{
  "version": 1,
  "topic": "TH08",
  "title": "Explore separator pressure and phase split on one synthetic feed",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Three-Stage Hydrocarbon Separator Train Calculator",
    "premise": "Fixed controls: Stage 1 absolute temperature = 330 K; Stage 2 absolute pressure = 2 MPa(a); Stage 2 absolute temperature = 300 K; Stage 3 absolute pressure = 0.5 MPa(a); Stage 3 absolute temperature = 280 K; Methane feed mole fraction = 0.5 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 = 0.05 dimensionless.",
    "formula": "Normalize original feed moles to one. Stage j removes NV,j=Nj*beta_j and sends only Nj+1=Nj*(1-beta_j) with composition xj to the next stage. Overall zi0=sum_j NV,j*yij+NL3*xi3. Separator pressure strictly decreases, while temperatures are prescribed independently.; For j=2,3, interstage heat Qj=Nj*(stage-equilibrium molar enthalpy minus previous liquid molar enthalpy), J/mol original feed. Stage 1 establishes initial enthalpy, so upstream conditioning duty is not included. Sum all removed vapor energy and final liquid energy and require overall residual<1e-4 J/mol original feed.; 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": "Stage 1 absolute pressure is varied within the supported input range. Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Stage 1 absolute pressure (MPa(a)) = 5",
        "explanation": "Fixed controls: Stage 1 absolute temperature = 330 K; Stage 2 absolute pressure = 2 MPa(a); Stage 2 absolute temperature = 300 K; Stage 3 absolute pressure = 0.5 MPa(a); Stage 3 absolute temperature = 280 K; Methane feed mole fraction = 0.5 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 = 0.05 dimensionless."
      },
      {
        "label": "Select the relation",
        "calculation": "Normalize original feed moles to one. Stage j removes NV,j=Nj*beta_j and sends only Nj+1=Nj*(1-beta_j) with composition xj to the next stage. Overall zi0=sum_j NV,j*yij+NL3*xi3. Separator pressure strictly decreases, while temperatures are prescribed independently.; For j=2,3, interstage heat Qj=Nj*(stage-equilibrium molar enthalpy minus previous liquid molar enthalpy), J/mol original feed. Stage 1 establishes initial enthalpy, so upstream conditioning duty is not included. Sum all removed vapor energy and final liquid energy and require overall residual<1e-4 J/mol original feed.; 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": "Stage 1 absolute pressure is varied within the supported input range. Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots."
      },
      {
        "label": "Substitute the values",
        "calculation": "p1 = 5 MPa(a); with the fixed controls above, the workflow evaluates Total separated vapor moles per feed mole = 0.809755941 dimensionless; Final liquid moles per feed mole = 0.190244059 dimensionless",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Total separated vapor moles per feed mole (dimensionless) = 0.809755941; Final liquid moles per feed mole (dimensionless) = 0.190244059",
        "explanation": "Every flash trial must remain at 180-450 K and 0.1-10 MPa absolute, with consistent mole fractions summing to one. Near-critical, vanishing-phase or failed closure states are rejected. Single-phase states are not given an invented vapor quality. Independent engine agreement is not experimental validation. Instantaneous equilibrium and the documented steady balance only. No machinery efficiency, transient behavior, separator sizing, phase residence time, mechanical safety approval or claimed field calibration. A rejected or unbracketed root is not extrapolated into an unsupported range. Exactly three once-through prescribed PT equilibrium stages, no recycle, heat-exchanger sizing, droplet carryover or residence-time design. Each must remain two-phase. No water decanter, C7+, gas recompression, upstream stage-1 conditioning duty or assumed separator efficiency."
