## 1 Introduction  
Microalgae are unicellular or pluricellular microscopic and photosynthetic microorganisms that may grow by employing solar energy in a more efficient way compared to land plants. They can be employed as a source of food, [1], in pharmaceuticals and cosmetics [2], in the bioremediation of wastewaters [3] and in general as a source of biomass.  
Microalgae cultivation may occur outdoors in open ponds. Among these, raceway ponds are the most commonly employed for mass cultivation [4], as they are generally cheap (production costs for microalgal biomass in a raceway can be estimated at around 1.6-1.8 \(\epsilon\) kg\({}^{-1}\)[5]), but have several disadvantages. In fact, in an outdoor cultivation facility, there is weak control of the operating parameters and risk of contamination, leading to poor mass production. Alternatively, microalgae can be grown indoors inside photobioreactors. Indoor photobioreactors are generally more expensive but ensure better control of growing conditions and, consequently, better productivity.  
Several studies of the design and optimization of photobioreactors to maximize biomass productivity are available [6; 7]. However, there are still several doubts about technical issues of concern and the economics of large scale microalgal cultivation. Most of the criticisms depend on the lack of reliable and reproducible parameters that strongly affect growth, productivity and, consequently, the industrial scale-up of the systems. Therefore, microalgae are usually not cultivated in their optimal conditions and this results in a gap between process operation and responses to the culture inputs, especially in an industrial environment in which productivity is largely lower than that which might be expected from lab experiments.  
The light available to the cells is the main parameter in optimizing microalgal cultivation [8].  
Several models describing microalgae response to light have been proposed in the literature, in some cases including investigation of mass transfer [9; 10]. [PERSON] et al. [11] suggested classification into three categories according to how the photosynthetic productivity is computed. One of the problems is that, in order to have strict control of the kinetic parameters, one should avoid self-shading effects that cause a non-homogeneous light distribution inside the reactor.  
To avoid this problem, a specific kind of reactor that allows a homogeneous light distribution inside should be employed to obtain the kinetic parameters. We refer to these kinds of reactors as quasi-isoactinic, meaning that the light distribution inside them is almost homogeneous [12]. When employing these reactors, it is fully possible to analyze the effect of a specific kind of illumination on a culture. This work proposes a Bechet type II photosynthetic model, able to predict the biomass productivity in reactors with different depths and geometries. In particular, a strain of _Nannochloropsis gaditana_, known for its lipid content, was employed for the experimental validation of the model. The kinetic parameters were obtained, for the first time, inside a \"quasi-isoactinic\" photobioreactor, in order to ensure an almost homogeneous light distribution. Then microalgae _Nannochloropsis gaditana_ were grown in photobioreactors with three different geometries to obtain experimental data to be compared with the model prediction.  
Model simulations in batch reactors are presented and discussed. Furthermore, biochemical analysis of proteins, carbohydrates, lipids, fatty acid characterization and carotenoids was performed on the biomass obtained through all the batch cultivations realized, and the results represent a complete characterization of _Nannochloropsis gaditana_ grown under different average light intensities.