The incorporation of variability and uncertainty evaluations in WWTP design by means of stochastic dynamic modeling: the case of the Eindhoven WWTP upgrade.

This paper illustrates how a dynamic model can be used to evaluate a plant upgrade on the basis of post-upgrade performance data. The case study is that of the Eindhoven wastewater treatment plant upgrade completed in 2006. As a first step, the design process based on a static model was thoroughly analyzed and the choices regarding variability and uncertainty (i.e. safety factors) were made explicit. This involved the interpretation of the design guidelines and other assumptions made by the engineers. As a second step, a (calibrated) dynamic model of the plant was set up, able to reproduce the anticipated variability (duration and frequency). The third step was to define probability density functions for the parameters assumed to be uncertain, and propagate that uncertainty with the dynamic model by means of Monte Carlo simulations. The last step was the statistical evaluation and interpretation of the simulation results. This work should be regarded as a 'learning exercise' increasing the understanding of how and to what extent variability and uncertainty are currently incorporated in design guidelines used in practice and how model-based post-project appraisals could be performed.

A GLUE uncertainty analysis of a drying model of pharmaceutical granules.

A shift from batch processing towards continuous processing is of interest in the pharmaceutical industry. However, this transition requires detailed knowledge and process understanding of all consecutive unit operations in a continuous manufacturing line to design adequate control strategies. This can be facilitated by developing mechanistic models of the multi-phase systems in the process. Since modelling efforts only started recently in this field, uncertainties about the model predictions are generally neglected. However, model predictions have an inherent uncertainty (i.e. prediction uncertainty) originating from uncertainty in input data, model parameters, model structure, boundary conditions and software. In this paper, the model prediction uncertainty is evaluated for a model describing the continuous drying of single pharmaceutical wet granules in a six-segmented fluidized bed drying unit, which is part of the full continuous from-powder-to-tablet manufacturing line (Consigma™, GEA Pharma Systems). A validated model describing the drying behaviour of a single pharmaceutical granule in two consecutive phases is used. First of all, the effect of the assumptions at the particle level on the prediction uncertainty is assessed. Secondly, the paper focuses on the influence of the most sensitive parameters in the model. Finally, a combined analysis (particle level plus most sensitive parameters) is performed and discussed. To propagate the uncertainty originating from the parameter uncertainty to the model output, the Generalized Likelihood Uncertainty Estimation (GLUE) method is used. This method enables a modeller to incorporate the information obtained from the experimental data in the assessment of the uncertain model predictions and to find a balance between model performance and data precision. A detailed evaluation of the obtained uncertainty analysis results is made with respect to the model structure, interactions between parameters and uncertainty boundaries.

Impact of influent data frequency and model structure on the quality of WWTP model calibration and uncertainty.

Application of activated sludge models (ASMs) to full-scale wastewater treatment plants (WWTPs) is still hampered by the problem of model calibration of these over-parameterised models. This either requires expert knowledge or global methods that explore a large parameter space. However, a better balance in structure between the submodels (ASM, hydraulic, aeration, etc.) and improved quality of influent data result in much smaller calibration efforts. In this contribution, a methodology is proposed that links data frequency and model structure to calibration quality and output uncertainty. It is composed of defining the model structure, the input data, an automated calibration, confidence interval computation and uncertainty propagation to the model output. Apart from the last step, the methodology is applied to an existing WWTP using three models differing only in the aeration submodel. A sensitivity analysis was performed on all models, allowing the ranking of the most important parameters to select in the subsequent calibration step. The aeration submodel proved very important to get good NH(4) predictions. Finally, the impact of data frequency was explored. Lowering the frequency resulted in larger deviations of parameter estimates from their default values and larger confidence intervals. Autocorrelation due to high frequency calibration data has an opposite effect on the confidence intervals. The proposed methodology opens doors to facilitate and improve calibration efforts and to design measurement campaigns.