      }
    ],
    "result": "Total separated vapor moles per feed mole (dimensionless) = 0.809755941; Final liquid moles per feed mole (dimensionless) = 0.190244059",
    "interpretation": "Every flash trial must remain at 180-450 K and 0.1-10 MPa absolute, with consistent mole fractions summing to one. Near-critical, vanishing-phase or failed closure states are rejected. Single-phase states are not given an invented vapor quality. Independent engine agreement is not experimental validation. Instantaneous equilibrium and the documented steady balance only. No machinery efficiency, transient behavior, separator sizing, phase residence time, mechanical safety approval or claimed field calibration. A rejected or unbracketed root is not extrapolated into an unsupported range. Exactly three once-through prescribed PT equilibrium stages, no recycle, heat-exchanger sizing, droplet carryover or residence-time design. Each must remain two-phase. No water decanter, C7+, gas recompression, upstream stage-1 conditioning duty or assumed separator efficiency.",
    "control": "Stage 1 absolute pressure (MPa(a))",
    "columns": [
      "Stage 1 absolute pressure (MPa(a))",
      "Total separated vapor moles per feed mole (dimensionless)",
      "Final liquid moles per feed mole (dimensionless)"
    ],
    "rows": [
      [
        3,
        0.8530002165634148,
        0.14699978343658524
      ],
      [
        4,
        0.8253355203723681,
        0.17466447962763193
      ],
      [
        5,
        0.8097559408033321,
        0.1902440591966679
      ],
      [
        6,
        0.8017106301307568,
        0.19828936986924317
      ],
      [
        7,
        0.79859295393963,
        0.2014070460603699
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Stage 1 absolute pressure (MPa(a)) = 3. Total separated vapor moles per feed mole (dimensionless): 0.853000217; Final liquid moles per feed mole (dimensionless): 0.146999783.",
      "Stage 1 absolute pressure (MPa(a)) = 4. Total separated vapor moles per feed mole (dimensionless): 0.82533552; Final liquid moles per feed mole (dimensionless): 0.17466448.",
      "Stage 1 absolute pressure (MPa(a)) = 5. Total separated vapor moles per feed mole (dimensionless): 0.809755941; Final liquid moles per feed mole (dimensionless): 0.190244059.",
      "Stage 1 absolute pressure (MPa(a)) = 6. Total separated vapor moles per feed mole (dimensionless): 0.80171063; Final liquid moles per feed mole (dimensionless): 0.19828937.",
      "Stage 1 absolute pressure (MPa(a)) = 7. Total separated vapor moles per feed mole (dimensionless): 0.798592954; Final liquid moles per feed mole (dimensionless): 0.201407046."
    ],
    "provenance": "Original recorded synthetic cases solved with the site's three-stage-separator-train 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 Total separated vapor moles per feed mole (dimensionless) without rounding intermediate values.",
        "answer": "p1 = 5 MPa(a); with the fixed controls above, the workflow evaluates Total separated vapor moles per feed mole = 0.809755941 dimensionless; Final liquid moles per feed mole = 0.190244059 dimensionless. Total separated vapor moles per feed mole (dimensionless) = 0.809755941. Every flash trial must remain at 180-450 K and 0.1-10 MPa absolute, with consistent mole fractions summing to one. Near-critical, vanishing-phase or failed closure states are rejected. Single-phase states are not given an invented vapor quality. Independent engine agreement is not experimental validation. Instantaneous equilibrium and the documented steady balance only. No machinery efficiency, transient behavior, separator sizing, phase residence time, mechanical safety approval or claimed field calibration. A rejected or unbracketed root is not extrapolated into an unsupported range. Exactly three once-through prescribed PT equilibrium stages, no recycle, heat-exchanger sizing, droplet carryover or residence-time design. Each must remain two-phase. No water decanter, C7+, gas recompression, upstream stage-1 conditioning duty or assumed separator efficiency."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Stage 1 absolute pressure (MPa(a)) changes from 3 to 7. Other controls remain as stated in the premise. Total separated vapor moles per feed mole (dimensionless) changes from 0.853000217 to 0.798592954."
