2.4.2. Long Term Ethanol Probabilities

The estimates for the current and potential use of forest biomass for biofuel are based on volumes (cords). Since green weights are imprecise and highly variable, cubic foot volumes or dry weight are assumed to be more reliable estimates of inventory, growth, and removals and changes over time [11]. Therefore, a conversion to oven-dried tons (ODT) was calculated to convert the timber and residue volumes (cords) to dry weights. The conversion factor is 1.21 ODTs/cord, which is the average conversion factor that is used in the Forest Age Class Change Simulator (FACCS) simulation model [42]. Since 1 short ton = 0.907 metric tonne, the conversion factor is recalculated as 1.21 × 0.907 = 1.097 tonnes of dry matter per cord. By assuming that forest residues have the same conversion rate with timber roundwood, the mass of ethanol ( *<sup>M</sup>TEtOH*, tonne) can be calculated as:

$$M\_{EtOH}^T = 1.097(\mathbf{Q}\_{timber}^T + \mathbf{Q}\_{residue}^T)(P\_{timber}^{hard}a\_{hard}^{mr} + P\_{timber}^{soft}a\_{soft}^{mr})\tag{5}$$

where the *αmr hard* represents the mass ratio of ethanol from hardwood and *αmr so f t* is the one from softwood.

With a density of 0.789 tonne/m<sup>3</sup> of ethanol [43], the tonnage of ethanol can be converted to liters through:

$$V\_{EtOH}^T = 1,390(Q\_{timber}^T + Q\_{residualer}^T)(P\_{timber}^{hard}a\_{hard}^{mr} + P\_{timber}^{soft}a\_{soft}^{mr})\tag{6}$$

where *VTEtOH* is the predicted volume (liters) of ethanol in year *T*.

For Michigan's case, Equation (4) and the values of *Phard timber* and *Pso f t timber* are substituted into Equations (5) and (6), the predicted mass (tonnes) and volume (liters) of ethanol in year *T* can be obtained by:

$$M\_{EtOH}^{T,MI} = Q\_{timber}^{T} (0.85a\_{hard}^{mr} + 0.28a\_{soft}^{mr})\tag{7}$$

$$V\_{EtOH}^{T,MI} = \mathcal{Q}\_{timber}^{T} (1, 077a\_{hard}^{mr} + 355a\_{soft}^{mr}) \tag{8}$$
