Trays efficiencies

Stage efficiency concepts are applicable only to devices in which the phases are contacted and then separated, that is, when discrete stages can be identified. This is not the case for packed columns or other continuous-contact devices. For these, the efficiency is already embedded into the design equation. 

Tray efficiency is the fractional approach to an equilibrium stage which is attained by a real tray. Ultimately, we require a measure of approach to equilibrium of all the vapor and liquid from the tray, but since the conditions at various locations on the tray may differ, we begin by considering the local or point efficiency of mass transfer at a particular place on the tray surface. 

y ocal is the concentration in equilibrium with xlocal, and equation (4-48) then 

Consider that the gas rises at a rate GM mole/(area)(time). Let the interfacial surface between gas and liquid be a area/volume of liquid-gas froth. As the gas rises a differential height dh[t the area of contact is a dht per unit active area of the tray. If, while of concentration y, it undergoes a concentration change dy in this height, and if the total quantity of gas is assumed to remain essentially constant, the rate of solute transfer is GM dy  

A method to estimate the overall volumetric mass-transfer coefficient at any point over the tray, Kya, is needed in order to use equation (4-52). Alternatively, Bennett et al. (1997) proposed the following correlation for estimating sieve-tray point efficiency  

To minimize vapor channeling, valve trays are designed to exceed a minimum unit reference (50). A unit reference is the ratio of the vapor rate to the vapor rate at which all the valves are open (Sec. 6.3.2). A minimum unit reference of 40, 60, and 80 percent is recommended for one-, two-, and four-pass trays, respectively (50). If the unit reference falls below the minimum, selected valves can be blanked, valve density can be reduced, or the ratio of light to heavy valves can be varied (7,50). 

As vapor rate is lowered below the weep point, the fraction of liquid falling through the holes increases until a condition is reached where all liquid fed onto a tray weeps through the holes and none reaches the downcomer. This condition is referred to as dump point or seal point. 

Below the dump point (100 percent weep), tray efficiency is a small fraction of its normal value, and mass transfer is extremely poor. Since no liquid enters the downcomers, they lose the liquid seal that prevents vapor from rising through them. Operation below the dump point can be accompanied by severe hydraulic instability due to unsealing of downcomers, as was demonstrated by field experience (76). The startup stability diagram (1), which defines the range of vapor and liquid rates needed for satisfactory startup, has the dump point as the lower limit- The tendency of dumping increases when (77-79) 

The most extensive studies on dumping were reported by Prince and Chan (77-79). The Chan and Prince dump-point correlation (Fig. 6,20 was recommended by Chase (30), The author has also had favorable experience with the correlation under conditions widely different from those used in its derivation. Alternatively, the dump point can be predicted from a weep rate correlation by setting the weep rate equal to 100 percent of the liquid entering the tray. However, little has been reported by either Lockett and Banik (56) or Hsieh and McNulty 63 about the reliability of dump-point predictions from their correlation. 

The total pressure drop across a tray is the sum of the pressure drop across the disperser unit, hd (dry hole for sieve trays dry valve for valve trays), and the pressure drop through the aerated mass hh i.e., 

Actual stages depend upon the tray efficiency, which will probably be the weakest number in the design. Using operating data from a similar system is certainly best where possible. Tables 1 and 2 give some shortcut correlations. 

Ludwig discusses new work by the A.I.Ch.E. which has produced a method more detailed than the previous shortcut methods. He states that some of the shortcut methods can be off by 15-50% as indicated by the A.I.Ch.E. work. The spread of the Drickamer and Bradford correlation shown in the Ludwig plot is about 10 points of efficiency or 5 efficiency points around the curve. Ludwig states that comparisons between shortcut and A.I.Ch.E. values indicate that deviations for the shortcut methods are usually on the safe or low side. 

Maxwell s correlation was generated from hydrocarbon data only. Ludwig states that the Drickamer and Bradford correlation is good for hydrocarbons, chlorinated hydrocarbons, glycols, glycerine and related compounds, and some rich hydrocarbon absorbers and strippers. 

Viscosity Centipoises Gunness and Other Data Plotted Versus Reciprocal Viscosity in Maxweli. (Average viscosity of iiquid on the piates) Drickamer and Bradford Correlation Plotted in Ludwig. (Molal average viscosity of the feed) 

Ludwig also presents correlations of O Connell. He warns that O Connell may give high results, Ludwig suggests using the O Connell absorber correlation only in areas where it gives a lower efficiency than the fractionator correlation of Drickamer and Bradford or O Connell. 

FIGURE 5.8 Implementing Murphree tray efficiency on the Y Xdiagram. 

This curve is constructed based on the definition of the tray vapor efficiency by marking off vertical segments between the operating line and the equilibrium curve such that 

Once this curve is in place, the graphical construction of stages proceeds as before. 

Distillation trays in a fractionator operate between 10 and 90 percent efficiency. It is the process person s job to make trays operate as close to 90-percent efficiency as possible. Calculating tray efficiency is sometimes 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. 3.3 is 100 percent. The efficiency of the tray in Fig. 3.4 is 0 percent. 

