A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve.
An energy crisis or energy shortage is any significant bottleneck in the supply of energy resources to an economy. In literature, it often refers to one of the energy sources used at a certain time and place, in particular, those that supply national electricity grids or those used as fuel in industrial development. Population growth has led to a surge in the global demand for energy in recent years. In the 2000s, this new demand – together with Middle East tension, the falling value of the US dollar, dwindling oil reserves, concerns over peak oil, and oil price speculation – triggered the 2000s energy crisis, which saw the price of oil reach an all-time high of $147.30 per barrel ($926/m3) in 2008.
Marion King Hubbert was an American geologist and geophysicist. He worked at the Shell research lab in Houston, Texas. He made several important contributions to geology, geophysics, and petroleum geology, most notably the Hubbert curve and Hubbert peak theory, with important political ramifications. He was often referred to as "M. King Hubbert" or "King Hubbert".
The Hubbert peak theory says that for any given geographical area, from an individual oil-producing region to the planet as a whole, the rate of petroleum production tends to follow a bell-shaped curve. It is one of the primary theories on peak oil.
Peak oil is the theorized point in time when the maximum rate of global oil production will occur, after which oil production will begin an irreversible decline. The primary concern of peak oil is that global transportation heavily relies upon the use of gasoline and diesel fuel. Switching transportation to electric vehicles, biofuels, or more fuel-efficient forms of travel may help reduce oil demand.
Colin J. Campbell was a British petroleum geologist who predicted that oil production would peak by 2007. He claimed the consequences of this are uncertain but drastic, due to the world's dependency on fossil fuels for the vast majority of its energy. His theories have received wide attention but are disputed and have not significantly changed governmental energy policies at this time. To deal with declining global oil production, he proposed the Rimini protocol.
In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function. The hyperbolic secant function is equivalent to the reciprocal hyperbolic cosine, and thus this distribution is also called the inverse-cosh distribution.
Oil depletion is the decline in oil production of a well, oil field, or geographic area. The Hubbert peak theory makes predictions of production rates based on prior discovery rates and anticipated production rates. Hubbert curves predict that the production curves of non-renewing resources approximate a bell curve. Thus, according to this theory, when the peak of production is passed, production rates enter an irreversible decline.
Backstop resources theory states that as a heavily used limited resource becomes expensive, alternative resources will become cheap by comparison, therefore making the alternatives economically viable options. In the long term, the theory implies faith that technological progress will allow backstop resources to be essentially unlimited, and that need will cause the development of new technologies to become cost effective. This idea is supported by economist Robert Solow who claimed that four-fifths of US economic growth could be attributed to technological development.
Jean H. Laherrère is a French petroleum engineer and consultant, best known as the co-author of an influential 1998 Scientific American article entitled The End of Cheap Oil.
The Hubbert linearization is a way to plot production data to estimate two important parameters of a Hubbert curve, the approximated production rate of a nonrenewable resource following a logistic distribution:
Peak gas is the point in time when the maximum global natural gas production rate will be reached, after which the rate of production will enter its terminal decline. Although demand is peaking in the United States and Europe, it continues to rise globally due to consumers in Asia, especially China. Natural gas is a fossil fuel formed from plant matter over the course of millions of years. Natural gas derived from fossil fuels is a non-renewable energy source; however, methane can be renewable in other forms such as biogas. Peak coal was in 2013, and peak oil is forecast to occur before peak gas. One forecast is for natural gas demand to peak in 2035.
Peak coal is the peak consumption or production of coal by a human community. Peak coal can be driven by peak demand or peak supply. Historically, it was widely believed that the supply-side would eventually drive peak coal due to the depletion of coal reserves. However, since the increasing global efforts to limit climate change, peak coal has been driven by demand. This is due in large part to the rapid expansion of natural gas and renewable energy. As of 2024 over 40% of all energy sector CO2 emissions are from coal, and many countries have pledged to phase-out coal.
The Export Land Model, or Export-Land Model, refers to work done by Dallas geologist Jeffrey Brown, building on the work of others, and discussed widely on The Oil Drum. It models the decline in oil exports that result when an exporting nation experiences both a peak in oil production and an increase in domestic oil consumption. In such cases, exports decline at a far faster rate than the decline in oil production alone.
Predicting the timing of peak oil involves estimation of future production from existing oil fields as well as future discoveries. The initial production model was Hubbert peak theory, first proposed in the 1950s. Since then, many experts have tried to forecast peak oil.
The reserves-to-production ratio is the remaining amount of a non-renewable resource, expressed in time. While applicable to all natural resources, the RPR is most commonly applied to fossil fuels, particularly petroleum and natural gas. The reserve portion (numerator) of the ratio is the amount of a resource known to exist in an area and to be economically recoverable. The production portion (denominator) of the ratio is the amount of resource produced in one year at the current rate.
Sustainability measurement is a set of frameworks or indicators used to measure how sustainable something is. This includes processes, products, services and businesses. Sustainability is difficult to quantify. It may even be impossible to measure as there is no fixed definition. To measure sustainability, frameworks and indicators consider environmental, social and economic domains. The metrics vary by use case and are still evolving. They include indicators, benchmarks and audits. They include sustainability standards and certification systems like Fairtrade and Organic. They also involve indices and accounting. They can include assessment, appraisal and other reporting systems. The metrics are used over a wide range of spatial and temporal scales. For organizations, sustainability measures include corporate sustainability reporting and Triple Bottom Line accounting. For countries, they include estimates of the quality of sustainability governance or quality of life measures, or environmental assessments like the Environmental Sustainability Index and Environmental Performance Index. Some methods let us track sustainable development. These include the UN Human Development Index and ecological footprints.
Peak minerals marks the point in time when the largest production of a mineral will occur in an area, with production declining in subsequent years. While most mineral resources will not be exhausted in the near future, global extraction and production has become more challenging. Miners have found ways over time to extract deeper and lower grade ores with lower production costs. More than anything else, declining average ore grades are indicative of ongoing technological shifts that have enabled inclusion of more 'complex' processing – in social and environmental terms as well as economic – and structural changes in the minerals exploration industry and these have been accompanied by significant increases in identified Mineral Reserves.
Decline curve analysis is a means of predicting future oil well or gas well production based on past production history. Production decline curve analysis is a traditional means of identifying well production problems and predicting well performance and life based on measured oil well production. Before the availability of computers, decline curve analysis was performed by hand on semi-log plot paper. Currently, decline curve analysis software on PC computers is used to plot production decline curves for petroleum economics analysis.
Oil and gas reserves denote discovered quantities of crude oil and natural gas that can be profitably produced/recovered from an approved development. Oil and gas reserves tied to approved operational plans filed on the day of reserves reporting are also sensitive to fluctuating global market pricing. The remaining resource estimates are likely sub-commercial and may still be under appraisal with the potential to be technically recoverable once commercially established. Natural gas is frequently associated with oil directly and gas reserves are commonly quoted in barrels of oil equivalent (BOE). Consequently, both oil and gas reserves, as well as resource estimates, follow the same reporting guidelines, and are referred to collectively hereinafter as oil & gas.
