The nonuniform distribution of vapor across a distillation plate causes a reduction in the Murphree plate efficiency. The magnitude of the reduction has been evaluated and the maximum effect occurs when the liquid mixing is intermediate between the perfectly mixed and the plug flow cases.The AlChE bubble-tray design manual ( 1 ) provides a method for calculating the Murphree plate efficiency (EMv) for binary systems for uniform vapor distribution across the plate. One of the causes given for the predicted efficiency bein below the measured value is a poor vapor liquid gradients, poor inlet arrangements and weir location. The numerous studies on the hydraulic gradient (2 to 6) all stress the reduction in vapor velocity through the plate near the liquid downcomer and higher vapor velocities near the discharge weir.A simple vapor distribution function such as a linear function agrees well with Bolles calculations (2). Let u be a dimensionless vapor mass flow rate defined by distribution. T a is can arise from a poor tray design, high where z is the distance to a int on the plate and Z is the total length of the plate E nwhere b = BZ/2Va, where 0 < b < 1 and B is the vapor velocity gradient across the plate. The value of b is restricted to the range 0 to 1 which allows for positive values of u throughout the plate, and a minimum positive velocity gradient of zero when the vapor is uniformly distributed.
MURPHREE PLATE EFFICIENCYThe Murphree plate efficiency is defined by where yav is the average vapor composition leaving the plate, y n + l is the vapor composition entering the plate, yon is the vapor composition in equilibrium with the liquid leaving the plate. The average vapor composition leaving the plate is given Substituting from Equations (1) and (2) Substituting yav from Equation ( EOG For a uniform vapor distribution b = 0 then u = 1 and which is in agreement with (7). To evaluate the integral in Equation (10) the dimensionless composition distribntion must be known, and this will depend on the degree of liquid mixing on the plate.
EDDY DIFFUSION M O D E LThe liquid mixing by an eddy dispersion model which assumes that the rate of back mixing is proportional to the concentration gradient on the plate is described in the manual (1 ) . A mass balance for the more volatile comonent over a vertical element of width dz has been given ! o r constant plate width and constant point efficiency by