      },
      {
        "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. Stage 1 absolute pressure is varied within the supported input range. Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots. Every flash trial must remain at 180-450 K and 0.1-10 MPa absolute, with consistent mole fractions summing to one. Near-critical, vanishing-phase or failed closure states are rejected. Single-phase states are not given an invented vapor quality. Independent engine agreement is not experimental validation. Instantaneous equilibrium and the documented steady balance only. No machinery efficiency, transient behavior, separator sizing, phase residence time, mechanical safety approval or claimed field calibration. A rejected or unbracketed root is not extrapolated into an unsupported range. Exactly three once-through prescribed PT equilibrium stages, no recycle, heat-exchanger sizing, droplet carryover or residence-time design. Each must remain two-phase. No water decanter, C7+, gas recompression, upstream stage-1 conditioning duty or assumed separator efficiency."
      }
    ]
  },
  "recorded": {
    "kind": "workflow",
    "workflow": "three-stage-separator-train",
    "parameter": "p1",
    "runs": [
      {
        "inputs": {
          "p1": 3,
          "T1": 330,
          "p2": 2,
          "T2": 300,
          "p3": 0.5,
          "T3": 280,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "outputs": [
            {
              "label": "Total separated vapor moles per feed mole",
              "value": 0.8530002165634148,
              "unit": "dimensionless"
            },
            {
              "label": "Final liquid moles per feed mole",
              "value": 0.14699978343658524,
              "unit": "dimensionless"
            },
            {
              "label": "Interstage heat per original feed mass",
              "value": -29.070870161875153,
              "unit": "kJ/kg"
            },
            {
              "label": "Maximum overall component balance error",
              "value": 2.7755575615628914e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Absolute overall energy residual",
              "value": 1.1368683772161603e-13,
              "unit": "J/mol feed"
            }
          ],
          "columns": [
            "Stage",
            "Pressure (MPa(a))",
            "Temperature (K)",
            "Stage feed (mol/mol original)",
            "Vapor removed (mol/mol original)",
            "Liquid forwarded (mol/mol original)",
            "Stage feed enthalpy (J/mol stage feed)",
            "Interstage heat (J/mol original feed)"
          ],
          "rows": [
            [
              1,
              3,
              330,
              1,
              0.8208506475367037,
              0.17914935246329633,
              -2597.4981899380864,
              0
            ],
            [
              2,
              2,
              300,
              0.17914935246329633,
              0.004660979816267958,
              0.17448837264702838,
              -20521.20167690577,
              -758.5642560444281
            ],
            [
              3,
              0.5,
              280,
              0.17448837264702838,
              0.027488589210443136,
              0.14699978343658524,
              -22180.51519800966,
              -197.12682093476087
            ]
          ],
          "rowLabels": [
            "Stage 1",
            "Stage 2",
            "Stage 3"
          ],
          "chart": {
            "xLabel": "Separator stage",
            "yLabel": "Moles per original feed mole",
            "xTicks": {
              "values": [
                1,
                2,
                3
              ],
              "text": [
                "1",
                "2",
                "3"
              ]
            },
            "series": [
              {
                "name": "Vapor removed",
                "x": [
                  1,
                  2,
                  3
                ],
                "y": [
                  0.8208506475367037,
                  0.004660979816267958,
                  0.027488589210443136
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Liquid forwarded",
                "x": [
                  1,
                  2,
                  3
                ],
                "y": [
                  0.17914935246329633,
                  0.17448837264702838,
                  0.14699978343658524
                ],
                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Three prescribed PT equilibrium separators; only each liquid stream feeds the next stage. Stage 1 defines the original feed enthalpy: its upstream conditioning duty is excluded. Interstage heat includes throttling/conditioning to the next PT state, not an assumed adiabatic valve. All streams use the same ideal-gas reference. No recycle, residence-time sizing, carryover or equipment design. C1-C6 PR with zero kij."
