Oil is one of the most valuable commodities on the planet, and even though use of renewable sources is increasing, it still provides a large proportion of the world’s energy. Our dependency on oil looks set to continue in the near future, but the past 150 years of oil drilling have left many reservoirs depleted and gaining access to those that remain is becoming increasingly difficult. Thankfully, mathematicians are helping to keep the oil flowing with models that map these buried reservoirs and techniques for boosting efficiency that are inspired by biological evolution.
Most oil reservoirs are found thousands of metres below the surface, making it impossible to observe or influence them directly, so mathematicians such as Jonathan Carter at Imperial College London have developed methods to describe reservoir structures and the flow of oil within them, allowing oil companies to produce the maximum yield possible.
Carter begins by constructing a three dimensional model of the reservoir based on data from seismic surveys. This model is then divided into a grid of cells, each of which holds values representing various properties of the reservoir, such as the ratio of water to oil, the capillary pressure or the permeability of the rock.
A typical reservoir model might contain 10 million cells, each describing the average properties of a piece of rock around the size of a large cargo container. While this is fine for describing the geological properties of a reservoir, the additional complexity of calculating oil flow means this level of detail is too high, and the grid has to be further averaged in a process known as upscaling. This creates a grid of 100,000 cells, each 100 times larger than in the previous grid. The model then calculates how oil and water flow in and out of each cell to build up a dynamic description of the entire reservoir.
At this broad level of detail, many important processes are not captured, but improvements can be made by using smaller cells for particularly complex regions of the reservoir and larger cells for areas that do not require as much detail. Building a multi
Oil is one of the most valuable commodities on the planet, and even though use of renewable sources is increasing, it still provides a large proportion of the world’s energy. Our dependency on oil looks set to continue in the near future, but the past 150 years of oil drilling have left many reservoirs depleted and gaining access to those that remain is becoming increasingly difficult. Thankfully, mathematicians are helping to keep the oil flowing with models that map these buried reservoirs and techniques for boosting efficiency that are inspired by biological evolution.
Most oil reservoirs are found thousands of metres below the surface, making it impossible to observe or influence them directly, so mathematicians such as Jonathan Carter at Imperial College London have developed methods to describe reservoir structures and the flow of oil within them, allowing oil companies to produce the maximum yield possible.
Carter begins by constructing a three dimensional model of the reservoir based on data from seismic surveys. This model is then divided into a grid of cells, each of which holds values representing various properties of the reservoir, such as the ratio of water to oil, the capillary pressure or the permeability of the rock.
A typical reservoir model might contain 10 million cells, each describing the average properties of a piece of rock around the size of a large cargo container. While this is fine for describing the geological properties of a reservoir, the additional complexity of calculating oil flow means this level of detail is too high, and the grid has to be further averaged in a process known as upscaling. This creates a grid of 100,000 cells, each 100 times larger than in the previous grid. The model then calculates how oil and water flow in and out of each cell to build up a dynamic description of the entire reservoir.
At this broad level of detail, many important processes are not captured, but improvements can be made by using smaller cells for particularly complex regions of the reservoir and larger cells for areas that do not require as much detail. Building a multi
