Java version of SUCCESS.BAS
See H.R. Bungay, BASIC Biochemical Engineering, BiLine Assoc., Troy,NY (1993), p. 8.2
Batch Mixed Cultures
The interactions of mixed cultures in batch systems are difficult
to interpret because there is no good reference point when so
many conditions and concentrations may be changing at once.
Not only are the numbers, types, and characteristics of the organisms
changing, but pH, redox potential, ionic strength, and concentrations of
nutrients, intermediates, and products are changing.
Holding sewage sludge under anaerobic conditions results in a
succession of microbial growth and death cycles where the
decay of cells provides nutrients for the next generation.
A highly oversimplified model for microbial succession is:
S ------> A ------> B ------> C ------> D ------> F
where S is the main nutrient and the different organisms are designated by A, B, C, and D. The final sludge is F.
Let us assume that S simply declines by a first-order reaction:
dS/dt = - k1 S
We further assume that the organisms grow in proportion to their food source and die by a first-order reaction. Some inefficiency is incorporated by the term with Kc.
dA/dt = k1 S - k2 A - Kc A
dB/dt = k2 A - k3 B - Kc B
dC/dt = k3 B - k4 C - Kc C
dD/dt = k4 C - k5 D - Kc D
dF/dt = k5 D
The coefficient Kc accounts for loss of mass to carbon dioxide.
The other coefficients are first-order rate constants.
In a real ecosystem, many different organisms would be
present, and each would feed on or derive benefit from
a complicated array of other organisms.
In this simulation, blue is the nutrient, red is Organism A, green is Organism B, orange is Organism C, magenta is Organism D, and the final sludge is not plotted. It increases with time and levels off. The figure just shows some concentrations versus time. There are also changes
in pH, oxidation/reduction potential, viscosity, and in concentrations
of other nutrients, intermediate biochemicals, and products of metabolism.