Simulating microbe mortality

It is important to capture microbe mortality in some simulations. This usually follows an exponential decay (1) where is the death rate. In the geochemistry module, kinetic species such as microbes are parameterised by their mole number, so the above equation reads:

As discussed on the main biogeochemistry page, this can only be implemented in the geochemistry module by making the microbe a kinetic species. Then a GeochemistryKineticRate UserObject may be used to simulate mortality by setting:

  • intrinsic_rate_constant = k/molar_mass

  • multiply_by_mass = true

  • eta = 0

  • direction = DEATH.

[UserObjects<<<{"href": "../../../syntax/UserObjects/index.html"}>>>]
  [rate_biomass_death]
    type = GeochemistryKineticRate<<<{"description": "User object that defines a kinetic rate.  Note that more than one rate can be prescribed to a single kinetic_species: the sum the individual rates defines the overall rate.  GeochemistryKineticRate simply specifies the algebraic form for a kinetic rate: to actually use it in a calculation, you must use it in the GeochemicalModelDefinition.  The rate is intrinsic_rate_constant * area_quantity * (optionally, mass of kinetic_species in grams) * kinetic_molality^kinetic_molal_index / (kinetic_molality^kinetic_molal_index + kinetic_half_saturation^kinetic_molal_index)^kinetic_monod_index * (product_over_promoting_species m^promoting_index / (m^promoting_index + promoting_half_saturation^promiting_index)^promoting_monod_index) * |1 - (Q/K)^theta|^eta * exp(activation_energy / R * (1/T0 - 1/T)) * Direction(1 - (Q/K)).  Please see the markdown documentation for examples", "href": "../../../source/userobjects/GeochemistryKineticRate.html"}>>>
    kinetic_species_name<<<{"description": "The name of the kinetic species that will be controlled by this rate"}>>> = methanogen
    intrinsic_rate_constant<<<{"description": "The intrinsic rate constant for the reaction"}>>> = 0.5E-9
    multiply_by_mass<<<{"description": "Whether the rate should be multiplied by the kinetic_species mass (in grams)"}>>> = true
    eta<<<{"description": "Eta parameter, which appears in |1 - (Q/K)^theta|^eta"}>>> = 0
    direction<<<{"description": "Direction of reaction.  Let Q = the activity product of the kinetic reaction, and K = the equilibrium constant of the reaction.  Then direction means the following.  both = dissolution and precipitation are allowed.  (Specifically, if Q < K then dissolution will occur, that is, the kinetic species mass will decrease with time.  If Q > K then precipitation will occur, that is, the kinetic species mass will increase with time.)  dissolution = if Q < K then dissolution will occur, and when Q > K then the rate will be set to zero so that precipitation will be prevented.  precipitation = if Q > K then precipitation will occur, and when Q < K then the rate will be set to zero so that dissolution will be prevented.  raw = the rate will not depend on sgn(1 - (Q/K)), which means dissolution will occur if intrinsic_rate_constant > 0, and precipitation will occur when intrinsic_rate_constant < 0.  death = the rate will not depend on sgn(1 - (Q/K)), which means dissolution will occur if intrinsic_rate_constant > 0, and precipitation will occur when intrinsic_rate_constant < 0, and, in addition, no reactants will be produced or consumed by this kinetic reaction (only the kinetic species mass will change)."}>>> = DEATH
  []
[]
(modules/geochemistry/test/tests/kinetics/bio_death.i)

Figure 1: Mortality of microbe using Eq. (1)