Trays pressure drop

The total pressure drop AP across a tray is defined by the general equation  

The third term is caused by the surface tension of the liquid. Usually this term can be neglected. The first term is the dry pressure drop due to the vapor flow through empty bubble caps. This term is defined in Eqn. (16.48). Similar to hdry we find  

The second term takes into account the pressure drop through the aerated liquid over and around the dispenser correspond to the clear liquid height. This pressure drop has a relationship with the liquid height on a tray. The method, commonly used, defines an aeration factor p, such that. 

The equation for Ptmy is stiongly related to the equation for Mi. Time constants can be derived directly from the pressure drop equation of tray / by linearization. The pressure drop is defined in Eqn. (16.59), it can be written as function of its independent variables  

This means that the pressure drop is determined by the mass on the tray, the impulse of the vapor flow and by the molar composition. For small variations one can write  

The dry pressure drop calculation is based on the orifice equation for gases, in which the pressure drop is proportional to the square of the vapor velocity through the orifice, and the vapor density. In terms of liquid head, the equation for sieve trays is written as 

In this equation h is in centimeters of clear liquid, Uq is the hole velocity in m/s, and Q is the orifice coefficient. The hole velocity is calculated from the vapor volumetric flow and the total hole area The orifice coefficient for sieve trays is a function of the ratio of total hole area to active tray area, and of the ratio of tray thickness to hole diameter. This function may be approximated by the equation (Smith, 1963), 

The weir height, h, is in centimeters and the weir length, is in meters. The liquid flow rate across the tray, is in cubic meters per minute. The relative froth density on the tray, ( ), defined as the ratio of clear liquid height to froth height, is given by another empirical equation  

The pressure drop due to surface tension is calculated on the assumption that the 

Taking /z in centimeters of clear liquid, o in dyne/cm, p in kg/m- and df, in centimeters, this equation may be written in the following form (Van Winkle, 1967)  

Uneven vapor flow bubbling-up through the tray deck will promote vapor-liquid channeling. This sort of channeling accounts for many trays that fail to fractionate up to expectations. To understand the cause of this channeling, we will have to quantify total tray pressure drop. 

On the other hand, bubble caps (or even the more ancient tunnel cap trays) are different, in that they do not depend on the vapor flow to retain the liquid level on the tray deck. More on this later. For now, just recall that we are dealing only with perforated tray decks. 

Vg = velocity of vapor or gas flowing through the sieve hole, ft/s 

K = an orifice coefficient, which can be as low as 0.3 for a smooth hole in a thick plate and 0.6 to 0.95 for various valve tray caps 

The weight of liquid on a tray is created by the weir height plus the crest height. We have defined the crest height (in inches of clear liquid) in Chap. 1, as 

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AP,rav = Tray pressure drop, inches of liquid ATi = Condensing side temperature difference, °F ATn, = Log mean temperature difference, °F Pf = Foam density, Ibs/ft ... 

Typical tray pressure drop, mmHg 2.5-8 Random Packings Size HETP... 

For stable tray operation, the hydraulic gradient should be less than one half the dry tray pressure drop. For conditions of high weir height and high Vq (Pv) the greater... 

This metliod calculates the dry tray pressure drop and allows for correcting the two-phase flow effects at various entrainment ratios. 

Fv = valve tray F-factor, ft- /min/valve Fvm = valve tray F-factor at the beginning of the valve open region, fr /min/valve g = gravitational constant, ft/s he = clear liquid height, in. ho = dry tray pressure drop, in. 

Compare calculated h j with value of dry tray pressure drop as given ... 

This is based on the correlation of Mayfield [45] where hjt (weep) = dry tray pressure drop at tray weep point, in. liquid. 

Set minimum design dry tray pressure drop 30% above the value of hdt (weep). 

Calculate wet tray pressure drop, determine effective head from Figure 8-130. 

Low tray pressure drop is required, as for vacuum systems. Design with extra caution under vacuum, since data correlations have not been checked in this region. 

Read Figure 8-130 effective head = 1.58 in. liquid Total Wet Tray Pressure Drop ht = 0.608 + 1.58 = 2.188 in. liquid Weep Point... 

Total wet tray pressure drop, h = 1.44 + 1.4 = 2.84 inches liquid... 

Orifice coefficient. Figure 8-129, read at 0.41 tray/hole gives Cq orifice coefficient = 0.75 Hole velocity = 347/8.66 = 40.06 fps Dry Tray pressure drop... 

Although Sutherland did not obtain an equation for total tray pressure drop, correlation at this time indicates that it follows the effective head concept of Hughmark. This is a limited evaluation because the data available did not indicate any clear liquid heights over about 0.75 in. 

Calculate the total wet tray pressure drop, using an assumed height of clear liquid on the tray of 0.5-in. minimum to 4-in. maximum (1 to 2-in. are usual values). 

Vh = vapor velocity through valve holes, ft/sec P = tray aeration factor, dimensionless AP = tray pressure drop, in. liquid pvm = valve metal density, tj = tray deck thickness, in. 

Figure 8-148. Typical operating valve tray pressure drop profile. Valves start to open at A, the closed balance point. Used by permission, Klein, G. F. Chem. Eng. V. 89, No. 9 (1982) p. 81 all rights reserved.

Closed and Open Loss Coefficients for Dry Tray Pressure Drop Equations 8-314 and 8-315... 

Beyond point B on the diagram, the pressure drop for the tray increases as the vapor rate increases. Use Equation 8-314 or 8-315 to determine the dry tray pressure drop, AP, in. liquid, Bolles [205] per Klein [201] ... 

Example 8-41 Procedure for Calculating Valve Tray Pressure Drop (after Klein [201])... 

Valve hole area 1.65 sq. ft. (separate calculation) = ho Tray pressure drop and froth height... 

Downcomer backup flooding results from pressure drop at bottom outlet of downcomer, causes liquid to backup in the downcomer and flood the tray above. Generally the cause is due to excessive tray pressure drop. 

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