Trays Murphree

This rate-based analysis of trayed columns gives an estimate of the number of overall gas phase mass transfer units corresponding to a given tray. The practical application of this analysis is to provide a means for estimating the tray Murphree vapor efficiency discussed in Section 14.3. 

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. 

The application of a 50 percent Murphree vapor-phase efficiency on a y-x magram is illustrated in Fig. 13-40. A pseudo-equilibrium cui ve is drawn halfway (on a vertical line) between the operating hnes and the true-equilibrium cui ve. The true-equilibrium cui ve is used for the first stage (the partial reboiler is assumed to be an equilibrium stage), but for 1 other stages the vapor leaving each stage is assumed to approach the equilibrium value only 50 percent of me way Consequently, the steps in Fig. 13-40 represent actual trays. 

When it is desired to compute, with rigorous methods, actual rather than equilibrium stages, Eqs. (13-69) and (13-94) can be modified to include the Murphree vapor-phase efficiency T ij, defined by Eq. (13-29). This is particularly desirable for multistage operations involving feeds containing components of a wide range ol volatility and/or concentration, in which only a rectification (absorption) or stripping action is provided and all components are not sharply separated. In those cases, the use of a different Murphree efficiency for each component and each tray may be necessary to compute recovery accurately. 

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

Data from bubble cap and perforated tray columns for the Murphree vapor plate efficiencies are correlated [86] ... 

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 ... 

The ratio Emv is shown graphically in Figure 11.56 where for any operating line AB the enrichment that would be achieved by an ideal plate is BC, and that achieved with an actual plate is BD. The ratio BD/BC then represents the plate efficiency. The efficiency may vary from point to point on a tray. Local values of the Murphree efficiency are designated Emv and Emi. 

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 ... 

Murphree vapor efficiency forjth component on nth tray... 

Aa Active area, same as bubbling area m2 ft2 Erriv. Em z Murphree tray efficiency, gas -/- -/-... 

Ea Murphree tray efficiency, -/- -/- Hol Height of an overall transfer m ft... 

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

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)]. 

Equation (14-135) is based on the assumption of constant molar overflow and a constant value of Emv from tray to tray. It needs to be applied separately to each section of the column (rectifying and stripping) because GM/LM, and therefore X, varies from section to section. Where molar overflow or Murphree efficiencies vary throughout a section of column, the section needs to be divided into subsections small enough to render the variations negligible. 

The point and Murphree efficiency definitions above are expressed in terms of vapor concentrations. Analogous definitions can be made in terms of liquid concentrations. Further discussion is elsewhere (Lockett, Distillation Tray Fundamentals, Cambridge University, Press, Cambridge, England, 1986). 

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. 

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. 

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],... 

Three parameters were identified and adjusted to validate the model against the experiments. The parameters are the heat losses, the nominal tray holdup and the Murphree tray efficiency (EM). Figure 4.16 shows how EM is adjusted to match the dynamic model prediction and experimental temperature profile measured on Plate 12. Figure 4.17 shows the comparison between the experimental and model prediction of ethanol composition in the reflux drum, middle vessel and in the bottom of the column. Figures 4.16-17 show a good match between the model prediction and experiments. 

Figure 4.16. Adjustment of Murphree Tray Efficiency. Dotted line Experiment. Full lines Model Predictions. [Barolo et al., 1998]a...

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. 

For tray columns, an alternative approach uses Murphree tray efficiencies (Sec, 7,1.1). This efficiency is easy to incorporate into an x-y diagram, and the diagram construction can he performed using actual rather than ideal stages. The Murphree tray efficiency is defined as... 

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... 

Most theoretical models incorporate the effects of vapor and liquid nonuniformity into the relationship between the Murphree and the point efficiency. Developing models for vapor-liquid contact on trays has been a fertile research area in the last couple of decades, with literally hundreds, maybe thousands of papers published on the subject. A thorough review is given by Lockett (12). 

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... 

The effective slope of the equilibrium curve, m, and therefore A. [Eq. (7.5)1 differs for each component. Therefore, each component has a different ratio of gas-phase resistance to liquid-phase resistance [Eq. (7.13)] and a different ratio of overall column efficiency to Murphree tray efficiency [Eq. (7.4)]. 

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