          ]
        }
      },
      {
        "inputs": {
          "p1": 4,
          "T1": 330,
          "p2": 2,
          "T2": 300,
          "p3": 0.5,
          "T3": 280,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "outputs": [
            {
              "label": "Total separated vapor moles per feed mole",
              "value": 0.8253355203723681,
              "unit": "dimensionless"
            },
            {
              "label": "Final liquid moles per feed mole",
              "value": 0.17466447962763193,
              "unit": "dimensionless"
            },
            {
              "label": "Interstage heat per original feed mass",
              "value": -30.494777802766578,
              "unit": "kJ/kg"
            },
            {
              "label": "Maximum overall component balance error",
              "value": 5.551115123125783e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Absolute overall energy residual",
              "value": 9.094947017729282e-13,
              "unit": "J/mol feed"
            }
          ],
          "columns": [
            "Stage",
            "Pressure (MPa(a))",
            "Temperature (K)",
            "Stage feed (mol/mol original)",
            "Vapor removed (mol/mol original)",
            "Liquid forwarded (mol/mol original)",
            "Stage feed enthalpy (J/mol stage feed)",
            "Interstage heat (J/mol original feed)"
          ],
          "rows": [
            [
              1,
              4,
              330,
              1,
              0.7627027607566108,
              0.2372972392433892,
              -3532.3475081719125,
              0
            ],
            [
              2,
              2,
              300,
              0.2372972392433892,
              0.025072217597072514,
              0.21222502164631668,
              -18405.946183617452,
              -838.114073114244
            ],
            [
              3,
              0.5,
              280,
              0.21222502164631668,
              0.03756054201868474,
              0.17466447962763193,
              -21266.778316182954,
              -164.3872926270288
            ]
          ],
          "rowLabels": [
            "Stage 1",
            "Stage 2",
            "Stage 3"
          ],
          "chart": {
            "xLabel": "Separator stage",
            "yLabel": "Moles per original feed mole",
            "xTicks": {
              "values": [
                1,
                2,
                3
              ],
              "text": [
                "1",
                "2",
                "3"
              ]
            },
            "series": [
              {
                "name": "Vapor removed",
                "x": [
                  1,
                  2,
                  3
                ],
                "y": [
                  0.7627027607566108,
                  0.025072217597072514,
                  0.03756054201868474
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Liquid forwarded",
                "x": [
                  1,
                  2,
                  3
                ],
                "y": [
                  0.2372972392433892,
                  0.21222502164631668,
                  0.17466447962763193
                ],
                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Three prescribed PT equilibrium separators; only each liquid stream feeds the next stage. Stage 1 defines the original feed enthalpy: its upstream conditioning duty is excluded. Interstage heat includes throttling/conditioning to the next PT state, not an assumed adiabatic valve. All streams use the same ideal-gas reference. No recycle, residence-time sizing, carryover or equipment design. C1-C6 PR with zero kij."
