NoninteractingSOA

{
  "reference": {
    "citation": "Seinfeld, J. H. and Pandis, S. N. (2006) Atmospheric Chemistry and Physics, 2nd Edition, Chapter 14, Section 14.5.2, Eqs. 14.6–14.18 — noninteracting SOA gas–particle partitioning model. Migrated from Aerosol.jl src/organic_aerosol.jl `NoninteractingSOA` (esm-cyz).",
    "notes": "source_ref: Aerosol.jl@main:src/organic_aerosol.jl:64\n\nUpstream `NoninteractingSOA` is an MTK `@component` with 3 constants (R_gas=8.314, zero_conc=0, zero_dimless=0), 5 parameters (a_i, p_i, M_i, M_ROG, T) and 7 variables (ΔROG, c_eq, c_total, ΔROG_threshold, c_aer, c_gas, X_p, Y). The equations are:\n  • c_eq ~ p_i * M_i / (R_gas * T)                                    [Eq. 14.7]\n  • c_total ~ a_i * (M_i / M_ROG) * ΔROG                              [Eq. 14.11]\n  • ΔROG_threshold ~ p_i * M_ROG / (a_i * R_gas * T)                  [Eq. 14.13]\n  • c_aer ~ max(0, c_total - c_eq)                                     [Eq. 14.9/14.10]\n  • c_gas ~ c_total - c_aer                                            [Eq. 14.6 rearranged]\n  • X_p ~ ifelse(c_total > 0, c_aer / c_total, 0)                     [Eq. 14.14]\n  • Y ~ ifelse(ΔROG > 0, c_aer / ΔROG, 0)                             [Eq. 14.16]\n\nESM representation:\n  ΔROG becomes the `delta_ROG` parameter (the external driving input). R_gas=8.314 and the zero-clamp literals are folded directly into expressions. The 4 primary computed quantities (c_eq, c_total, delta_ROG_threshold, c_aer) are ESM `state` variables with equations in the `equations` array; the 3 diagnostic quantities (c_gas, X_p, Y) are ESM `observed` variables with embedded expressions referencing the state variables. This matches `features: variables, parameters, observed` in the migration tracker.\n\nAcausality note: all 7 equations are purely algebraic (no ODEs). The system has no cycles in the topological substitution order: c_eq and c_total depend only on parameters; delta_ROG_threshold depends only on parameters; c_aer depends on c_eq and c_total; c_gas, X_p, Y depend on c_aer and c_total. The ESS substitution loop resolves all states without a DAE solver.\n\nPhysics note: c_aer = max(0, c_total − c_eq) implements the threshold behaviour — no aerosol forms until c_total ≥ c_eq, i.e. until delta_ROG ≥ delta_ROG_threshold. Above the threshold the excess condensate equals c_total − c_eq.\n\nTolerance rationale (model-level rel=1e-9): purely algebraic system; all outputs are analytic functions of the 6 parameters with no time integration. Floating-point round-off is ~1e-15. rel=1e-9 leaves comfortable headroom."
  },
  "tolerance": {
    "rel": 1e-09
  },
  "variables": {
    "a_i": {
      "type": "parameter",
      "units": "1",
      "default": 0.05,
      "description": "Molar yield of product i (dimensionless fraction of reacted ROG that becomes product i)"
    },
    "p_i": {
      "type": "parameter",
      "units": "Pa",
      "default": 1.01325e-05,
      "description": "Vapor pressure of pure condensed product i at temperature T"
    },
    "M_i": {
      "type": "parameter",
      "units": "kg/mol",
      "default": 0.18,
      "description": "Molecular weight of product i"
    },
    "M_ROG": {
      "type": "parameter",
      "units": "kg/mol",
      "default": 0.15,
      "description": "Molecular weight of the parent reactive organic gas (ROG)"
    },
    "T": {
      "type": "parameter",
      "units": "K",
      "default": 298.0,
      "description": "Temperature"
    },
    "delta_ROG": {
      "type": "parameter",
      "units": "kg/m^3",
      "default": 1e-05,
      "description": "Reacted reactive organic gas (ROG) concentration. The primary driving input. Aerosol forms only when delta_ROG >= delta_ROG_threshold."
    },
    "c_eq": {
      "type": "unknown",
      "units": "kg/m^3",
      "description": "Equilibrium gas-phase saturation concentration of product i (Eq. 14.7). Equals p_i * M_i / (R_gas * T); depends only on parameters."
