A CAES storage plant comprising an air compressor, underground compressedair storage, gas turbine with a combustor, and an HRSG is operating as follows: • Electric power output of peaking gas turbine–generator train is Pel = 100 MWe • Storage cavern charging period (compression) duration is

Question

A CAES storage plant comprising an air compressor, underground compressed air storage, gas turbine with a combustor, and an HRSG is operating as follows:

• Electric power output of peaking gas turbine–generator train is [latex]P_{el}[/latex] = 100 MWe
• Storage cavern charging period (compression) duration is [latex] au_{c}[/latex] = 5 h
• Power generation period duration is [latex] au_{g}[/latex] = 8 h
• Compressor intake is at [latex]t_{1}[/latex] = 15°C and [latex]p_{1}[/latex] = 100 kPa and discharge is at [latex]p_{2}[/latex] = 6.4 MPa
• Supplementary firing raises the compressed-air temperature to a turbine inlet temperature [latex]t_{3}[/latex] of 1050°C
• Fuel: natural gas with an LHV of 49 MJ/kg
• Compressor and turbine isentropic efficiencies [latex]\eta_{ic}[/latex] and [latex]\eta_{it}[/latex] are 0.85 and 0.8, respectively

Assuming a constant specific heat for the air of 1.05 kJ/(kg K) in the entire temperature range, calculate (i) the required energy storage capacity, (ii) the mass of air required for the storage, (iii) the total fuel requirements for the generation period per hour, (iv) the volume of the air storage cavern, (v) the air flow rate, and (vi) the fuel flow rate.

Accepted Answer

1. The required energy storage capacity is equal to the total energy input to the gas turbine train during the power generation period. Thus, taking into account the energy losses during generation

[latex]Q_{s}=P\mathbf{\mathrm{\bf~t}}_{g}/\mathbf{h}_{it}\,=\,100 imes8/0.8\,=\,1000\,\,\mathrm{MW}\,\mathrm{h}[/latex]

2. With [latex]T_{1}[/latex] = 15°C + 273 = 288 K, air temperature after isentropic (reversible) and actual (irreversible) zero compression with a pressure ratio [latex]\beta[/latex] = [latex]p_{2}[/latex]/[latex]p_{1}[/latex] = 6.4 MPa/0.1 MPa = 64, respectively,

[latex]T_{2s}\,=\,T_{1}\mathbf{b}^{(k-1)/k}\,=\,288 imes64^{(1.4-1)/1.4}\,=\,945\ \mathrm{K}[/latex]

[latex]T_{2}\,=\,T_{1}+(T_{2s}-T_{1})/\mathbf{h}_{ic}\,=\,288+(945-288)/0.85=\,1061\,\mathrm{K}[/latex]

3. With the gas turbine inlet temperature [latex]T_{3}[/latex] = 1050°C + 273 = 1323 K, the fuel–air ratio is given by

[latex]{f}\,=\,c_{p}(T_{3}-T_{2})/\mathrm{LHV}\mathrm{ }=\,1.05 imes(1323-1061)/49,000=\,0.0056\mathrm{1\,kg/kg}[/latex]

4. Mass of air required

[latex]m_{a}\,=\,Q_{s}/c_{p}\Delta T\,=\,1 imes1 0^{6}\,\mathrm{kW}\,\mathrm{h} imes3600\,\,\mathrm{s/h}\,/[1.05\,\mathrm{kJ} /\mathrm{kg}\,\,\mathrm{k} imes(1323-288)\,\mathrm{K}][/latex]

= 3,312,629 kg

5. Total fuel requirements

[latex]m_{f}\;=\;f\;m_{a}\;=\;0.00561 imes3,312,629=18,584\;{\mathrm{kg}}[/latex]

6. Fuel mass flow rate per hour of generation

[latex]m_{f} [/latex]= 18,584 kg/8 h = 2323 kg/h

7. Air density at [latex]p_{2}[/latex] = 6.4 MPa and [latex]T_{2}[/latex] = 1061 K

[latex]{\bf r}_{2}\,=\,p_{2}/\mathrm{RT}_{2}\,=\,6.4 imes10^{6}\mathrm{~Pa~}/\left[287 \,\mathrm{J}/(\mathrm{kg~}\mathrm{K}) imes1061\mathrm{~K} ight]\,=\,21.02\mathrm{~kg/m^{3}}\,[/latex]

8. Cavern volume required

[latex]V_{c}\,=\,m_{a}/{\bf r}_{2}\,=\,3,312,629\;\mathrm{kg/21.}02\;\mathrm{kg/m^{3}}\,=\,157,594\;\mathrm{m^{3}}[/latex]

9. Average air flow to the cavern during 5 h of compression

[latex]V_{a,a v}=157,594\mathrm{~m^{3}/5~h=31},518.8\mathrm{~m^{3}/h}=8.755\mathrm{~m^{3}/s}[/latex]

It is more reasonable to employ a two-stage intercooled compression and two-stage reheat expansion.
Example 11.3 presents the performance calculation of a CAES system for a utility-scale power plant.

Question 11.2: A CAES storage plant comprising an air compressor, undergrou......

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