Ecological Archives A019-028-A2

Stephen R. Mitchell, Mark E. Harmon, and Kari E. B. O'Connell. 2009. Forest fuel reduction alters fire severity and long-term carbon storage in three Pacific Northwest ecosystems. Ecological Applications 19:643–655.

Appendix B. Biofuels analysis calculations.

I. Energy Conversions

Energy can be obtained through the combustion of woody biomass, ethanol, and automotive fossil fuel, and all of these materials emit C upon combustion. However, the amount of C emitted for each unit of energy derived from their combustion varies due to the differences in potential energy of each material. In the below calculations we estimated ratios of the amount of C emitted per unit energy between biofuels (woody biomass and bioethanol) and automotive fossil fuel. This was done to establish a conversion efficiency among our C based energy sources to ascertain how much biofuels C must be emitted for a certain amount of energy compared to how much fossil fuel C must be emitted for the same amount of energy.

Note that we have assumed maximum energy conversion efficiencies. We did this because biofuels are currently an area of intense research, and it was unlikely that we could provide a conversion efficiency that would not be outdated shortly after publication. We also assumed, only for the sake of simplicity, that no C would be emitted during the process of harvesting the biomass. Consequently, our calculations give an estimate of the shortest possible time to an offset of ecosystem C reduction.

Biomass Energy Conversion Efficiency

1. To calculate the conversion efficiency of woody biomass energy C to fossil fuel energy C, we first obtained estimates of the amount of energy in woody biomass and fossil fuel.

Wood biomass energy content†: 20 GJ t-1 (t = 1 ton)

Fossil fuel energy content†: 43.50 GJ t-1 (Lower Heating Value)

2. Next, we obtained estimates of the amount of C in woody biomass and fossil fuel.

C ratio in fossil fuel* = 0.85 t C / t fossil fuel

C ratio in biomass** = 0.50 t C / t biomass

3. Finally, we calculated the ratio between the energy output for each unit of C emitted between biomass and fossil fuel.

Ratio of C emissions per unit energy = (20 GJ t-1 / 0.5 t C emissions) / (43.50 GJ t-1 / 0.85 t C emissions) = 0.7816 Conversion Efficiency for Biomass-Derived C.

Ethanol Conversions

1. To calculate the conversion efficiency of ethanol energy C to fossil fuel energy C, we first obtained estimates of the amount of ethanol that can come from 1 Mg C.

Ethanol production from dry biomass‡ = 455 liters of ethanol from 1 Mg dry biomass

Fraction of C in dry biomass = 0.5

Increase in efficiency for ethanol compared to fossil fuels § = 15%

455 liters of ethanol from 1 Mg dry biomass / 0.5 = 910 liters of ethanol from 1 Mg C

2. Next, we found the ratio in volumetric energy content between ethanol and fossil fuel.

Ratio in volumetric energy content between ethanol and fossil fuel † = 75,670 Btu gal-1/131,800 Btu gal-1 * 1.15 = 0.6602

3. We then multiplied this ratio by our estimate of the amount of potential ethanol production per Mg C to obtain the amount of ethanol-derived fossil fuel energy per Mg C emissions.

910 liters ethanol per Mg C * 0.6602 = 600.78 liters of ethanol-derived fossil fuel energy per Mg C emissions.

4. Finally, we found the amount of C emitted per unit fossil fuel energy and used it to calculate the ratio between the energy outputs for each unit of C emitted for ethanol and fossil fuel.

Fossil fuel energy per unit C emitted by combustion† = 1547 liters of fossil fuel energy per Mg C emissions.

600.78 liters of ethanol-derived fossil fuel energy per Mg C emissions / 1547 liters of fossil fuel energy per Mg C emissions = 0.3884 Conversion Efficiency for Ethanol-Derived C.

II. C Accumulation Statistics from STANDCARB

Coast Range

Mean C storage of an unharvested stand (control group) = 1082.21 Mg C ha-1

C harvested from a previously unharvested stand via a clear-cut = 332.36 Mg C ha-1

Mean C storage for a stand with UR+OT+PF applied every 25 years = 757.30 Mg C ha-1

Mean annual harvestable C accumulation for a stand with UR+OT+PF applied every 25 years = 2.46 Mg C ha-1yr-1

West Cascades

Mean C storage of an unharvested stand (control group) = 798.08 Mg C ha-1

C harvested from a previously unharvested stand via a clear-cut = 268.01 Mg C ha-1

Mean C storage for a stand with UR+OT+PF applied every 25 years = 403.67 Mg C ha-1

Mean annual harvestable C accumulation for a stand with UR+OT+PF applied every 25 years = 2.21 Mg C ha-1yr-1

III. Time for Biofuel Offsets to Exceed Ecosystem C Reductions.

Once conversion efficiencies were established, we took the modeled estimate of the average amount of biomass produced every year under the fuel reduction treatment conditions and multiplied it by the conversion efficiency to establish the amount of fossil fuel C that was being offset each year, assuming that all biomass removed was utilized for biofuels. This is shown in the below calculations for the west Cascades and Coast Range, once for biomass and once for ethanol.

Coast Range Biomass and Ethanol Offsets

Mean Annual C Offset for Biomass

2.46 Mg C ha-1 yr-1 * 0.7816 = 1.92 Mg C ha-1 yr-1 mean C offset by biomass each year for UR+OT+PF applied every 25 years (MFRI=500) in the Coast Range.

Mean Annual C Offset for Ethanol

2.46 Mg C ha-1 yr-1 * 0.3884 = 0.96 Mg C ha-1 yr-1 mean C offset by ethanol each year for UR+OT+PF applied every 25 years (MFRI=500) in the Coast Range.

