Mathematical Modeling of Microalgae–mineralization–human Structure within the Environment Regeneration System for the Biosphere Compatible City

Modern fast growing megacities and urban agglomerations exert extremely high environmental load. One of the biggest problems of megalopolises is the human organic waste disposal. Under current technology, waste utilization requires enormous extent of sewer networks and large areas of treatment plants, which deform the natural landscapes and is expensive to operate. Organization of local recycling of organic waste is crucially important at creation of new urban objects satisfying the principle of biosphere compatibility. In addition, it should be noted, that with the rising of building tallness in modern cities the use of centralized water systems leads to excessive overruns of electricity by pumping equipment, therefore the local effluent regeneration systems is the optimal solution for skyscrapers. Making a start from successful design experience of closed ecological life support systems, which were initially created for long-duration space flights, our research implements the idea to realize closed circle for flows of substances and energy for utilization of human waste and improving air quality within residential building. We focus on small volume treatment facilities designed for 20-30 people. The main difference of our system is the high degree of closure of flows. Thus, the hardest part is to balance all technological processes. To solve this problem we suggest using rather complicated and accurate modelling founded on non-stationary partial differential equations describing the laws of matter conservation as a basis of an automatic control system. In this article, we present a mathematical model to simulate and control processes of transport phenomena in the system microalgae-mineralization-human. The model includes flow equations, the equations of reaction-advection-diffusion on a stratified set (linked 1D and 2D domains)