Tray efficiency computer modeling

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

Based on an average tray efficiency of 90 percent for the hydrocarbons, the eqiiilibniim-based model calculations were made with 36 equilibrium stages. The results for the distillate and bottoms compositions, which were very close to those computed by the rate-based method, were a distillate with 0.018 mol % ethylbenzene and less than 0.0006 mol % styrene, and a bottoms product with only a trace of methanol and 0.006 mol % toluene. 

In general, distillation columns should be operated at a low pressure. For example, Fig. 3.3 shows an isobutane-normal butane stripper. This fractionator is performing poorly. A computer simulation of the column has been built. The column has 50 actual trays. But in order to force the computer model to match existing operating parameters (reflux rate, product compositions), 10 theoretical separation stages (i.e., 10 trays, each 100 percent efficient) must be used in the model. This means that the trays are developing an actual tray efficiency of only 20 percent. 

A detailed model of the pilot-plant MVC was derived and validated against experimental data in a previous study (Barolo et al., 1998 and also see Chapter 4). The model consists of material and energy balances, vapour liquid equilibrium on trays (with Murphree tray efficiency to account for tray nonideal behaviour), liquid hydraulics based on the real tray geometry, reflux subcooling, heat losses, and control-law calculations based on volumetric flows. The model provides a very accurate representation of the real process behaviour, but is computationally expensive for direct use within an optimisation routine. Greaves et al. (2003) used this model as a substitute of the process. 

It is worth pointing out that the composition of the vapor above the froth can be calculated without computing the component efficiencies. As noted later, the use of component efficiencies may well be the cause of convergence difficulties that have been encountered when using these multicomponent tray efficiency models in column simulations. ... 

I rechecked my computer model for the tower. With an assumed 80 percent tray efficiency, which is normal for this service at the observed reflux ratio, a 1 percent butane in the gasoline would be expected. To force my computer model to match the observed 4 percent... 

When you set up a computer model for any distillation process, you must select a tray efficiency. Tray efficiencies (for mechanically intact trays) vary from 30 to 90 percent. Experience is the only guide in making the least wrong selection. 

I had arbitrarily manipulated tray efficiency and relative volatility to force my computer model to match the observed plant data. It might seem that by arbitrarily selecting both the relative volatility and tray efficiency for my computer model, my calculations would be little better than a guess. 

The design of absorbers (and strippers) typically involves a computer-assisted, Iray-by-tray. heat- and material-balance calculation to determine the required number of equilibrium stages, which arc then related to the required number of actual trays by an estimated tray efficiency. More recently, a non-equilibrium stage model has been developed for computer application which considers actual trays (or sections of packing) and performs a heat and material balance for each phase on each actual tray, based on mass and heat transfer rates on that tray. 

In order for a process to be controllable by machine, it must represented by a mathematical model. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as well as the parameters of sensing devices, control valves, and control instruments. The process as a whole then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process models then the computer can be made to optimize the operation continually. 

Downcomer mixing. The AIChE model assumes that liquid along the downcomer length is perfectly mixed. A recent study using a tracer injection technique (174) showed that in large trays, the downcomer liquid is unmixed. A computational analysis (174) showed that efficiency reduction due to an unmixed downcomer is relatively small, but will intensify in the presence of liquid stagnant regions on the tray. 

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