How about the 10 trays shown in Fig. 3.5 Calculate their average efficiency (the answer is 10 percent). As the vapor temperature rising from the top tray equals the liquid temperature draining from the bottom tray, the 10 trays are behaving as a single perfect tray with 100-percent efficiency. But as there are 10 trays, each tray, on average, acts like one-tenth of a perfect tray. 

In this chapter, we discuss problems that contribute to tray deck flooding. 

Since efficiencies vary from one section to another, it is best (12) to apply Eq. (7.1) separately for each section (e.g., rectifying and stripping). In practice, efficiency data and prediction method are often too crude to give a good breakdown between the efficiencies of different sections, and Eq. (7.1) is applied over the entire column. 

Alternative definitions of tray efficiency are sometimes used. Lockett (12) reviewed the pros and cons of several efficiency definitions, He cited the industiy s experience that the more rigorous and theoretically correct a deiimtion is, the more difficult it is to use. For instance, the Sttuidart efficiencies are often considered the soundest fundamentally, but apparently have never been used for a design. For the design and operation engineer, the overall column (or section) efficiency is by far the most important. 

Flgur 7.1 Point and Murphree efficiencies, (o) Point Murphree, 

Murphree tray efficiency (120) is the same as point efficiency, except that it applies for file entire tray instead of to a single point (Fig. 7.1), 

If both liquid and vapor are perfectly mixed, liquid composition on the tray is uniform and so is vapor composition, The Murphree tr efficieno will then 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 xl, on the tray (Fig. 7.16). This frequently lowers y relative to y , thus enhancing tray efficiency lEcp (7.3)] compared to point efficiency, y may even drop belowy in thi case, exceeds 100 percent [Eq. (7,3)]. 

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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. 

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. 

The rate-based model gave a distillate with 0.023 mol % ethylbenzene and 0.0003 mol % styrene, and a bottoms product with essentially no methanol and 0.008 mol % toluene. Miirphree tray efficiencies for toluene, styrene, and ethylbenzene varied somewhat from tray to tray, but were confined mainly between 86 and 93 percent. Methanol tray efficiencies varied widely, mainly from 19 to 105 percent, with high values in the rectifying section and low values in the stripping section. Temperature differences between vapor and liquid phases leaving a tray were not larger than 5 F. 

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. 

Design data for separation of the particular or similar mixture in a packea column are not available. Design procedures are better estabhshed for tray-type columns than for packed columns. This is particularly so with respect to separation efficiency since tray efficiency can be estimated more accurately than packed height equivalent to a theoretical stage (HETP). 

Computation of Tower Height The required height of a gas-absorption or stripping tower depends on (1) the phase equilibria involved, (2) the specified degree of removal of the solute from the gas, and (3) the mass-transfer efficiency of the apparatus. These same considerations apply both to plate towers and to packed towers. Items 1 and 2 dictate the required number of theoretic stages (plate tower) or transfer units (packed tower). Item 3 is derived from the tray efficiency and spacing (plate tower) or from the height of one transfer unit (packed tower). Solute-removal specifications normally are derived from economic considerations. 

Tray Efficiencies in Plate Absorbers and Strippers Compn-tations of the nnmber of theoretical plates N assnme that the hqnia on each plate is completely mixed and that the vapor leaving the plate is in eqnihbrinm with the liqnid. In actnal practice a condition of complete eqnihbrinm cannot exist since interphase mass transfer reqnires a finite driving-force difference. This leads to the definition of an overall plate efficiency... 

AiCbE Researcb Committee, Tray Efficiency in Distillation Columns, final report. University of Delaware, Newark, 1958. 

In distillation towers, entrainment lowers the tray efficiency, and 1 pound of entrainment per 10 pounds of liquid is sometimes taken as the hmit for acceptable performance. However, the impact of entrainment on distiUation efficiency depends on the relative volatility of the component being considered. Entrainment has a minor impact on close separations when the difference between vapor and liquid concentration is smaU, but this factor can be dominant for systems where the liquid concentration is much higher than the vapor in equilibrium with it (i.e., when a component of the liquid has a very lowvolatiUty, as in an absorber). 

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. 

Defining tray efficiency as the difference between the actual and the equilibrium vaporization, the efficiency is ... 

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. 

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. 

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. 

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. 

For high values of a, low tray efficiency usually results. 

Presaturators. A presaturator to provide lean oil/gas contact prior to feeding the lean oil into the tower can be a good way of getting more out of an older tower. Absorber tray efficiencies ran notoriously low. A presaturator that achieves equilibrium can provide the equivalent of a theoretical tray. This can easily equal 3-4 actual trays. Some modem canned computer distillation/absorp-tion programs provide a presaturator option. 

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

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. 

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

Tray efficiency —70% is usually conservative (it is usually a good idea to put a few extra trays—say 10% extra)... 

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