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Register a new userOptimizing microalgal productivity in raceway ponds through a controlled mixing device
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This paper focuses on mixing strategies to enhance the growth of microalgae in a raceway pond. The flow is assumed to be laminar and the Han model describing the dynamics of the photosystems is used as a basis to determine growth rate as a function of light history. A device controlling the mixing is assumed, which means that the order of the cells along the different layers can be rearranged at each new lap according to a permutation matrix P. The order of cell depth hence the light perceived is consequently modified on a cyclical basis. The dynamics of the photosystems are computed over K laps of the raceway with permutation P. It is proven that if a periodic regime is reached, it will be periodic immediately after the first lap, which enables to reduce significantly the computational cost when testing all the permutations. In view of optimizing the production, a functional corresponding to the average growth rate along depth and for one lap is introduced. A suboptimal but explicit solution is proposed and compared numerically to the optimal permutation and other strategies for different cases. Finally, the expected gains in growth rate are discussed.
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This paper focuses on mixing strategies to enhance the growth rate in an algal raceway system. A mixing device, such as a paddle wheel, is considered to control the rearrangement of the depth of the algae cultures hence the light perceived at each lap. The dynamics of the photosystems after a rearrangement is accounted for by the Han model. Our approach consists in considering permanent regimes where the strategy is parametrized by a permutation matrix which modifies the order of the layers at the beginning of each lap. It is proven that the dynamics of the photosystems is then periodic, with a period corresponding to one lap of the raceway whatever the order of the considered permutation matrix is. An objective function related to the average growth rate over one lap is then introduced. Since N ! permutations (N being the number of considered layers) need to be tested in the general case, it can be numerically solved only for a limited number of layers. Consequently, we propose a second optimization problem associated with a suboptimal solution of the initial problem, which can be determined explicitly. A sufficient condition to characterize cases where the two problems have the same solution is given. Some numerical experiments are performed to assess the benefit of optimal strategies in various settings.
We consider a coupled physical-biological model describing growth of microalgae in a raceway pond cultivation process, accounting for hydrodynamics. Our approach combines a biological model (based on the Han model) and shallow water dynamics equations that model the fluid into the raceway pond. We present an optimization procedure dealing with the topography to maximize the biomass production over one lap or multiple laps with a paddle wheel. On the contrary to a widespread belief in the microalgae field, the results show that a flat topography is optimal in a periodic regime. In other frameworks, non-trivial topographies can be obtained. We present some of them, e.g., when a mixing device is included in the model.
We present a coupled model describing growth of microalgae in a raceway cultivation process, accounting for hydrodynamics. Our approach combines a biological model (based on the Han model) and shallow water dynamics equations that model the fluid into the raceway. We then describe an optimization procedure dealing with the topography to maximize the biomass production over one cycle (one lap of the raceway). The results show that non-flat topographies enhance microalgal productivity.
This paper focuses on mixing strategies and designing shape of the bottom topographies to enhance the growth of the microalgae in raceway ponds. A physical-biological coupled model is used to describe the growth of the algae. A simple model of a mixing device such as a paddle wheel is also considered. The complete process model was then included in an optimization problem associated with the maximization of the biomass production. The results show that non-trivial topographies can be coupled with some specific mixing strategies to improve the microalgal productivity.
A detailed empirical analysis of the productivity of non financial firms across several countries and years shows that productivity follows a non-Gaussian distribution with power law tails. We demonstrate that these empirical findings can be interpreted as consequence of a mechanism of exchanges in a social network where firms improve their productivity by direct innovation or/and by imitation of other firms technological and organizational solutions. The type of network-connectivity determines how fast and how efficiently information can diffuse and how quickly innovation will permeate or behaviors will be imitated. From a model for innovation flow through a complex network we obtain that the expectation values of the productivity level are proportional to the connectivity of the network of links between firms. The comparison with the empirical distributions reveals that such a network must be of a scale-free type with a power-law degree distribution in the large connectivity range.
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