Experimental study of flow pattern and liquid velocity distribution by the tracer technique in a two-meter diameter single pass sieve half-tray using air-water system reveals that there exist highly non-ideal flowing behavior. Typical residence-time distribution curves covering the whole tray deck are presented

from which four flow regions can be observed

a main channelling region of non-uniform flow

a sideway region of accompanied subsidiary flow

a small region of backward flow and a complete mixing region next to the inlet weir. The tray models available in the present literature seem incapable to simulate all these complicated hydrodynamic phenomena in a large tray. An eddy diffusion model with consideration of non-uniform liquid velocity field has been developed from the basic partial differential equation of mass transfer by introducing a velocity distribution function j. Since the experimental liquid velocity profile follows approximately the exponential rule

function j can be taken in similar form with two experimentally determined constants which are dependent on the flowing condition. The non-linear partial differential equation is solved by the method of finite element. For this purpose

the equation should be transformed into elliptic form by mullipying an integrating factor (B) which is equal to exp[PejZ] where Pe is Peclet number and Z is dimensionless flow length. A computer program is designed according to this method to predict numerically the concentration profiles in the whole tray deck as well as the Murphree tray efficiencies under various operating conditions. Typical computed results are presented and discussed.