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Modelling, parameter estimation, optimisation and control of transport and reaction processes in bioreactors.
ŠTUMBAUER, Václav
With the significant potential of microalgae as a major biofuel source of the future, a considerable scientific attention is attracted towards the field of biotechnology and bioprocess engineering. Nevertheless the current photobioreactor (PBR) design methods are still too empirical. With this work I would like to promote the idea of designing a production system, such as a PBR, completely \emph{in silico}, thus allowing for the in silico optimization and optimal control determination. The thesis deals with the PBR modeling and simulation. It addresses two crucial issues in the current state-of-the-art PBR modeling. The first issue relevant to the deficiency of the currently available models - the incorrect or insufficient treatment of either the transport process modeling, the reaction modeling or the coupling between these two models. A correct treatment of both the transport and the reaction phenomena is proposed in the thesis - in the form of a unified modeling framework consisting of three interconnected parts - (i) the state system, (ii) the fluid-dynamic model and (iii) optimal control determination. The proposed model structure allows prediction of the PBR performance with respect to the modelled PBR size, geometry, operating conditions or a particular microalgae strain. The proposed unified modeling approach is applied to the case of the Couette-Taylor photobioreactor (CTBR) where it is used for the optimal control solution. The PBR represents a complex multiscale problem and especially in the case of the production scale systems, the associated computational costs are paramount. This is the second crucial issue addressed in the thesis. With respect to the computational complexity, the fluid dynamics simulation is the most costly part of the PBR simulation. To model the fluid flow with the classical CFD (Computational Fluid Dynamics) methods inside a production scale PBR leads to an enormous grid size. This usually requires a parallel implementation of the solver but in the parallelization of the classical methods lies another relevant issue - that of the amount of data the individual nodes must interchange with each other. The thesis addresses the performance relevant issues by proposing and evaluation alternative approaches to the fluid flow simulation. These approaches are more suitable to the parallel implementation than the classical methods because of their rather local character in comparison to the classical methods - namely the Lattice Boltzmann Method (LBM) for fluid flow, which is the primary focus of the thesis in this regard and alternatively also the discrete random walk based method (DRW). As the outcome of the thesis I have developed and validated a new Lagrangian general modeling approach to the transport and reaction processes in PBR - a framework based on the Lattice Boltzmann method (LBM) and the model of the Photosynthetic Factory (PSF) that models correctly the transport and reaction processes and their coupling. Further I have implemented a software prototype based on the proposed modeling approach and validated this prototype on the case of the Coutte-Taylor PBR. I have also demonstrated that the modeling approach has a significant potential from the computational costs point of view by implementing and validating the software prototype on the parallel architecture of CUDA (Compute Unified Device Architecture). The current parallel implementation is approximately 20 times faster than the unparallized one and decreases thus significantly the iteration cycle of the PBR design process.
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Microalgal Growth Problem for the Photosynthetitc Factory and its Optimization: An Overview and Further Analysis
Čelikovský, Sergej
The overview of the micro-algal growth problem for the photosynthetic factory and its optimal control solution is presented here. First, the model description and its properties like Haldan steady state dynamics, light integration property and the forward invariance of the set of biologically well-de ned states are described. This shows that the model meets basic experimentally based requirements. Further, its optimal control problem is formulated and solved analytically for the one dimensional singular perturbation based reduction. Properties of the optimal control for the reduced model are discussed and compared with some experimental observations. Among them, the general biotechnological paradigm that on large time intervals the optimal solution is, in certain sense, almost constant, is substantiated. As a new original result of this paper, the explicit solvable di erentiable equation for the unsaturated part of the optimal control is derived.
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Optimization of Algae Population Growth Using Markov Chains and
Zouharová, Martina ; Kalčevová, Jana (advisor) ; Černý, Michal (referee)
The thesis deals with the task of refining the constructional and operational parameters of a tubular photobioreactor in order to maximise the growth rate of algae contained in the cultivation suspension. It builds on a basic growth model of the Porhydrium sp. alga, and focuses on the optimization of external irradiance, which is one of the key determinants of algae growth. Two distinct methodological approaches are applied: analytic approach, which employs Markov Chains, and simulation approach, which relies on agent-based simulations. In the analytic part, we introduce the construction of state transition matrix for a Markov Chain that accounts for varying irradiance inside the photobioreactor (in contrast to constant-irradiance methods that have been published so far). In the simulation part, we devised an agent-based model of algae population that enables us to analyze the system behaviour while interactively changing the model parameters. In the context of the results from both the analytic and simulation part, we conclude by suggesting the optimal level of external irradiance.
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