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Question 11.4: A TES has a capacity of 50 kWh over a temperature range from......

A TES has a capacity of 50 kWh over a temperature range from 40°C to 60°C.
Two SHS media, water and rock, or one LHS medium and lauric acid can be used in the TES system. Determine the required mass and volume of each storage medium.
The properties of the storage media are as follows:

Water Rock Lauric Acid
Density ρ (kg/m³) 1000 1600 1007
Specific heat c (kJ/[kg K]) 1.6
Heat of fusion h_{f} (kJ/kg) – – 177
Bed void fraction ε – 0.4 –
Fusion temperature (°C) – – 49

 

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1. Storage energy density per unit mass of lauric acid, water, and rock bed (subscripts a, w, and r), respectively, are

q_{a}\,=\,c_{a}(t_{\mathrm{max}}-t_{\mathrm{min}})+h_{f}\ \ =\,1.6\times(60-40)+177\,=\,209\ \mathrm{kJ} /\mathrm{kg}

 

q_{w}\,=\,c_{w}(t_{\mathrm{max}}-t_{\mathrm{min}})\,=\,4.19\times(60-40)=83.8\ \mathrm{kJ} /\mathrm{kg}

 

q_{r}\,=\,c_{r}(t_{\mathrm{max}}-t_{\mathrm{min}})\,=\,0.8\times(60-40)\,=\,16\mathrm{~kJ}/\mathrm{kg}

2. Masses and volumes of storage media: lauric acid (a), water (w), and rock bed (r), respectively, are

m_{a}\,=\,Q/q_{a}\,=\,50\,\mathrm{kWh}\times3600\,\,{\mathrm{s/h}}/209\,\,\mathrm{kJ}/\mathrm{kg}\,=\,861.2\,\,\mathrm{kg}

 

V_{a}\,=\,m_{\mathrm{a}}/{\bf r}_{\mathrm{a}}\,=\,861.2/1\mathbf{0}07 \,=\,0.855\,\,\mathrm{m}^{3}

 

m_{w}\,=\,Q/q_{w}\,=\,50\,\mathrm{~kW~h}\times3600\,\,{\mathrm{s/h}}/83.8\,\mathrm{~kJ/kg}\,=\,2148\,\mathrm{~kg}

 

V_{\mathrm{w}}=2148/1000=2.148\mathrm{~m}^{3}

 

m_{r}\,=\,Q/q_{r}\,=\,50\,\mathrm{kW}\,\mathrm{h}\times3600\,\,s/\mathrm{h}/16\,\mathrm{kJ}/\mathrm{kg}\,=\,11,250\,\,\mathrm{kg}

 

V_{r}=m_{r}/[\mathbf{r}_{r}(1-\mathbf{e})]=11250\,\,/\,[1600\times(1-0.4)]=11.72\,\mathrm{m}^{3}

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