Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

Optimization of the electrodialytic phosphorus recovery from sewage sludge ash

Phosphorus (P) is becoming a scarce element due to the decreasing availability of primary sources. Therefore, recover P from secondary sources, e.g. waste streams, have become extremely important. Sewage sludge ash (SSA) is a reliable secondary source of P. The use of SSAs as a direct fertilizer has very restricted legislation due to the presence of inorganic contaminants. Furthermore, the P present in SSAs is not in a plant-available form. The electrodialytic (ED) process is one of the methods under development to recover P and simultaneously remove heavy metals. The present work aimed to optimize the P recovery through a 2 compartment electrodialytic cell. The research was divided in three independent phases. In the first phase, ED experiments were carried out for two SSAs from different seasons, varying the duration of the ED process (2, 4, 6 and 9 days). During the ED treatment the SSA was suspended in distilled water in the anolyte, which was separated from the catholyte by a cation exchange membrane. From both ashes 90% of P was successfully extracted after 6 days of treatment. Regarding the heavy metals removal, one of the SSAs had a better removal than the other. Therefore, it was possible to conclude that SSAs from different seasons can be submitted to ED process under the same parameters. In the second phase, the two SSAs were exposed to humidity and air prior to ED, in order to carbonate them. Although this procedure was not successful, ED experiments were carried out varying the duration of the treatment (2 and 6 days) and the period of air exposure that SSAs were submitted to (7, 14 and 30 days). After 6 days of treatment and 30 days of air exposure, 90% of phosphorus was successfully extracted from both ashes. No differences were identified between carbonated and non-carbonated SSAs. Thus, SSAs that were exposed to the air and humidity, e.g. SSAs stored for 30 days in an open deposit, can be treated under the same parameters as the SSAs directly collected from the incineration process. In the third phase, ED experiments were carried out during 6 days varying the stirring time (0, 1, 2 and 4 h/day) in order to investigate if energy can be saved on the stirring process. After 6 days of treatment and 4 h/day stirring, 80% and 90% of P was successfully extracted from SSA-A and SSA-B, respectively. This value is very similar to the one obtained for 6 days of treatment stirring 24 h/day.

Modeling and optimization of extracellular polysaccharides production by Enterobacter A47

Polysaccharides are gaining increasing attention as potential environmental friendly and sustainable building blocks in many fields of the (bio)chemical industry. The microbial production of polysaccharides is envisioned as a promising path, since higher biomass growth rates are possible and therefore higher productivities may be achieved compared to vegetable or animal polysaccharides sources. This Ph.D. thesis focuses on the modeling and optimization of a particular microbial polysaccharide, namely the production of extracellular polysaccharides (EPS) by the bacterial strain Enterobacter A47. Enterobacter A47 was found to be a metabolically versatile organism in terms of its adaptability to complex media, notably capable of achieving high growth rates in media containing glycerol byproduct from the biodiesel industry. However, the industrial implementation of this production process is still hampered due to a largely unoptimized process. Kinetic rates from the bioreactor operation are heavily dependent on operational parameters such as temperature, pH, stirring and aeration rate. The increase of culture broth viscosity is a common feature of this culture and has a major impact on the overall performance. This fact complicates the mathematical modeling of the process, limiting the possibility to understand, control and optimize productivity. In order to tackle this difficulty, data-driven mathematical methodologies such as Artificial Neural Networks can be employed to incorporate additional process data to complement the known mathematical description of the fermentation kinetics. In this Ph.D. thesis, we have adopted such an hybrid modeling framework that enabled the incorporation of temperature, pH and viscosity effects on the fermentation kinetics in order to improve the dynamical modeling and optimization of the process. A model-based optimization method was implemented that enabled to design bioreactor optimal control strategies in the sense of EPS productivity maximization. It is also critical to understand EPS synthesis at the level of the bacterial metabolism, since the production of EPS is a tightly regulated process. Methods of pathway analysis provide a means to unravel the fundamental pathways and their controls in bioprocesses. In the present Ph.D. thesis, a novel methodology called Principal Elementary Mode Analysis (PEMA) was developed and implemented that enabled to identify which cellular fluxes are activated under different conditions of temperature and pH. It is shown that differences in these two parameters affect the chemical composition of EPS, hence they are critical for the regulation of the product synthesis. In future studies, the knowledge provided by PEMA could foster the development of metabolically meaningful control strategies that target the EPS sugar content and oder product quality parameters.