    },
    "c_total": {
      "type": "unknown",
      "units": "kg/m^3",
      "description": "Total mass concentration of product i (gas + aerosol) produced from the reacted ROG (Eq. 14.11). Linear in delta_ROG."
    },
    "delta_ROG_threshold": {
      "type": "unknown",
      "units": "kg/m^3",
      "description": "Threshold reacted ROG concentration below which no aerosol forms (Eq. 14.13). Equals p_i * M_ROG / (a_i * R_gas * T); depends only on parameters."
    },
    "c_aer": {
      "type": "unknown",
      "units": "kg/m^3",
      "description": "Aerosol-phase mass concentration of product i (Eq. 14.9/14.10). Zero below the formation threshold; equals c_total − c_eq above it."
    },
    "c_gas": {
      "type": "unknown",
      "units": "kg/m^3",
      "description": "Gas-phase mass concentration of product i (Eq. 14.6 rearranged). Equals c_total − c_aer; equals c_total below the threshold, approaches c_eq above it."
    },
    "X_p": {
      "type": "unknown",
      "units": "1",
      "description": "Mass fraction of product i in the aerosol phase (Eq. 14.14, dimensionless). Zero when no total product is present."
    },
    "Y": {
      "type": "unknown",
      "units": "1",
      "description": "Aerosol mass yield (Eq. 14.16, dimensionless). Fraction of reacted ROG that partitions into the aerosol phase: Y = c_aer / delta_ROG. Zero when delta_ROG = 0."
    }
  },
  "equations": [
    {
      "lhs": "c_eq",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "p_i",
              "M_i"
            ]
          },
          {
            "op": "*",
            "args": [
              8.314,
              "T"
            ]
          }
        ]
      }
    },
    {
      "lhs": "c_total",
      "rhs": {
        "op": "*",
        "args": [
          "a_i",
          {
            "op": "/",
            "args": [
              "M_i",
              "M_ROG"
            ]
          },
          "delta_ROG"
        ]
      }
    },
    {
      "lhs": "delta_ROG_threshold",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "p_i",
              "M_ROG"
            ]
          },
          {
            "op": "*",
            "args": [
              "a_i",
              8.314,
              "T"
            ]
          }
        ]
      }
    },
    {
      "lhs": "c_aer",
      "rhs": {
        "op": "max",
        "args": [
          0,
          {
            "op": "-",
            "args": [
              "c_total",
              "c_eq"
            ]
          }
        ]
      }
    },
    {
      "lhs": "c_gas",
      "rhs": {
        "op": "-",
        "args": [
          "c_total",
          "c_aer"
        ]
      }
    },
    {
      "lhs": "X_p",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": ">",
            "args": [
              "c_total",
              0
            ]
          },
          {
            "op": "/",
            "args": [
              "c_aer",
              "c_total"
            ]
          },
          0
        ]
      }
    },
    {
      "lhs": "Y",
      "rhs": {
        "op": "ifelse",
        "args": [
          {
            "op": ">",
            "args": [
              "delta_ROG",
              0
            ]
          },
          {
            "op": "/",
            "args": [
              "c_aer",
              "delta_ROG"
            ]
          },
          0
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "default_conditions",
      "description": "Default parameter set: delta_ROG = 1e-5 kg/m³ (~10 μg/m³), well above the threshold (~1.23e-8 kg/m³). c_total = a_i*(M_i/M_ROG)*delta_ROG = 0.06*1e-5 = 6e-7. c_aer = 6e-7 − c_eq = 5.9926385590e-7. Y = c_aer/delta_ROG = 0.059926386. X_p = c_aer/c_total = 0.99877309.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "delta_ROG": 1e-05
      },
      "assertions": [
        {
          "variable": "c_eq",
          "time": 0.0,
          "expected": 7.3614409591e-10,
          "tolerance": {
            "rel": 1e-06
          }
        },
        {
          "variable": "c_total",
          "time": 0.0,
          "expected": 6e-07,
          "tolerance": {
            "rel": 1e-09
          }
        },
        {
          "variable": "delta_ROG_threshold",
          "time": 0.0,
          "expected": 1.2269068265e-08,
          "tolerance": {
            "rel": 1e-06
          }
        },
        {
          "variable": "c_aer",
          "time": 0.0,
          "expected": 5.992638559e-07,
          "tolerance": {
            "rel": 1e-06
          }
        },
        {
          "variable": "c_gas",
          "time": 0.0,
