Alma Mašić

Persistence in a Single Species CSTR Model with Suspended Flocs and Wall Attached Biofilms

We consider a mathematical model for a bacterial population in a continuously stirred tank reactor (CSTR) with wall attachment. This is a modification of the Freter model, in which we model the sessile bacteria as a microbial biofilm. Our analysis indicates that the results of the algebraically simpler original Freter model largely carry over. In a computational simulation study, we find that the vast majority of bacteria in the reactor will eventually be sessile. However, we also find that suspended biomass is relatively more efficient in removing substrate from the reactor than biofilm bacteria.

Estimation of nitrite in source-separated nitrified urine with UV spectrophotometry

Monitoring of nitrite is essential for an immediate response and prevention of irreversible failure of decentralized biological urine nitrification reactors. Although a few sensors are available for nitrite measurement, none of them are suitable for applications in which both nitrite and nitrate are present in very high concentrations. Such is the case in collected source-separated urine, stabilized by nitrification for long-term storage. Ultraviolet (UV) spectrophotometry in combination with chemometrics is a promising option for monitoring of nitrite. In this study, an immersible in situ UV sensor is investigated for the first time so to establish a relationship between UV absorbance spectra and nitrite concentrations in nitrified urine. The study focuses on the effects of suspended particles and saturation on the absorbance spectra and the chemometric model performance. Detailed analysis indicates that suspended particles in nitrified urine have a negligible effect on nitrite estimation, concluding that sample filtration is not necessary as pretreatment. In contrast, saturation due to very high concentrations affects the model performance severely, suggesting dilution as an essential sample preparation step. However, this can also be mitigated by simple removal of the saturated, lower end of the UV absorbance spectra, and extraction of information from the secondary, weaker nitrite absorbance peak. This approach allows for estimation of nitrite with a simple chemometric model and without sample dilution. These results are promising for a practical application of the UV sensor as an in situ nitrite measurement in a urine nitrification reactor given the exceptional quality of the nitrite estimates in comparison to previous studies.

A Modeling and Simulation Study of the Role of Suspended Microbial Populations in Nitrification in a Biofilm Reactor

Many biological wastewater treatment processes are based on bacterial biofilms, i.e. layered aggregates of microbial populations deposited on surfaces. Detachment and (re-)attachment leads to an exchange of biomass between the biofilm and the surrounding aqueous phase. Traditionally, mathematical models of biofilm processes do not take the contribution of the suspended, non-attached bacteria into account, implicitly assuming that these are negligible due to the relatively small amount of suspended biomass compared to biofilm biomass. In this paper, we present a model for a nitrifying biofilm reactor that explicitly includes both types of biomass. The model is derived by coupling a reactor mass balance for suspended populations and substrates with a full one-dimensional Wanner–Gujer type biofilm model. The complexity of this model, both with respect to mathematical structure and number of parameters, prevents a rigorous analysis of its dynamics, wherefore we study the model numerically.Our investigations show that suspended biomass needs to be considered explicitly in the model if the interests of the study are the details of the nitrification process and its intermediate steps and compounds. However, suspended biomass may be neglected if the primary interests are the overall reactor performance criteria, such as removal rates. Furthermore, it can be expected that changes in the biofilm area, attachment, detachment, and dilution rates are more likely to affect the variables primarily associated with the second step of nitrification, while the variables associated with the first step tend to be more robust.

Global parameter optimization for biokinetic modeling of simple batch experiments

Environmental process modeling is challenged by the lack of high quality data, stochastic variations, and nonlinear behavior. Conventionally, parameter optimization is based on stochastic sampling techniques to deal with the nonlinear behavior of the proposed models. Despite widespread use, such tools cannot guarantee globally optimal parameter estimates. It can be especially difficult in practice to differentiate between lack of algorithm convergence, convergence to a non-global local optimum, and model structure deficits. For this reason, we use a deterministic global optimization algorithm for kinetic model identification and demonstrate it with a model describing a typical batch experiment. A combination of interval arithmetic, reformulations, and relaxations allows globally optimal identification of all (six) model parameters. In addition, the results suggest that further improvements may be obtained by modification of the optimization problem or by proof of the hypothesized pseudo-convex nature of the problem suggested by our results. Display Omitted Objective function bounds for global biokinetic parameter optimization are proven.Global deterministic parameter estimation of a six-parameter model is possible.Globally optimal parameters are obtained to fit the model to experimental data.

