Even though the transition to renewable energy sources is sourced by reducing carbon emissions and limiting the world's temperature increase to 1.5˚C degrees, which are the target of the Paris Climate Agreement, there may be another reason behind this world’s transition: the possibility of fossil fuel depletion. In this article, I would like to clarify the reality of this possibility with mathematical concepts. Afterwards, what can be done in case it happens will be discussed.
Fossil fuels are composite mixtures of fossilized plant and animal remains that have been buried in the ground for millions of years. Fossil fuels, which have a high carbon content due to their origin, require tens of millions of years to form. For this reason, fossil fuels are classified as non-renewable energy sources. There are three main sources of fossil energy: oil, coal and natural gas. We are fully and utterly reliant on fossil fuels, even more than most of us know. Everything we use in our daily life is made up of oil or contains oil. Automobiles, steel, cement, roads, farm machinery, food, health care item, even Starbucks paper cups which are lined with a thin layer of oil-based polyethene plastic, are a limited list of the oil products. As we consider the produced product then by now, we have burnt a lot of oil and we will. Since oil is the product we use most, I will continue to evaluate the depletion of fossil fuels over oil.
According to Alice Friedemann’s notes, the era of cheap and easy oil ended in 2005 when conventional oil plateaued.This also means that just being discovered an oil reservoir is not enough for an oil well drilling to be put into process. Reservoirs are evaluated considering whether they will bring economic profit when the system is built on it. Again Friedemann states that the cost and difficulty of obtaining oil will increase from now on. The analysis of geologic and engineering data with reasonable certainty under existing economic and operating conditions demonstrates that total proved world oil reserves are estimated to be a little over 1.6 trillion barrels. The Worldometer also shows lively how much oil is left in the world based on the sources of British Petroleum (BP) and Energy Information Administration (EIA). Therefore, unless a crunch discovery will be made, we may agree right here that oil is a finite energy source. (Or presumably, let’s assume the oil is finite.)
In mathematics, a real sequence <xn> is a sequence whose codomain is the set of real numbers. <xn> is called bounded if and only if there exist elements of real numbers, m and M, such that m ≤ xi and xi ≤ M for every i that are elements of natural numbers. Here, let xi denote the total oil reservoir size in the world per year, i denote the years, and let <xn> be a sequence of oil reservoir sizes. Since we assumed the oil is finite, the <xn> is bounded by the zero-amount of oil and maximum amount of oil. Let us order the elements of sequences and put it a set T. A theorem states that an ordered, non-empty, finte set T has always a maximal (M) and a minimal element (m). This is to say that we will reach the maximum reservoir size at any year undoubtedly. We will call that “peak oil” when xj = M for a j that is an element of natural numbers.
Peak oil does not imply that oil will run out. It signifies that world oil production has peaked, and there will be less available in the future. Peak oil means that some current uses of oil will no longer be possible. If we consider the current 7.8 billion people burn one cubic mile of oil every year and the increasing population over the years, the peak point points out the problem that the oil will be insufficient but does not imply it will run out. In other words, we could not prove that oil will run out, but we have proven that oil will be insufficient after a while.
If we are nearing or past of the peak oil, a fossil free alternative should be commercialized in a nutshell. However, to create new energy systems and related infrastructure, massive volumes of oil will be required. It is impossible to build without oil, whether it is nuclear, photovoltaics, wind, hydro, or batteries. Therefore, we urgently need to comprehend that now is the moment to redeploy the remaining oil by allocating it solely to purposes where there are no easy substitutes and transitioning to a simpler world utilizing other fossil fuels.
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