{
  "version": 1,
  "topic": "TH11",
  "title": "What a heavier C7 plus assumption changes in a synthetic flash",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Four-Cut Gamma C7+ Characterization and PR Flash Calculator",
    "premise": "Fixed controls: Equilibrium absolute pressure = 2 MPa(a); Equilibrium absolute temperature = 350 K; C7+ specific gravity (60/60 F) = 0.85 dimensionless; Methane feed mole fraction = 0.45 dimensionless; Ethane feed mole fraction = 0.15 dimensionless; Propane feed mole fraction = 0.15 dimensionless; n-Butane feed mole fraction = 0.1 dimensionless; n-Pentane feed mole fraction = 0.05 dimensionless; n-Hexane feed mole fraction = 0.03 dimensionless; C7+ feed mole fraction = 0.07 dimensionless; Conditional gamma distribution shape = 2 dimensionless; Common methane / heavy-cut interaction parameter = 0 dimensionless.",
    "formula": "Condition a shifted gamma distribution to 100-300 g/mol, shift=100, shape=alpha. Fit scale b to the supplied conditional mean using incomplete-gamma moments. Four quantile bins each carry 0.25 of C7+ moles; their representative molecular weights are conditional first moments, not bin midpoints. Reconstructed mean must close within 1e-7 g/mol.; MW-SG variant: Tb=97.58*M^0.3323*SG^0.04609 K. Tc=(5/9)*554.4*exp(-1.3478e-4*M-0.61641*SG)*M^0.2998*SG^1.0555 K. M is g/mol, SG dimensionless; no Pedersen fallback.; Pc(bar)=0.068947*45203*exp(-0.0018078*M-0.3084*SG)*M^-0.8063*SG^1.6015. Retain NeqSim's rounded conversion coefficient for reference reproducibility, then convert bar to Pa exactly.; Edmister omega=(3/7)*log10(Pc(Pa)/101325)/(Tc/Tb-1)-1. This is NeqSim calcAcentricFactor2, not its Kesler-Lee default. Watson Kw=(1.8*Tb(K))^(1/3)/SG uses Rankine.; Classical Peng-Robinson, standard quadratic alpha: a=sum_i sum_j xi*xj*sqrt(ai*aj)*(1-kij), b=sum_i xi*bi. The matrix is symmetric with zero diagonal. Available database coefficients and common user-assumed coefficients are distinguished; there is no volume translation or hidden parameter tuning.",
    "variables": "C7+ measured molar-average molecular weight is varied within the supported input range. A deliberately bounded four-cut approximation over 100-300 g/mol, not a complete Whitson C7-to-C80 assay. Every cut uses the same supplied 60/60 F SG. Reject an unbracketed mean, retained gamma probability below 1e-6, Tb>=Tc or omega outside 0-1. Shape does not determine aromaticity or a measured carbon-number distribution.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "C7+ measured molar-average molecular weight (g/mol) = 200",
        "explanation": "Fixed controls: Equilibrium absolute pressure = 2 MPa(a); Equilibrium absolute temperature = 350 K; C7+ specific gravity (60/60 F) = 0.85 dimensionless; Methane feed mole fraction = 0.45 dimensionless; Ethane feed mole fraction = 0.15 dimensionless; Propane feed mole fraction = 0.15 dimensionless; n-Butane feed mole fraction = 0.1 dimensionless; n-Pentane feed mole fraction = 0.05 dimensionless; n-Hexane feed mole fraction = 0.03 dimensionless; C7+ feed mole fraction = 0.07 dimensionless; Conditional gamma distribution shape = 2 dimensionless; Common methane / heavy-cut interaction parameter = 0 dimensionless."
