The assumptions inherent in a calculation of overall efficiency of a photosynthetic process are based on areal insolation, capture, and conversion, and are analyzed relative to a sequentially accumulating loss of photons that are not gainfully utilized for the production of product. When accounting for the ultimate contingent of photons that are converted, the loss at each process step is a percentage fraction of the total available from the previous step. The descriptions below follow the sequence of process conversion steps and reflect the accumulating losses and resultant efficiencies illustrated in Fig. 2. Values described below are summarized in Table 3.
PAR radiation fraction
The analysis assumes that only the solar radiation reaching the ground is available for conversion and the cumulative loss is computed with respect to this boundary value. Although the average total solar radiation reaching the ground varies throughout the world, we assume that the relative efficiency of each subsequent step in the conversion process is location-independent to a first-order approximation. The energy fraction of solar radiation reaching the ground that lies in the PAR range does vary with location and time of day. Results obtained from NREL models (Gueymard 2005; Bird and Riordan 1984) indicate that the PAR radiation fraction ranges from about 47–50% in the southwest USA. For the calculations performed in this article, we use a value of 48.7% for PAR radiation fraction to remain consistent with Zhu et al. (2008), resulting in a loss of 51.3%.
In the direct process, once reactors are inoculated, cells must be grown up to high density before the production phase. Thereafter, the process is continuous for an extended period. Based on pilot experience, we assume an 8-week process time, 3 days of growth at doubling times ~3 h followed by 53 days of production with no biomass accumulation, before the reactors must be emptied and reinoculated. Direct production of a fungible product minimizes downstream processing. This results in a reactor availability loss of about 5%.
In the case of an algal biomass process, energy and carbon are dedicated to batch growth and stress-induced triglyceride accumulation, followed by harvesting and downstream processing. The DOE Algal Biomass report process summary indicates that the algal growth phase is followed by an equal triglyceride accumulation phase, which would indicate a cycling efficiency loss of 50%. Coupled growth and triglyceride process would result in an approximate 20% loss (see Fig. 3; Sheehan et al. 1998) which we take here.
Reactor surface reflection
Any process using an enclosed reactor must account for reflective and refractive losses as light passes through the outward facing surface. A 15% loss is estimated for the direct process to account for light reflected away from the reactor. The reactor is assumed to have two layers of plastic containing the organisms (an outer protective layer and an inner container), resulting in three air/plastic interfaces that light must pass through before reaching the culture. Each of these interfaces will result in about a 5% reflective Fresnel loss, assuming no antireflective coating is used. For the algal open pond, a single air/water interface results in about a 2% reflective Fresnel loss.
According to Zhu et al. (2008), about 10% of the incoming PAR radiation is reflected away by a plant or culture, with most of this reflection occurring at the green wavelengths. This loss is applied to all cases, including the theoretical maximum.
Not all photons that enter a reactor are available for conversion. For instance, it may be too costly to maintain the reactor in a condition in which it can convert every photon, such as early in the morning and late in the day when solar radiation is very diffuse. Likewise, depending on how the reactor temperature is maintained, the organisms may not be at optimal production temperature early in the morning. In addition, at very high intensity levels, the organisms may not be able to convert all of the photons. Based on models that integrate solar and meteorological data with a thermal and production model, we estimate that about 15% of the incoming photons will not be available for conversion for the direct case. We assign a comparable loss to the algal open pond.
The main fractional loss in photosynthetic conversion results from energy-driven metabolism. Because the photosynthetic process is ultimately exothermic, the available energy contained in the product formed by metabolism is a fraction of that contained in the incoming photons. The remaining energy is dissipated as heat into the culture. For the production of alkane, we calculated that ~12 photons are required to reduce each molecule of CO2. Assuming an average PAR photon energy of 226 kJ/mol and a heating value of 47.2 MJ/kg for alkane, the photosynthetic conversion efficiency is about 25% (equivalent to a loss of 74.8%). For the simpler triglyceride, we assume only eight photons are required to reduce each molecule of CO2, but that the product consists of half triglyceride (heating value ≈37 kJ/kg) and half simple biomass (heating value ≈15.6 kJ/kg), resulting in a photosynthetic conversion efficiency of about 29.8%. This value for algal open ponds is considered to be very conservative, with the actual value likely a few percent lower. Finally, for the theoretical maximum, we use the value computed in Zhu et al. (2008) for a maximum photosynthetic efficiency of 29.1% (obtained by combining the loss for photochemical inefficiency and carbohydrate synthesis).
Maintenance energy is a variable that may affect photoefficiency by drawing away energetic currencies of ATP and NADPH for cell division, repair, and other functions not directly associated with product formation. The maintenance energy in any given process situation depends on rates of metabolism, cell division, etc., as shown in differences in measured values in dividing versus resting cells (Pirt 1965; Pirt 1975). A batch bioprocess, therefore, wherein cell division and product formation are proceeding simultaneously versus a continuous process where growth is minimized and carbon is partitioned to a secreted product may differ considerably in maintenance energy. However, because the concept and measurement are controversial, we have attributed a 5% loss to the analyses of all three scenarios.
Under illumination, eukaryotic photosynthetic organisms, e.g., plants and algae, lose efficiency because of respiratory metabolism in the mitochondria. Because cyanobacteria have no subcellular organelles and the engineered organisms are partitioning nearly all fixed carbon to product, we have assumed negligible respiration loss in the direct process and have also zeroed out this loss in the theoretical practical maximum scenario. The algal open-pond analysis includes a 30% loss for mitochondrial respiration. This value is based on the plant value used by Zhu et al. (2008).
According to Zhu et al. (2008), processes at atmospheric CO2 concentrations, such as an open algal pond, will have a substantial loss (≈49%) due to photorespiration. This loss is minimized at high-CO2 levels (>1%) maintained in the enclosed direct process (see text for explanation).
Biomass versus fuel production
In the direct process, most fixed-carbon output is in the form of a chemical product from a cloned heterologous pathway. For the algal process, we assume a generous value for oil yield of 50% by weight and thus apply a 50% loss to productivity.
The losses discussed above are summarized in Table 3. We define conversion factor as (1 – loss factor) for each of the above losses. For instance, the conversion factor for cellular maintenance (loss = 5%) is 95%. Total conversion efficiency, as shown in Fig. 2, is computed by taking the product of each of the conversion factors computed from the values in Table 3.