Mass transfer during gas absorption in a vertical gas-liquid slug flow with small bubbles in liquid plugs T. Elperin, A. Fominykh Abstract A model is developed for the analysis of mass transfer during isothermal absorption in a vertical gas- liquid slug ¯ow at large Reynolds numbers with liquid plugs containing small bubbles. Simple formulas for mass ¯ux from the N -th unit cell of gas-liquid slug ¯ow and for total mass ¯ux from N unit cells are derived. In the lim- iting case the derived formulas for mass transfer during gas absorption in a slug ¯ow with liquid plugs containing small bubbles recover the derived expressions for mass transfer in slug ¯ow without small bubbles in the liquid plugs. Using the developed model recommendations con- cerning the design of the absorber operating in a slug ¯ow regime are suggested. List of symbols A cross section area of a channel, m 2 c concentration of a soluble gas, kg m 3 D coef®cient of molecular diffusion in a liquid phase, m 2 s 1 D g coef®cient of molecular diffusion in a gaseous phase, m 2 s 1 d diameter of channel, m d b diameter of spherical bubble, m g acceleration of gravity, m s 2 k number of spherical bubbles in a liquid plug L ` length of a liquid plug, m L g length of a Taylor bubble, m L c length of a unit cell in gas-liquid slug ¯ow, m N number of unit cells N ` dimensionless number Q c mass ¯ux, kg s 1 Q cN mass ¯ux from the N-th cell, kg s 1 Q cRN total mass ¯ux from N cells, kg s 1 Q cRN0 total mass ¯ux from N cells, free from small gas bubbles, kg s 1 Q ` liquid volumetric ¯ow rate, m 3 s 1 Q g gas volumetric ¯ow rate, m 3 s 1 S surface area of a slug, m 2 S b surface area of a spherical bubble, m 2 U 1 velocity of a gas slug rising in a stagnant ¯uid, m s 1 y; z coordinates, m Greek symbols b coef®cient of mass transfer for gas slug, m s 1 b b coef®cient of mass transfer for a spherical bubble, ms 1 u void fraction r surface tension, N m 1 m ` kinematics viscosity of ¯uid, m 2 s 1 Subscripts ` liquid g gas 1 value at in®nity 0 value at inlet s value at interface 1 Introduction A number of studies deal with experimental and theoret- ical investigations of mass transfer during gas absorption by water from a single slug and in a gas-liquid slug ¯ow. The importance of the problem stems from the wide use of absorption technologies in chemical engineering, gas mixtures separation, industrial gas cleaning. Investigation of diffusion-controlled mass transfer from slugs is relevant not only to gas-liquid systems in a slug ¯ow regime but also to ¯uidization (see, e.g. Guedes de Carvalho and Da- vidson [1] and Guedes de Carvalho et al. [2]). In the ®rst studies on mass transfer from a single short slug (Agnew and Becker [3±4]) the rates of absorption of nitrogen and oxygen by water were measured. Later absorption of car- bon dioxide from a single slug rising in a tube ®lled with water was measured by van Heuven and Beek [5]. Filla [6], Nakoryakov et al. [7] and Petukhov and Fominykh [8] measured mass transfer coef®cient for the stationary slugs of carbon dioxide in descending water ¯ow. Later Niranjan et al. [9] used a tube inversion technique for slug gener- ation and measured mass transfer coef®cients for a pure carbon dioxide slug rising in Newtonian and non-New- tonian liquids. A tube inversion technique for measure- ment of liquid-phase mass transfer coef®cient from a gas slug in inclined tubes was used by Nigam et al. [10]. Sena Esteves and Guedes de Carvalho [11] measured mass transfer coef®cients during absorption of carbon dioxide by water for long slugs with values L g =d up to 38. Heat and Mass Transfer 33 (1998) 489±494 Ó Springer-Verlag 1998 489 Received on 28 July 1997 T. Elperin A. Fominykh Pearlstone Center for Aeronautical Engineering, Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel Correspondence to: T. Elperin