To develop efficient vessels with a disperse solid phase, which can be blown-out by the gases that react with the charge and transmit heat (drying of granular materials, regeneration of air in special mounts, gasification of powdered fuel, trapping of the valuable or harmful components of a gas passed through special porous absorbers, etc.), it is necessary to know the distribution of the gas in the layers of the disperse materials [1][2][3]. Experimental methods of determining local gas velocities in granular layers are insufficiently reliable and extremely time-consuming.The simplest problems involving the filtration spread of gas in a layer, and the conditions under which local gushing occurs (a system of jets penetrating a granular layer ) have been solved for the plane and axisymmetric cases [4--6], and these solutions are being successfully employed in the design of chemical reactors with a disperse charge.In a number of cases of practical significance, gas is introduced to these reactors not in the direction of its basic flow in the vessel, but through a lateral port, which is skewed with respect to the vessel's base. The disperse material may be situated directly on the impenetrable base, or on a grid separating it from the base by a drainage slot, which is required for realization of the corresponding production process in some cases, and effectively contributes to hydrodynamic stabilization of the filtration flow of gas over a shorter initial section of the reactor, and markedly reduces head losses associated with the lateral entry of gas to the vessel in other cases.Rational design of a vessel, in which active interaction between the gas and charge is realized in the zone of a hydrodynamically stabilized essentially homogeneous (over the cross section of the vessel) gas flow in the axial direction, is possible when the length of the initial section is known. The height of the vessel may be, among other things, minimized as a result of a limited reduction in the indicated length (for example, for a given height of the gas-entry port above the base of the vessel).The effectiveness of the drainage slot, which may be filled with a "highly permeable" disperse material, is characterized by dimensionless hydraulic-conduction parameter 0 -the ratio of the hydraulic resistance of the layer of disperse material in the vessel to the hydraulic resistance of a drainage slot of the same length: 0 = k20H0(kl0a) -I . If the drainage slot is an empty space between the grid and base, 0 = ~/03(12k10a) -1. Here, kl0 and k20 are the permeabilities, respectively, of the charge in the apparatus and the porous material under the grid, tx is the viscosity of the gas, H 0 is the height of the drainage slot, and a is the width of the vessel.Lyubin et al. [7] analyzed the hydrodynamic stabilization of plane filtration flows in a layer of disperse material with different schemes employed to introduce gas to a vessel through a port of f'mite width with allowance for the influence exerted by a drainage slot in the base of the vesse...