Scale-up of photo-bioreactors for microalgae cultivation by π-theorem

Robust microalgae cultivation at industrial scale needs complex scale-up of photobioreactors since the same yields obtained at lab-scale are hardly reached during pilot or industrial production. In this paper we propose a procedure based on Buckingham π-theorem to perform the scale-up of photobioreactors used to cultivate Chlorella Vulgaris fed by CO2 and wastewater rich in glycerol. This theoretical approach is usually overlooked in favor of the synergy of modeling tailored on the process and piloting, but it grants excellent generalizability. An experimental campaign at three levels was designed and carried out to evaluate the characteristic dimensionless numbers individuated by the theoretical formulation. Since scale-up regards both geometrical dimensions and type of reactor, passing from lab-scale stirred tanks (STRs) to pilot scale tubular and airlift, particular attention was devoted to defining characteristic lengths inside the dimensionless numbers. Moreover, since scale-up also regards the operating mode, scaling from discontinuous to semi-continuous to continuous, some interesting dimensionless numbers arise other than Re, Sh ,Da. They are mainly related to the type of biological process and its operating mode and are the ratios O2/CO2 and T/Topt, the ratio between the incident light intensity and the saturation constant, the absorbance, the ratio between the final and the initial concentration c/c0, the ratio between the maximum increase in cell population and its initial concentration, the ratio between the estimated specific kinetic constant and a variable representing the characteristic time of mixing inside the chosen reactor. Preliminary outdoor tests confirmed the operability of the scaled-up airlift reactors reaching c/c0 = 5.3 – 7.5, with c = 1.15 g L-1 at extraction intervals of 5 days. They were operated under optimal light conditions of incident light greater than Chlorella v. saturation constant and absorbance A = 40 and at incipient churn flow (Re = 10000 - 11000) with dimension of fluegas bubbles around 5 mm, apt to guarantee Sh = 1500-2500; and with a calculated Da around 25.