Impact on sludge inventory and control strategies using the benchmark simulation model no. 1 with the Bürger-Diehl settler model

Fractional order-based hierarchical controller design and evaluation with Bürger-Diehl settler model in a total nitrogen removal wastewater treatment process

The primary objective of this study was to establish two-level structured control techniques based on the globally known benchmark simulation model no. 1 (BSM1) and the Bürger-Diehl settler model in order to improve effluent quality. The latter was based on the activated sludge model no. 1 (ASM1), while the classic Takacs model was superseded by the more recent Bürger-Diehl settler model with enhanced predictive potential. A two-level hierarchical control structure was considered to maintain the dissolved oxygen concentration basing on the ammonia levels and also a nitrate controller was considered to improve nitrogen removal efficiency. Fractional order PI controllers were considered at the secondary level and advanced control techniques, namely, MPC and fuzzy, were implemented at the primary level. Two advance control schemes, being, FPI-MPC and FPI-fuzzy were designed in the present work. The controllers were designed based on the plant model which was identified using prediction-error minimization method. It was observed that the implemented control strategies in consideration with the plant modifications showed a profound impact in improving the plant performance in terms of the effluent quality. FPI-fuzzy resulted in noticeable 60% and 53% reduction in total nitrogen violations for dry and storm climatic conditions, respectively.

An improved 1D reactive Bürger-Diehl settler model for secondary settling tank denitrification

An improved 1D reactive settler model is pursued in order to increase the understanding of reactive settling processes and obtain a better prediction of the nitrogen mass balance in wastewater treatment systems. The developed model is based on the 1D Bürger-Diehl settler model with compression function and the Activated Sludge Model No. 1 biological reactions. Specific attention was paid in the model development phase to optimal selection of settling velocity functions and integration of the correct clarifier geometry. A unique measurement campaign was carried out with different operational scenarios to quantify the denitrification in a secondary settling tank. A detailed step-wise calibration effort demonstrated that by choosing an appropriate settling velocity function (power-law structure) and considering the true clarifier geometry allows to accurately capture the biomass concentration profile, total sludge mass, sludge blanket height, and the reaction rates. The resulting model is able to accurately describe total suspended solids (TSS) and nitrate concentration profiles throughout a settling tank under different operational conditions. As such the model can be applied in further scenario analysis and system optimization. PRACTITIONER POINTS: A unique measurement campaign was carried out to obtain detailed data for a reactive settler model development. A 1-D reactive settler model is developed based on the Bürger-Diehl framework including ASM1 biokinetics and the clarifier geometry. An extensive calibration and model selection effort was performed. The model accurately predicts measured concentration profiles in the settling tank. The developed model can be integrated in a plant-wide model to properly calculate the nitrogen mass balance of a WRRF.

Densification of activated sludge for better settling performances: experimental characterization in batch column and model parameters calibration

Conventional activated sludge (CAS) and densified sludge obtained using hydro-cyclone selective wasting were compared at a full-scale water resources recovery facility. The densified tested sludge, containing around 30-50% of aerobic granules, showed enhanced settleability with low and stable sludge volume index (SVI) compared to CAS, which suffered recurrent filamentous bulking. Further in-depth batch settling tests were carried out using a 40 cm diameter column fitted with ultrasonic transducers to monitor both sludge blanket height and vertical velocity profiles. Hindered settling and compression parameters were calibrated from the experiment for latter modelling use. Test sludge displayed more than doubled settling velocities compared to CAS, with hindered settling velocities remaining >3 m·h^-1 even at high solids concentrations of 6.85 g·L^-1. The compression regime was attained at much higher critical concentration for the test sludge. It also displayed enhanced thickening properties, with concentrations obtained after 30 min of settling being 20.9 and 8.5 g·L^-1 respectively for test and control sludge. This allows for a substantial reduction of recirculation rates in practice. These results open perspectives in optimizing existing plant operation as well as clarifier design and modelling using densified sludge.

Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense

To lower the concentration of organic pollutants in the effluent stream, wastewater must be treated before being discharged into the environment. The question of whether wastewater treatment facilities can successfully reduce the concentration of micropollutants found in their influent streams is becoming increasingly pressing. The removal of micropollutants in treatment plants is investigated using a model that incorporates biodegradation and sorption as the key processes of micropollutant removal. This article provides the mathematical analysis of the wastewater model that describes the removal of micropollutant in treatment plants under a non-local operator in Caputo sense. The positivity of the solution is presented for the Caputo fractional model. The steady state’s solution of model and their stability is presented. The fixed point theorems of Leray–Schauder and Banach are used to deduce results regarding the existence of the solution of the model. Ulam–Hyers (UH) types of stabilities are presented via functional analysis. The fractional Euler method is used to find the numerical results of the proposed model. The numerical results are illustrated via graphs to show the effects of recycle ratio and the impact of fractional order on the evolution of the model.

A review of flux identification methods for models of sedimentation

Most models of sedimentation contain the nonlinear hindered-settling flux function. If one assumes ideal conditions and no compression, then there exist several theoretically possible ways of identifying a large portion of the flux function from only one experiment by means of formulas derived from the theory of solutions of partial differential equations. Previously used identification methods and recently published such, which are based on utilizing conical vessels or centrifuges, are reviewed and compared with synthetic data (simulated experiments). This means that the identification methods are evaluated from a theoretical viewpoint without experimental errors or difficulties. The main contribution of the recent methods reviewed is that they, in theory, can identify a large portion of the flux function from a single experiment, in contrast to the traditional method that provides one point on the flux curve from each test. The new methods lay the foundation of rapid flux identification; however, experimental procedures need to be elaborated.

Quantifying the sources of uncertainty when calculating the limiting flux in secondary settling tanks using iCFD

Solids-flux theory (SFT) and state-point analysis (SPA) are used for the design, operation and control of secondary settling tanks (SSTs). The objectives of this study were to assess uncertainties, propagating from flow and solids loading boundary conditions as well as compression settling behaviour to the calculation of the limiting flux (J_L) and the limiting solids concentration (X_L). The interpreted computational fluid dynamics (iCFD) simulation model was used to predict one-dimensional local concentrations and limiting solids fluxes as a function of loading and design boundary conditions. A two-level fractional factorial design of experiments was used to infer the relative significance of factors unaccounted for in conventional SPA. To move away from using semi-arbitrary safety factors, a systematic approach was proposed to calculate the maximum SST capacity by employing a factor of 23% and a regression meta-model to correct values of J_L and X_L, respectively - critical for abating hydraulic effects under wet-weather flow conditions.

On constitutive functions for hindered settling velocity in 1-D settler models: Selection of appropriate model structure

Advanced 1-D models for Secondary Settling Tanks (SSTs) explicitly account for several phenomena that influence the settling process (such as hindered settling and compression settling). For each of these phenomena a valid mathematical expression needs to be selected and its parameters calibrated to obtain a model that can be used for operation and control. This is, however, a challenging task as these phenomena may occur simultaneously. Therefore, the presented work evaluates several available expressions for hindered settling based on long-term batch settling data. Specific attention is paid to the behaviour of these hindered settling functions in the compression region in order to evaluate how the modelling of sludge compression is influenced by the choice of a certain hindered settling function. The analysis shows that the exponential hindered settling forms, which are most commonly used in traditional SST models, not only account for hindered settling but partly lump other phenomena (compression) as well. This makes them unsuitable for advanced 1-D models that explicitly include each phenomenon in a modular way. A power-law function is shown to be more appropriate to describe the hindered settling velocity in advanced 1-D SST models.

Concentration-driven models revisited: towards a unified framework to model settling tanks in water resource recovery facilities

A new perspective on the modelling of settling behaviour in water resource recovery facilities is introduced. The ultimate goal is to describe in a unified way the processes taking place both in primary settling tanks (PSTs) and secondary settling tanks (SSTs) for a more detailed operation and control. First, experimental evidence is provided, pointing out distributed particle properties (such as size, shape, density, porosity, and flocculation state) as an important common source of distributed settling behaviour in different settling unit processes and throughout different settling regimes (discrete, hindered and compression settling). Subsequently, a unified model framework that considers several particle classes is proposed in order to describe distributions in settling behaviour as well as the effect of variations in particle properties on the settling process. The result is a set of partial differential equations (PDEs) that are valid from dilute concentrations, where they correspond to discrete settling, to concentrated suspensions, where they correspond to compression settling. Consequently, these PDEs model both PSTs and SSTs.

