This article discusses the mathematical modeling of the hydrodynamic structure of flows in the apparatus for cultivating chlorella and the parametric identification of the mathematical model. Since in the considered reactor there is rather active longitudinal and radial mixing, the diffusion model is still more acceptable. However, such a model is described by partial differential equations and is associated with certain difficulties associated with determining the coefficients of radial and longitudinal diffusion. Therefore, when describing such phenomena, it makes sense to resort to the cell model. The mathematical description of the hydrodynamic structure of flows in the form of a cell model consists of a system of linear differential equations of the first order. On the basis of the obtained kinematic equations and the control of the hydrodynamic structure of flows in the reactor, a generalized mathematical model of the microalgae cultivation process is being drawn up. The model of the process under consideration obtained by analytical methods is a system of equations describing various aspects of the research object, taking into accounts the kinetic parameters and real hydrodynamic regimes. These specific values of the coefficients can be used to solve various engineering problems.

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Oil and gas fields in natural conditions are rarely of homogeneous nature. Given the chaotic nature of changes in rock mass permeability within a single layer, its significant parts (areas) can be considered uniform in permeability. If significant in sizes homogeneous zones (regions) are distinguished within the formation, the parameters of such a macro-inhomogeneous formation significantly affect the characteristics of the filtration flows. The area of zonal inhomogeneity consists of the parts of different permeability. Within the same zone, the permeability is on average the same, but differs from the permeability of adjacent zones.