          ]
        }
      },
      {
        "inputs": {
          "p1": 5,
          "T1": 330,
          "p2": 2,
          "T2": 300,
          "p3": 0.5,
          "T3": 280,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "outputs": [
            {
              "label": "Total separated vapor moles per feed mole",
              "value": 0.8097559408033321,
              "unit": "dimensionless"
            },
            {
              "label": "Final liquid moles per feed mole",
              "value": 0.1902440591966679,
              "unit": "dimensionless"
            },
            {
              "label": "Interstage heat per original feed mass",
              "value": -28.787577776287023,
              "unit": "kJ/kg"
            },
            {
              "label": "Maximum overall component balance error",
              "value": 2.7755575615628914e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Absolute overall energy residual",
              "value": 2.2737367544323206e-13,
              "unit": "J/mol feed"
            }
          ],
          "columns": [
            "Stage",
            "Pressure (MPa(a))",
            "Temperature (K)",
            "Stage feed (mol/mol original)",
            "Vapor removed (mol/mol original)",
            "Liquid forwarded (mol/mol original)",
            "Stage feed enthalpy (J/mol stage feed)",
            "Interstage heat (J/mol original feed)"
          ],
          "rows": [
            [
              1,
              5,
              330,
              1,
              0.7100537875510105,
              0.28994621244898955,
              -4235.702742385191,
              0
            ],
            [
              2,
              2,
              300,
              0.28994621244898955,
              0.05529177459325178,
              0.23465443785573778,
              -16489.237463711106,
              -815.931505834528
            ],
            [
              3,
              0.5,
              280,
              0.23465443785573778,
              0.0444103786590699,
              0.1902440591966679,
              -20747.74616038422,
              -130.44646824904208
            ]
          ],
          "rowLabels": [
            "Stage 1",
            "Stage 2",
            "Stage 3"
          ],
          "chart": {
            "xLabel": "Separator stage",
            "yLabel": "Moles per original feed mole",
            "xTicks": {
              "values": [
                1,
                2,
                3
              ],
              "text": [
                "1",
                "2",
                "3"
              ]
            },
            "series": [
              {
                "name": "Vapor removed",
                "x": [
                  1,
                  2,
                  3
                ],
                "y": [
                  0.7100537875510105,
                  0.05529177459325178,
                  0.0444103786590699
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Liquid forwarded",
                "x": [
                  1,
                  2,
                  3
                ],
                "y": [
                  0.28994621244898955,
                  0.23465443785573778,
                  0.1902440591966679
                ],
                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Three prescribed PT equilibrium separators; only each liquid stream feeds the next stage. Stage 1 defines the original feed enthalpy: its upstream conditioning duty is excluded. Interstage heat includes throttling/conditioning to the next PT state, not an assumed adiabatic valve. All streams use the same ideal-gas reference. No recycle, residence-time sizing, carryover or equipment design. C1-C6 PR with zero kij."
          ]
        }
      },
      {
        "inputs": {
          "p1": 6,
          "T1": 330,
          "p2": 2,
          "T2": 300,
          "p3": 0.5,
          "T3": 280,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "outputs": [
            {
              "label": "Total separated vapor moles per feed mole",
              "value": 0.8017106301307568,
              "unit": "dimensionless"
            },
            {
              "label": "Final liquid moles per feed mole",
              "value": 0.19828936986924317,
              "unit": "dimensionless"
            },
            {
              "label": "Interstage heat per original feed mass",
              "value": -25.245650841681535,
              "unit": "kJ/kg"
            },
            {
              "label": "Maximum overall component balance error",
              "value": 2.7755575615628914e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Absolute overall energy residual",
              "value": 1.0231815394945443e-12,
              "unit": "J/mol feed"
            }
          ],
          "columns": [
            "Stage",
            "Pressure (MPa(a))",
            "Temperature (K)",
            "Stage feed (mol/mol original)",
            "Vapor removed (mol/mol original)",
            "Liquid forwarded (mol/mol original)",
            "Stage feed enthalpy (J/mol stage feed)",
            "Interstage heat (J/mol original feed)"
          ],
          "rows": [
            [
              1,
              6,
              330,
              1,
              0.6591365659287516,
              0.3408634340712484,
              -4794.747974249588,
              0
            ],
            [
              2,
              2,
              300,
              0.3408634340712484,
              0.09439163101869534,
              0.24647180305255306,
              -14711.905993465907,
              -720.3054166174626
            ],
            [
              3,
              0.5,
              280,
              0.24647180305255306,
              0.048182433183309906,
              0.19828936986924317,
              -20488.52860964275,
              -109.633388364319
            ]
          ],
          "rowLabels": [
            "Stage 1",
            "Stage 2",
            "Stage 3"
          ],
          "chart": {
            "xLabel": "Separator stage",
            "yLabel": "Moles per original feed mole",
            "xTicks": {
              "values": [
                1,
                2,
                3
              ],
              "text": [
                "1",
                "2",
                "3"
              ]
            },
            "series": [
              {
                "name": "Vapor removed",
                "x": [
                  1,
                  2,
                  3
                ],
                "y": [
                  0.6591365659287516,
                  0.09439163101869534,
                  0.048182433183309906
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Liquid forwarded",
                "x": [
                  1,
                  2,
                  3
                ],
                "y": [
                  0.3408634340712484,
                  0.24647180305255306,
                  0.19828936986924317
                ],
                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Three prescribed PT equilibrium separators; only each liquid stream feeds the next stage. Stage 1 defines the original feed enthalpy: its upstream conditioning duty is excluded. Interstage heat includes throttling/conditioning to the next PT state, not an assumed adiabatic valve. All streams use the same ideal-gas reference. No recycle, residence-time sizing, carryover or equipment design. C1-C6 PR with zero kij."
