Calculating the heat loss of an Aquifer Thermal Energy Storage
Department of Mathematics & Computer Science @ Eindhoven University of Technology
In the search for ways to improve the climate, a new technology is being used in The Netherlands for about 20 years: Aquifer Thermal Energy Storage (ATES), also known as a heat-cold storage system. This technology uses geothermal sources — the heat of the Earth — for water heating, and thereby reduces CO2 emissions. TU/e also has a heat-cold storage system in use, saving around two million KWh of electricity annually and over 300,000 m3 of gas.
An open ATES system consists of two tubes, approximately 100 meters apart, with a depth of 25 to 250 meters. One tube leads to a cold water source between 6 and 9 degrees Celsius. The other tube leads to a source of hot water between 14 and 17 degrees Celsius. When hot water is desired, cold water is pumped through the “cold tube”, so that the water is propelled through groundwater flow to the hot spring. Here the water heats up and is pumped back through the ‘hot tube’, for example to be used for the heating of a building.
The research
As is customary with relatively young technologies, ATES systems are already in use but not yet optimized. In order to make progress and be able to deploy the technology on a larger scale, TU/e’s Mathematics and Computer Science PhD student Arthur Vromans conducts research into heat loss of ATES systems. This research is part of the Mathematics of Planet Earth program of the Netherlands Organization for Scientific Research (NWO).
The challenge in creating the mathematical model to calculate heat loss from ATES systems is the large number of factors that affect the water. Consider the earth’s composition and the density of the earth in the tube, and the concrete mix from which the tube is made. This information is known on a level of sand grains, which means that heat loss can in fact be calculated. But to calculate this information for a tube of tens to hundreds of meters, supercomputers are needed.
The solution to this is to use a mathematical model in which the data are averaged: homogenization.
Homogenization is a technique in which effects on a small scale, for example, micron size, are averaged to effective coefficients usable on a large scale, for example, over distances of meters. Homogenization is highly suitable on blends and their properties, so that, for example, the fluidity of concrete can be determined.
In everyday life, everyone is using homogenization. If you look at the screen of a TV, smartphone or computer, each pixel will create all possible colors out of the three basic colors red, green and blue. Because a pixel is very small, we see a composite color; a sort of average of the three basic colors. Only when we are relatively close to the pixel, we can see effects that indicate composite colors from the three basic colors.
In the case of an ATES system, homogenization enables us to determine material constants for the average properties of a water-sand mixture, allowing calculation over a longer distance rather than at sand grain level. This makes it possible to do calculations with a normal computer instead of using a supercomputer.
For testing the mathematical model, the sewage was the ideal test environment. There, the same process takes place as in the tubes of ATES systems. A liquid (in this case gas) comes into contact with the concrete wall of the sewage, nests in it, and a chemical reaction takes place, a process that takes place over a longer period of time: concrete degradation. The data obtained from the sewage has shown that the mathematical model has mathematical properties that are physically necessary to calculate heat loss in ATES systems in the future.
The future
Determining the mathematical one-dimensional model for concrete degradation was the first small but important step in calculating heat loss from ATES systems. In a nutshell, the future steps are as follows; expanding the concrete corrosion model with heat loss, making a three-dimensional model, visualizing the model and then validating the model.
A process that could last several years, but what will form the basis to calculate any further questions. For example, to calculate the actual heat loss, to determine the ideal composition of the concrete, the distance of the tubes from each other and ideal maintenance schedules. Calculations that engineers will use in the future to build the most efficient ATES system, which ensures the greatest possible positive contribution to improving the climate. But first, the sewer will probably benefit from this research, before ATES systems do.
