Analysis of the productivity of a continuous algal culture system

We describe a first-principles analysis of a system for the continuous culture of the green alga Scenedesmus obliquus under light-limiting conditions. According to this analysis, the productivity of the algal culture is given by the relation Y = E(m)I(0)AK(1 - e(-alphacl)) - GRcV, where Y = yield (g cells/h), E(m) = 0.20 (the maximum attainable photosynthetic conversion on an energy basis), A = illuminated area (m(2)), K = 0.156[(g cells/h/W), the energy equivalent of the algae], I(0) = light intensity (W/m(2)), alpha = extinction coefficient (L/cm/g),c = cell concentration (g/L), I = light path (cm), R = respiration rate (g carbon/g cells/h), V = culture volume (L), and G = ratio of g cells to g carbon (2.04). This formula is completely determined and has no free adjustable parameters. Using parameter values determined independently, the model accurately predicted the relationship of productivity to cell density in the culture system.