Note: Because this example
includes reactants, it requires the RT Module. If you are using the CT
Module, you will not be able to open the file.
To illustrate the manner in which GoldSim can be used to represent complex higher order reactions, let's consider a problem involving Monod kinetics. Monod kinetics has been applied in systems where a microorganism population increases because a contaminant present in the environment supports the microorganism's growth. This particular example file, Monod.gsm, can be found in the Contaminant Transport Examples folder in your GoldSim directory (accessed by selecting File | Open Example... from the main menu).
Note: Because this example
includes reactants, it requires the RT Module. If you are using the CT
Module, you will not be able to open the file.
Assume we have a Cell containing 1 m3 of Water, with an initial concentration of contaminant (4.6 g/m3), and an initial concentration of microorganisms (1E10 cells/m3). Assume a cell has a mass of 1E-10 g. If the system follows Monod kinetics, the rate of change of the contaminant and the microorganisms with time can be described as follows:
and
where:
|
(Bugs) |
= concentration of microorganisms (cells/L3); |
|
[contam] |
= concentration of contaminant (mol/L3); |
|
μmax |
= maximal growth rate (1/T); |
|
Km |
= Monod constant (mol/L3); and |
|
Y |
= constant yield (cells/mol). |
This would be represented in GoldSim as follows:
1. Define two species (Contaminant and Bugs);
2. Specify that the Contaminant has Bugs as a daughter product, with a stoichiometry equal to the yield, Y (2E14 cell/mole). Because stoichiometry factors are dimensionless, Y must be divided by Avogadro's number, resulting in a stoichiometry factor of 3.321E-10 mole/mole).
3. The rate of change of the contaminant can be rewritten in terms of mass concentrations as:
where:
|
ccontam |
= the concentration of the contaminant (M/L3); |
|
cBugs |
= the concentration of the microorganisms (M/L3); |
|
Mbugs |
= the mass of a single microorganism (M/cell); and |
|
MWcontam |
= the molecular weight of the contaminant (M/mole). |
The k' term defined above can then be entered as the pseudo first-order decay rate for the contaminant. Assume umax is equal to 0.7 hr-1, Km is equal to 6.4E-3 mole/m3, and the molecular weight of the contaminant is equal to 100 g/mol. Note that the "molecular weight" of the microorganisms is 1E-10 g/cell x Avogadro's number = 6.02E13 g/mol.
4. Define a single Cell containing 1 m3 of Water;
5. Define an initial mass of contaminant in the Cell of 4.6 g, and an initial quantity of microorganisms of 1E10 cells. Assume the mass of one cell is equal to 1e-10 g.
6. Specify the simulation settings and run the model.
Note that defining the decay rate as a function of the concentrations creates a recursive model (since the concentration is a function of the decay rate, and the decay rate is a function of the concentration). Hence, when you do this, you must utilize a previous value element.
The output of this model, in the form of a time history of the contaminant and microorganism concentrations, is shown below:
