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

Abstract

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.

Fast reliable simulations of secondary settling tanks in wastewater treatment with semi-implicit time discretization

“…Such a discretization of PDE (17) has been made in detail by Bürger et al [20] and we refer to that publication for all implementation details. Here, we only review the concepts necessary for describing the semi-implicit time-discretization method in Section 4.…”

“…While algorithms for efficient computation of (26) for general constitutive functions are provided by Bürger et al [20], it is an advantage when the primitive of d comp can be obtained as a closed-form expression. This is the case with the particular choice of f bk in (4) and σ e in (7).…”

“…1 (ASM1) by Henze et al [14,15] and most of the setup in the Benchmark Simulation Model no. 1 (BSM1) by Alex et al [16], Copp [17], Gernaey et al [18], but substituted the SST simulation model by Takács et al [19], for the one by Bürger et al [20,13], which we call the BD simulation model. This is based on PDE theory, in contrast to most of the traditional simulation models (e.g.…”

“…These phenomena are related to the spatial discretization. All implementation details of the BD model were provided by Bürger et al [20] and the evaluations made by Bürger et al [21] were related to differences between two alternative spatial discretizations. After the spatial discretization, the BD model is on a method-of-lines (MOL) form as a system of ODEs.…”

“…The subprocess of continuous sedimentation, which contains concentration discontinuities, is modelled by a degenerate parabolic conservation PDE with spatially discontinuous coefficients. A spatial discretization of this PDE described in Bürger et al (2013) results in a large system of method-of-lines ODEs for the entire plant and simulation can be performed by integration in time. In practice, standard time integration methods available in commercial simulators are often used.…”