We consider the problem of regulating the air quality in underground extraction rooms for mining industry. This is a challenging control problem where the flow dynamics, the interconnections between subsystems and the time-varying topology have to be taken into account along with real-time computation constraints. Our work is focused on the deep pit part of the ventilation system, which brings fresh air at a specified pressure to the extraction levels. The flow interactions and main automation elements are first presented, with a real-time engineering model of the complete mine ventilation system. A novel control-oriented model focused on the pressure dynamics is then introduced, as a convective-resistive partial differential equation (PDE) with multiple inputs where the time-varying transport coefficients are estimated based on the distributed measurements. A fast predictive controller (FPC) is finally proposed to compensate the pressure losses due to friction and multiple flow exhausts thanks to the ventilation pit input pressure regulation. Simulation results illustrate the efficiency of the modeling and control algorithms.