Tray efficiency examples

Kremser-Brown-Sherwood Method — No Heat of Absorption, 108 Absorption — Determine Component Absorption in Fixed Tray Tower, 108 Absorption — Determine Number of Trays for Specified Product Absorption, 109 Stripping — Determine Theoretical Trays and Stripping or Gas Rate for a Component Recovery, 110 Stripping — Determine Stripping-Medium Rate for Fixed Recovery, 111 Absorption — Edmlster Method, 112 Example 8-33 Absorption of Hydrocarbons with Lean Oil, 114 Inter-cooling for Absorbers, 116 Absorption and Stripping Efficiency, 118 Example 8-34 Determine Number of Trays for Specified Product Absorption, 118 Example 8-35 Determine Component Absorption in Fixed-Tray Tower, 119 Nomenclature for Part 2, 121... 

Determine the effects of tray hydraulics on the efficiency. Tray hydraulics will affect efficiency adversely only if submergence, hole size, open tray area, and weir configuration are outside the recommended limits outlined in the previous example. Since that is not the case, no adverse effects need be expected. 

In practice the tray efficiency is estimated from a model that combines information about the tray hydrodynamics, with a model for the point efficiency that is defined analogously to the tray efficiency but applied to a narrow vertical slice of the froth (see Fig. 12.1). The Murphree vapor-phase point efficiency, for example, is defined by... 

Fractional equihbrium stages have meaning. The 11.4 will be divided by a tray efficiency, and the rounding to an integral number of actual trays should be done after that division. For example, if the average tray efficiency for the process being modeled in Fig. 13-36 were 80 percent, then the number of actual trays required would be 11.4/0.8 = 14.3, which would be rounded to 15. 

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. 

Example 12 Estimation of Plate Efficiency For the conditions of Examples 9 and 11, estimate the point efficiency of the tray. Additional property data ... 

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 is one example of the first interaction. Figure 30-6 is a representation of a distillation tray. 

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. 

Better examples of shortcut design methods developed from property data are fractionator tray efficiency, from viscosity " and the Clausius-Clapeyron equation which is useful for approximating vapor pressure at a given temperature if the vapor pressure at a different temperature is known. The reference states that all vapor pressure equations can be traced back to this one. 

Example 8-13 Estimating Distillation Tray Efficiency by Equations 8-7OA and 8-7OB (used by permission of McFarland et al. [86])... 

Tray efficiency is calculated as previously demonstrated and will not be repeated, except that normally stripping tray efficiencies run lower than rectification efficiencies. For ammonia-water stripping such as this example most over-all efficiencies run 50-60%. 

Example 8-42 Mass Transfer Efficiency Calculation for Baffle Tray Column (used by permission [211])... 

Kunesh [126] presents tm overview of the basis for selecting rsuidom packing for a column application. In first deciding between a trayed tower or a packed one, a comparative performance design and its mechanical interpretation should be completed, considering pressure drop, capacity limitations, performance efficiencies (HETP), material/heat balances for each alternate. For one example relating to differences in liquid distribution performance, see Reference 126. 

As the potentialities of liquid extraction as a separation method were developed, the need for efficient, continuously operated, multistage equipment became apparent. It was natural therefore to turn to devices which had been so successful in other similar fluid-contacting operations, such as the bubble-tray tower and the packed tower of distillation. These devices have proved to be disappointing in liquid-extraction service, however for example, bubble-tray towers provide tray efficiencies in liquid-extraction operations of less than 5% (S7), and conventional packed towers show heights of transfer units of 10 to 20 ft. or more (T3). 

HETP is another quantity that is used to express the efficiency of a device for carrying out a separation, particularly in which mass is transferred by a stage-wise action rather than a differential contact. For example, in a tray column, the HETP value is the tray spacing divided by the fractional overall tray efficiency. 

As might be expected, the vapour phase may offer the controlling resistance to mass transfer in high pressure distillations. Values for tray efficiencies at elevated pressure are scarce [23, 24]. The prediction of tray efficiency may be approached in several ways. One way is to utilize field performance data taken for the same system in very similar equipment. Unfortunately such data are seldom available. When they are available, and can be judged as accurate and representative, they should be used as a basis for efficiency specification [25], Another way is to utilize laboratory-or pilot-plant efficiency data. For example a small laboratory-Oldershaw tray-column can be used with the same system. Of course, the results must be corrected for vapour-and liquid mixing effects to obtain overall tray efficiencies for large-scale design [26], Another approach is the use of empirical or fundamental mass-transfer models [27-30],... 

A notable feature of high-pressure distillation is the high efficiency that is usually obtained on trays. Figures close to 100% are not uncommon. However, the efficiency of trayed columns has been shown to increase only from atmospheric pressure up to a pressure of 11.5 bar. At higher operating pressures, the efficiency of the trays decreases with increasing pressure. There is an entrainment of vapour in the liquid phase which is carried back down the column. For example, for a C4-hydrocarbon separation the tray efficiency will be reduced by 16% as the pressure is raised from 11.5 bar to 27.6 bar. 

Distillation trays in a fractionator operate between 10 and 90 percent efficiency. It is the process person s job to make them operate as close to 90 percent efficiency as possible. Calculating tray efficiency is simple. Compare the vapor temperature leaving a tray to the liquid temperature leaving the trays. For example, the efficiency of the tray shown in Fig. 1.2 is 100 percent. The efficiency of the tray in Fig. 1.3 is 0 percent. 

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 narrow-trough vapor distributor shown in Fig. 7.4 is intended to disperse the vapor evenly across the bottom of the packed bed. The width of the chimney does not exceed 6 in. The older-style chimney trays, which may have had a few large round or square chimneys, reduced the separation efficiency of the packing. To work properly, the vapor distributor has to have a reasonable pressure drop, in comparison to the pressure drop of the packed bed. For example, if the expected pressure drop of a 12-ft packed bed is 10 in of liquid, the pressure drop of the vapor distributor ought to be about 3 to 4 in of liquid. 

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. 

A factor that is of concern with bubblecap trays is the development of a liquid gradient from inlet to outlet which results in corresponding variation in vapor flow across the cross section and usually to degradation of the efficiency. With other kinds of trays this effect rarely is serious. Data and procedures for analysis of this behavior are summarized by Bolles (in Smith, 1963, Chap. 14). There also are formulas and a numerical example of the design of all features of bubblecap trays. Although, as mentioned, new installations of such trays are infrequent, many older ones still are in operation and may need to be studied for changed conditions. 

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