BETAdsorption

{
  "reference": {
    "citation": "Seinfeld, J. H. and Pandis, S. N. (2006) Atmospheric Chemistry and Physics, 2nd Edition, Chapter 14, Section 14.5.3, Eq. 14.45 — BET multilayer adsorption isotherm. Migrated from Aerosol.jl src/organic_aerosol.jl `BETAdsorption` (esm-1c7).",
    "notes": "source_ref: Aerosol.jl@main:src/organic_aerosol.jl:279\nUpstream `BETAdsorption` is an MTK `@component` with two parameters (V_m, c_BET), and two variables (S, V). The equation is:\n  • V ~ V_m * c_BET * S / ((1 - S) * (1 + (c_BET - 1) * S))  (Eq. 14.45 — BET isotherm)\nThe equation is algebraic (no derivatives), making this an observed-only component.\n\nObservability classification: observed-only — the single output V is given by an algebraic equation. Test scenarios use `time_span: [0, 1]` and sample at t=0.\n\nESM representation note: in the upstream MTK component S 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/wildland_fire/midflame_wind.esm where all inputs are parameters and only algebraic outputs are states). Tests vary S via `parameter_overrides`, and the `saturation_sweep` example sweeps S as a parameter dimension.\n\nTolerance rationale (model-level rel=1e-9): observed-only algebraic system (no ODE integration); the equation involves multiplication, division, and addition. Floating-point round-off is ~1e-15. 1e-9 leaves comfortable headroom."
  },
  "tolerance": {
    "rel": 1e-09
  },
  "variables": {
    "V_m": {
      "type": "parameter",
      "units": "m^3",
      "default": 1.0,
      "description": "Gas volume for monolayer formation"
    },
    "c_BET": {
      "type": "parameter",
      "units": "1",
      "default": 10.0,
      "description": "BET constant for the adsorbing surface (dimensionless)"
    },
    "S": {
      "type": "parameter",
      "units": "1",
      "default": 0.5,
      "description": "Gas-phase saturation ratio p/p_sat (dimensionless). Input parameter — the observed-only model has one algebraic equation for V given S."
    },
    "V": {
      "type": "unknown",
      "units": "m^3",
      "description": "Volume of gas adsorbed"
    }
  },
  "equations": [
    {
      "lhs": "V",
      "rhs": {
        "op": "/",
        "args": [
          {
            "op": "*",
            "args": [
              "c_BET",
              "V_m",
              "S"
            ]
          },
          {
            "op": "*",
            "args": [
              {
                "op": "+",
                "args": [
                  1,
                  {
                    "op": "*",
                    "args": [
                      -1,
                      "S"
                    ]
                  }
                ]
              },
              {
                "op": "+",
                "args": [
                  1,
                  {
                    "op": "*",
                    "args": [
                      {
                        "op": "+",
                        "args": [
                          -1,
                          "c_BET"
                        ]
                      },
                      "S"
                    ]
                  }
                ]
              }
            ]
          }
        ]
      }
    }
  ],
  "tests": [
    {
      "id": "default_conditions",
      "description": "Default conditions: V_m = 1.0 m^3, c_BET = 10.0, S = 0.5. V = 1.0*10.0*0.5 / ((1-0.5)*(1+9*0.5)) = 5.0/2.75 = 1.8181818181818181 m^3.",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "S": 0.5
      },
      "assertions": [
        {
          "variable": "V",
          "time": 0.0,
          "expected": 1.8181818181818181,
          "tolerance": {
            "rel": 1e-06
          }
        }
      ]
    },
    {
      "id": "low_saturation",
      "description": "Low saturation regime: S = 0.001, V approaches V_m * c_BET * S = 0.01 m^3 (linear approximation).",
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_overrides": {
        "S": 0.001
      },
      "assertions": [
        {
          "variable": "V",
          "time": 0.0,
          "expected": 0.009921,
          "tolerance": {
            "rel": 0.0001
          }
        }
      ]
    }
  ],
  "analyses": [
    {
      "id": "saturation_sweep",
      "description": "Sweep saturation ratio from 0.01 to 0.99 to show the characteristic BET isotherm shape (multilayer adsorption as S approaches 1).",
      "initial_state": {},
      "parameters": {
        "V_m": 1.0,
        "c_BET": 10.0
      },
      "time_span": {
        "start": 0.0,
        "end": 1.0
      },
      "parameter_sweep": {
        "type": "cartesian",
        "dimensions": [
          {
            "parameter": "S",
            "range": {
              "start": 0.01,
              "stop": 0.99,
              "count": 50
            }
          }
        ]
      },
      "plots": [
        {
          "id": "bet_isotherm",
          "type": "line",
          "description": "BET isotherm: V/V_m vs S — shows monolayer completion at intermediate S and multilayer adsorption as S → 1.",
          "x": {
            "variable": "S",
            "label": "S (p/p_sat)"
          },
          "y": {
            "variable": "V",
            "label": "V (m^3)"
          }
        }
      ]
    }
  ]
}