The basic principle of CAES involves the following steps:
• Compression: Air is compressed adiabatically (i.e., without significant heat transfer to or from the surroundings) using an air compressor, which increases its temperature.
• Cooling: The compressed air is then cooled to ambient temperature using a heat exchanger, removing the heat generated during compression and reducing its volume further.
• Storage: The cooled compressed air is then stored in a suitable underground storage facility, such as a salt cavern, depleted gas reservoir, or an aquifer.
• Expansion: When needed, the stored compressed air is expanded back to a lower pressure through a turbine, converting its stored potential energy into kinetic energy.
• Power generation: The expanded air passes through a generator, where it causes the rotor to spin and produce electricity.
• Heat recovery: The exhaust air from the turbine still contains some energy in the form of heat, which can be recovered using a heat exchanger to pre-heat the air entering the compressor. This improves the overall efficiency of the system.
To illustrate the formula, consider a CAES system with the following parameters:
• Initial air pressure: 1 atm
• Final air pressure: 10 atm
• Initial air temperature: 25°C
• Final air temperature: 35°C
• Turbine efficiency: 80%
• Generator efficiency: 90%
• Overall efficiency of the air compressor and heat exchanger: 85%
1. Compression work: The work required to compress the air can be calculated using the formula:
Work of compression = (P2V2 - P1V1)/n,
where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and 'n' is the polytropic exponent for air (approximately 1.4).
2. Cooling work: Assuming the cooling process is isobaric (constant pressure) and assuming perfect heat transfer, the work required to cool the compressed air is:
Cooling work = m * C_v * (T2 - T1),
where T1 and T2 are the initial and final temperatures, m is the mass of air, and C_v is the specific heat of air at constant volume (approximately 718 J/kg-K).
3. Heat recovery: The heat that can be recovered from the exhaust air of the turbine can be calculated using:
Heat recovery = m * C_p * (T3 - T4), where T3 is the exhaust temperature, T4 is the temperature of the air entering the compressor, and C_p is the specific heat of air at constant pressure (approximately 1004 J/kg-K).
4. Power generation: The power generated by the turbine is given by:
Power = m * (h1 - h2) *n,
where h1 and h2 are the specific enthalpies of the air at the inlet and outlet of the turbine, and $\eta$ is the turbine efficiency.
The overall system efficiency can then be calculated as:
System efficiency = (Power output / Work of compression + Cooling work)
By plugging in the given numerical values, calculate each of these quantities and determine the overall system efficiency of the CAES system.