      },
      {
        "label": "Select the relation",
        "calculation": "Condition a shifted gamma distribution to 100-300 g/mol, shift=100, shape=alpha. Fit scale b to the supplied conditional mean using incomplete-gamma moments. Four quantile bins each carry 0.25 of C7+ moles; their representative molecular weights are conditional first moments, not bin midpoints. Reconstructed mean must close within 1e-7 g/mol.; MW-SG variant: Tb=97.58*M^0.3323*SG^0.04609 K. Tc=(5/9)*554.4*exp(-1.3478e-4*M-0.61641*SG)*M^0.2998*SG^1.0555 K. M is g/mol, SG dimensionless; no Pedersen fallback.; Pc(bar)=0.068947*45203*exp(-0.0018078*M-0.3084*SG)*M^-0.8063*SG^1.6015. Retain NeqSim's rounded conversion coefficient for reference reproducibility, then convert bar to Pa exactly.; Edmister omega=(3/7)*log10(Pc(Pa)/101325)/(Tc/Tb-1)-1. This is NeqSim calcAcentricFactor2, not its Kesler-Lee default. Watson Kw=(1.8*Tb(K))^(1/3)/SG uses Rankine.; Classical Peng-Robinson, standard quadratic alpha: a=sum_i sum_j xi*xj*sqrt(ai*aj)*(1-kij), b=sum_i xi*bi. The matrix is symmetric with zero diagonal. Available database coefficients and common user-assumed coefficients are distinguished; there is no volume translation or hidden parameter tuning.",
        "explanation": "C7+ measured molar-average molecular weight is varied within the supported input range. A deliberately bounded four-cut approximation over 100-300 g/mol, not a complete Whitson C7-to-C80 assay. Every cut uses the same supplied 60/60 F SG. Reject an unbracketed mean, retained gamma probability below 1e-6, Tb>=Tc or omega outside 0-1. Shape does not determine aromaticity or a measured carbon-number distribution."
      },
      {
        "label": "Substitute the values",
        "calculation": "M = 200 g/mol; with the fixed controls above, the workflow evaluates Vapor mole fraction = 0.821170907 dimensionless; Vapor mass fraction = 0.54114372 dimensionless",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Vapor mole fraction (dimensionless) = 0.821170907; Vapor mass fraction (dimensionless) = 0.54114372",
        "explanation": "MW=100-300 g/mol, SG=0.65-0.90, shape=0.5-10; the conditional mean must also be achievable at that shape. At least two feed fractions >=0.001; C7+ is 0.004-0.99. T=180-450 K and p=0.1-10 MPa(a) are software bounds, not a validated accuracy envelope. No water, N2, CO2, H2S, solids, multiple liquids, volume shifts or density matching. Only methane/heavy-cut pairs share the user k_heavy (-0.2 to 0.4). All other pairs are zero. Properties use the pinned NeqSim Riazi-Daubert MW-SG variant plus explicit Edmister omega, not a silent Pedersen or Kesler-Lee fallback. Neither a solved flash nor a fitted parameter is proof of physical accuracy."
      }
    ],
    "result": "Vapor mole fraction (dimensionless) = 0.821170907; Vapor mass fraction (dimensionless) = 0.54114372",
    "interpretation": "MW=100-300 g/mol, SG=0.65-0.90, shape=0.5-10; the conditional mean must also be achievable at that shape. At least two feed fractions >=0.001; C7+ is 0.004-0.99. T=180-450 K and p=0.1-10 MPa(a) are software bounds, not a validated accuracy envelope. No water, N2, CO2, H2S, solids, multiple liquids, volume shifts or density matching. Only methane/heavy-cut pairs share the user k_heavy (-0.2 to 0.4). All other pairs are zero. Properties use the pinned NeqSim Riazi-Daubert MW-SG variant plus explicit Edmister omega, not a silent Pedersen or Kesler-Lee fallback. Neither a solved flash nor a fitted parameter is proof of physical accuracy.",
    "control": "C7+ measured molar-average molecular weight (g/mol)",
    "columns": [
      "C7+ measured molar-average molecular weight (g/mol)",
      "Vapor mole fraction (dimensionless)",
      "Vapor mass fraction (dimensionless)"
    ],
    "rows": [
      [
        160,
        0.8308344829268548,
        0.589111881884612
      ],
      [
        180,
        0.8252841345598947,
        0.5633749340499484
      ],
      [
        200,
        0.8211709065062422,
        0.5411437201833701
      ],
      [
        210,
        0.8195682560648943,
        0.5311118172323331
      ],
      [
        220,
        0.8182105001797494,
        0.521683495890791
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "C7+ measured molar-average molecular weight (g/mol) = 160. Vapor mole fraction (dimensionless): 0.830834483; Vapor mass fraction (dimensionless): 0.589111882.",
      "C7+ measured molar-average molecular weight (g/mol) = 180. Vapor mole fraction (dimensionless): 0.825284135; Vapor mass fraction (dimensionless): 0.563374934.",
      "C7+ measured molar-average molecular weight (g/mol) = 200. Vapor mole fraction (dimensionless): 0.821170907; Vapor mass fraction (dimensionless): 0.54114372.",
      "C7+ measured molar-average molecular weight (g/mol) = 210. Vapor mole fraction (dimensionless): 0.819568256; Vapor mass fraction (dimensionless): 0.531111817.",
      "C7+ measured molar-average molecular weight (g/mol) = 220. Vapor mole fraction (dimensionless): 0.8182105; Vapor mass fraction (dimensionless): 0.521683496."
