Trays column diameter calculation

Formulation of the mathematical model here adopts the usual assumptions of equimolar overflow, constant relative volatility, total condenser, and partial reboiler. Binary variables denote the existence of trays in the column, and their sum is the number of trays N. Continuous variables represent the liquid flow rates Li and compositions xj, vapor flow rates Vi and compositions yi, the reflux Ri and vapor boilup VBi, and the column diameter Di. The equations governing the model include material and component balances around each tray, thermodynamic relations between vapor and liquid phase compositions, and the column diameter calculation based on vapor flow rate. Additional logical constraints ensure that reflux and vapor boilup enter only on one tray and that the trays are arranged sequentially (so trays cannot be skipped). Also included are the product specifications. Under the assumptions made in this example, neither the temperature nor the pressure is an explicit variable, although they could easily be included if energy balances are required. A minimum and maximum number of trays can also be imposed on the problem. 

Figure 6.7 gives flowsheet conditions and equipment sizes. Based on a feed flowrate of 2000 kmol/h and a feed composition of 6 mol% THF, the column diameters calculated by Aspen s Tray Sizing lae 1.36 and 1.43 m. The total number of stages in each column is set at 17 since the separations are fairly easy. Feed tray locations are shown in the figure. The economizers are sized using minimum approach temperatures of 10-15°C and overall... 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

Methods for quick sizing trayed fractionation and absorption column diameter have been reduced here to equations to facilitate programming for calculators or computers. Three methods are discussed and it is not a bad idea to compare results with all three. 

To determine the column (with trays) diameter, an approach [130] is to (1) assume 0 hours (2) solve for V, Ib/hr vapor up the column at selected, calculated, or assumed temperature and pressure (3) calculate column diameter using an assumed reasonable vapor velocity for the type of column internals (see section in this volume on Mechanical Designs for Tray Performance ). 

This is the boilup rate, which is approximately 3.3 ft vapor/sec. An approximately 1 ft 0 in. diameter column can handle this rate however, because it is in the usual size for a packed tower (or cartridge trays), the diameter must be checked using the packed tower calculations in Chapter 9 of this volume. 

In order to develop a method for the design of distillation units to give the desired fractionation, it is necessary, in the first instance, to develop an analytical approach which enables the necessary number of trays to be calculated. First the heat and material flows over the trays, the condenser, and the reboiler must be established. Thermodynamic data are required to establish how much mass transfer is needed to establish equilibrium between the streams leaving each tray. The required diameter of the column will be dictated by the necessity to accommodate the desired flowrates, to operate within the available drop in pressure, while at the same time effecting the desired degree of mixing of the streams on each tray. 

The method of calculation introduced in this chapter not only allows an exact determination of the column diameter for nonpulsed sieve tray columns, but also allows a good estimation of the diameters of pulsed and stirred extractors. For the latter, however, more exact specific equations exist for the flooding point, see for example [1,4]. 

The downcomer area required for trays not only increases with the liquid-flow-rate, but also with the difficulty in achieving separation between the vapour and the liquid phases. The volume required for the downcomer (downcomer residence time) increases at a lower surface tension and a smaller density difference between vapour and liquid. Because of the large downcomer area required to handle the high liquid flow rates typical of high-pressure distillations, a trayed column cross-sectional area may be 40% to 80% greater than the active tray area calculated from the vapour flow rates for such distillations. Thus, the downcomer area becomes a significant factor in the determination of the diameter of a tray column. 

Calculate the column diameter, D, for tray columns, from Equation 1.21.6T and for packed columns from Equation 6.21,6P. 

Calculate a preliminary column diameter from Equations 6.23.1 and 6.23.2 by assuming a superficial velocity of 2 ft/s. If D < 2.5 ft, select a packed column. Otherwise, select a tray column. 

The column height, given by Equation 6.21.7T for tray columns or by Equation 6.21.7P for packed columns, depends on the column diameter, which we will now calculate. From the ideal gas law, the volumetric air flow rate. 

The calculation of column diameter for distillation and absorption columns %h,6 is usually based on the flooding velocity, which, in turn, requires values of the flooding capacity factor, Cf- Fair s flooding-capacity plot for sieve trays [1] correlates the flooding capacity factor with a flow parameter Flv for each tray-spacing value, t, as shown in Figure 2. The flow parameter involves the liquid mass flow, LMi, and vapor mass flow, F v (both in lb/ s), as well as the densities of the two streams. 

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. Calculated tray efficiencies for determination of actual trays can be lost by any unbalanced and improperly designed tray. 

The next step is to determine the flooding vapor velocity, which is a function of the vapor and liquid flow rates and their densities. The design vapor velocity is then calculated by multiplying the flooding vapor velocity by a flood factor such as 0.85. The vapor velocity is based on the vapor volumetric flow and the net flow area between the trays, that is, the column cross-sectional area minus the area blocked by the downcomers. With known vapor velocity, vapor flow, and fraction of the column cross section occupied by the downcomers, the net area can be calculated. The total area is then calculated, from which the tray diameter is determined. The actual column diameter is obtained by rounding off the tray diameter to the next larger standard size. The vapor velocity is then adjusted to the new diameter to calculate the expected flood factor. 

Many of the correlations presented here are of general applicability although some may be particularly suited for certain tray types as indicated. The main objectives are to determine the tray or column diameter for a given application, to calculate the tray liquid holdup and the pressure drop between the trays, and to check for flooding (entrainment and downcomer) and weeping. 

The column has 3 m diameter sieve trays with 0.5 cm diameter holes and 10% hole area. The tray spacing is 45 cm. Assuming a foaming factor of 0.85, calculate the vapor flood velocity at the top tray. Check if the column diameter is acceptable. The fraction of flood velocity should be within a 60-85% range. 

Determine by hand calculations the column diameter, then the following items with the diameter rounded up to the next standard tray diameter, available in 0.25 m increments. Recommend possible design modifications for situations where unacceptable column operation is indicated. 

Example 18.6. A sieve-plate column operating at atmospheric pressure is to produce nearly pure methanol from an aqueous feed containing 40 mole percent methanol. The distillate product rate is 5800 kg/h. (a) For a reflux ratio of 3.5 and a plate spacing of 18 in., calculate the allowable vapor velocity and the column diameter. b) Calculate the pressure drop per plate if each sieve tray is in, thick with j-in, holes on a -in. triangular spacing and a weir height of 2 in. (c) What is the froth height in the downcomer ... 

Because of the need for internal access to columns with trays, a packed column is generally used if the diameter calculated from equation (4-33) is less than 60 cm. Tray spacing must be specified to compute column diameter, as shown by equation (4-32). On the other hand, recommended values of tray spacing depend on column diameter, as summarized in Table 4.3. Therefore, calculation of the tower diameter involves an iterative procedure (a) an initial value of tray spacing is chosen (usually, t = 0.6 m) (b) the tower diameter is calculated based on this value of tray spacing (c) the value of t is modified as needed according to the recommendations of Table 4.3 and the current estimate of D (d) the procedure is repeated until conver-... 

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