Biogeochemical Cycles - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 179

The kinetic equation for indirect photolysis is

dC / dt = - k 2 CX = - k p C (4.85)

where
k 2 = indirect photolysis rate constant

X = concentration of the nontarget intermediary

k p = overall pseudo-first-order rate constant for sensitized photolysis

4.2.4.7 Biodegradation

If the microbial community has adapted to the contaminant, the Michaelis-Menten
equation can be used to represent the rate of biotransformation as

k b = ( µ max X )/( Y ( k s + c )) (4.86)

where
c

= concentration of chemical being biodegraded [ µ g m −3 ]

µ max = maximum growth rate of the culture [yr −1 ]

X = biomass concentration of the microorganisms [cells.m −3 ]

Y = yield coefficient [cells produced per mass toxicant removed]

k s = half-saturation constant [ µ g.m −3 ]

k b = biological transformation rate constant [m 3 cells −1 year −1 ]

When c << k s , then

k b = ( µ max X )/( Y ⋅ k s ) = k b 2 ⋅ X (4.87)

where k b 2 is the second-order biotransformation rate constant [m 3 cells −1 year −1 ].
For systems where the microbial population is relatively constant, the transfor-
mation rate equation reduces to a pseudo-first-order rate expression. 45
If pseudo-first-order rates are unavailable, or if they must be extrapolated to
different bacterial conditions, then the second-order approach can be used. It is
generally assumed that bacterial populations are unaffected by the presence of the
pollutant compound at low concentrations. Second-order kinetics for dissolved,
DOC-sorbed, and sediment-sorbed chemical can also be considered:

K BW = P ac ( t ) Σ i Σ j k bij f ij j = 1, 2 (4.88)

K BS = P ac ( t ) Σ i Σ j k bij f ij j = 3 (4.89)

where
K BW = total biodegradation rate constant in the water column [day −1 ]

K BS = total biodegradation rate constant on sediment [day −1 ]

k bij = second-order biodegradation rate constant for species i , phase j [ml cell −1 day −1 ]

P ac (t ) = active bacterial population density in segment [cell ml −1 ]

f ij = fraction of chemical as species i in phase j