problem more difficult? P9-20B Alternative Energy Source.25 In the summer of 2009, ExxonMobil decided to invest 600 million dollars on developing algae as an alternative fuel. Algae would be grown and their oil extracted to provide an energy source. It is estimated that one acre of a biomass pond can provide 6,000 gallons of gasoline per year, which would require the capture of a CO2 source more concentrated than air (e.g., fuel gas from a refinery) and also contribute to the sequestration of CO2. The biomass biosynthesis during the day is Sunlight + CO2 + H2O + Algae More Algae + O2 Consider a 5,000-gallon pond with perforated pipes into which CO2 is injected and slowly bubbled into the solution to keep the water saturated with CO2. The doubling time during the day is 12 h at high-noon sunlight and zero during the night. As a first approximation, the growth during the 12 hours of daylight law is rg = fCC Run Cs (g/dm3) D (day!1) Cc (g/dm3) 1 01 10. 0.9 2 03 1.5 0.7 3 04 1.6 0.6 4 10 1.8 40. 25 The contributions of John Benemann to this problem are appreciated. CO2 Figure P9-20.1 Commercial microalgae production in open raceway, paddle-wheel mixed ponds. Courtesy of Cyanotech Co., Hawaii. Chapter 9 Supplementary Reading 397 with f = sunlight = sin ( t/12) between 6 a.m. and 6 p.m., otherwise f = 0, CC is the algae concentration (g/dm3) and = 0.9 day1 (assumes constant CO2 saturation at 1 atm is 1.69g/kg water). The pond is 30-cm deep and for effective sunlight penetration, the algae concentration cannot exceed 200 mg/dm3. (a) Derive an equation for the ratio of the algae cell concentration CC at time t to initial cell concentration CC0, i.e., (CC/CC0). Plot and analyze (CC/CC0) versus time up to 48 hours. (b) If the pond is initially seeded with 0.5 mg/dm3 of algae, how long will it take the algae to reach a cell density (i.e., concentration) of 200 mg/dm3, which is the concentration at which sunlight can no longer effectively penetrate the depth of the pond? Plot and analyze rg and CC as a function of time. As a first approximation, assume the pond is well mixed. (c) Suppose the algae limit the suns penetration significantly even before the concentration reaches 200 mg/dm3 with e.g., = 0 (1 CC/200). Plot and analyze rg and CC as a function of time. How long would it take to completely stop growth at 200 mg/dm3? (d) Now, lets consider continuous operation. Once the cell density reaches 200 mg/dm, one-half of the pond is harvested and the remaining broth is mixed with fresh nutrient. What is the steady-state algae productivity in gm/year, again assuming the pond is well mixed? (e) Now consider a constant feed of waste water and removal of algae at a dilution rate of one reciprocal day. What is the mass flow rate of algae out of the 5,000 gallon pond (g/d)? Assume the pond is well mixed. (f) Now consider that the reaction is to be carried out in an enclosed, transparent reactor. The reactor can be pressurized with CO2 up to 10 atm with KS = 2 g/dm3. Assume that after the initial pressurization, no more CO2 can be injected. Plot and analyze the algae concentration as a function of time. (g) An invading algae can double twice as fast as the strain you are cultivating. Assume that it initially is at 0.1 mg/l concentration. How long until it is the dominant species (over 50% of the cell density)?