444006526487,
          0.033177440908913725,
          4.440892098500626e-16,
          0.3202432988315994
        ],
        [
          276.5,
          0.29722779702186314,
          0.12477186503199279,
          0.17245593198987033,
          0.8537617131943762,
          0.10704483565117268,
          0.03919345115445121,
          4.440892098500626e-16,
          0.31850599341298313
        ],
        [
          278,
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          0.11040348029626372,
          0.1665805689123263,
          0.8298572104021256,
          0.12392052983846946,
          0.04622225975940495,
          4.440892098500626e-16,
          0.31678743589456776
        ],
        [
          279.5,
          0.2521941249661011,
          0.09288898499806593,
          0.1593051399680352,
          0.8023472668930306,
          0.14323371690156703,
          0.054419016205402335,
          2.220446049250313e-16,
          0.3150873244318062
        ],
        [
          281,
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          0.15020961950120507,
          0.7707433976754651,
          0.16529725726254252,
          0.06395934506199238,
          2.220446049250313e-16,
          0.3134053636252307
        ],
        [
          282.5,
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          0.13870011272451144,
          0.7345015012643046,
          0.19045706668373033,
          0.07504143205196499,
          4.440892098500626e-16,
          0.3117412643493445
        ],
        [
          284,
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          0.010312202638200402,
          0.12390808722042362,
          0.6930169337209624,
          0.21909475948659604,
          0.08788830679244157,
          0,
          0.310094743586936
        ],
        [
          285.5,
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          0.673036161204591,
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          0.3084655242686159
        ],
        [
          287,
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          0.09134743629145542,
          0.6603183922699561,
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        [
          288.5,
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          0.6456579377985263,
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          0,
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        ],
        [
          290,
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          2.2251597418657106e-16,
          0.0457764353823234,
          0.6287834656864701,
          0.2095944885621565,
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        [
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        [
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        [
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        [
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        [
          297.5,
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        [
          299,
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        [
          300.5,
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          0,
          0,
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          0.2,
          0,
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        [
          302,
          0,
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          0,
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          0,
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        [
          303.5,
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          0.2,
          0,
          0.29017102859535365
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        [
          305,
          0,
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          0,
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        [
          306.5,
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          0.2,
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        [
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        [
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        [
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        [
          312.5,
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          0,
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          0.2,
          0,
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        [
          314,
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        [
          315.5,
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          0,
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          0.2,
          0.2,
          0,
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        [
          317,
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        [
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        [
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      ],
      "chart": {
        "xLabel": "Temperature (K)",
        "yLabel": "Moles solid / initial feed mole",
        "includeZero": false,
        "series": [
          {
            "name": "C18 crystal",
            "x": [
              275,
              276.5,
              278,
              279.5,
              281,
              282.5,
              284,
              285.5,
              287,
              288.5,
              290,
              291.5,
              293,
              294.5,
              296,
              297.5,
              299,
              300.5,
              302,
              303.5,
              305,
              306.5,
              308,
              309.5,
              311,
              312.5,
              314,
              315.5,
              317,
              318.5,
              320
            ],
            "y": [
              0.13665547948705964,
              0.12477186503199279,
              0.11040348029626372,
              0.09288898499806593,
              0.07132117556031758,
              0.04441932410820558,
              0.010312202638200402,
              0,
              5.503459214038881e-17,
              1.024148868339959e-16,
              2.2251597418657106e-16,
              0,
              0,
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              0,
              0,
              0,
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              0,
              0,
              0,
              0,
              0,
              0,
              0,
              0,
              0
            ]
          },
          {
            "name": "C20 crystal",
            "x": [
              275,
              276.5,
              278,
              279.5,
              281,
              282.5,
              284,
              285.5,
              287,
              288.5,
              290,
              291.5,
              293,
              294.5,
              296,
              297.5,
              299,
              300.5,
              302,
              303.5,
              305,
              306.5,
              308,
              309.5,
              311,
              312.5,
              314,
              315.5,
              317,
              318.5,
              320
            ],
            "y": [
              0.1772366982704048,
              0.17245593198987033,
              0.1665805689123263,
              0.1593051399680352,
              0.15020961950120507,
              0.13870011272451144,
              0.12390808722042362,
              0.108517439945384,
              0.09134743629145542,
              0.07071536664476591,
              0.0457764353823234,
              0.015408883392852643,
              0,
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              0,
              0,
              0,
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              0,
              0,
              0,
              0,
              0
            ]
          }
        ]
      },
      "warnings": [
        "One nonideal regular-solution liquid and two separate pure crystals; globally convex liquid domain enforced, not a solid solution or a crude-oil wax calibration. C18: 301.5 K / 61.500 kJ/mol; C20: 309.6 K / 69.000 kJ/mol, matched Barbillon et al. rows in NIST. Constant molar volumes and Hildebrand parameters are supplied assumptions (defaults are illustrative). Zero fusion heat-capacity difference, no solid polymorphs, vapor, pressure correction, asphaltenes or joint VLLS. External pressure must maintain a liquid solvent throughout the interval."
      ]
    }
  }
}