Mathematical Modelling of Phosphorus Accumulation in Photo-Biological Treatment Plants of a Biosphere-Compatible City

We develop the idea of creating wastewater treatment facilities for biosphere compatible buildings with maximum-closed cycles with respect to water and energy. The idea started from experiments with closed-loop ecological Life Support Systems for space flights carried out in the 60s-80s last century. Water recycling is accomplished by functioning the microalgae-bacteria human ecosystem. One of the problems for systems of this type is high energy-consumption. However, besides water purification from nutrients, that organization of the purification process has multiple advantages, such as carbon dioxide recycling, wastewater disinfection, etc. One of the major benefits is the opportunity to get third-generation biofuels from algae. The closure of the system with respect to energy is performed by biofuel combustion. Thus, there is an objective to cultivate such an amount of biomass, which allows producing enough volume of biofuel. In projects, which have been presented on the exhibitions recently, for that goal phosphorus-containing reagents are used. However, nowadays, depletion of phosphorus deposits is one of the most serious problems threatening food security, since its variously estimated deposits are enough only for a period of 30-80 years. One solution to this problem is to create a phosphorus closed-loop cycle system. We present the mathematical model describing the dynamics of phosphorus accumulation in the partially closed-loop biological system. The model can be used as a basis for the automatic control system of the photo-biological treatment plants to ensure energy independence of a residential building.