Prediction, trays

Robinson, C. S., and Gilliland, E. R., Elements of Fractional Distillation, McGraw-Hill, 1950, p. 348. Rice, V. L., Way to Predict Tray Temperatures, Hydr. Proc., August 1984, p. 83. 

The example reflects the prime difficulty often encountered by tray designers inconsistent predictions from different correlations. The three entrainment flood correlations used gave predictions that widely differed the differences were up to 50 to 60 percent- Another inconsistency was in the weep-dump prediction. These inconsistencias stem from the empiricism associated with prediction methods. Our understanding of tray hydrodynamics has still a very long way to go before it can provide us with models that reliably predict tray performance from first principles. 

A rigorous nonlinear dynamic model of the column is used on-line to predict compositions. The measured flowrates of the manipulated variables (reflux and heat input) are fed into the model. The differential equations describing the system are integrated to predict all compositions and tray temperatures. The predicted tray temperatures are compared with the actual measured tray temperatures, and the differences... 

The next step in predicting tray efficiency for design would be to take into account the effects of 1) tray and tower configuration and 2) hydraulic conditions on the tray. For the effects of the former, one can refer to a comprehensive treatise by W. K. Lewis, In this somewhat idealized study, the advantage of plug flow of liquid across the tray and its flow direction for the liquid on each tray is shown. Such an arrangement can produce Murphree tray efficiencies as high as 150% from a point efficiency of 80%. 

Equation 12.1.8 relates the entering and exiting vapor mole fractions through the overall number of transfer units. To predict tray performance, therefore, we need to estimate this quantity. A working relationship for may be obtained by combining Eq. 12.1.10 with Eq. 7.3.15 for to give... 

With a more mechanistic model for predicting tray point efficiency, Garcia and Fair showed a better fit to a large database than did the older Chan-Fair model. A parity plot for the Garcia-Fair work is given in Figure 12.64. The newer method is more complex, however, and requires a fairly elaborate computer program. 

A general, approximate, short-cut design procedure for adiabatic bubble tray absorbers has not been developed, although work has been done in the field of nonisothermal and multicomponent hydrocarbon absorbers. An analytical expression which will predict the recovery of each component provided the stripping factor, ie, the group is known for each component on each tray of the column has been developed (102). This requires knowledge... 

Rate of Mass Transfer in Bubble Plates. The Murphree vapor efficiency, much like the height of a transfer unit in packed absorbers, characterizes the rate of mass transfer in the equipment. The value of the efficiency depends on a large number of parameters not normally known, and its prediction is therefore difficult and involved. Correlations have led to widely used empirical relationships, which can be used for rough estimates (109,110). The most fundamental approach for tray efficiency estimation, however, summarizing intensive research on this topic, may be found in reference 111. 

A pseudo-convective heat-transfer operation is one in which the heating gas (generally air) is passed over a bed of solids. Its nse is almost exchisively limited to drying operations (see Sec. 12, tray and shelf dryers). The operation, sometimes termed direct, is more aldu to the coudnctive mechanism. For this operation, Tsao and Wheelock [Chem. Eng., 74(13), 201 (1967)] predict the heat-transfer coefficient when radiative and conductive effects are absent by... 

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. 

Tbe best-established theoretical method for predicting E is that of tbe AlCbE [Buhhle-Tray Design Manual, American Institute of Chemical Engineers, New York, 1958). It is based on tbe sequential prediction of point efficiency, Murpbree efficiency, and overall column efficiency ... 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

Tray efficiency 0 j is supposed to represent a measure of the deviation from equilibrium-stage mass transfer assuming backmixed trays. However, the estimate of tray efficiency requires accurate knowledge of the equihbrium vaporization constant. Any deviations between the actual equihbrium relation and that predicted by the database will be embodied in the tray efficiency estimate. It is a tender trap to accept tray efficiency as a true measure of the mass transfer hmitations when, in fact, it embodies the uncertainties in the database as well. 

Aside from the fundamentals, the principal compromise to the accuracy of extrapolations and interpolations is the interaction of the model parameters with the database parameters (e.g., tray efficiency and phase eqiiilibria). Compromises in the model development due to the uncertainties in the data base will manifest themselves when the model is used to describe other operating conditions. A model with these interactions may describe the operating conditions upon which it is based but be of little value at operating conditions or equipment constraints different from the foundation. Therefore, it is good practice to test any model predictions against measurements at other operating conditions. 

Considerable work on methods for pre-predicting fractionator tray efficiency continues to the present. Shortcut methods from the past differed rather widely.The... 

This suggests that caution must be exercised when establishing a tray efficiency for any type contacting device by (1) using actual test data if available for some similar system or (2) comparing several methods of predicting efficiency, and (3) possible use of a more conservative efficiency than calculated to avoid the possibility of ending up with a complete column with too few actual trays—a disastrous situation if not discovered prior to start-up operations. 

Ryan et. al. [185] examined the prediction of misting and bubbling in towers, tray and packed, and assessed the impact. 

Kister and Haas [184] recommend using 25 dynes/cm in Equation 8-286 when the actual surface tension is a 25 dynes/cm. This correlation is reported [94, 184] to give better effects of physical properties, and predicts most sieve and valve tray entrainment flood data to 15 to 20%, respectively. 

American Institute of Chemical Engineers, Bubble Tray Design Manual, Prediction of Fractionation Efficiency, Amer. Inst. Chem. Engrs. (1958). 

Fair, J. R, How to Predict Sieve Tray Entrainment and Flooding, Pelro/Chem Engr. SepL (1961), p. 45. 

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