          ]
        }
      },
      {
        "inputs": {
          "p1": 7,
          "T1": 330,
          "p2": 2,
          "T2": 300,
          "p3": 0.5,
          "T3": 280,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "outputs": [
            {
              "label": "Total separated vapor moles per feed mole",
              "value": 0.79859295393963,
              "unit": "dimensionless"
            },
            {
              "label": "Final liquid moles per feed mole",
              "value": 0.2014070460603699,
              "unit": "dimensionless"
            },
            {
              "label": "Interstage heat per original feed mass",
              "value": -20.48049016552829,
              "unit": "kJ/kg"
            },
            {
              "label": "Maximum overall component balance error",
              "value": 2.7755575615628914e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Absolute overall energy residual",
              "value": 1.1368683772161603e-12,
              "unit": "J/mol feed"
            }
          ],
          "columns": [
            "Stage",
            "Pressure (MPa(a))",
            "Temperature (K)",
            "Stage feed (mol/mol original)",
            "Vapor removed (mol/mol original)",
            "Liquid forwarded (mol/mol original)",
            "Stage feed enthalpy (J/mol stage feed)",
            "Interstage heat (J/mol original feed)"
          ],
          "rows": [
            [
              1,
              7,
              330,
              1,
              0.6067560035977106,
              0.39324399640228935,
              -5256.794016773854,
              0
            ],
            [
              2,
              2,
              300,
              0.39324399640228935,
              0.1423659995718989,
              0.25087799683039047,
              -13041.456747254377,
              -569.8291192226307
            ],
            [
              3,
              0.5,
              280,
              0.25087799683039047,
              0.049470950770020554,
              0.2014070460603699,
              -20404.075672576804,
              -103.45728721677345
            ]
          ],
          "rowLabels": [
            "Stage 1",
            "Stage 2",
            "Stage 3"
          ],
          "chart": {
            "xLabel": "Separator stage",
            "yLabel": "Moles per original feed mole",
            "xTicks": {
              "values": [
                1,
                2,
                3
              ],
              "text": [
                "1",
                "2",
                "3"
              ]
            },
            "series": [
              {
                "name": "Vapor removed",
                "x": [
                  1,
                  2,
                  3
                ],
                "y": [
                  0.6067560035977106,
                  0.1423659995718989,
                  0.049470950770020554
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Liquid forwarded",
                "x": [
                  1,
                  2,
                  3
                ],
                "y": [
                  0.39324399640228935,
                  0.25087799683039047,
                  0.2014070460603699
                ],
                "mode": "lines+markers"
              }
            ]
          },
          "warnings": [
            "Three prescribed PT equilibrium separators; only each liquid stream feeds the next stage. Stage 1 defines the original feed enthalpy: its upstream conditioning duty is excluded. Interstage heat includes throttling/conditioning to the next PT state, not an assumed adiabatic valve. All streams use the same ideal-gas reference. No recycle, residence-time sizing, carryover or equipment design. C1-C6 PR with zero kij."
          ]
        }
      }
    ]
  }
}