Tray efficiency point

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. 

As vapor rates decrease, the tray activity also decreases. There eventually comes a point at which some of the active devices (valves or bubble caps) become inactive. Liquid passing these inactive devices gets very little contact with vapor. At very low vapor rates, the vapor activity will concentrate only in certain sections of the tray (or, in the limit, one bubble cap or one valve). At this point, it is possible that liquid may flow across the entire active area without ever contacting a significant amount ot vapor. This will result in very low tray efficiencies for a distillation process. Nothing can be done with a bubble cap tray to compensate for this. 

Murphree [85] developed point and overall distillation tray efficiencies, which are examined in detail in Reference 2. The expressions are [59] ... 

Biddulph [90] emphasizes the importance of using point efficiencies rather than tray efficiencies or overall column efficiencies, due to the wide fluctuations that often exist. 

Sakata [180] evaluates the degree of mixing of the liquid as it flows across a tray and its effect on the tray efficiency, Figure 8-30. For plug flow the liquid flows across the tray with no mixing, while for partial or spot mixing as it flow s over the tray, an improved tray efficiency can be expected. For a completely mixed tray liquid, the point efficiency for a small element of the tray, Eog> tray efficiency, E V, are equal. 

Mols of distillate or overhead product, lb mols/hr or batch distillation, mols Mols component, i, in distillate Vaporization efficiency of steam distillation Overall column efficiency Overall tray efficiency Eqg = Murphree point efficiency, fraction Murphree plate/tray efficiency, = E ... 

Figure 8-137 is used for estimating the entrainment-flood point. Liquid particle entrainment is generally considered as reducing tray efficiency (performance). 

Tray efficiency is as high as for bubble caps and almost as high as sieve trays. It is higher than bubble caps in some systems. Performance indicates a close similarity to sieve trays, since the mechanism of bubble formation is almost identical. The real point of concern is that the efficiency falls off quickly as the flow rate of vapor through the holes is reduced close to the minimum values represented by the dump point, or point of plate initial activation. Efficiency increases as the tray spacing increases for a given throughput. 

Higher efficiencies are obtained for operating conditions within 85-95% of the tray flood point. 

This analysis refers to a small area for vertical flow, and Emv is therefore the point or local Murphree efficiency. The relation between this point efficiency and the tray efficiency depends on the nature of the liquid mixing on the tray. If there is complete mixing of the liquid, x = xn for the liquid, and ye and y will also be constant over a horizontal plane. The tray efficiency EMv = Emv. With no mixing of the liquid, the liquid may be considered to be in plug flow. If ye = mx + b and Emv is taken as constant over tray, it may be shown" 91 that ... 

M.J. Lockett and I.S. Ahmed, Tray and point efficiencies from a 0.6 meter diameter distillation column, Chem. Engng. Res. Des., 61 (1983) 110-118. 

It is a characteristic of process equipment, that the best operation is reached, at neither a very high nor a very low loading. The intermediate equipment load that results in the most efficient operation is called the the best efficiency point. For distillation trays, the incipient flood point corresponds to the best efficiency point. We have correlated this best efficiency point, for valve and sieve trays, as compared to the measured pressure drops in many chemical plant and refinery distillation towers. We have derived the following formula ... 

K = 0.18 to 0.25 tray operation close to its best efficiency point K = 0.35 to 0.40 tray suffering from entrainment—increase in reflux rate, noticeably reduces tray efficiency K = >0.5 tray is in fully developed flood—opening a vent on the overhead vapor line will blow out liquid, with the vapor K = 0.10 to 0.12 tray deck is suffering from low tray efficiency, due to tray deck leaking... 

For a tray to function reasonably close to its best efficiency point, the dry tray pressure drop must be roughly equal ( 50 percent) to the hydraulic tray pressure drop ... 

Figure 3.5 illustrates this relationship. Point A is the incipient flood point. In this case, the incipient flood point is defined as that operating pressure that maximizes the temperature difference across the tower at a particular reflux rate. How, then, do we select the optimum tower pressure, to obtain the best efficiency point for the trays Answer—look at the temperature profile across the column. 

Dumping As gas velocity is lowered below the weep point, the fraction of liquid weeping increases until all the liquid fed to the tray weeps through the holes and none reaches the downcomer. This is the dump point, or the seal point. The dump point is well below the range of acceptable operation of distillation trays. Below the dump point, tray efficiency is slashed, and mass transfer is extremely poor. Operation below the dump point can be accompanied by severe hydraulic instability due to unsealing of downcomers. 

Murphree Tray Efficiency [Ind. Eng. Chem. 17, 747 (1925)] This is the same as point efficiency, except that it applies to the entire tray instead of to a single point (Fig. 14-40b) ... 

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)]. 

Lewis (loc. cit.) was the first to derive quantitative relationships between the Murphree and the point efficiency. He derived three mixing cases, assuming plug flow of liquid in all. The Lewis cases give the maximum achievable tray efficiency. In practice, efficiency is lower due to liquid and vapor nonuniformities and liquid mixing. 

Example 12 Estimating Tray Efficiency For the column in Example 9, estimate the tray efficiency, given that at the relative volatility near the feed point is 1.3 and the viscosity is 0.25 cP. 

Enter an alpha value if you have chosen F or T for the method. Enter a K value for a light key component if you chose A. Input the factor alpha or K. Alpha is defined as simply the light key K divided by the heavy key K component. The K factor is simply the particular component s vapor phase mole fraction divided by its liquid mole fraction. The alpha value is therefore a ratio of the chosen two key components. These key components should be those that readily point to how well the fractionator is doing its job of separation. For example, for a depropanizer tower, choose propane as the light key component and butane as the heavy key, since you wish to separate the propane from the butane to make a propane product specification. For a multicomponent system, you may try several components to determine a controlling alpha and/or to factor an average tray efficiency. 

Equation (3.48) is known as point efficiency, having been given in a number of publications, one notable one being Distillation Principles and Design Procedures [7]. Equation (3.48) is the two-film method of predicting the ETF tray one-point efficiency, and refers to a small element of a tray that must be converted to a Murphree efficiency (Eq. 3.47) [8],... 

Above the weep point, W = 0 and fw = 0. At the dump point (Sec. 6.2.14], all liquid weeps from the tray, and fw 1.0. It was stated (50,70) that when weeping across the tray is uniform, the decrease in tray efficiency is usually considered acceptable with a weep fraction of up to 0.1. 

Figure 7.3 shows the sequence of steps converting phase resistances into a tray efficiency. Gas and liquid film resistances are added to give the point efficiency (Sec. 7.1,2), Had both vapor and liquid on the tray been perfectly mixed, the Murphree tray efficiency would have equaled the point efficiency (see Sec. 7,1.1). Since the phases are not perfectly mixed, a model of the vapor- and liquid-mixing patterns is... 

In order to convert point efficiencies to Murphree tray efficiencies, the Chan and Fair correlation uses the same general mixing model as the AIChE model (125). This model uses Lewis case 1 (Sec. 7.1.3), i.e., mixed vapor and plug flow of liquid. In addition, some liquid back-mixing is assumed and correlated via an eddy diffusion coefficient. The model gives... 

Using the slopes of the equilibrium curve obtained in (4) above, and the appropriate mixing model, convert point to Murphree tray efficiencies. 

The calculated point efficiency must be converted to overall column efficiency, which will lower its value and make it closer to the O Connell prediction. The calculated value of Eog is slightly higher than obtained experimentally (Eog = 0.83-0.92) at the University of Delaware for bubblecap trays (Annual Progress Report of Research Committee, Tray Efficiencies in Distillation Columns, AIChE, New York, 1955). 

---