The PFROI is equivalent to the QA 2nd O EROI and is calculated using Equation (14). This relation serves as a standard way to compare energy and cost analyses at a systems level. By doing so, the energetic profitabil­ity of an energy system (which is the most important metric for researchers interested in global energy production and consumption or thermodynam­ics of energy systems) can be compared with the financial profitability of an energy system (which is most important to businesses and investors).

The cost of growing algae was calculated for the Experimental Case by applying electricity and material prices, yielding a total cost of growth of $105.2/kLp. With 2.1 g of bio-oil produced from each kL of processed

URE 2: The EROI and PFROI for the Experimental Case and the Highly Productive Case decline as more inputs are considered. The curves are presented for illustration only, as the curve shapes are unknown.

volume, these cultivation costs are $40,000/L of bio-oil ($150,000/gal). The Highly Productive Case data results in a total cultivation cost of $0.42/kLp, which is equivalent to $0.42/kg of algae or $1.6/L of bio-oil ($6.1/gal) based on the bio-oil productivity calculated above (210 g bio — oil/kLp). The combined cost of processing and refining was calculated to be $7.71/kLp and $0.13/kLp for the Experimental and Highly Productive Cases, respectively (cf. Tables 1A and 2A). Based on the resulting bio-oil productivities, these values correspond to $2900/L of bio-oil ($11,000/gal)
and $0.5/L of bio-oil ($1.9/gal) for these cases, respectively. Davis et al. present a comprehensive techno-economic analysis of a similar production system (including capital costs) and determined that operating costs for both open-pond and enclosed bioreactor settings would be near $1.3/L of bio-oil ($5/gal) [16]. This result is similar to the total operating cost of the Highly Productive Case ($2.1/L of bio-oil, $7.99/gal). In the Experimental Case, 2.1 g of bio-oil were produced per kLp (0.0026 L/kLp) and 41.6 g of methane were produced per kLp. Assuming market prices of $0.66/L of bio-oil ($0.66/L, $0.83/kg) and $4/MMBtu of methane ($0.21/kg) yields revenues of $0.0017/kLp for bio-oil and $0.0087/kLp for methane in the Experimental Case (yielding $0.010/kLp of total revenue). In the Highly Productive Case, 210 g (0.26 L) of bio-oil and 150 g of methane are pro­duced for each kLp, resulting in $0.17/kLp of bio-oil revenue and $0.03/ kLp of methane revenue. Until 2012, a production subsidy of $0.13/L was provided for corn ethanol in the United States, and if an equal subsidy was provided for algal fuels, the production plant would gain incremental income of $0.0004/kLp for the Experimental Case and $0.035/kLp for the Highly Productive Case.

The partial financial returns on investment (PFROI) are calculated from Equation (14) for the Experimental Case and the Highly Productive Case to be 9.2 * 10-5 and 0.37, respectively. The challenge in obtaining a PFROI greater than 1 is growing, processing, and refining high-yield biomass cheaply, especially since many of the costs scale directly with biomass productivity (e. g., nutrient costs increase as biomass productivity increases). The overall FROI would be lower than the PFROI as capital, labor, and distribution costs will be significant expenses, which are not included in the PFROI. For example, Lundquist et al. and Davis et al. provide analyses for capital costs of similar production systems and dem­onstrate that capital costs might contribute roughly 50% of the total cost for open-pond systems (this fraction increases substantially for bioreac­tors) [16,52]. Figure 2 illustrates the relationships between the EROI, QA EROI, and PFROI with respect to the number of inputs that are considered in the analysis, and is based on the work of Henshaw, King, and Zarnikau in relating EROI to full business costs, or cash flows [53]. For a given biofuel output, as more inputs are included in the calculations, the return on investment values decrease.