The physical characteristics of the flow of a gaseous mixture with solid inclusions in a counterflow with a liquid in a cylindrical pipe is of major interest in analyzing production equipment and processes, making it possible to formulate proposals relative to improvement in the quality and effectiveness of distillation columns. This paper cites results of analyses in the above-indicated problem based on analysis of forces that develop as a result of particle-particle interaction, and particle interaction with the surrounding medium, and forces that develop as a result of particle collisions. The frequency of particle-particle collisions, which limits the adequacy of this model with consideration of solid-particle concentrations, is based on the analyses. Experimental data are obtained for different regimes: in a fluidization regime, where a liquid and gaseous mixture with solid inclusions are delivered from below into a counterflow within the vessel, and in a film regime. More precise definitions, which made it possible to improve the adequacy for the processes under investigations, were made in reducing the experimental data.Mass-transfer units [2, 3] used for hydrodynamic and hydroaerodynamic testing of packed vessels in a three-phase medium are examined for experimental determination of empirical data to compare with computed model data in [1]. A schematic of one of these plants is shown in Fig. 1, and consists of the following components: vertical column vessel, fan with an air duct, and water-supply, -heating, -distribution, and -collection systems. Heat-and mass-transfer characteristics of the packing are studied on this unit during evaporative cooling with indirect contact in an air-water system under counterflow conditions.Column 1 with a diameter of 400 mm has downcomer type of detachable support-distribution grating 2. Packing 3 fills a plate. The layer of packing was set in motion by an ascending gas flow delivered by high-pressure fan 4, and made it possible to effect linear gas velocities of from 1 to 4 m/sec within the column.Liquid from tank 12 was fed by pump 13 through special sprayer 5 uniformly over the surface of the packing, and owing to its irregular movement, created a stable hydrodynamic layer on the surface of the downcomer plate. The liquid then entered the lower section of the vessel, where it was discharged by pump 11 into tank 12. The specific irrigation surface attained 1-5 m 3 /m 2 ·h.The sheets enclosing column 1 are made of acrylic plastic, permitting observation of the three-phase layer, and also measurement of its dynamic height.The following were measured during the course of the hydrodynamic investigations: the hydraulic resistance of the plate with a three-phase layer of irrigated packing, the dynamic height of the layer, and the volume of liquid maintained in the layer.The flow rate of air was measured by Pitot tube 9, which was connected to micromanometer 10. The error of the measurements was ±1.5%.

A mechanical model of the motion of component phases in a cylindrical pipe is used as a kinematic approximation for investigation of the interaction that occurs in a three-phase medium with movement of a top-fed liquid and a bottom-fed gaseous mixture with solid inclusions in a countercurrent flow with the liquid within a cylindrical pipe. Kinetic equations derived with consideration of the stress tensor in the particle phase are based on the model. Numerical calculations for various boundary conditions linked to porosity, which was varied from zero to the maximum value (0.65), were performed within the framework of the model. These results indicated that pressure variation leads to significant changes in the structure of the fluidized bed and ascending flow. Pressure dependencies of the temperature and velocity at the center of the pipe and in the near-boundary region close to the wall are investigated.The mechanical behavior of an air-fluidized flow can be described by forces that influence the interaction between particles. The contacts are not permanent, since clusters are recombined as the ensemble of particles moves. Because there are no absolutely elastic surfaces for the particles, the forces possess both tangential and normal components, and the surfaces at the contact may slide one with respect to the other. In the case when the ensembles of particles are spread throughout the entire volume and are moving rapidly, individual contacts are short-lived, and can be treated as impingements, like the collisions between molecules in a liquid or gas. In the opposite case, the contacts are semi-permanent when deformation is small and stacking density high, and normal reactive forces and tangential friction forces dominate at these sliding contacts.Johnson and Jackson [1] propose the derivation of a pressure tensor for an ensemble of particles in constitutive relationships. Combination of tangential forces developing as a result of interaction between particles and the surrounding medium, and forces developing as a result of particle impingement are based on the method. In our study, we modified the pressure tensor, and obtained one in constitutive relationships for the intermediate case when the frequency of inter-particle impingement is rather high, i.e., the adequacy of this model is limited by the concentrations of solid particles (far from zero).In analyzing models, Walton and Braun [2] examined the movement of particles with mutual contacts of arbitrary duration. These models, however, examine plane shear perpendicular to the flow, in which the periodicity of the variables is used to limit the number of particles in the moving flow. Other authors [3][4][5][6] resort to the use of a continuous model of an ensemble of particles with consideration of their interaction for the treatment of more complex situations. In our study, the kinetic energy of the random motion of solid particles plays the role of internal energy, which is related to the "solid-particle temperature" denoted by θ. The value of θ exerts a m...

Reduction of experimental data obtained in fluidization and film regimes is required in the building of adequate models representing the feed of a gaseous mixture with solid inclusions into a liquid counterflow within a vessel. Reduction to a small-dimensional model permitting effective computer implementation is performed, proceeding from equations of the conservation of the radial moment of solid particles and the conservation of energy with the inclusion of laws governing the conservation of axial moments of the gas and solid particles. Results of numerical calculations within the framework of the refined model simulating MEA cleaning in a counterflow column make it possible to draw a conclusion concerning the potential for optimization of geometric characteristics of the vessel employed. Temperature fluctuations in the effective zone, i.e., structuring of the counterflow along the radius of the effective channel, may be observed when the parameters of the model are varied and the temperature on the boundary of the column is increased. Among other things, the results of the study permit assessment of the reduction in operational effectiveness of the packing in a selected regime.Reduction of experimental data obtained in fluidization and film regimes when a gaseous mixture with solid inclusion is fed into a counterflow with a liquid in a vessel is required for the development of adequate models. Reduction to a small-dimensional model that permits effective computer realization is performed below, proceeding from equations of the conservation of the radial moment of solid particles and conservation of energy with inclusion of laws governing the axial moments of the gas and solid particles. Results of numerical analyses within the framework of the refined model simulating MEA cleaning in a counterflow column enable us to conclude the potential for optimization of the geometric characteristics of the vessel under investigation. Temperature fluctuations in the effective zone, i.e., structuring of the counterflow along the radius of the effective channel, may be observed when the parameters of the model are varied and the temperature is increased on the boundary of the column. Among other things, these considerations make it possible to evaluate the reduction in operating effectiveness of the packing for a selected regime. To test the model described in [1], we examined MEA cleaning in a counterflow column. Basic equations of the model of a vertical flow of a gaseous mixture with solid inclusions in a cylindrical pipe are presented in dimensionless coordinates with consideration of particle-particle interaction and interaction of the particles with the surrounding medium, and the forces that develop as a result of particle collisions. The model includes equations of the conservation of the axial