ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
ass Transfer in Packed Towers EFFECT OF LIQUID CONCENTRATION ON LIQUID FILM COEFFICIENT JOHN W. TIERNEY, JR.', LEROY F. STUTZMAN, AND ROBERT L. DAILEADER2 Chemical Engineering Department, Norlhwestern University, Evanston, 111.
P'4cKE
+ Dtowers are often used in the chemical industries to effect the transfer of a chemical component from a liquid to a gas or from a gas to a liquid. I n operation, the gas is admitted a t the bottom of a vertical toner and the liquid a t the top. The packing serves to distribute the liquid over the area of the column and to provide numerous changes in direction and velocity for each phase. In the design of such units, the principal problem is to determine the length of time the phases must be in contact to accomplish the desired transfer. This involves the liquid and gas rates, tower height, and t'he rate of transfer. The rate of transfer can be expressed as the product of a driving force (concentration difference) and a transference or reciprocal resistance (mass transfer coefficient). According to the two-film theory, the over-all mass transfer coefficient can be considered as consisting of two individual coefficients in series-one for each phase. Further, the concentration gradients are steep only near the interface between phases, and most of the resistance to transfer can be considered as concentrated in a thin film adjacent to the interface. At t'he interface itself, equilibrium is assumed. The problem of Obtaining a general correlation for individual mass transfer coefficients in terms of physical properties of the phase, flow rates, packing, etc., has been investigated by many trorlters. The work described in this paper was undertaken to determine the effect of one of these variables-the liquid phase concent,ration-on the liquid film mass transfer coefficient. The work of other investigators on liquid film mass transfer coefficients can be briefly summarized as follows: The liquid film mass transfer coefficient multiplied by the interhas been reported to be a funcfacial area per unit volume, k~a, tion of L , the liquid rate expressed as pounds per unit crosssectional area of empty tower, raised to a power between 0.5 and 1.0 ( 7 , 9, 11-13) and independent of gas rate. Sherwood and Holloway ( 1 3 ) report, t ~ proportional a to DL,the liquid diffusivity, raised to the 0.5 power; while Scheibel(12) recommends an exponent of 1.0. Gaffney and Drew ( 3 ) used an exponent of 0.58 for D L to correlate data obtained by passing organic solvents and water through a bed packed with solid organic pellets. Scheibel (18) reports an effect of liquid composition on k ~ but a attributes it to changes in liquid diffusivity with concentration for the ketone-water syst'ems used. Since the highest liquid composition reported is about 2 mole %, little effect would be expected. Hobson and Thodos ( 5 ) used a log mean inert composition across the liquid film to correlate their data, but, again, dilute solutions were used, and the necessity for the presence of the concentration term is not definitely shown. The effect of concentration on the liquid film mass transfer coefficient has been largely ignored by most workers. This is due primarily to the fact that virtually all of the experiments have been performed with very dilute solutions-for which concentration effects are small. The experiment described in this paper was designed, therefore, to measure t,he liquid film transfer coefficient throughout a range of concentration and to minimize as much as possible the effect of other variables, such as liquid and gas rate. The method 1 2
Present addrees, Pure Oil Co., Crystal Lake, Ill. Present address, Standard Oil Co. (New Jersey), Linden -N. J.
August 1954
selected consists essentially of measuring the over-all coefficient for mass transfer and the gas film coefficient and then obtaining t'he liquid film coefficient from them. The measurement, of the gas film coefficient requires a knowledge of the interface composition. Actual experimental measurement of this quantity is virtually impossible; but, if the liquid is a pure material, the interface composition is known. Hence, for the particular composition where the mole fraction of the diffusing component is equal to 1, the gas film coefficient equals the over-all coefficient and can be measured. Also, since the gas film coefficient is essentially a function of the state of mot,ion of the gas relative to the liquid (gas rate, liquid rate, and packing) and of the properties of the gas film (viscosity, density, and diffusivity), the gas film coefficient will not change with liquid composition, provided these conditions are not changed. The method used, therefore, was to measure the gas film coefficient a t a particular gas and liquid rate by evaporating the pure liquid and then, without changing the column in any way, to measure the over-all coefficient for various liquid compositions, using the same gas and liquid rates. I n t,his Ray the state of motion of the gas is kept constant relative to the liquid. T o ensure that the physical propert,ies of the gas film remained the same, a relatively nonvolatile liquid n-as used-the vapor pressure was less than 7 mm. of mercury-and the gas film consisted essentially of air for all liquid compositions. This assumes that koa is not affected by the properties of the liquid film. Actually, as the concentration in the liquid changes, its viscosity will also change. An increase in viscosity mould presumably- result in a thickening of the liquid flowing over the packing and a decrease in a. However, the cross-sectional area available for gas flow will siniultaneously decrease, causing an increase in ic,. I n the absence of any information concerning the relative importance of theso effects, it has been assumed that k,a remains constant for the range of viscosity changes encountered in this work. The measurement of the over-all coefficient for mass t'ransfer (which, for the particular case of a pure liquid, is equal to the gas film coefficient) requires that the inlet and outlet liquid compositions, inlet and outlet gas compositions, and gas and liquid rates be known. The liquid composition can be determined by analysis, and the gas and liquid rates can be measured relatively easily. By making the inlet gas composition zero, the only unknown is the exit gas composition, which was determined as follows. The tower was mounted on a scale and provision was made for all liquid removed from the bottom of the tower to be added again at the top. I n this way the amount of liquid in the systemismaintained constant, except for that lost by evaporation. The scale reading was maintained constant by the addition of fresh ,liquid from a buret. The amount of liquid evaporated is thus equal to the amount added t o the syst'em. Since the amount and composition of the liquid added and the gas rate are known, the exit composition can be calculated. This procedure assumes that the ratio of components in the exit gas is the same as that in the liquid added to the system. This will only be true for one particular circulating liquid composition. If one component is present in greater proportion in the liquid added to the system
INDUSTRIAL AND ENGINEERING CHEMISTRY
1595
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT tometer. The instrument does not read the refractive index directly but meaaures an angle that is related to the refractive index. The difference in refractive index between the pure compounds was approximately 200 minutes, as measured by the instrument. A micrometer screwj provided for reading differences, was divided into tenths of a minute. The technique used vias to measure the difference in refractive index in minutes of instrument reading, 0, between the unknown and pure I-butanol. Duplicate samples checked within 0.2 minutes. Fourteen samples covering the entire concentrat,ion range were prepared by direct weighing, and these known values of mole fraction mere compared with those obtained using the refractometer and the equations based on the additivity of molar refractions. The average deviation was 0.0003 mole fraction units. Figure I is a photograph of the apparatus showing the relative location of the various it'ems. The tower used was a 3.24-inch-inside-diameter glass column, 13 inches long, supported by a ring stand. A stopper was inserted in the bottom to form a liquid collection chamber and to support the packing. Glass marbles (450) with an average diameter of 0.485 inch were used for packing. The packed height was 4.31 inches, as measured from the lower support to a flat piece of metal placed on top of the packing. The tower assembly was mounted on one arm of a Toledo balance which had a direct reading scale: as shown in Figure 1. The scale range TTas 500 grams in I-gram divisions. Readings between divisions could he estimated to gram, while deflections from a fixed point could be noted for even smaller weighh. To connect the tower, Fvhich was mounted on the scale, t
