Non-Renewable means Limited

Our (post-)industrial society is addicted to consuming non-renewable resources, to fossil fuels in form of coal, gas and oil. We use them to get from A to B in our cars, trucks, ships and planes, to heat our homes in the cold seasons, to generate nitrogen-based fertilizers, to generate light and to power our electronic devices.

Billions of car engines and household heatings are consuming oil and gas which has been created over millions of years. Because these fossil fuels have been generated over millions of years, they have a high energy density and are hard to replace. Ed Conway writes in his book “Material World” [1]

“Coal has about twice the energy density – in other words the amount of energy that can be released per kg of weight – of wood. Kerosene, refined from crude oils, has nearly twice the energy density of coal. And a higher energy density means you can carry less fuel and go greater distances”

The relentless exploitation of fossil fuels and non-renewable resources enabled our modern capitalistic societies to function in the last decades. But even very simple models show that the society as we know it can not last long. Drug addicts know that the repeated consumption of the drug will ruin their lives, but they are consuming them anyway. For us it is similar: we know that the addiction to oil and gas will ruin the world we live in, including the climate, but we are doing it anyway.

I have asked claude.ai to create a very simple model which describes resource depletion, energy generation and pollution over time. As more and more resources are consumed to generate energy, the pollution goes up, until the resource is depleted and the pollution reached its maximum. It is perhaps the most simple way to model the exploitation of non-renewable resources. If the exploitation is happening through exponential growth even giant amounts of resources can be turned quickly into waste and pollution.

Try it yourself here (It works best on a desktop screen, not on a small mobile screen. The HTML and JS source code should be simple to understand). The collapse in this model when the resources have been deleted happens quite quickly in a few years after peak production is reached. It uses exponential growth. If we consider that the modern capitalistic economy is based on exponential growth, it is obvious that even very large amounts of non-renewable resources can be exploited and totally depleted in a short time, in logarithmic time complexity O(log n). The biggest oil fields like the Ghawar oil field in Saudi Arabia, the Prudhoe Bay oil field in Alaska and the Cantarell oil field in Mexico are in fact already past their peak of production, the North Field gas field in Qatar is not far away from its peak.

If we do not want to turn our planet into a giant junkyard [3] while destroying the climate and making it uninhabitable, we need to use renewable energy in a sustainable economy [4]. There does not seem to be another way. Asked for a simple model of a sustainable resource, claude.ai suggested logistic functions where we have eventually an equilibrium of consumption and regeneration:

You can try this model here. Basically these two models correspond to the models M212 (“Exploitation of resources”) and M214 (“Sustainable use of renewable resources”) in Hartmut Bossel’s book [5] from 30 years ago. We knew all of this for a long time, at least since the first “Limits to Growth” research 50 years ago. And yet like an addict our society is unable to change.

[1] Ed Conway, Material World, WH Allen, 2023
[2] Donella H. Meadows et al, Limits to Growth
[3] Adam Minter, Junkyard Planet, Bloomsbury Press 2013
[4] Eklas Hossain and Slobodan Petrovic, Renewable Energy Crash Course: A Concise Introduction, Springer, 2021
[5] Hartmut Bossel, Modellbildung und Simulation (in German), Vieweg, 1994