Trays determining number required

In the case of plate columns, a heat balance may be performed over each plate and the resulting temperature determined. For adiabatic operation, where no heat is removed from the system, the temperature of the streams leaving the absorber will be higher than those entering, due to the heat of solution. This rise in temperature lowers the solubility of the solute gas so that a large value of Lm/Gm and a larger number of trays will be required than for isothermal operation. 

The simplest distillation models to set up are the shortcut models. These models use the Fenske-Underwood-Gilliland or Winn-Underwood-Gilliland method to determine the minimum reflux and number of stages or to determine the required reflux given a number of trays or the required number of trays for a given reflux ratio. These methods are described in Chapter 11. The shortcut models can also estimate the condenser and reboiler duties and determine the optimum feed tray. 

Step off the stages to determine the required number of trays and the optimum feed trays below the side draw. 

A distillation column is designed to separate a 70-30 mole percent mixture to produce a distillate product with 97.5% mole component 1 and a bottoms product with 20% mole component 1. The column has a partial condenser and reboiler and operates at 1 atm pressure. Determine the required number of theoretical trays and the optimum feed location at a reflux ratio of 1.5. Calculate the recovery of component 1 in the distillate. Calculate the recovery at the same distillate purity and reflux ratio if the feed is introduced three trays below the optimum feed tray. Use thermodynamic data from Problem 6.1. 

The same separation would require a minimum reflux ratio of 0.6. Existing pumping facilities can deliver a reflux rate of 275 kmol/h. Determine the required number of theoretical stages. What minimum overall tray efficiency is needed to make the specified separation with the existing column ... 

If the distillation were to be started at twice the minimum reflux ratio, determine the required number of stages. If the initial charge is 100 kmol and the distillate rate is 10 kmol/h, calculate the reflux rate, the amounts of distillate and residue, and the residue composition as a function of time. Irrespective of tray hydraulics and reboiler and condenser capacity constraints, when should the distillation be stopped Assume negligible tray holdups and use shortcut methods. 

To determine the required size of an absorption or stripping nrtl, it is necessary to know not only the equilibrium soluhility of the solute in the solvent and the material balance atound the column bas also the rate at which solute is transferred from one phase to the other within the tower. This rale directly affects the volume of packing needed in a packed tower, the degree of dispersion requited in a spray contactor, and (somewhat less directly) the number of trays required in a nay tower. The last effect occurs as a result of the influence of mass transfer rms on tray efficiency which is discussed in a later section. Because of its direct effect ou packed tower design and the importance of this type of contactor in absoiption. this discussion of mass transfer is aimed primarily at the packed tower case. A more detailed review of mass transfer theoty is given in Chapter 2. 

Knowledge about the regularities of the trajectory bundles arrangement under the finite reflux provides an opportunity to develop the reliable and fast-acting algorithm to fulfill design calculations of distillation to determine the required number of trays for each section. 

The design of absorbers (and strippers) typically involves a computer-assisted, Iray-by-tray. heat- and material-balance calculation to determine the required number of equilibrium stages, which arc then related to the required number of actual trays by an estimated tray efficiency. More recently, a non-equilibrium stage model has been developed for computer application which considers actual trays (or sections of packing) and performs a heat and material balance for each phase on each actual tray, based on mass and heat transfer rates on that tray. 

After actual theoretical trays are determined (see Actual reflux and theoretical stages) one needs to estimate the actual physical number of trays required in the distillation column. This is usually done by dividing the actual theoretical trays by the overall average fractional tray efficiency. Then a few extra trays are normally added for offload conditions, such as a change in feed composition. 

Determining the number of theoretical and actual trays in a distillation column is only part of the design necessary to ensure system performance. The interpretation of distillation, absorption, or stripping requirements into a mechanical vessel with internal components (trays or packing, see Chapter 9) to carry out the function requires use of theoretical and empirical data. The costs of this equipment are markedly influenced by the column diameter and the intricacies of the trays, such as caps, risers, weirs, downcomers, perforations, etc. Calcvdated tray efficiencies for determination of actual trays can be lost by any unbalanced and improperly designed tray. 

As with distillation, the correlation for overall tray efficiency for absorbers, given in Equation 10.7, should only be used to derive a first estimate of the actual number of trays. More elaborate and reliable methods are available, but these require much more information on tray type and geometry and physical properties. If the column is to be packed, then the height of the packing is determined from Equation 9.64. As with distillation, the height equivalent of a theoretical plate (HETP) can vary... 

A direct-contact gas cooler system operates as follows Approximately 35,000 lb/hr of bone-dry air is passed over hot trays. The air is heated from 150°F to 325°F as it passes over the trays. It exits from the unit with a due point of 105°F. The hot air is sent to a direct-contact cooler, where its temperature is reduced back to 150°F. During the cooling stage, the air is dehumidified with water that is heated frpm 75°F to 105°F. The unit is rated at 3.5 inches of water pressure drop (a) Determine the number of diffusion units needed for this operation and (b) Establish the required dimensions for the direct-contact cooling tower (Hint Use standard low-pressure-drop data from the literature. Some of the older literature give pressure drop data for simple fill. See Sherwood, T. K. and C. E. Reed [6]. 

By varying the geometries in the program, an optimum design can be achieved. The choice of column diameter was a critical decision in the optimization procedure. In order to evaluate the effect of changing the column diameter, various column diameters were used and the number of trays required was determined. The results of these test runs are shown in Table G.l... 

The number of trays is determined by dividing the theoretical number of stages, which is obtained from the relationships in Section III, by the appropriate tray efficiency. It is best to use experimental efficiency data for the system when available, but caution is required when extending such data to column design, because tray efficiency depends on tray geometry, liquid and gas loads, and physical properties, and these may vary from one contactor to another. In the absence of data, absorption efficiency can be estimated using O Connell s empirical correlation. This correlation should not be used outside its intended range of application. 

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