I cannot speak one way or the other to the implementation of a full cyclic model as a desirable course of action. I did however want to dive deeper into the world of Python by trying to make a mathematical model of the Carbon Cycle in the original post. I hope to refine it some more in the next few days/weeks. Regardless, I do think there is a way to integrate the cycle and patches.
If we determine the mass composition of each bin (I.e. for the mantle 4.07e24 kg Carbon, xxx kg nitrogen, xxx kg oxygen, etc), we can create mass ratios (I.e. 4.07e24 kg Carbon/xxx total mass of mantle). Every patch can correspond to specific bins it comes into contact with (I.e. an abyssal pitch would come into contact with the deep ocean and crustal bins). Each patch could then access an element in accordance with the ratios available to its local bins. I envision the math working out to something along the lines of:
Patch Carbon = (Carbon Ratio of Bin 1) * (Mass Fraction of Patch Composed of Bin 1) + … + (Carbon Ratio of Bin X) * (Mass Fraction of Patch Composed of Bin X)
That way the bins directly impact patches and patches respond to changes in their local bins that might be on a different timeline from others. This can be further complicated to include the local biological component of the carbon cycle, which can store and release carbon like regular bins. These bio-bins have access to a maximum of “Patch Carbon” to store each “round” but can release any stored amount of carbon in accordance with their metabolic activity (possibly derived from the AutoEvo calculations).
Each Bin could then lose or gain carbon to any biological populations associated with it.
I apologize if this was not particularly coherent, I have not quite settled out the mathematics in the Python model.