Calculating Tray Efficiency

The mathematical model developed to describe the nitric acid absorption process isdiscussed in detail in Section G.2. It uses a tray-by-tray approach that incorporates reaction-mass balance corrections and heat balance calculations. Tray efficiency calculations are also included in the model, the efficiency being a function of the tray geometry and gas velocity. Rate equations and other data specific to the nitric acid/nitrous gas system are applied. 

Data specific to tray type must be established next, but these inputs will be discussed later. The data inputted for the next six prompts are the same for all tray types and are primarily for tray efficiency calculations. If tray efficiency or tray liquid residence time values are not desired, these inputs may be skipped (i.e., remain as zero values). However, for bubble cap and sieve trays, the SURF TENS DYN/CM prompt is for active area tray flood calculation. This value should therefore be inputted. 

Step 1. The first step in the procedure is to determine the key component equilibrium curve slope M. This is for one component only. You must choose a light key and a heavy key component for this tray efficiency calculation. Select components that are keys in the fractionator split. A single K = Y/X equilibrium value is to be applied to absorbers and strippers as this M value. The change of Y per the change of X is sought out for the light key component. 

In another study, Grayson examined the effect of K-values on bubble-point, dew-point, equilibrium flash, distillation, and tray efficiency calculations. He noted a wide range of sensitivity of design calculations to variations in K-values. 

Tray inspection after installation or during a unit turnaroimd is a lot more important than the selection of the best tray efficiency calculation model. 

CO2 Tray Efficiencies Calculated by AMSIM Simulation Program for Ttiree Amine Solutions... 

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. 

Rigorous calculation results combined with plant data can be used to back calculate column tray efficiencies for... 

Distillation design is based on the theoretical consideration that heat and mass transfer from stage to stage (theoretical) are in equilibrium [225-229]. Actual columns with actual trays are designed by establishing column tray efficiencies, and applying these to the theoretical trays or stages determined by the calculation methods to be presented in later sections. 

This applies to any pair of components. My experience suggests adding +1 theoretical tray for the reboiler, thus making the total theoretical trays perhaps a bit conservative. But, they must be included when converting to actual trays using the selected or calculated tray efficiency ... 

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. 

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%. 

Calculate fraction absorbed for each component, assuming a fixed overall tray efficiency for an... 

Many designs are set up by assuming the number of theoretical trays, using best available information for tray efficiencies and then calculating the expected performance. A series of such studies might be made. 

Calculate tray efficiency for C3H4. Using O Connell s correlation ... 

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

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. 

The calculations made thus far are of theoretical trays, that is, trays on which vapor-liquid equilibrium is attained for all components. Actual tray efficiencies vary widely with the kind of system, the flow rates, and the tray construction. The range can be from less than 10% to more than 100% and constitutes perhaps the greatest uncertainty in the design of distillation equipment. For hydrocarbon fractionation a commonly used efficiency is about 60%. Section 13.14 discusses this topic more fully. 

Overall column efficiency can be calculated from the Murphree tray efficiency by using the relationship developed by Lewis [Ind. Eng. Chem. 28, 399 (1936)]. 

The dry Murphree efficiency calculated thus far takes into account the vapor and liquid resistances and the vapor-liquid contact patterns, but is uncorrected for the effects of entrainment and weeping. This correction converts the dry efficiency to a "wet or actual Murphree tray efficiency. Colburn [Eq. (14-98), under "Entrainment ] incorporated the effect of entrainment on efficiency, assuming perfect mixing of liquid on the tray. 

Most efficiency data reported in the literature are obtained at total reflux, and there are no indirect VLE effects. For measurements at finite reflux ratios, the indirect effects below compound the direct effect of Fig. 14-42. Consider a case where apparent < OW and test data at a finite reflux are analyzed to calculate tray efficiency. Due to the volatility difference Rmin.apparent > hmin,tme- Since the test was conducted at a fixed reflux flow rate, (R/Rmia)appaieot < (R/RmiIJtme- A calculation based on the apparent R/Rmin will give more theoretical stages than a calculation based on the true R/Rmin. This means a higher apparent efficiency than the true value. 

Stage 6 The number of moles of nitric acid formed as the gas passes through the liquid mixture on the plate is calculated. This calculation includes a term that effectively describes the tray efficiency. The moles of acid formed are given by ... 

Select the method of calculation for tray efficiency. Two methods are presented the O Connell method and the two-film method. In the programs accompanying this book, you may select the O Connell method by entering either an F for fractionator or an A for absorbers. In 1946, O Connell [4] published curves on log-log plots showing both absorber and fractionator efficiencies vs. equilibrium-viscosity-density factored equations. Separate curves for absorbers and fractionators were given. Such data have been curve-fit using a modified least-squares method in conjunction with a log scale setup. The fit is found to be reasonably close to the O Connell published curves. 

Campbell s series [5] states that many authors recommend, as do I, the O Connell method for hydrocarbons. You may select the two-film method by entering T. The Fractionation Research Institute (FRI) has for more than 30 years used and proven a much more thorough method called the two-film method, which is equally applicable to both fractionators and absorbers [6], The FRI method accounts for the actual tray internal configuration and fluid dynamics, making it far superior to the O Connell method. I have therefore produced a type of two-film method for determining tray efficiency that has been checked to be within 3% accuracy of hundreds of answers calculated with the FRI method. Called the Erwin two-film method, it is recommended for all types of trays and will also calculate the liquid tray residence time in seconds. This method is included in the three tray computer program executable files in the CD accompanying this book. 

Input the liquid viscosity in centipoise. The liquid here is that on the subject tray. This is an important factor in determining tray efficiency. The value should be entered accurately and derived from reliable data sources, such as a reliable computer program for tray-to-tray fractionation calculations. Values greater than the normal range may occur, causing lower tray efficiencies. 

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. 

St is calculated by any of the methods in Chaps. 2 to 6- Once the tray efficiency is known, the number of actual trays can be obtained from... 

Rigorous testing of a plant column is generally the most reliable method of obtaining tray efficiency. Test procedures are outside the scope of this book and are addressed in a companion book(l) and elsewhere (130). Alternative methods of obtaining tray efficiency are calculation and scaleup (or scale-down). Calculation is addressed in this section scaleup in Sec. 7.3. 

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