A sensitivity and model reduction analysis of one-dimensional secondary settling tank models under wet-weather flow and sludge bulking conditions
Introduction
The activated sludge process is the most widely used technique to remove organic matter and reduce nutrients such as nitrogen and phosphorus in wastewater treatment plants (WWTPs). Generally, efficient solids–liquid separation techniques are needed to provide low turbidity effluent by removing the biomass from the liquid, and the secondary settling tanks (SSTs), where biomass is settled by gravity, are the most commonly used [1]. Mathematical modeling approaches, where the activated sludge models, comprised of a set of ordinary differential equations (ODEs), are coupled with the SST models, comprised of a set of partial differential equations (PDEs), are being increasingly used in wastewater treatment process studies for three purposes (1) learning, which means the model simulation results are able to improve the understanding of wastewater treatment process; (2) design, the model can be used to evaluate various design alternatives via simulation, and (3) process optimization and control, simulating different sceneries to optimize the process efficiency and avoid possible failure problems [2], [3], [4].
The family of activated sludge models [5], [6], [7] provide a comprehensive description of the significant biological processes of the activated sludge system, and are widely accepted in the research and industrial communities as a useful tool for scientific study and practical applications. However, compared with the well-developed scientific knowledge on characterizing the metabolic processes and contaminant removal in the bioreactor, various settling behavior occurring in the SST still remain poorly understood, thus making the SST model a potential error source in process simulation [8]. The one-dimensional (1-D) 10-layer model, also known as the Takács model [9], is the most commonly used SST model and has been implemented in most commercial simulators as a reference model. Although the Takács model has achieved a degree of success in predicting the SST performance, its shortcomings are not negligible, such as the insufficient description of various settling behaviors and inaccuracy of numerical solutions, which have been demonstrated in previous studies [8], [10], [11], [12], [13].
In last two decades, to compensate for the limitations of the Takács model, several advanced SST models have been developed as alternatives, which can be classified into three groups based on their advantages:
- 1.
First-order hindered-only models with reliable numerical techniques: for these models, the model formula remains the same as the Takács model, considering only the hindered settling behavior, but using more reliable numerical techniques. Reliable techniques such as the Godunov numerical flux, the Yee–Roe–Davis (YRD) numerical flux, and finer discretization levels (more than 30-layers), are used to construct both numerically and physically acceptable solutions [10], [13], [14].
- 2.
Second-order hindered–compression models additionally accounting for compression settling: the improved understanding of activated sludge rheology has facilitated the development of phenomenological theory of sedimentation-consolidation. The phenomenological theory is then expressed in the compression model, which allows a more rigorous description of the compression settling behavior [15], [16]. Compared with the hindered-only model, the hindered–compression model is expected to provide more realistic predictions of the sludge blanket level and the underflow concentration.
- 3.
Second-order hindered–dispersion models additionally accounting for hydraulic dispersion: for these models, an explicit hydraulic dispersion term is added to the model formula to account for the potential impact of hydraulics on the biomass settling behavior [17], [18]. The hydraulic dispersion model possesses the advantage of simulating the hydraulics of SSTs over a wider range of dynamic flow conditions [17], [19]. From the numerical point of view, adding the explicit flow-dependent dispersion term also decreases the difficulty in solving the hindered–dispersion model.
Despite the advantages of the Bürger–Diehl model, its practical application is limited, which can be attributed to two main reasons:
- (1)
The difficulty of calibration: great efforts have been made to facilitate model calibration, for example by evaluating the hindered-only and hindered–dispersion models, Ramin et al. [18], [22] identified the potential parameter subsets suitable for the calibration of WWTP models under various simulation conditions. However, calibrating the 1-D SST models accounting for the compression settling still remains a challenge due to the insufficient understanding of the influence of compression settling on the SST performance.
- (2)
The increased implementation complexity and computation burden: technically, the currently used hindered-only, hindered–compression and hindered–dispersion models can be considered as the sub-models of the Bürger–Diehl model, and their successful applications in SST simulation implies that the Bürger–Diehl model in some cases can be reduced to these sub-models without sacrificing the quality of prediction. However, how to reliably reduce the Bürger–Diehl model, particularly under non-ideal flow and settling conditions, still remains unclear.
In this study, we provided a comprehensive sensitivity and model reduction analysis of the Bürger–Diehl model under non-ideal flow and settling conditions. The Benchmark Simulation Model No. 1 (BSM1) [23] is used as the simulation platform, because of its well documented model inputs. The influence of the uncertainty of model parameters to the variance of model outputs, such as the sludge blanket level, is quantified by using global sensitivity analysis (GSA), and the reliability of the Bürger–Diehl model reduction is evaluated based on uncertainty analysis.
The main objectives of this paper are (i) identify the suitable parameter subsets for the Bürger–Diehl model calibration under non-ideal flow and settling conditions; (ii) evaluate the influence of imposed flow and settling conditions on the sensitivity of the Bürger–Diehl model outputs to the parameters; (iii) demonstrate how reliable reduction of the Bürger–Diehl model can be achieved based on GSA results; (iv) assess the reliability of the Bürger–Diehl model reduction for different modeling purposes based on uncertainty analysis results.
Section snippets
Model structure and simulation condition description
As shown by Fig. 1, BSM1 is used as the simulation platform, where ASM1 is combined with the SST model to describe the biological and settling processes of the activated sludge system. For further details about ASM1, the reader is referred to literature [5]. With regards to the SST model, the Bürger–Diehl model is used to replace the Takács model.
The formula of the Bürger–Diehl model can be expressed as Eq. (1) on the basis of the mass and momentum conservation:
Global sensitivity analysis of the Bürger–Diehl model under non-ideal flow and settling conditions
In this section, the GSA results of Bürger–Diehl model are provided in order to identify the potential parameter subsets suitable for model calibration. Table 2 shows the sensitivity measures (Si and STi) of the Bürger–Diehl model under the wet-weather condition (scenario 1). The high sensitivity indices (Si > 0.01) of v0 and rh indicate their strong influence on the model outputs as well as implying the important role hindered settling plays in determining the SST performance. In contrast, the
Conclusions
In the last decade, great efforts have been made to improve the SST simulation. In this study, by using the Benchmark Simulation Model No. 1 as the simulation platform, we provide the sensitivity and reduction analysis of the Bürger–Diehl model under non-ideal flow and settling conditions. The following specific conclusions can be made:
- 1.
Based on the GSA results, the important parameters are identified for the Bürger–Diehl model calibration under non-ideal flow and settling conditions. All model
Acknowledgments
The present study was supported in part by the National Science Foundation (NSF), Award 1134355. Ben Li. received a fellowship from the University of California, Los Angeles (UCLA).
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