    ],
    "provenance": "Original recorded synthetic cases solved with the site's gamma-c7-plus-flash 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 Vapor mole fraction (dimensionless) without rounding intermediate values.",
        "answer": "M = 200 g/mol; with the fixed controls above, the workflow evaluates Vapor mole fraction = 0.821170907 dimensionless; Vapor mass fraction = 0.54114372 dimensionless. Vapor mole fraction (dimensionless) = 0.821170907. MW=100-300 g/mol, SG=0.65-0.90, shape=0.5-10; the conditional mean must also be achievable at that shape. At least two feed fractions >=0.001; C7+ is 0.004-0.99. T=180-450 K and p=0.1-10 MPa(a) are software bounds, not a validated accuracy envelope. No water, N2, CO2, H2S, solids, multiple liquids, volume shifts or density matching. Only methane/heavy-cut pairs share the user k_heavy (-0.2 to 0.4). All other pairs are zero. Properties use the pinned NeqSim Riazi-Daubert MW-SG variant plus explicit Edmister omega, not a silent Pedersen or Kesler-Lee fallback. Neither a solved flash nor a fitted parameter is proof of physical accuracy."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "C7+ measured molar-average molecular weight (g/mol) changes from 160 to 220. Other controls remain as stated in the premise. Vapor mole fraction (dimensionless) changes from 0.830834483 to 0.8182105."
      },
      {
        "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. C7+ measured molar-average molecular weight is varied within the supported input range. A deliberately bounded four-cut approximation over 100-300 g/mol, not a complete Whitson C7-to-C80 assay. Every cut uses the same supplied 60/60 F SG. Reject an unbracketed mean, retained gamma probability below 1e-6, Tb>=Tc or omega outside 0-1. Shape does not determine aromaticity or a measured carbon-number distribution. MW=100-300 g/mol, SG=0.65-0.90, shape=0.5-10; the conditional mean must also be achievable at that shape. At least two feed fractions >=0.001; C7+ is 0.004-0.99. T=180-450 K and p=0.1-10 MPa(a) are software bounds, not a validated accuracy envelope. No water, N2, CO2, H2S, solids, multiple liquids, volume shifts or density matching. Only methane/heavy-cut pairs share the user k_heavy (-0.2 to 0.4). All other pairs are zero. Properties use the pinned NeqSim Riazi-Daubert MW-SG variant plus explicit Edmister omega, not a silent Pedersen or Kesler-Lee fallback. Neither a solved flash nor a fitted parameter is proof of physical accuracy."
      }
    ]
  },
  "recorded": {
    "kind": "workflow",
    "workflow": "gamma-c7-plus-flash",
    "parameter": "M",
    "runs": [
      {
        "inputs": {
          "p": 2,
          "T": 350,
          "M": 160,
          "SG": 0.85,
          "z1": 0.45,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.03,
          "z7": 0.07,
          "alpha": 2,
          "k_heavy": 0
        },
        "result": {
          "outputs": [
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 37.045707993561734,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 41.548878800000004,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction",
              "value": 0.8308344829268548,
              "unit": "dimensionless"
            },
            {
              "label": "Vapor mass fraction",
              "value": 0.589111881884612,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum component balance error",
              "value": 2.7755575615628914e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 3.1765961594487635e-7,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum relative EOS pressure residual",
              "value": 2.1606683731079102e-13,
              "unit": "dimensionless"
            },
            {
              "label": "Conditional gamma scale",
              "value": 31.036950990432647,
              "unit": "g/mol"
            },
            {
              "label": "Unconditioned probability retained between 100 and 300 g/mol",
              "value": 0.9881630910209175,
              "unit": "dimensionless"
            },
            {
              "label": "Reconstructed C7+ mean molecular weight",
              "value": 160.00000000000003,
              "unit": "g/mol"
            }
          ],
          "columns": [
            "Feed z (mol/mol)",
            "Vapor composition (mol/mol)",
            "Vapor allocation (mol/mol feed)",
            "Liquid 1 composition (mol/mol)",
            "Liquid 1 allocation (mol/mol feed)",
            "MW (g/mol)",
            "Critical temperature (K)",
            "Critical pressure (MPa(a))",
            "Acentric factor"
          ],
          "rows": [
            [
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            ],
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            ],
            [
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            [
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            [
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            [
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          ],
          "rowLabels": [
            "Methane",
            "Ethane",
            "Propane",
            "n-Butane",
            "n-Pentane",
            "n-Hexane",
            "C7+ cut 1",
            "C7+ cut 2",
            "C7+ cut 3",
            "C7+ cut 4"
          ],
          "chart": {
            "xLabel": "Component",
            "yLabel": "Mole fraction",
            "xTickAngle": -45,
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5,
                6,
                7,
                8,
                9,
                10
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "nC4",
                "nC5",
                "nC6",
                "H1",
                "H2",
                "H3",
                "H4"
              ]
            },
            "series": [
              {
                "name": "Feed",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6,
                  7,
