## 2 Materials and Methods
### Physical Cultivation Environment, Inorganic Nutrients, Irradiance Measurements and Computations  
During the cultivation sessions, water was sampled every workday (Monday-Friday and occasionally also during weekends) to measure temperature, pH, irradiance, in vivo Chla and cell concentration. Every second day, concentrations of the nutrients nitrate, nitrite, phosphate, silicate and sometimes ammonia were measured [86]. The first years (until December 2017) a Seal Analytical auto analyzer was applied, while from June 2018 we analyzed samples by using Merck kits and modifications adapted to measurement in a plate reader (Table 2). This allowed for nutrient concentrations being available 2 h after sampling, whereafter eventual adjustments in the added quantities of nutrients to the cultures could be done the same day. Occasionally in vitro Chla, oxygen and other parameters were sampled. During cultivation sessions in the 300 m\({}^{3}\) reactor temperature, salinity, pH, CO\({}_{2}\), turbidity and irradiance sub-surface and incident upon the reactor were also logged continuously (Table 2). Irradiance logging was performed with a cosine atmospheric pyranometer (400-700 nm) sensor placed above the reactor, in addition to cosine and scalar (spherical) subsurface (0.7 m) 400-700 nm quantum ones (Table 2). The cultivation sessions were started using diatom cells from our own in-house stock culture collection. The species making up this collection were all isolated from the Arctic Barents Sea or the northernmost part of the North Norwegian coast. These monoclonal stock cultures are maintained and diluted with pasteurized f/2 or f/10 growth medium [87] with additional silicate added (12.3 umol Si(OH)4 L\({}^{-1}\)) in temperature and irradiance controlled culture cabinets. Storage temperature was 6-8 \({}^{\circ}\)C and scalar irradiance was kept at ca. 10 umol m\({}^{-2}\) s\({}^{-1}\). Photoperiod was 14:10 (L:D) and the cultures were kept in 40 mL. Nunc cell cultivation flasks. When new mass cultivation sessions were started, inocula from the stock collections were transferred to 10 and 20 L polypropylene containers filled with f/10 medium. The containers were kept in culture cabinets with same temperature and photoperiod as the stock cultures while irradiance was increased to >15 umol m\({}^{-2}\) s\({}^{-1}\). When cell concentrations were >ca. 20 mill L\({}^{-1}\), the cultures were transferred to one of the 6 m\({}^{3}\) reactors and ca. 1000 L filtrated seawater was added together with Yara Kristalon and Si-solution. Thereafter volume was added until the reactor was full and desired cell concentrations were reached. If cultivation in the 300 m\({}^{3}\) reactor was initiated, the 6 m\({}^{3}\) reactor thus functioned as inocula. From mid  
Figure 2: The main components of the microalgae cultivation system integrated in the production line at the ferrosilicon producer Finnfjord AS. 2020, addition of factory fume to the 300 m\({}^{3}\) was regulated with a solenoid valve that was controlled by the logged pH so that pH was kept between 7.9 and 7.5. The spherical sensor pointed downwards (with bulb mount up) while the cosine sensor pointed upwards. In an ideal illumination situation with diffuse light from all directions, the cosine sensor should always show lower readings than the spherical one. However, in a reactor the illumination units can shadow and variable ratios between direct and diffuse radiation can occur. Therefore, in some few instances where the cosine sensor showed higher values, this was taken as mean irradiance at 0.7 m.  
The diffuse light attenuation coefficient (\(k\)) of a suspension is a measure of the energy removed from a fixed-length light beam by both scattering and absorption.