Chemical Engineering Science 59 (2004) 2899–2912 www.elsevier.com/locate/ces Simulation of algae growth in a bench scale internal loop airlift reactor Xiaoxi Wu a , Jose C. Merchuk b; * a Department of Biotechnology and Bioengineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel b Department of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel Received 18 June 2003; received in revised form 11 February 2004; accepted 19 February 2004 Abstract The growth of red marine alga Porphyridium sp. cultivated in an internal loop airlift (ALR) photobioreactor was simulated. The model proposed integrates a dynamic formulation of the kinetics of photosynthesis, photoinhibition, and the uid dynamics of the ALR, including shear stress eects on the kinetics of growth. The kinetic parameters obtained previously for a system under dened light/dark cycles were used, and satisfactory agreement was found. The maintenance term was modied to take into account the detrimental eects of shear stress in the bioreactor on the rate of growth. A hybrid method for approximate solution of the equations is proposed. The conditions of gas ow rate and illuminance required for positive growth were found. This is the rst mathematical model that predicts the eect of gas ow rate, column height, column diameter, and cross-sectional areas on the productivity of a photosynthetic process in an airlift bioreactor. Extrapolations done using the model indicate the possibility of predicting the optimal diameter for an assembly of ALR photobioreactors. ? 2004 Elsevier Ltd. All rights reserved. Keywords: Photobioreactors; Mathematical modeling; Fluid dynamics; Photoinhibition; Algal growth; Large-scale production 1. Introduction One of the most important factors that control cell growth in a photobioreactor is light availability. As described by Lambert–Beer’s Law, light intensity decays exponentially as it penetrates into an optically dense culture. In highly dense cultures, while the region close to the light source receives plenty of light, some zones in the reactor may remain in the dark due to optical absorption and self-shading of the cells. In this region, the light intensity is too weak to maintain positive growth of the cells, and the net biomass production would be negative. Increasing the volumetric surface area (reducing the cul- ture depth) to avoid such negative eect results in higher installation costs. In the present approach, ordered mix- ing is suggested instead. Ordered mixing forces the cells to experience periodical light/dark cycles. The eect of the light/dark cycles has been studied previously (Lee and Pirt, 1981; Merchuk et al., 1998; Wu and Merchuk, 2001), and it was found that under high PFD, periodical light/dark cycles ∗ Corresponding author. Tel.: +972-8-6461768; fax: +972-8-6472916. E-mail address: jcm@bgumail.bgu.ac.il (J.C. Merchuk). might enhance growth. A dynamic model was developed and was studied under well-dened uid dynamics conditions (Wu and Merchuk, 2001). For modeling a photobioreactor with this approach, uid dynamics should be integrated with the dynamic behavior of the photosynthetic elements, to give the overall kinetics of the process. This approach was fol- lowed elsewhere to simulate the growth in a bubble column (Wu and Merchuk, 2002). Agreement of experimental data and model prediction was achieved. An airlift reactor (ALR) is a pneumatically agitated de- vice that provides dened pattern of bulk circulation of u- ids, through channels specically designed for this purpose (Merchuk and Gluz, 1999). If the volumes enclosed by an- nulus and draft tube can be regarded as illuminated and dark regions, respectively, this ow pattern gives dened light/dark cycles for photosynthetic cells culture. However, because of the nature of the decay in illuminance mentioned above, the description of the annulus as an “illuminated re- gion” is in most cases an oversimplication. Local dier- ences in PFD will appear as one departs from the illumi- nated surface. Hence, the cell trajectories in the light zone, i.e., the liquid ow patterns in the downcomer, are required in order to describe properly the light story of a photosyn- thetic cell. An optical trajectory tracking system (OTTS), a 0009-2509/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2004.02.019