Murphree

This is the one case where the overall column efficiency can be related analytically to the Murphree plate efficiency, so that the actual number of plates is calculable by dividing the number of theoretical plates through equation 86 ... 

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. 

Murphree vapor plate efficiency, see equation 82 poiat value of plate efficiency... 

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

Stage Efficiency The use of the Murphree plate ejficiency is par-ticulany convenient on y-x diagrams. The Murphree efficiency is defined for the vapor phase as... 

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. 

FIG. 13-40 Application of a 50 percent Murphree vapor-phase efficiency to each stage (excluding the rehoiler) in the column. Each step in the diagram corresponds to an actual stage. 

Another implementation of homotopy-continuation methods is the use of problem-dependent homotopies that exploit some physical aspect of the problem. Vickeiy and Taylor [AIChE J., 32, 547 (1986)] utilized thermodynamic homotopies for K values and enthalpies to gradually move these properties from ideal to ac tual values so as to solve the MESH equations when veiy nonideal hquid solutions were involved. Taylor, Wayburn, and Vickeiy [I. Chem. E. Symp. Sen No. 104, B305 (1987)] used a pseudo-Murphree efficiency homotopy to move the solution of the MESH equations from a low efficiency, where httle separation occurs, to a higher and more reasonable efficiency. 

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. 

E = Murphree vapor efficiency, corrected for recycle of hqiiid entrainment... 

Ejfects of Gas and Liquid Mixing As noted previously, it is necessary in most instances to convert point efficiency E g to Murphree plate efficiency E, ,. This is true because of incomplete mixing only in small laboratoiy or pilot-plant columns, under special conditions, is the assumption E g = E, , likely to be valid. For a crossflow plate with no hquid mixing there is plug flow of hquid. For this condition of liquid flow, Lewis [Ind. Eng. Chem., 28, 399 (1936)] analyzed effects of gas mixing on efficiency. He considered three cases ... 

FIG. 14-42 Overall (Murphree) efficiency and pressure drop data for several devices using the same test mixture (ethylbenzene/styrene). See text for details. [Billet, Conrad, and Giuhh, Instn. Chem. Engrs. Symp. Ser. No. 32, 5, 111 (1979).]... 

FIG. 14-43 Overall (Murphree) efficiencies of sieve plates with hole/active area ratios of 0.08 and 0.14. Efficiency values greater than 1.0 (100%) result from crossflow effects (Figs. 14-38, 14-39). [Yanagi and Sakata, Ind. Eng. Chem., Proc. Des. Devel., 2i, 712 (J.9S2).] Reproduced with permission, copyright 1982 American Chemical Society. 

Emd Murphree dispersed-phase m Slope of equilibrium hue iu Dimensionless Dimeusionless... 

During filling, the catalyst is distributed uniformly to avoid the possibility of channeling that coiild lead to poor heat transfer, poor conversion, and harm to the catalyst because of hot spots. During startup, sudden surges of flow may disturb the bed and are to be avoided. For instance, in a study of a hydrodesulfuiizer by Murphree et al. (Ind. Eng. Chem. Proc. Des. size unit varied between 47 and 80 percent with different modes of loading and startup. 

Gayle, J.B., Dalton, C.C., Martin, H.L., and Murphree, W.D., Review of Selected Aspects of the Meteoroid Hazard, George C. Marshall Space Fligh Center Report No. MDWG-63-1, Huntsville, AL, 54 pp., February 1963. 

The Houdry fixed-bed cyclic units were soon displaced in the 1940s by the superior Fluid Catalytic Cracking process pioneered by Warren K. Lewis of MIT and Eger Murphree and his team of engineers at Standard Oil of Newjersey (now Exxon). Murphree and his team demonstrated that hundreds of tons of fine catalyst could be continuously moved like a fluid between the cracking reactor and a separate vessel for... 

Murphree, E. V., et al. (194S). Improved Fluid Process for Catalytic Cracking. Transactions of the American Institute of CheinicaJ Engineers 41 19-20. 

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] ... 

Solving the problem defined in the following table will show the equations for estimating system physical properties and their relation to the calculation of Murphree vapor plate efficiencies ... 

Murphree vapor plate efficiency is calculated two ways ... 

D = molecular diffusion coefficient, sq ft/hr Em = Murphree vapor plate efficiency, %... 

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 ... 

Kappe C. O., Murphree S. S., Padwa A. Synthetic Applications of Fnran Diels-Alder Chemistry Tetrahedron 1997 53 14179-14233... 

---