West Cascades Biomass and Ethanol Offsets

Mean Annual C Offset for Biomass

2.21 Mg C ha-1 yr-1 * 0.7816 = 1.73 Mg C ha-1 yr-1 mean C offset by biomass each year for UR+OT+PF (MFRI=230) in the west Cascades

Mean Annual C Offset for Ethanol

2.21 Mg C ha-1 yr-1 * 0.3884 = 0.86 Mg C ha-1 yr-1 mean C offset by ethanol each year for UR+OT+PF applied every 25 years (MFRI=230) in the west Cascades.

IV. Time for Biofuel Offsets to Exceed Ecosystem C Reductions.

After the average amount of C offset was calculated, we calculated how long it would take for C offsets from biofuels to result in a net offset of potential atmospheric C emissions. Calculations for the amount of time required to reach equilibrium were performed for two different land-use histories. The first assumed that the stand was currently managed under the fuel reduction treatment scenario described above. We estimated time to equilibrium for this scenario by calculating the difference between the mean C storage of the control group and the mean C storage of the fuel reduction treatment group before dividing that by our estimate of C that was being offset each year by biofuels production.

The second land-use history assumed that the stand was old growth before being converted via clear-cut to a second-growth forest, utilizing C removed in the clear-cut for biofuels. We estimated time to equilibrium for this scenario by multiplying the amount of C removed in a clear-cut by the conversion efficiency factor and subtracting this quantity, along with the mean C storage of the fuel reduction treatment group, from the mean C storage of the control group before dividing that by our estimate of C that was being offset each year by biofuels production. These calculations are shown in the calculations below for the west Cascades and Coast Range, once for biomass and once for ethanol.

Coast Range Years to Reach Equilibrium for Biomass and Ethanol

Years to Reach Equilibrium for Biomass

(1082.21 Mg C ha-1 - 757.30 Mg C ha-1) / 1.92 Mg C ha-1 yr-1 = 169.22 yr to reach equilibrium via biomass for UR+OT+PF applied every 25 years (MFRI=500) in the Coast Range.

Years to Reach Equilibrium for Biomass (when converted from old-growth)

(1082.21 Mg C ha-1 - 757.30 Mg C ha-1 - 332.36 Mg C ha-1 * 0.7816) / 1.92 Mg C ha-1 yr-1 = 33.93 yr to reach equilibrium via biomass for UR+OT+PF applied every 25 years (MFRI=230) in the Coast Range.

Years to Reach Equilibrium for Ethanol

(1082.21 Mg C ha-1 - 757.30 Mg C ha-1)/ 0.96 Mg C ha-1 yr-1 = 338.48 yr to reach equilibrium via ethanol for UR+OT+PF applied every 25 years (MFRI=500) in the Coast Range.

Years to Reach Equilibrium for Ethanol (when converted from old-growth)

(1082.21 Mg C ha-1 - 757.30 Mg C ha-1 - 332.36 Mg C ha-1 * 0.3884) / 1.11 Mg C ha-1 yr-1 = 176.42 yr to reach equilibrium via ethanol for UR+OT+PF applied every 25 years (MFRI=230) in the Coast Range.

West Cascades Years to Reach Equilibrium for Biomass and Ethanol

Years to Reach Equilibrium for Biomass

(798.0804 Mg C ha-1 - 403.67 Mg C ha-1)/ 1.73 Mg C ha-1 yr-1 = 227.98 yr to reach equilibrium via biomass for UR+OT+PF (MFRI=230) in the west Cascades.

Years to Reach Equilibrium for Biomass (when converted from old-growth)

(798.0804 Mg C ha-1 - 403.67 Mg C ha-1 - 268.01 Mg C ha-1 * 0.7816) / 1.73 Mg C yr-1 = 106.89 yr to reach equilibrium via biomass for UR+OT+PF (MFRI=230) in the west Cascades.

Years to Reach Equilibrium for Ethanol

(798.08 Mg C ha-1 - 403.67 Mg C ha-1)/ 0.86 Mg C ha-1 yr-1 = 458.62 years to reach equilibrium via ethanol for UR+OT+PF applied every 25 years (MFRI=230) in the west Cascades.

Years to Reach Equilibrium for Ethanol (when converted from old-growth)

(798.0804 Mg C ha-1 - 403.67 Mg C ha-1 - 268.01 Mg C ha-1 * 0.3884) / 0.86 Mg C ha-1 yr-1 = 337.57 years to reach equilibrium via ethanol for UR+OT+PF applied every 25 years (MFRI=230) in the west Cascades.

Sources

† Data taken from Wright et al. (2006)

‡ Data taken from Galbe and Zacchi (2002)

*Data from EIA (1994)

** Data taken from Waring and Schlessinger (1985)

§ Data taken from Bailey (1996)

LITERATURE CITED

Bailey, B. K. 1996. Performance of ethanol as a transportation fuel. Paghes 37-60 in C. E. Wyman, Editor. Handbook on bioethanol: production and utilization. Taylor and Francis, Bristol, Pennsylvania, USA.

EIA. 1994.  Emissions of Greenhouse Gases in the United States 1987-1992, Energy Information Administration, U.S. Department of Energy. Washington, DC. November, 1994. DOE/EIA 0573.

Galbe, M., and G. Zacchi. 2002. A review of the production of ethanol from softwood. Applied Microbiology and Biotechnology 59:618–628.

Waring, R. H., and W. H. Schlesinger. 1985.  Forest ecosystems: concepts and management.  Academic Press, Orlando, Florida, USA.

Wright, L., B. Boundy, B. Perlack, S. Davis, and B. Saulsbury.  2006.  Biomass energy data book: edition 1.  Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA. 


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