The paper deals with photosynthetic microorganism growth modelling and simulation in a distributed parameter system. Main result concerns the development and comparison of two modelling frameworks for photo-bioreactor modelling. The first "classical" approach is based on PDE (reaction-turbulent diffusion system) and finite difference method. The alternative approach is based on random walk model of transport by turbulent diffusion. The complications residing in modelling of multi-scale transport and reaction phenomena in microalgae are clarified and the solution is chosen. It consists on phenomenological state description of microbial culture by the lumped parameter model of photosynthetic factory (PSF model) in the re-parametrized form, published recently in this journal by Papáček, et al. (2009). Obviously both approaches lead to the same simulation results, nevertheless they provide different advantages.

a b s t r a c tThe development of a distributed parameter model of microalgae growth is presented. Two modelling frameworks for photo-bioreactor modelling, Eulerian and Lagrangian, are discussed and the complications residing in the multi-scale nature of transport and reaction phenomena are clarified. It is shown why is the mechanistic two time-scale model of photosynthetic factory the adequate model for biotechnological purposes. For a special laboratory Couette-Taylor bioreactor with cylindrical geometry, we reached reliable simulation results using a steady-state Eulerian approach and the finite difference scheme. Moreover, we prove numerically that the resulting photosynthetic production rate in this reactor goes, for growing inner cylinder angular velocity, to a certain limit value, which depends on the average irradiance only.

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