AbsorptivePartitioning

{
  "reference": {
    "citation": "Seinfeld, J. H. and Pandis, S. N. (2006) Atmospheric Chemistry and Physics, 2nd Edition, Chapter 9, Section 9.4, Eq. 9.23 — absorptive partitioning of a semivolatile organic between gas and particle phases. Migrated from Aerosol.jl src/organic_aerosol.jl `AbsorptivePartitioning` (esm-aez).",
    "notes": "source_ref: Aerosol.jl@main:src/organic_aerosol.jl:125\nUpstream `AbsorptivePartitioning` is an MTK `@component` with two parameters (K_om, C_oa), one input variable (C_tot), and one output variable (F_p). The equation is:\n  • F_p ~ K_om * C_oa * C_tot / (1 + K_om * C_oa)  (derived from Eq. 9.23)\nThe equation is algebraic (no derivatives), making this an observed-only component.\n\nDerivation: the partition equilibrium F_p / A_g = K_om * C_oa (Eq. 9.23) combined with mass balance C_tot = F_p + A_g gives F_p = K_om * C_oa * C_tot / (1 + K_om * C_oa), where A_g is gas-phase concentration and F_p is particle-phase concentration.\n\nObservability classification: observed-only — the single output F_p is given by an algebraic equation in terms of inputs K_om, C_oa, C_tot. Test scenarios use `time_span: [0, 1]` and sample at t=0.\n\nESM representation note: in the upstream MTK component C_tot is an `@variable` supplied externally as the input; in this .esm it is represented as a `parameter` (not a state) so the system is well-posed under the schema's equation-count rule (one equation per state) and to match the observed-only pattern used elsewhere in this rig (see components/aerosol/organic/bet.esm). Tests vary C_tot via `parameter_overrides`, and the `partitioning_sweep` example sweeps K_om as a parameter dimension.\n\nTolerance rationale (model-level rel=1e-9): observed-only algebraic system (no ODE integration); the equation involves only multiplication and division. Floating-point round-off is ~1e-15. 1e-9 leaves comfortable headroom."
  },
  "tolerance": {
    "rel": 1e-09
  },
  "variables": {
    "K_om": {
      "type": "parameter",
      "units": "m^3 ug^-1",
      "default": 1.0,
      "description": "Mass-based partition coefficient for absorptive partitioning into organic aerosol"
    },
    "C_oa": {
      "type": "parameter",
      "units": "ug m^-3",
      "default": 10.0,
      "description": "Total absorbing organic aerosol mass concentration"
    },
    "C_tot": {
      "type": "parameter",
      "units": "ug m^-3",
      "default": 1.0,
      "description": "Total concentration of the compound (gas + particle phases). Input parameter — the observed-only model has one algebraic equation for F_p given C_tot."
    },
    "F_p": {
      "type": "unknown",
      "units": "ug m^-3",
      "description": "Particle-phase (aerosol) concentration of the compound"
    }
  },
  "equations": [
    {
      "lhs": "F_p",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "K_om",
              "C_oa",
              "C_tot"
            ]
          },
          {
            "op": "+",
            "args": [
              1,
              {
                "op": "*",
                "args": [
                  "K_om",
                  "C_oa"
                ]
              }
            ]
          }
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "default_conditions",
      "description": "Default conditions: K_om = 1.0 m³/µg, C_oa = 10.0 µg/m³, C_tot = 1.0 µg/m³. F_p = 1.0*10.0*1.0 / (1 + 1.0*10.0) = 10.0/11.0 = 0.9090909090909091 µg/m³.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "C_tot": 1.0
      },
      "assertions": [
        {
          "variable": "F_p",
          "time": 0.0,
          "expected": 0.9090909090909091,
          "tolerance": {
            "rel": 1e-06
          }
        }
      ]
    },
    {
      "id": "low_partitioning",
      "description": "Low partition coefficient (mostly gas phase): K_om = 0.001 m³/µg, C_oa = 10.0 µg/m³, C_tot = 1.0 µg/m³. F_p = 0.001*10.0*1.0 / (1 + 0.001*10.0) = 0.01/1.01 = 0.009900990099009901 µg/m³.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "K_om": 0.001,
        "C_tot": 1.0
      },
      "assertions": [
        {
          "variable": "F_p",
          "time": 0.0,
          "expected": 0.009900990099009901,
          "tolerance": {
            "rel": 1e-06
          }
        }
      ]
    },
    {
      "id": "high_partitioning",
      "description": "High partition coefficient (mostly particle phase): K_om = 100.0 m³/µg, C_oa = 10.0 µg/m³, C_tot = 1.0 µg/m³. F_p = 100.0*10.0*1.0 / (1 + 100.0*10.0) = 1000.0/1001.0 = 0.999000999000999 µg/m³.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "K_om": 100.0,
        "C_tot": 1.0
      },
      "assertions": [
        {
          "variable": "F_p",
          "time": 0.0,
          "expected": 0.999000999000999,
          "tolerance": {
            "rel": 1e-06
          }
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "partitioning_sweep",
      "description": "Sweep partition coefficient K_om from 0.001 to 1000 m³/µg (log scale) to show transition from gas-dominated (K_om*C_oa << 1) to particle-dominated (K_om*C_oa >> 1) regimes.",
      "initial_state": {},
      "parameters": {
        "C_oa": 10.0,
        "C_tot": 1.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "K_om",
            "range": {
              "start": 0.001,
              "stop": 1000.0,
              "count": 50
            }
          }
        ]
      },
      "plots": [
        {
          "id": "partitioning_curve",
          "type": "line",
          "description": "Absorptive partitioning: F_p vs K_om — shows sigmoid transition from gas-dominated (low K_om) to particle-dominated (high K_om) regime.",
          "x": {
            "variable": "K_om",
            "label": "K_om (m³/µg)"
          },
          "y": {
            "variable": "F_p",
            "label": "F_p (µg/m³)"
          }
        }
      ]
    }
  ]
}