Estimation of heterogeneity of the atmospheric air velocity field in adsorbers of front-end purification units for air separation plants

Assuming unidirectional motion of compressed atmospheric air through a vertical cylindrical adsorbent with a fixed granular layer of the front-end purification unit adsorbent, the mathematical model for estimating the heterogeneity of a hydrodynamic velocity field in the radial and axial directions in a turbulent regime is proposed. The model is based on the boundary layer approximation of the Darcy–Brinkman–Forchheimer phenomenological equation. The steady-state flow at low permeability of the granular layer is identified using the collocation method, and the approximate analytical solution is obtained which justifies the applicability of an ideal displacement mode when describing the carrier medium motion. Numerical integration of a boundary value problem of the model equation using the finite-difference method with Richardson extrapolation confirms the conclusion validity. The structure of an accelerated turbulent flow having constant flow velocity in the input section shows that for small Forchheimer coefficients, the Darcy–Brinkman equation is used to obtain the analytical ratio for calculating the length of the initial hydrodynamic section. The proposed mathematical model for estimating the heterogeneity of the velocity field in adsorbers with a stationary dispersed layer is applicable for a laminar flow regime. Testing of this approach by assessing velocity field uniformity for a mass-produced front-end purification unit of air separation plants has shown its efficiency.