Calculators › Renewables and on-site generation Wet biomass useful-heat cost calculator
Wet biomass useful-heat cost
Compare purchased wet mass on a common useful-heat basis: dry-fuel heat is reduced by the modeled moisture burden before applying the stated useful efficiency.
Units IP (US) SI (metric)
c useful = c ton × 1 , 000 , 000 2000 × [ ( 1 − w ) × H dry − w × H evap ] × η c_{\text{useful}} = \frac{c_{\text{ton}} \times 1{,}000{,}000}{2000 \times \left[\left(1 - w\right) \times H_{\text{dry}} - w \times H_{\text{evap}}\right] \times \eta} c useful = 2000 × [ ( 1 − w ) × H dry − w × H evap ] × η c ton × 1 , 000 , 000 c useful = c tonne × 1 , 000 , 000 1000 × [ ( 1 − w ) × H dry − w × H evap ] × η c_{\text{useful}} = \frac{c_{\text{tonne}} \times 1{,}000{,}000}{1000 \times \left[\left(1 - w\right) \times H_{\text{dry}} - w \times H_{\text{evap}}\right] \times \eta} c useful = 1000 × [ ( 1 − w ) × H dry − w × H evap ] × η c tonne × 1 , 000 , 000
Calculator
Enter the values you know and leave one box empty. Calculate finds the empty one, the result or any input.
Worked example
Given
c ton c_{\text{ton}} c ton 110 $/short ton w w w 0.3 fraction H dry H_{\text{dry}} H dry 7,800 Btu/lb dry fuel H evap H_{\text{evap}} H evap 1,100 Btu/lb moisture η \eta η 0.78 fraction c useful = 110 × 1 , 000 , 000 2000 × [ ( 1 − 0.3 ) × 7800 − 0.3 × 1100 ] × 0.78 ≈ 13.745 c_{\text{useful}} = \frac{110 \times 1{,}000{,}000}{2000 \times \left[\left(1 - 0.3\right) \times 7800 - 0.3 \times 1100\right] \times 0.78} \approx 13.745 c useful = 2000 × [ ( 1 − 0.3 ) × 7800 − 0.3 × 1100 ] × 0.78 110 × 1 , 000 , 000 ≈ 13.745
Given
c tonne c_{\text{tonne}} c tonne 150 $/tonne w w w 0.32 fraction H dry H_{\text{dry}} H dry 18,000 kJ/kg dry fuel H evap H_{\text{evap}} H evap 2,500 kJ/kg moisture η \eta η 0.8 fraction c useful = 150 × 1 , 000 , 000 1000 × [ ( 1 − 0.32 ) × 18 , 000 − 0.32 × 2500 ] × 0.8 ≈ 16.39 c_{\text{useful}} = \frac{150 \times 1{,}000{,}000}{1000 \times \left[\left(1 - 0.32\right) \times 18{,}000 - 0.32 \times 2500\right] \times 0.8} \approx 16.39 c useful = 1000 × [ ( 1 − 0.32 ) × 18 , 000 − 0.32 × 2500 ] × 0.8 150 × 1 , 000 , 000 ≈ 16.39
Symbols and units
Symbol Meaning Unit
c useful c_{\text{useful}} c useful useful heat unit cost $/MMBtu c ton c_{\text{ton}} c ton as-received short-ton purchase price $/short ton w w w as-received moisture mass fraction fraction H dry H_{\text{dry}} H dry dry fuel heating value Btu/lb dry fuel H evap H_{\text{evap}} H evap modeled moisture heating and evaporation burden Btu/lb moisture η \eta η useful transfer efficiency after moisture burden fraction
Symbol Meaning Unit
c useful c_{\text{useful}} c useful useful heat unit cost $/GJ c tonne c_{\text{tonne}} c tonne as-received metric-tonne purchase price $/tonne w w w as-received moisture mass fraction fraction H dry H_{\text{dry}} H dry dry fuel heating value kJ/kg dry fuel H evap H_{\text{evap}} H evap modeled moisture heating and evaporation burden kJ/kg moisture η \eta η useful transfer efficiency after moisture burden fraction
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