          "expected": 7.3614409591e-10,
          "tolerance": {
            "rel": 1e-06
          }
        },
        {
          "variable": "Y",
          "time": 0.0,
          "expected": 0.05992638559,
          "tolerance": {
            "rel": 1e-06
          }
        },
        {
          "variable": "X_p",
          "time": 0.0,
          "expected": 0.9987730932,
          "tolerance": {
            "rel": 1e-06
          }
        }
      ]
    },
    {
      "id": "ten_times_threshold",
      "description": "delta_ROG = 10 × delta_ROG_threshold = 1.2269068265e-7 kg/m³. At this loading c_total = 10 × c_eq, so c_aer = 9 × c_eq. Y = 9 × a_i*(M_i/M_ROG)/10 = 0.054 (exact). X_p = 9/10 = 0.9 (exact). c_gas = c_eq (exact).",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "delta_ROG": 1.2269068265e-07
      },
      "assertions": [
        {
          "variable": "c_total",
          "time": 0.0,
          "expected": 7.3614409591e-09,
          "tolerance": {
            "rel": 1e-06
          }
        },
        {
          "variable": "c_aer",
          "time": 0.0,
          "expected": 6.6252968632e-09,
          "tolerance": {
            "rel": 1e-06
          }
        },
        {
          "variable": "c_gas",
          "time": 0.0,
          "expected": 7.3614409591e-10,
          "tolerance": {
            "rel": 1e-06
          }
        },
        {
          "variable": "Y",
          "time": 0.0,
          "expected": 0.054,
          "tolerance": {
            "rel": 1e-08
          }
        },
        {
          "variable": "X_p",
          "time": 0.0,
          "expected": 0.9,
          "tolerance": {
            "rel": 1e-08
          }
        }
      ]
    },
    {
      "id": "below_threshold",
      "description": "delta_ROG = 1e-9 kg/m³, well below the threshold (~1.23e-8 kg/m³). c_total = 6e-11 < c_eq = 7.36e-10, so c_aer = max(0, negative) = 0. All product remains in the gas phase: c_gas = c_total = 6e-11. Y = 0, X_p = 0.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "delta_ROG": 1e-09
      },
      "assertions": [
        {
          "variable": "c_total",
          "time": 0.0,
          "expected": 6e-11,
          "tolerance": {
            "rel": 1e-09
          }
        },
        {
          "variable": "c_aer",
          "time": 0.0,
          "expected": 0.0,
          "tolerance": {
            "abs": 1e-20
          }
        },
        {
          "variable": "c_gas",
          "time": 0.0,
          "expected": 6e-11,
          "tolerance": {
            "rel": 1e-09
          }
        },
        {
          "variable": "Y",
          "time": 0.0,
          "expected": 0.0,
          "tolerance": {
            "abs": 1e-20
          }
        },
        {
          "variable": "X_p",
          "time": 0.0,
          "expected": 0.0,
          "tolerance": {
            "abs": 1e-15
          }
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "rog_loading_sweep",
      "description": "Sweep reacted ROG concentration from 1e-10 to 1e-4 kg/m³ (log scale) to show the threshold behaviour and approach to the mass-yield plateau Y → a_i*(M_i/M_ROG) = 0.06 at high loading. Below the threshold (~1.23e-8 kg/m³) no aerosol forms; above it aerosol concentration grows quasi-linearly.",
      "initial_state": {},
      "parameters": {
        "a_i": 0.05,
        "p_i": 1.01325e-05,
        "M_i": 0.18,
        "M_ROG": 0.15,
        "T": 298.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "delta_ROG",
            "range": {
              "start": 1e-10,
              "stop": 0.0001,
              "count": 80,
              "scale": "log"
            }
          }
        ]
      },
      "plots": [
        {
          "id": "aerosol_yield_vs_rog",
          "type": "line",
          "description": "Aerosol mass yield Y vs. reacted ROG (log scale). Shows Y = 0 below the threshold and approach to a_i*(M_i/M_ROG)=0.06 at high loading.",
          "x": {
            "variable": "delta_ROG",
            "label": "ΔROG (kg/m³)"
          },
          "y": {
            "variable": "Y",
            "label": "Y (aerosol mass yield)"
          }
        },
        {
          "id": "aerosol_conc_vs_rog",
          "type": "line",
          "description": "Aerosol mass concentration c_aer vs. reacted ROG (log-log scale). Shows zero below the threshold and linear growth above it.",
          "x": {
            "variable": "delta_ROG",
            "label": "ΔROG (kg/m³)"
          },
          "y": {
            "variable": "c_aer",
            "label": "c_aer (kg/m³)"
          }
        }
      ]
    }
  ]
}