                  8,
                  9,
                  10
                ],
                "y": [
                  0.45,
                  0.15,
                  0.15,
                  0.1,
                  0.05,
                  0.03,
                  0.017499999999999998,
                  0.01750000000000001,
                  0.017499999999999995,
                  0.017500000000000005
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Vapor",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6,
                  7,
                  8,
                  9,
                  10
                ],
                "y": [
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                  0.00003090538175392778,
                  0.000010742494215989103,
                  0.0000026746788045928796
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Liquid 1",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6,
                  7,
                  8,
                  9,
                  10
                ],
                "y": [
                  0.03831283252277361,
                  0.04538802873191068,
                  0.10641260594370076,
                  0.15033516728379878,
                  0.1316952684421818,
                  0.1147505213380534,
                  0.10297632362506284,
                  0.1032971910911083,
                  0.10339621849652592,
                  0.10343584252488383
                ],
                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Numerical closure is not measured-PVT validation. PR with the stated interaction matrix; no volume translation, reactions or solids. Single-phase states are not assigned an invented vapor quality.",
            "Four equal-probability cuts of a gamma distribution conditioned to 100-300 g/mol, with its scale fitted to the measured conditional mean. All cuts share the supplied SG. This is a bounded approximation, not a C30+ assay. PT-only: the internal ideal-reference gauge is not a heavy heat-capacity model."
          ]
        }
      },
      {
        "inputs": {
          "p": 2,
          "T": 350,
          "M": 180,
          "SG": 0.85,
          "z1": 0.45,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.03,
          "z7": 0.07,
          "alpha": 2,
          "k_heavy": 0
        },
        "result": {
          "outputs": [
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 38.38812376235492,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 42.9488788000004,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction",
              "value": 0.8252841345598947,
              "unit": "dimensionless"
            },
            {
              "label": "Vapor mass fraction",
              "value": 0.5633749340499484,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum component balance error",
              "value": 2.7755575615628914e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 7.740151986013188e-8,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum relative EOS pressure residual",
              "value": 2.1606683731079102e-13,
              "unit": "dimensionless"
            },
            {
              "label": "Conditional gamma scale",
              "value": 46.07960628913417,
              "unit": "g/mol"
            },
            {
              "label": "Unconditioned probability retained between 100 and 300 g/mol",
              "value": 0.930402751650804,
              "unit": "dimensionless"
            },
            {
              "label": "Reconstructed C7+ mean molecular weight",
              "value": 180.0000000000057,
              "unit": "g/mol"
            }
          ],
          "columns": [
            "Feed z (mol/mol)",
            "Vapor composition (mol/mol)",
            "Vapor allocation (mol/mol feed)",
            "Liquid 1 composition (mol/mol)",
            "Liquid 1 allocation (mol/mol feed)",
            "MW (g/mol)",
            "Critical temperature (K)",
            "Critical pressure (MPa(a))",
            "Acentric factor"
          ],
          "rows": [
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          "rowLabels": [
            "Methane",
            "Ethane",
            "Propane",
            "n-Butane",
            "n-Pentane",
            "n-Hexane",
            "C7+ cut 1",
            "C7+ cut 2",
            "C7+ cut 3",
            "C7+ cut 4"
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          "chart": {
            "xLabel": "Component",
            "yLabel": "Mole fraction",
            "xTickAngle": -45,
            "xTicks": {
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              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "nC4",
                "nC5",
                "nC6",
                "H1",
                "H2",
                "H3",
                "H4"
              ]
            },
            "series": [
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                "y": [
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              {
                "name": "Vapor",
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              {
                "name": "Liquid 1",
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                  5,
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                "y": [
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          "warnings": [
            "Numerical closure is not measured-PVT validation. PR with the stated interaction matrix; no volume translation, reactions or solids. Single-phase states are not assigned an invented vapor quality.",
            "Four equal-probability cuts of a gamma distribution conditioned to 100-300 g/mol, with its scale fitted to the measured conditional mean. All cuts share the supplied SG. This is a bounded approximation, not a C30+ assay. PT-only: the internal ideal-reference gauge is not a heavy heat-capacity model."
          ]
        }
      }
    ]
  }
}