## 1 Introduction  
Over the past century, mankind's activities have continuously induced carbon release into the atmosphere. This massive carbon discharge has induced global warming and climate change. Having not taken early measures to reduce carbon dioxide emissions, humanity has now turned to negative emission technologies to try to attenuate the most dire consequences of climate change. With this goal in mind, two actions have to be led simultaneously: carbon capture and carbon emission reduction. In this view, biotechnological approaches seem relevant. First, they contribute to shifting oil-based productions toward bio-based productions. Second, they can contribute to carbon capture through photosynthesis. In this domain, the most evident approach is afforestation, which may be the easiest solution to deploy from a technical point of view. Yet, several drawbacks hinder its practical applicability: large area requirement, slow capture mechanism, likely reduction in local biodiversity, and possible competition with food crops. Consequently, microalgae may appear as an alternative, as they grow faster than higher plants (generation time spanning from several hours to days), show a higher photosynthetic efficiency (4.6% for C3 plants, 6% for C4 plants [1], and up to an optimistic 15% for microalgae [2]), and can be grown on non-arable lands, or even oceans. The two main ways of leading microalgal carbon capture are biotechnological cultivation of microalgae and ocean fertilization. This work applies to the first category, as the second may appear as a last-resort measure belonging to the geoengineering approaches. Indeed, ocean fertilization raises concern from an ecological standpoint, while its carbon sequestration potential is questionable. Among other issues, ocean fertilization could disturb local biodiversity by promoting algal bloom, which would hinder the oceanic carbon pump and foster ocean acidification [2]. Microalgal biotechnology has drawn considerable attention from scholars and engineers for decades thanks to its numerous qualities. Among them, one can cite high protein content for food and feed application [3]; lipids for biofuels [4]; and advanced molecules for cosmetic and pharmaceutical use [5]. In addition to producing natural molecules, microalgae also deliver ecosystem services, such as wastewater remediation [6] and, of course, carbon capture [7; 8]. Considering both these aspects, it seems that microalgal bioprocesses naturally have a low impact on the environment and could potentially reach carbon neutrality with proper optimization. Aiming toward the development of large-scale microalgal bioprocesses, the concept of biorefinery has been thought out to improve the valorization of microalgal biomass, which is otherwise far from economically viable [6; 9]. As a side benefit of these bioprocesses, many authors investigate the carbon capture potential of a culture through the lens of a green biofuel production process [10; 11; 12] or highly CO2-tolerant species growing on industrial fumes [13; 14]. However, if the potential of carbon capture in this context is rightfully emphasized, the question of the carbon footprint of such a process is rarely evaluated. While potentially relevant if led naturally [15; 16], the often-made claim on carbon capture associated with microalgal bioprocesses should be discussed [17]. Previous works have focused on maximizing the carbon sequestration capacity of industrial algal processes, such as the production of pigments [18], without calculating the carbon emission of the process. While it stands to reason that photosynthetic processes involving artificial light cannot lead to net negative emission, the actual extent of compensation attained by an industrial process has to be assessed with more care. Previous works have focused on supplying an adequate amount of carbon dioxide to foster cultures. In this work, we propose quantifying the net carbon balance of such a process by considering microalgae carbon capture and process carbon footprint.