A method-of-lines formulation for a model of reactive settling in tanks with varying cross-sectional area

Reactive settling denotes the process of sedimentation small solid particles dispersed in a viscous fluid with simultaneous reactions between components that constitute and liquid phases. This is particular importance for simulation control secondary tanks (SSTs) water resource recovery facilities (WRRFs), formerly known as wastewater treatment plants. A spatially one-dimensional model reactive an SST formulated by combining mechanistic compression biokinetic reactions. In addition, cross-sectional area tank allowed to vary function height. The final system strongly degenerate parabolic, nonlinear partial differential equations (PDEs)that include discontinuous coefficients describe feed, underflow overflow mechanisms, well singular source terms feed mechanism. finite difference scheme derived first deriving method-of-lines formulation (discrete space, continuous time), then passing fully discrete time discretization. advantage this its compatibility common practice development software WRRFs. main mathematical result invariant-region property, which implies physically relevant numerical solutions are produced. Simulations denitrification SSTs illustrate