Efficiency, tray compositions

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. 

Analysts must recognize the above sensitivity when identifying which measurements are required. For example, atypical use of plant data is to estimate the tray efficiency or HTU of a distillation tower. Certain tray compositions are more important than others in providing an estimate of the efficiency. Unfortunately, sensor placement or sample port location are usually not optimal and, consequently, available measurements are, all too often, of less than optimal use. Uncertainty in the resultant model is not minimized. 

This overall flow pattern in a distillation column provides countercurrent contacting of vapor and hquid streams on all the trays through the column. Vapor and liquid phases on a given tray approach thermal, pressure, and composition equilibriums to an extent dependent upon the efficiency of the contac ting tray. 

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. 

After actual theoretical trays are determined (see Actual reflux and theoretical stages) one needs to estimate the actual physical number of trays required in the distillation column. This is usually done by dividing the actual theoretical trays by the overall average fractional tray efficiency. Then a few extra trays are normally added for offload conditions, such as a change in feed composition. 

The HETP (Height Equivalent to a Theoretical Plate (stage or plate)) is the tray spacing divided by the fractional overall tray efficiency [82]. The transfer unit concept has been useful for generalized correlations [89]. Because packed towers operate with continuously changing compositions through the packed height, the concept... 

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. 

The tray temperatures in our preflash tower, shown in Fig. 4.4, drop as the gas flows up the tower. Most of the reduced sensible-heat content of the flowing gas is converted to latent heat of evaporation of the downflowing reflux. This means that the liquid flow, or internal reflux rate, decreases as the liquid flows down the column. The greater the temperature drop per tray, the greater the evaporation of internal reflux. It is not unusual for 80 to 90 percent of the reflux to evaporate between the top and bottom trays in the absorption section of many towers. We say that the lower trays, in the absorption section of such a tower, are drying out. The separation efficiency of trays operating with extremely low liquid flows over their weirs will be very low. This problem is commonly encountered for towers with low reflux ratios, and a multicomponent overhead product composition. 

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. 

If both liquid and vapor are perfectly mixed, liquid and vapor compositions on the tray are uniform, and the Murphree tray efficiency will coincide with the point efficiency at any point on the tray. In practice, a concentration gradient exists in the liquid, and x at the tray outlet is lower than x on the tray (see Fig. 14-40b). This frequently lowers y relative to t/ , thus enhancing tray efficiency [Eq. (14-134)] compared with point efficiency. The value of y may even drop below yn. In this case, Emv exceeds 100 percent [Eq. (14-134)]. 

Generally, trays work better in applications requiring high flows, because plate efficiencies increase with increased vapor velocities, and therefore increase the influence of the reflux to feed ratio on overhead composition. Column dynamics is a function of the number of trays, because the liquid on each tray must overflow its weir and work its way down the column. Therefore, a change in composition will not be seen at the bottoms of the tower until some time has passed. 

Three parameters were identified and adjusted to validate the model against the experiments. The parameters are the heat losses, the nominal tray holdup and the Murphree tray efficiency (EM). Figure 4.16 shows how EM is adjusted to match the dynamic model prediction and experimental temperature profile measured on Plate 12. Figure 4.17 shows the comparison between the experimental and model prediction of ethanol composition in the reflux drum, middle vessel and in the bottom of the column. Figures 4.16-17 show a good match between the model prediction and experiments. 

A stagnant film model is used for two-phase boundaries (1-2), which in effect, isolates the mass transfer process to a thin region at the interface stagnant film. Once the expressions for entropy production in terms of pressure, temperature, and composition are available a transformation is made to process variables such as reflux ratio, column height, packing or tray geometry, column diameter and column efficiency. Results of this design optimization model are compared with the results obtained via traditional methods. 

In plant or pilot tests, separation data are analyzed by computer simulation that reproduces test conditions. The number of theoretical stages in the simulation is varied until the simulated product compositions and temperature profile match those measured. Tray efficiency is determined from the number of stages that give a good match to test data. 

In the above procedure, errors in VLE are compensated by equivalent errors in tray efficiency. If the relative volatility calculated by the simulation is too high, fewer stages will be needed to match the measured test compositions, i.e., efficiency will be lower. Scaleup will be good as long as the VLE and efficiency errors continue to equally offset each other. This requires that process conditions (feed composition,... 

---