Shape constrained splines as transparent black-box models for bioprocess modeling

Identification of mathematical models is an important task for the design and optimization of biokinetic processes. The Monod rate law is often chosen by default, although this rate law is restrictive and cannot capture all biokinetic process dynamics, which ultimately reduces the predictive capability of the resulting models. This paper proposes an alternative rate-law structure consisting of a flexible black-box spline function that is forced to obey a predefined shape. This way, the difficult task of searching through potentially incomplete rate-law libraries can be circumvented. A simulated case study is used to illustrate the applicability of the method and its superiority to represent unconventional growth conditions, where neither Monod nor Tessier kinetics are appropriate.

On optimization of substrate removal in a bioreactor with wall attached and suspended bacteria.

We investigate the question of optimal substrate removal in a biofilm reactor with concurrent suspended growth, both with respect to the amount of substrate removed and with respect to treatment process duration. The water to be treated is fed externally from a buffer vessel to the treatment reactor. In the two-objective optimal control problem, the flow rate between the vessels is selected as the control variable. The treatment reactor is modelled by a system of three ordinary differential equations in which a two-point boundary value problem is embedded. The solution of the associated singular optimal control problem in the class of measurable functions is impractical to determine and infeasible to implement in real reactors. Instead, we solve the simpler problem to optimize reactor performance in the class of off-on functions, a choice that is motivated by the underlying biological process. These control functions start with an initial no-flow period and then switch to a constant flow rate until the buffer vessel is empty. We approximate the Pareto Front numerically and study the behaviour of the system and its dependence on reactor and initial data. Overall, the modest potential of control strategies to improve reactor performance is found to be primarily due to an initial transient period in which the bacteria have to adapt to the environmental conditions in the reactor, i.e. depends heavily on the initial state of the dynamic system. In applications, the initial state, however, is often unknown and therefore the efficiency of reactor optimization, compared to the uncontrolled system with constant flow rate, is limited.

On the Use of Shape-Constrained Splines for Biokinetic Process Modelling

Identification of mathematical models is an important task for the design and the optimization of biokinetic processes. Monod or Tessier growth-rate models are often chosen by default, although these models are not able to represent the dynamics of all bacterial growth processes. This imperfect representation then affects the quality of the model prediction. This paper introduces an alternative approach, which is based on constraints such as monotonicity and concavity and the use of shape-constrained spline functions, to describe the substrate affinity with high parametric flexibility. This way, the difficult task of searching through potentially incomplete rate-model libraries can be circumvented. A simulated case study is used to illustrate the superiority of the proposed method to represent non-ideal growth conditions, where neither Monod nor Tessier kinetics offer a good approximation.

Outlier detection in UV/Vis spectrophotometric data

Abstract UV/Vis spectrophotometers have been used to monitor water quality since the early 2000s. Calibration of these devices requires sampling campaigns to elaborate relations between recorded spectra and measured concentrations. In order to build robust calibration data sets, several spectra must be recorded per sample. This study compares two approaches – principal component analysis and data depth theory – to identify outliers and select the most representative spectrum (MRS) among the repetitively recorded spectra. Detection of samples that contain outliers is consistent between the methods in more than 70% of the samples. Identification of spectra as outliers is consistent in more than 95% of the cases. The identification of MRS differs depending on the approach used. In their current form, both of the proposed approaches can be used for outlier detection and identification. Further studies are suggested to combine the methods and develop an automated ranking and sorting system.

Identification of Biokinetic Models Using the Concept of Extents

The development of a wide array of process technologies to enable the shift from conventional biological wastewater treatment processes to resource recovery systems is matched by an increasing demand for predictive capabilities. Mathematical models are excellent tools to meet this demand. However, obtaining reliable and fit-for-purpose models remains a cumbersome task due to the inherent complexity of biological wastewater treatment processes. In this work, we present a first study in the context of environmental biotechnology that adopts and explores the use of extents as a way to simplify and streamline the dynamic process modeling task. In addition, the extent-based modeling strategy is enhanced by optimal accounting for nonlinear algebraic equilibria and nonlinear measurement equations. Finally, a thorough discussion of our results explains the benefits of extent-based modeling and its potential to turn environmental process modeling into a highly automated task.

A Chemostat Model with Wall Attachment: The Effect of Biofilm Detachment Rates on Predicted Reactor Performance

We consider a previously introduced mathematical model of chemostat with suspended and wall attached growth and exchange of biomass via biofilm detachment and reattachment. In this study we investigate the role of the specific choice of a biomass detachment criterion. We find that this choice does greatly affect output parameters such as biomass in the system, but it does not affect strongly effluent concentration and hence the prediction of reactor performance.