## 1 Introduction  
Anaerobic digestion (AD) is one of the oldest biological process for the valorization of organic wastes into biogas [1,2]. AD consists of a sequence of processes that involve microorganisms that in the absence of oxygen break organic matter down producing biogas. Over the last decades, digestion capacity in Europe has been increasing rapidly [2]. Many industrial digesters have been built in European countries such as Italy, France, being Germany the largest producer. Anaerobic digestion plants have increased up to 18,202 in 2018, achieving a production of 63,511 GWh ofbiogas. The main product obtained from AD is biogas that consists mainly of 50-75% CH\({}_{4}\) and 25-50% CO\({}_{2}\) that can be converted into electricity and heat (Combined Heat and Power plants; CHP), injected in the Natural Gas Grid, or used as transportation fuel, whereas the digestate (residues after digestion) typically are used as crop fertilizer and/or soil amendment [3,4]. For a better management of digestates they are often separated into solid and liquid fractions. Solid-liquid separation of digestate presents many advantages, allowing a better management. The solid fraction, which is rich in dry matter, N and P; is often used as soil amendment to return nutrients back to the fields [4,5]. The liquid fraction has been reported to have high contents in K and N, mainly in its form of ammonia, and it is characterized for a higher N/P ratio than in the solid fraction and generally used as liquid crop fertilizer [5,6]. Nonetheless, large amounts of digestate are currently produced due to the increased number of biogas plants operated, especially in some intensive livestock's area. Digestate engenders some environmental problems related to the greenhouse-gas emissions during storage, its intensive transportation needs [4,7], and due to the leaching or evaporation of nutrients during land application [8,9]. Moreover, the use of digestate on agricultural land is regulated by European EU Directive 91/676/EC, that stablish Nitrate Vulnerable Zones (NVZ) where the annual amount of nitrogen that is applied to the land by spreading does not exceed 170 kg per hectare. For all these reasons, digestate management has become a major bottleneck of the biogas industry and several alternative digestate valorization routes are under investigation [4,10,11]. One promising solution for the recovery of nutrients in the liquid digestate is microalgae cultivation [8,12,13]. Indeed, microalgae can efficiently remove the nutrients from digestate while producing high-value biomass that can be used for the production of biochemical, biomaterials, fertilizers and/or biofuels [12,14,15]. Since digestates are rich in macronutrients (N, P, K, S, Ca and Mg) [16,17,18] and thanks to its ability to uptake nutrients from media, microalgae seem a potential solution to remediate nutrients present in liquid digestate from agricultural biogas plants. For instance, [PERSON] et al. (2016) have investigated the cultivation of _Chlorella vulgaris_ on different anaerobic digestates deriving from municipal wastewater, sewage sludge or agro-waste treatment plants in closed photobioreactor [13]. Nonetheless, considering microalgae cultivation on liquid digestate, two major issues should be addressed as the high turbidity of liquid digestate caused by suspended materials and its high ammonia content that can significantly affect the microalgae growth efficiency [8,11,19]. [PERSON] and [PERSON] (2016) reported that concentration of total ammonia nitrogen (TAN) varying from 50 to 260 mg/L of TAN can inhibit the microalgae growth [11]. For these purposes, two mains strategies that have been investigated in literature data are dilution of the digestate with water [12,13] or liquid digestate treatments to alleviate its toxicity [8,15,19].Until now, diverse technologies of reactors have been used in microalgae cultivation by means of open systems raceway, tubular, column and flat photobioreactors [20], with _Chlorella_ sp.