Practical identifiability and uncertainty analysis of the one-dimensional hindered-compression continuous settling model

The practical application of the one-dimension hindered-compression settling models remains a challenge, since the model calibration strongly depends on experimental observations with limited information. In this study, the identifiability of parameter subsets of the hindered-compression models is evaluated for various experimental layouts. Global sensitivity analysis is used to preliminarily select the influential parameters which can be reasonably estimated, while the identifiability analysis of parameter subsets is conducted based on the local sensitivity functions and collinearity measures. The batch settling curve observations are informative for calibrating hindered parameters, and to determine the compression parameters, the concentration profile observations may need to be collected. For different experimental layouts, at least three parameters are identifiable, and the number of identifiable parameters can potentially increase to five, if both batch settling curve and concentration observations are available. The parameter subset identifiability is sensitive to the choice of initial parameter values, and determining the initial values of hindered parameters and gel concentration by measuring the hindered settling velocities and the top concentration of the static sediment respectively allows efficient reduction of the sensitivity. Parameter subset estimates are sensitive to the values of fixed parameters, and reliable estimation of identifiable parameter subsets is possible to significantly decrease model prediction uncertainties.

On time discretizations for the simulation of the batch settling-compression process in one dimension

The main purpose of the recently introduced Bürger-Diehl simulation model for secondary settling tanks was to resolve spatial discretization problems when both hindered settling and the phenomena of compression and dispersion are included. Straightforward time integration unfortunately means long computational times. The next step in the development is to introduce and investigate time-integration methods for more efficient simulations, but where other aspects such as implementation complexity and robustness are equally considered. This is done for batch settling simulations. The key findings are partly a new time-discretization method and partly its comparison with other specially tailored and standard methods. Several advantages and disadvantages for each method are given. One conclusion is that the new linearly implicit method is easier to implement than another one (semi-implicit method), but less efficient based on two types of batch sedimentation tests.

Characterizing shallow secondary clarifier performance where conventional flux theory over-estimates allowable solids loading rate

The performance characteristics of relatively shallow (3.3 and 3.7 m sidewater depth in 30.5 m diameter) activated sludge secondary clarifiers were extensively evaluated during a 2-year testing program at the City of Akron Water Reclamation Facility (WRF), Ohio, USA. Testing included hydraulic and solids loading stress tests, and measurement of sludge characteristics (zone settling velocity (ZSV), dispersed and flocculated total suspended solids), and the results were used to calibrate computational fluid dynamic (CFD) models of the various clarifiers tested. The results demonstrated that good performance could be sustained at surface overflow rates in excess of 3 m/h, as long as the clarifier influent mixed liquor suspended solids (MLSS) concentration was controlled to below critical values. The limiting solids loading rate (SLR) was significantly lower than the value predicted by conventional solids flux analysis based on the measured ZSV/MLSS relationship. CFD analysis suggested that this resulted because mixed liquor entering the clarifier was being directed into the settled sludge blanket, diluting it and also creating a 'thin' concentration sludge blanket that overlays the thicker concentration sludge blanket typically expected. These results indicate the need to determine the allowable SLR for shallow clarifiers using approaches other than traditional solids flux analysis. A combination of actual testing and CFD analyses are demonstrated here to be effective in doing so.

Steady-state analysis of activated sludge processes with a settler model including sludge compression

A reduced model of a completely stirred-tank bioreactor coupled to a settling tank with recycle is analyzed in its steady states. In the reactor, the concentrations of one dominant particulate biomass and one soluble substrate component are modelled. While the biomass decay rate is assumed to be constant, growth kinetics can depend on both substrate and biomass concentrations, and optionally model substrate inhibition. Compressive and hindered settling phenomena are included using the Bürger-Diehl settler model, which consists of a partial differential equation. Steady-state solutions of this partial differential equation are obtained from an ordinary differential equation, making steady-state analysis of the entire plant difficult. A key result showing that the ordinary differential equation can be replaced with an approximate algebraic equation simplifies model analysis. This algebraic equation takes the location of the sludge-blanket during normal operation into account, allowing for the limiting flux capacity caused by compressive settling to easily be included in the steady-state mass balance equations for the entire plant system. This novel approach grants the possibility of more realistic solutions than other previously published reduced models, comprised of yet simpler settler assumptions. The steady-state concentrations, solids residence time, and the wastage flow ratio are functions of the recycle ratio. Solutions are shown for various growth kinetics; with different values of biomass decay rate, influent volumetric flow, and substrate concentration.