A nonrenewable source is based in a storage, a limited quantity of energy. If we use the example of a dead log, it is a storage of wood available to be eaten by beetles. The population of beetles will increase exponentially as they eat the log and the quantity of log will decrease. As the log is used up, the quantity of beetles decreases too.
In the diagram (Figure II-3a) E is the nonrenewable source, the dead log. The amount the log decreases is proportional to the quantity of log (E) and the quantity of beetles (Q); the equation for the decrease in log is:
DE = - K*E*Q
In a period of time, like a week, the amount of log will be the amount started with plus the change:
E = E + DE
The change in quantity of beetles is also proportional to the quantity of log (E) and the quantity of beetles (Q). The net increase of beetles (K1*E*Q) is their growth and reproduction (K2*E*Q) minus the effort used to get their food (K3*E*Q). The decrease in beetles, their death rate, is proportional to their quantity (K4*Q). Therefore, the change in quantity of beetles (Q) over time is their growth minus their death. The equation is:
DQ = K1*E*Q - K4*Q
At the end of a week the number of beetles will be the number at the beginning of the week plus the change:
Q = Q + DQ.
You get a graph (Figure II-3b) when you run the program. We have graphed both the change in the log (E) and the change in beetles (Q). Notice that the log does not decrease much until the population of beetles increases fast and then the log gets used up quickly.
Examples of Nonrenewable Models
This model represents any system with a limited source, which is used up. An economic example is a mining town living on a limited source of gold ore. As the ore is mined, the town grows on its revenues from the gold. When the mine runs out, the town economy decreases until everyone leaves and it becomes a "ghost town."
A person given an inheritance could fit this model. He uses the money to go on more and more trips. As the money runs out, his trips decrease and then cease.
"What if" Experiments
COMPUTER MINIMODELS AND SIMULATION EXERCISES
FOR SCIENCE AND SOCIAL STUDIES
Howard T. Odum* and Elisabeth C. Odum+
* Dept. of Environmental Engineering Sciences, UF
+ Santa Fe Community College, Gainesville
Center for Environmental Policy, 424 Black Hall
University of Florida, Gainesville, FL, 32611
Copyright 1994
Autorização concedida gentilmente pelos autores para publicação na Internet
Laboratório de Engenharia Ecológica e Informática Aplicada - LEIA - Unicamp
Enrique Ortega
Mileine Furlanetti de Lima Zanghetin
Campinas, SP, 20 de julho de 2007