The 2nd O EROI for the Experimental Case and the Highly Productive Case, which have been reported previously by Beal et al. [14], are 9.2 * 10-4 ± 3.3 * 10-4 (cf. [19] for uncertainty analysis) and 0.22, respec­tively.

For algal biofuels to be produced commercially, the EROI must be competitive with that of conventional fuels (e. g., over the last few decades the EROI for oil and gas, including industrial capital, has typically been 10-20 [36] with delivered gasoline between 5 and 10 [37]). Several other studies have presented hypothetical energy analyses of algal biofuel pro­duction, and although the scope and systems evaluated vary, each of these studies has also found that without discounted inputs, the EROI is not competitive with conventional fuels [11,15,17,27,38]. The 2nd O EROI results from this study are plotted in Figure 2, along with the first-order EROI, which only includes direct energy inputs (and thereby neglects en­ergy embedded in material inputs).

For the Experimental Case, 90% (2308 kJ/Lp) of the total energy in­put (2572 kJ/Lp) was associated with bioreactor lighting, air compression (for supplying CO2), and pond mixing; all of which are considered to be artifacts of inefficient research-scale growth methods. Conversely, in the Highly Productive Case, which modeled efficient growth equipment, em­bedded energy in nutrients accounted for 85% (63 kJ/Lp) of the total energy
input (75 kJ/Lp). The Highly Productive Case assumes 8 kg of CO2, 70 g of nitrogen, and 8 g of phosphorus consumed per kg of algae produced.

Based on conservation of mass, the minimum possible CO2, nitrogen, and phosphorus consumption can be approximated as 1.8 kg, 70 g, and 8 g per kg of generic algal biomass, respectively [2,15,17,44-46]. Using these minimum data, and the associated energy equivalents (with values of 7.3 MJ/kg CO2, 59 MJ/kg N, and 44 MJ/kg P [15,19,46-51]), the mini­mum possible energy embedded in the (full-price) nutrients alone requires more energy (17.7 kJ/Lp) than the total energy produced (16.6 kJ/Lp), which prevents a positive net energy yield, and illustrates the need to use waste forms of nutrients. The energy embedded in carbon, nitrogen, and phosphorus is dependent on the stoichiometric requirement and energy intensity of production for each element. However, the embedded energy in these elements is independent of growth rate [14], demonstrating the limited ability for growth optimization to alter the overall EROI for algal biofuels.

The EROI was adjusted using quality factors reported by Beal et al. [14] that were calculated according to the price of each input, yielding a QA 2nd O EROI that directly parallels the PFROI analysis. For the Experi­mental Case and the Highly Productive Case, the QA 2nd O EROI was 9.2 x 10-5 and 0.36, respectively [14].