Countercurrent-flow columns are widely used in production processes in the chemical industry and their application in ecological engineering is of increasing importance. A theoretical model is presented here that allows mass transfer to be described in terms of packing geometry and physical properties which influence the gas-liquid or vapour-liquid systems in absorption, desorption and rectification columns. The relationships derived from the model can be applied to all countercurrent-flow columns, regardless of whether the packing has been dumped at random or arranged in a geometric pattern. Mass Transfer in the Liquid PhaseThe geometry and dimensions of modern packings are the main parameters that govern the flow of various phases and thus also the column efficiency. The liquid must flow in the form of a thin film and be distributed as uniformly as possible over the entire cross-section of the column in order to ensure large throughputs, effective mass transfer and moderate pressure drops. The surface of the packing should be wetted as much as possible and the countercurrent flow of gas should also be uniformly distributed over the column cross-section. Thus, the factors that govern the fluid dynamics and mass transfer of a column are the physical properties of the system, its capacity range and the shape and structure of the packing [I].The efficiency of a packing is influenced by the length of flow path I, which has to be traversed before the surface of the liquid in contact with the gas is renewed. Since the liquid is continually remixed at the points of contact with the packing, according to Higbie, the mass transfer in the liquid phase occurs by non-steady state diffusion, Eq. (1). DL is the diffusion coefficient of the transferring component and the time rL necessary for the renewal of interfacial area is determined by Eq. (2) Gravity and shear forces in the film are maintained at equilibrium with the frictional forces by the shear stress rv in the gas or vapour flow at the surface of the film, Eq. (4).In Eq. (4), ev is the gas density, iiv the average effective gas velocity and wL the drag coefficient for the gas-liquid or vapour-liquid countercurrent flow. (4)r,= -+wLeviiV 2 .Integration of Eq. (3) and substitution of the frictional force of the gas, acting at the surface of the liquid, by Eq. (4), lead theoretically to Eq. (5), valid for the liquid hold-up hL at and below the loading point [2-41. In Eq. (9, uL is the liquid load based on the column cross-section and a the total surface area of the packing.(2)Combining Eqs (I), (2) and (5) gives rise to Eq. (6) for the volumetric mass transfer coefficient &aph and Eq. (7) for the height of a transfer unit HTUL on the liquid-side, with CL being a constant, characteristic of the shape and structure of the packing 12, 5 , 61.If the packing is regarded as a large number of Chmnels through which the liquid of density QL and viscosity 4' L flows as a film with a local velocity iiL,s countercurrent to

No abstract

Up to now, the only equations that were known for calculating mass transfer during twophase countercurrent flow in packed columns were those that apply to the range extending up to the loading point. The gas and liquid streams flow separately through the column below but not above this point. Above it, the shear stress in the gas stream supports an increasing quantity of liquid in the column, with the result that the liquid holdup greatly increases. Finally, at the flood point, the liquid accumulates to such an extent that column instability occurs. Mass transfer in this upper loading range can be described if these fluid dynamic relationships are taken into consideration. The algorithm that is presented here for its prediction is based on theoretical and experimental studies. Fluid DynamicsA model that describes the fluid dynamic relationships in packed columns with countercurrent flow of the gas and liquid phases was developed in a previous work by Billet -31. It allows the flow conditions to be described UP to the flood point. The assumption made was that the void It follows from this that the local velocity lzL,s is given by (3) and the average effective liquid velocity in the film lzL, by fraction in a bed of packing could be represented by a multiplicity of vertical channels through which the liquidflows downwards in the form of a film countercurrent to the ascending gas stream. This model also permits mass transfer in the loading range up to the flood point to be determined.If a gas flows countercurrent to a liquid film and the inertia forces are neglected, the shear and gravity forces at the surface of the film s = so, as defined by Eq. (l), are in equilibrium with the shear forces t in the gas stream in accordance with Eq. ( 2 ) ' ) , = -eL'g ds where uL,s is the local liquid velocity in the film, qL is the dynamic viscosity of the liquid, QL is the density of the liquid, g is the acceleration due to gravity, uv is the average effective gas velocity, ev is the gas density, and (vL is the resistance factor for two-phase flow.The loading point in two-phase countercurrent flow is reached whenever the gas velocity is just so high that iiL,s becomes zero at the surface of the film s = so. In view of this fact, Eq. (5) can be derived from the void fraction E , the specific surface a of the bed of packing, and the liquid holdup h, = sou corresponding to the gas velocity at the loading point u~,~. The term vS for the resistance factor in Eq. (5) is described by Eq. (6); and that for the liquid holdup hL,s by Eq. (7). In the derivation of Elq. (5), the terms uv = ziV(&-kL) and uL = aLhL were introduced to allow for the fundamental relationship between the superficial gas and liquid velocities uv and uL and the figures obtained for the average effective gas and liquid velocities iiV and iiL from Eqs (3) and (4) [2 -51.

The correct choice of packing is of decisive importance for optimum process efficiency in the operation of two-phase countercurrent columns. An important criterion for this choice is the pressure drop in the gas flow. Theoretical relationships are derived for calculating the pressure drop in beds with dry and trickle packings. It has been demonstrated by comprehensive experiments that these relationships allow the pressure drop to be determined more accurately than by previous methods. The experiments were performed at the Department of Thermal Separation Processes of Bochum University on 54 different packed beds, using 24 different systems.In order to describe the flow in a packed trickle bed, it is assumed that the bed is equivalent to a multiplicity of flow channels through which the liquid of density') eL and viscosity vL flows downwards as a film of thickness so at a local velocity iiL,s. If inertia forces are neglected, gravity and shear forces in the laminar-flow film, Eq. (l), are held in equilibrium with the frictional forces by the shear stress rv in the vapour at the surface of the film, Eq. (2). In Eq. (2), ev is the gas density, Uv the average effective gas velocity and II/ the resistance coefficient for gas flow [ 3 ] : 1) List of symbols at the end of the paper. 0930-75 16/91/0204-0089 $03.50+ .25/0

This contribution presents the determination of liquid hold-up in gadliquid two-phase countercurrent columns filled with random or structured packings. The equations resulting from the established physical relationships are verified against the values for liquid hold-up determined experimentally on 56 different column packings and 16 gadliquid systems. The experimental and calculated results agree well, with only slight deviations. This also applies to the range between the loading and flooding points for two-phase countercurrent flow.