A consistent modelling methodology for secondary settling tanks: a reliable numerical method.

The consistent modelling methodology for secondary settling tanks (SSTs) leads to a partial differential equation (PDE) of nonlinear convection-diffusion type as a one-dimensional model for the solids concentration as a function of depth and time. This PDE includes a flux that depends discontinuously on spatial position modelling hindered settling and bulk flows, a singular source term describing the feed mechanism, a degenerating term accounting for sediment compressibility, and a dispersion term for turbulence. In addition, the solution itself is discontinuous. A consistent, reliable and robust numerical method that properly handles these difficulties is presented. Many constitutive relations for hindered settling, compression and dispersion can be used within the model, allowing the user to switch on and off effects of interest depending on the modelling goal as well as investigate the suitability of certain constitutive expressions. Simulations show the effect of the dispersion term on effluent suspended solids and total sludge mass in the SST. The focus is on correct implementation whereas calibration and validation are not pursued.

Fundamental nonlinearities of the reactor-settler interaction in the activated sludge process.

The activated sludge process can be modelled by ordinary and partial differential equations for the biological reactors and secondary settlers, respectively. Because of the complexity of such a system, simulation models are most often used to investigate them. However, simulation models cannot give general rules on how to control a complex nonlinear process. For a reduced-order model with only two components, soluble substrate and particulate biomass, general results on steady-state solutions have recently been obtained, such as existence, uniqueness and stability of solutions. The aim of the present paper is to utilize those results to formulate some implications of practical importance. In particular, strategies are described for the manual control of the effluent substrate concentration subject to the constraint that the settler is maintained in normal operation (with a sludge blanket in the thickening zone) in steady state. Such strategies contain how the two control parameters, the recycle and waste volumetric flow ratios, should be chosen for any (steady-state) values of the input variables.