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- Bürger, Raimund, et al.
(författare)
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A consistent modelling methodology for secondary settling tanks: A reliable numerical method.
- 2013
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Ingår i: Water Science and Technology. - : IWA Publishing. - 0273-1223 .- 1996-9732. ; 68:1, s. 192-208
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Tidskriftsartikel (refereegranskat)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.
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| 2. |
- Bürger, Raimund, et al.
(författare)
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A consistent modelling methodology for secondary settling tanks in wastewater treatment
- 2011
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Ingår i: Water Research. - : Elsevier BV. - 1879-2448 .- 0043-1354. ; 45:6, s. 2247-2260
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solideliquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models.
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| 3. |
- Bürger, Raimund, et al.
(författare)
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On reliable and unreliable numerical methods for the simulation of secondary settling tanks in wastewater treatment
- 2012
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Ingår i: Computers & Chemical Engineering. - : Elsevier BV. - 1873-4375 .- 0098-1354. ; 41, s. 93-105
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Tidskriftsartikel (refereegranskat)abstract
- Abstract in UndeterminedA 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.
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| 4. |
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| 5. |
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| 6. |
- Torfs, Elena, et al.
(författare)
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Impact on sludge inventory and control strategies using the Benchmark Simulation Model No. 1 with the Bürger-Diehl settler model
- 2015
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Ingår i: Water Science and Technology. - : IWA Publishing. - 0273-1223 .- 1996-9732. ; 71:10, s. 1524-1535
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Tidskriftsartikel (refereegranskat)abstract
- An improved one-dimensional (1-D) model for the secondary clarifier, i.e. the Bürger-Diehl model, was recently presented. The decisive difference to traditional layer models is that every detail of the implementation is in accordance with the theory of partial differential equations. The Bürger-Diehl model allows accounting for hindered and compressive settling as well as inlet dispersion. In this contribution, the impact of specific features of the Bürger-Diehl model on settler underflow concentration predictions, plant sludge inventory and mixed liquor suspended solids based control actions are investigated by using the benchmark simulation model no. 1. The numerical results show that the Bürger-Diehl model allows for more realistic predictions of the underflow sludge concentration, which is essential for more accurate wet weather modelling and sludge waste predictions. The choice of secondary settler model clearly has a profound impact on the operation and control of the entire treatment plant and it is recommended to use the Bürger-Diehl model as of now in any wastewater treatment plant modelling effort.
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| 7. |
- Torfs, Elena, et al.
(författare)
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Towards improved 1-D settler modelling: calibration of the Bürger model and case study
- 2013
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Ingår i: Proceedings of 86th Annual Water Environment Federation Technical Exhibition and Conference (WEFTEC 2013).
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Konferensbidrag (refereegranskat)abstract
- 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.
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