fix nufeb/growth/het command

Syntax

fix ID group-ID nufeb/growth/het sub-ID sub-Ks o2-ID o2-Ks no2-ID no2-Ks no3-ID no3-Ks keyword value ...

  • ID = user-assigned name for the fix

  • group-ID = ID of the group atoms to apply the fix to

  • sub-ID = substrate ID for organic substrate

  • sub-Ks = half-velocity constant (Ks) for organic substrate

  • o2-ID = substrate ID for oxygen

  • o2-Ks = half-velocity constant (Ks) for oxygen

  • no2-ID = substrate ID for nitrite

  • no2-Ks = half-velocity constant (Ks) for nitrite

  • no3-ID = substrate ID for nitrate

  • no3-Ks = half-velocity constant (Ks) for nitrate

  • zero or more keyword/value pairs may be appended

  • keyword = growth or yield or decay or maintain

growth value = maximum growth rate
yield value = yield coefficient
decay value = decay rate
maintain value = maintenance coefficient
epsyield value = yield coefficient for EPS production
anoxic value = reduction factor in anoxic condition
epsdens value = EPS density

Examples

#--- examples/biofilm-heterotroph ---#

group HET type 1
grid_style nufeb/chemostat 4 sub o2 no2 no3 4e-6

fix f_ghet HET nufeb/growth/het sub 4e-3 o2 2e-4 no2 3e-4 no3 3e-4 growth 6.9e-5 yield 0.61


#--- examples/biofilm-anammox ---#

fix growth_het HET nufeb/growth/het sub 4e-3 o2 2e-4 no2 0.5e-3 no3 0.5e-3 &
growth 6.9444e-5 yield 0.63 maintain 4.63e-6 decay 9.17e-7 anoxic 0.8

Description

Perform microbial growth to the atoms defined in group-ID. The affected atoms are considered as heterotrophic bacteria, having a spherical shape (atom_style coccus) with outer mass and outer diameter to represent their EPS (Extracellular Polymeric Substance) shells.

The model assumes that heterotrophs grow by consuming organic substrate in oxygenated conditions or nitrate in anoxic denitrifying conditions. Additionally, the model takes into account microbial decay and endogenous respiration processes.

The fix is called at each biological step (see run_style nufeb) to update atom and grid attributes. The value of the substrate ID keyword XX-ID must be consistent with the name defined in the grid_style chemostat command. The following forward Euler method is implemented to update the mass (m) and outer mass (om) of each atom in the group:

\[ \begin{align}\begin{aligned}m' & = m + \mu \cdot \Delta t\\om' & = om + \mu_{EPS} \cdot \Delta t\end{aligned}\end{align} \]

The specific growth rates \(\mu\) and EPS secretion rate \(\mu_{EPS}\) are calculated based on the equations described in (Ofiteru, I.D., et al, 2013):

\[ \begin{align}\begin{aligned}\mu & = r1 + r2 + r3 - r4 - r5 - r6 - b_{decay}\\\mu_{EPS} & = \frac{Y_{EPS}}{Y} \cdot (r1 + r2 +r3)\\r1 & = \mu_{max} \cdot \frac{S_{sub}}{S_{sub} + Ks_{sub}} \cdot \frac{S_{o2}}{S_{o2} + Ks_{o2}}\\r2 & = \eta \mu_{max} \cdot \frac{S_{sub}}{S_{sub} + Ks_{sub}} \cdot \frac{S_{no3}}{S_{no3} + Ks_{no3}} \cdot \frac{Ks_{o2}}{S_{o2} + Ks_{o2}}\\r3 & = \eta \mu_{max} \cdot \frac{S_{sub}}{S_{sub} + Ks_{sub}} \cdot \frac{S_{no2}}{S_{no2} + Ks_{no2}} \cdot \frac{Ks_{o2}}{S_{o2} + Ks_{o2}}\\r4 & = b_{maint} \cdot \frac{S_{o2}}{S_{o2} + Ks_{o2}}\\r5 & = \frac{1}{1.17} \cdot \eta \cdot b_{maint} \cdot \frac{S_{no2}}{S_{no2} + Ks_{no2}} \cdot \frac{Ks_{o2}}{S_{o2} + Ks_{o2}}\\r6 & = \frac{1}{2.86} \cdot \eta \cdot b_{maint} \cdot \frac{S_{no3}}{S_{no3} + Ks_{no3}} \cdot \frac{Ks_{o2}}{S_{o2} + Ks_{o2}}\end{aligned}\end{align} \]

where:

  • \(b_{decay}\) is the decay rate (decay)

  • \(Y\) is the yield coefficient (yield)

  • \(Y_{EPS}\) is the yield coefficient for EPS secretion (epsyield)

  • \(\mu_{max}\) is the maximum growth rate (growth)

  • \(S_{sub}, S_{o2}, S_{no2}, S_{no3}\) are the local concentrations of organic substrate, oxygen, nitrite and nitrate, respectively, at the grid cell in which atom resides

  • \(Ks_{sub}, Ks_{o2}, Ks_{no2}, Ks_{no3}\) are the half-velocity constants for organic substrate (sub-Ks), oxygen (o2-Ks), nitrite (no2-Ks) and nitrate (no3-Ks), respectively

  • \(\eta\) is the reduction factor of the atoms in anoxic condition (anoxic)

  • \(b_{maint}\) is the maintenance coefficient (maintain)

The new mass and outer mass are then used to update the diameter and outer diameter of the atoms. If fix nufeb/diffusion_reaction is applied, the fix also update substrate utilisation (reaction) rates in all the affected grid cells:

\[ \begin{align}\begin{aligned}R_{sub} & = -\frac{1}{Y} \cdot (r1 + r2 + r3) \cdot X\\R_{o2} & = -(\frac{1-Y-Y_{EPS}}{Y} \cdot r1 + r4) \cdot X\\R_{no3} & = -(\frac{1-Y-Y_{EPS}}{2.86 Y} \cdot r2 + r5) \cdot X\\R_{no2} & = -(\frac{1-Y-Y_{EPS}}{1.17 Y} \cdot r3 + r6) \cdot X\end{aligned}\end{align} \]

where:

  • \(R_{sub}, R_{o2}, R_{no2}, R_{no3}\) are the utilisation rates of organic substrate, oxygen, nitrite and nitrate in the affected grid cells, respectively

  • \(Y\) is the yield coefficient (yield)

  • \(X\) is the heterotrophs biomass density in grid cell

Restrictions

This fix is not compatible with the following commands:

(Ofiteru, I.D., et al 2013) Ofiteru, I.D., et al., Multi-scale modelling of bioreactor-separator system for wastewater treatment with two-dimensional activated sludge floc dynamics, Water Research (2013)