Monod type differenctial equations

[grockson]

I having a problem with unit check on a differential equation i am trying to test.
Attached is the workbench for the model

[grockson]

Dear all, Could any one ( Bob) assist with this workbench

[bob@vensim.com]

I am not sure what the question is - the model has as yet no units or equations. Biomass should probably be in Kg or Tonne - and its temperature determined by ambient temp and internal organic activity. The equations and units for the internal organic activity are beyond me (my compost piles never work right). But you probably want the equivalent of population (a level) for different organisms consuming different types of organic materials (levels) in order to create new ones (also levels). The temperature change is then determined by the activities of the bacteria and other consumers relative to the total mass.

I hope that is helpful.

[grockson]

I have detailed the equation as mush as possible. The temperature terms have been left out to make it look simple, although temperature is affecting the microbial growth rates. The units have also been attached although, i tried to use a simpler unit system.

Home it meet you interest to discuss or make your contribution.

Best regards

[grockson]

Hi Bob, Were the equations enough to explain my goal?

Hope to hear from you.

George

[bob@vensim.com]

I did take a look at the equations but I don't know enough about the chemistry to comment on units of measurement - it seems that will require more in depth knowledge. I did note that the CO2 equation must also be a d/dt equation or it simply does not make sense.

[grockson]

Monod type differenctial equations

Dear Bob,

I could assume that CO2 should also have a d/dt. how do i represent such a flow system. Also CO2 feeds equation 7 in the attached document which explains the conceptual model. I which to keep temperature(T) constant for the time being.

Even without the CO2 equation incorporated, i am realizing high explosion of X (mesophilic and Thermophilic), coupled with a negative S


hope to here from you.

[bob@vensim.com]

I still don't follow the question. You can enter a differential equation in the form

d/dt X = aX

as

X = INTEG(a*X,init X)
init X = 1

That is, the differential equations translate directly but the initial conditions must be specified. You should be able to to that for this problem.

[grockson]

Dear Bob,

You are right in this respect, and that is what I have been doing. Unfortunately, the values keep exploding in both the negative and positive directions. I will keep trying.

Thanks

[Edited on 5-16-2008 by grockson]

[bob@vensim.com]

Switch to Runge-Kutta 4 with variable step size - if might just be an integration error. Otherwise one of the constants may be wrong.

[grockson]

Dear Bob,

Who do I locate this; switching to Runge-Kutta 4 (cause I am a beginner)? Hope to here from you.

[bob@vensim.com]

Click on Set to set up a simulation then in the toolbar where it says Euler click and it should toggle to RK4 Auto (there are some other choices in Pro/DSS).

[grockson]

Dear Bob,

What I am currently using is a PLE, I have recommended the Software for purchase by my university, but this could take some time ( Typical of Africa). I will continue to review the equations, option and fine-tune the equation