Local tray efficiency

Based on the simulated concentration distribution as shown in Fig. 4.11, the local tray efficiencies can be obtained. The simulated tray efficiency by area average for run 16552 is 33.4 % in comparison with the experimental value of 36 %. More simulated tray efficiencies at different mV/L are compared with the experimental measurements as shown in Fig. 4.12, in which reasonable agreement can be seen between them. 

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 ... 

This is the local efficiency or point efficiency, and because a liquid concentratjna gradient is not involved, it cannot have a valne greater than 1,0. Thus, it is a more fundemeatal concept, but it suffers in application since concentration profiles of operating trays are difficult to predict. As in tha case of the Murphrea tray efficiency, it is possible to use a liquid-phase point efficiency. 

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. 

Three types of tray or plate efllciency are used overall tray efficiency Eq, Murphree tray efficiency E , and point or local tray efllciency E ff (sometimes called Murphree point efficiency). These will be considered individually. 

Murphree tray efficiency The bulk-average concentrations of all the local pencils of gas of Fig. 6.21 SLrey +, and> . The Murphree efficiency of the entire tray is then [see Eq. (5.39)]... 

The point efficiency is an essential information in distillation design and operation. The tray efficiency can be calculated by the CMT models presented in this chapter it shows that the tray efficiency is in connection with the tray structure, flow pattern, and operating conditions, and thus, it is only referred to a specific distillation column under specific condition. On the other hand, the point efficiency, which depends on only the local condition of vapor-liquid contact and the physical properties of the system, is the better way to evaluate the feasibility of using distillation tray column for the separation. 

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. 

The electroresistivity probe, recently proposed by Burgess and Calder-bank (B32, B33) for the measurement of bubble properties in bubble dispersions, is a very promising apparatus. A three-dimensional resistivity probe with five channels was designed in order to sense the bubble approach angle, as well as to measure bubble size and velocity in sieve tray froths. This probe system accepts only bubbles whose location and direction coincide with the vertical probe axis, the discrimination function being achieved with the aid of an on-line computer which receives signals from five channels communicating with the probe array. Gas holdup, gas-flow specific interfacial area, and even gas and liquid-side mass-transfer efficiencies have been calculated directly from the local measured distributions of bubble size and velocity. The derived values of the disper-... 

It would be possible to do design work integrating local efficiencies for each tray through the entire tower, though calculating the detailed work required would be a lengthy procedure. 

The effects of tray leakage and liquid entrainment in the vapor stream may need to be taken into account. For bubble cap trays, tray leakage is normally of no significance. Entrainment, on the other hand, can decrease separation markedly. Quantitative prediction of entrainment is sometimes possible however, the effect of entrainment is usually combined with the effect of vapor velocity on local efficiency, using the results of experimental full-scale studies, such as those performed by FRI. 

DISTILLATION PLATE EFFICIENCY. The two-film theory can be applied to mass transfer on a sieve tray to help correlate and extend data for tray effieiency. The bubbles formed at the holes are assumed to rise through a pool of liquid that is vertically mixed and has the local composition x. The bubbles change in composition as they rise, and there is assumed to be no mixing of the gas phase in the vertical direction. For a unit plate area with a superficial velocity the moles transferred in a thin slice dz are... 

Calculate the effect of the change in slope of the equilibrium line on the local efficiency in a sieve-tray distillation column. Use the benzene-toluene system as an example, and predict / for plates where the mixture is mostly toluene and for those where it is mostly benzene, starting with an estimated value of for the middle of the column. 

Gas absorption can be carried out in a column equipped with sieve trays or other types of plates normally used for distillation. A column with trays is sometimes chosen instead of a packed column to avoid the problem of liquid distribution in a large diameter tower and to decrease the uncertainty in scaleup. The number of theoretical stages is determined by stepping off plates on a y-x diagram, and the number of actual stages is then calculated using an average plate efficiency. The plate and local efficiencies are defined in the same way as for distillation [Eqs. 

Figure 4.10 is a schematic representation of one tray of a multitray tower. The tray n is fed from tray n - 1 above by liquid of average composition x and it delivers liquid of average composition xn to the tray below. At the place under consideration, a pencil of gas of composition yn+, local rises from below and, as a result of mass transfer, leaves with a concentration yn local. At the place in question, it is assumed that the local liquid concentration xlgcal is constant in the vertical direction. The point efficiency is then defined by... 

The bulk-average concentration of all the local pencils of gas of Figure 4.10 are yn+l and yn. The efficiency of the entire tray, also known as the Murphree effi -ciency, is then... 

On a column tray, the gas and liquid flow crosscurrently, therefore, one has to distinguish between the efficiencies Eg and Eg. Eg is a local variable point efficiency on a particular tray with a gas liquid dispersion layer, describing the conditions along a stream line of the gas... 

Point efficiency. The point or local efficiency Ej p on a tray is defined as... 

For the development of the process model various physical and chemical phenomena occurring in each process unit has to be known. Most important phenomena in chemical production plants are reaction kinetics, heat and mass transfer, phase equilibrium and hydraulics. Reactors require kinetic and mass transfer models that describe how local concentrations and temperature affect the reaction rates. Separation processes require knowledge of phase equilibria (vapor/liquid, liquid/liquid) and knowledge of heat and mass transfer. Very often some specific knowledge of the equipment are also required like capacities and efficiencies of distillation trays. 

---