GPS-X Technical Reference

Attached Growth Models 220
Mathematical Model
The mathematical equations used within each layer of the biofilm are provided in the
corresponding Model matrix (for example, see Appendix A for the mantis model). The
equation used for the diffusion of the state variables from the bulk liquid into the biofilm
is provided below. The diffusion through the biofilm is described by Fick's second law
and supplemented with biological reactions:
Equation 7.1
where:
Aa = surface area of biofilm through which transport is occurring (m 2 )
δL
S j L
t
S j BLi
S o
Q L
K M
K ML
= thickness of attached liquid layer (m)
= substrate conc. in liquid film horizontal section (mg/L)
= time (days)
= substrate concentration at biofilm liquid interface section j
(mg/L)
= saturated liquid-film substrate concentration (mg/L)
= volumetric flow rate of attached liquid layer (L/d)
= mass transfer coefficient from liquid to biofilm (m/d)
= oxygen transfer coefficient from air to liquid film (m/d)
GPS-X Technical Reference