Towards improved 1-D settler modelling : calibration of the Bürger model and case study

Recently, Burger et al. (2011) developed a new 1-D SST model which allows for more realistic predictions of the sludge settling behaviour than traditional 1-D models used to date. However, the addition of a compression function in this new 1-D model complicates the model calibration. This study aims to report advances in the calibration of this novel 1-D model. Data of the evolution of the sludge blanket height during batch settling experiments were collected at different initial solids concentrations. Based on the linear slopes of the batch settling curves the hindered settling velocity functions by Vesilind (1968) and Takacs et al. (1991) were calibrated. Although both settling velocity functions gave a good fit to the experimental data, very large confidence intervals were found for the parameters of the settling velocity by Takacs. Global sensitivity analysis showed that it is not possible to find a unique set of parameter values for the settling function by Takacs based on experimental data of the hindered settling velocity. Subsequently, the calibrated Vesilind settling velocity was implemented in the 1-D model by Burger et al. (2011) and the parameters of the additional compression function were calibrated by fitting the model by Burger et al. (2011) to the batch settling curves. Simulation results showed that while the 1-D model by Takacs et al. (1991) underpredicted the experimental data of sludge blanket heights, the model by Burger et al. (2011) was able to predict the experimental data far more accurately. However, a global sensitivity analysis showed that no unique optimum for the combined set of hindered and compression parameters could be found

Conservation Laws, Numerical Schemes and Control Strategies for Sedimentation and Wastewater Treatment

A consistent theme throughout this thesis is quasilinear partial differential equations (PDEs) appearing in one-dimensional models of sedimentation for solid-liquid separation of suspensions. We mainly focus on continuous sedimentation in so-called clarifier-thickeners (CTs), which are found in mineral processing and wastewater treatment. In addition to complications with shocks and non-unique solutions that are standard for quasilinear first-order PDEs, the considered CT models offer challenges such as spatially discontinuous fluxes and strongly-degenerate diffusion terms. We are primarily concerned with numerical methods for two CT models: one previously published scalar PDE model relying on the assumption that all suspended solids have the same settling properties, and one system of strongly coupled PDEs that accounts for solids with non-homogeneous settleability. A method of Godunov type is proposed for the scalar model. This method has been well received by the wastewater community and it is implemented both on benchmark simulation platforms and in commercial software. During the development of numerical schemes for the second model, we encounter a hyperbolic system with a delicate feature: a nonlinear contact field. Generalising the problem setting to a family of systems, also containing the celebrated Aw-Rascle-Zhang traffic flow model, we construct a novel random sampling scheme to capture discontinuities with jumps along curves in such fields. Convergence to weak solutions of the hyperbolic system is proved for that scheme. The research presented also covers steady-state analyses and design of control strategies for stand-alone CTs and for a wastewater treatment plant with a biological reactor preceding the sedimentation process. The plant-wide models of interest are given as systems of ordinary differential equations for the reactor coupled to some PDEs for the CT

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

A reduced-order ODE-PDE model for the activated sludge process in wastewater treatment: Classification and stability of steady states

Most wastewater treatment plants contain an activated sludge process, which consists of a biological reactor and a sedimentation tank. The purpose is to reduce the incoming organic material and dissolved nutrients (the substrate). This is done in the biological reactor where micro-organisms (the biomass) decompose the substrate. The biomass is then separated from the water in the sedimentation tank under continuous in- and outflows. One of the outflows is recirculated to the reactor. The governing mathematical model describes the concentration of substrate and biomass as functions of time for the biological reactor, and as functions of time and depth for the sedimentation tank. This gives rise to a system of two ODEs for the reactor coupled with two spatially one-dimensional PDEs for the sedimentation tank. The main mathematical difficulty lies in the nonlinear PDE modeling the continuous sedimentation of the biomass. Previous analyses of models of the activated sludge process have included excessively simplifying assumptions on the sedimentation process. In this paper, results for nonlinear hyperbolic conservation laws with spatially discontinuous flux function are used to obtain a classification of the steady states for the coupled system. Their stability to disturbances are investigated and some phenomena are demonstrated by a numerical simulation

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

The bio-kinetic and sedimentation processes of wastewater treatment plants can be modelled by a large system of coupled nonlinear ordinary and partial differential equations (ODEs and PDEs). 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. Shortages of such methods are here shown, such as the smearing of shock waves by Runge–Kutta methods and long execution times. A semi-implicit time discretization, which is described in detail, provides substantially shorter computational times and is more efficient than standard methods

On reliable and unreliable numerical methods for the simulation of secondary settling tanks in wastewater treatment

Abstract in Undetermined A one-dimensional model for the sedimentation-compression-dispersion process in the secondary settling tank can be expressed as a nonlinear strongly degenerate parabolic partial differential equation (PDE), which has coefficients with spatial discontinuities. Reliable numerical methods for simulation produce approximate solutions that converge to the physically relevant solution of the PDE as the discretization is refined. We focus on two such methods and assess their performance via simulations for two scenarios. One method is provably convergent and is used as a reference method. The other method is less efficient in reducing numerical errors, but faster and more easily implemented. Furthermore, we demonstrate some pitfalls when deriving numerical methods for this type of PDE and can thereby rule out certain methods as unsuitable; among others, the wide-spread Takacs method. (c) 2012 Elsevier Ltd. All rights reserved

Modeling and controlling clarifier–thickeners fed by suspensions with time-dependent properties

A one-dimensional model of the process of continuous sedimentation in a clarifier–thickener unit is presented. The governing model is expressed as a system of two nonlinear partial differential equations for the solids volume fraction and the varying settling velocity of the solids as functions of depth and time. This model extends the well-known model for the dynamics of a flocculated suspension in a clarifier–thickener advanced by Bürger et al. (2005). Operating charts are calculated to be used for the control of steady states, in particular, to keep the sediment level and the underflow volume fraction at desired values. A numerical scheme and a simple regulator are proposed and numerical simulations are performed

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