Number of Trays and Feed Location

The number of trays in each column section (rectifying or stripping) is determined by the required fractionation in that section at a given L/V ratio. This ratio, which is directly related to the reflux ratio, is usually limited by practical considerations such as economically acceptable reboiler and condenser duties. Also, the reflux ratio is limited by tray hydraulics considerations, discussed in Chapters 14 and 15. Column flooding can occur if the vapor or liquid velocities become excessive. The total column trays and feed location are set once the number of trays in each section is known. 

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The azeotropic column feed flow rate was adjusted from that used in the previous study (216 kmol/h) to correspond to the 1000 kmol/h of fermenter broth fed to the beer still used in the present study. With a distillate composition of 85 mol% ethanol, this feed flow rate is 62.44 kmol/h. With this flow rate and with the number of trays and feed locations stated above, the reboiler duty (QR2) in the azeotropic column is 1.597 MW and the reboiler duty in the recovery column is 0.7122 MW. 

Products The molar flow rate of the product stream S2 is set to 4 kgmol/h. One needs to enable the minimum reflux calculations in the shortcut column to see the minimum number of tray and feed location. Once this option is selected then running the simulation, generates a text report. The required results are under the Summary of Underwood Calculations section in the report as shown in Figure 6.11. The stream property table is shown in Figure 6.12 where exit streams molar flow rate and conditions are obtained. 

The complete definition of column performance when the number of stages and feed location are fixed requires two specifications (Section 5.2.2). In studying the effect of reflux ratio on separation, other parameters, including product rates, are assumed constant. In Y-X graphical representation, a fixed product rate is implied by fixing the 7-line slope. This slope depends on the feed thermal conditions at feed tray temperature and pressure (Section 5.2.2). The column pressure is fixed, but its temperature depends on the product rates. Therefore, in order to maintain a fixed product rate, the (/-line slope must be held constant. The actual product rates corresponding to a given (/-line slope are calculated by material balance once the product compositions have been determined. 

A distillation column with an attached side stripper is used to separate a feed stream F into products A, B, and C, as shown in the diagram. The main column has a total condenser and a partial reboiler, and the side stripper has a partial reboiler. The columns are existing units with fixed number of trays and feed and draw locations. The external feed, a product of an upstream unit, is of fixed flow rate, composition, and thermal conditions. The pressure in the columns is determined independently and is not available as a variable. Using basic modules representation, determine the degrees of freedom of this system. What variables would you specify to define the performance of these columns ... 

First, a steady state model was built. The three reactors are modelled as CSTR and PFR rectors while the reaction kinetics are modelled with the available standard Arrhenius kinetic expressions in HYSYS.PLANT with the kinetic data available in the literature (see Ref. [45-48]). The four separation columns are modelled and simulated, at steady state, as full rigorous distillation columns based on the specifications of the inlet streams, colunms pressure profiles, required number of trays and feed tray location. Moreover, two more specifications are required for each column with both reboiler and condenser. These specifications could be the duties, reflux flow rate, draw streams rates, composition fractions, column recovery, etc. 

Guess a total number of trays and feed tray location. 

Once one has proposed alternative configurations for systems of separation devices to effect a desired separation, one must then design these devices so the various alternatives may be compared. For a distillation column, the first set of design decisions is to choose the number of trays, the feed tray location, and the reflux ratio at which to operate it. For a binary separation, the McCabe-Thiele diagram (or the concepts behind it) is an indispensable aid in making these decisions. 

To redistribute the stages in the remaining sections, a shortcut simulation is used to find out the required number of trays, the feed tray location and the minimum reflux ratio for each column in the sequence. To make use of the existing column with the same number of trays (24 trays) iterations are required to adjust the sum of the rectifying sections in each column equal to 24 (number of trays in the main column). Finally, the sequence of the simple columns is merged into a complex column. The main column is not changed, but the side strippers and pump arounds need to be relocated or adjusted. 

The steady-state simulation of distillation columns in Aspen Plus discussed in previous sections took a rating approach to the problem. Specific values for the total number of trays and the feed-tray location were selected, and the required reflux ratio and reboiler duty were determined for this specific configuration, subjected to attaining the desired product specifications. Then, economics must be used to find what the optimum tray configuration is. 

Since there is no recycle flow back to the first preconcentrator column, this standalone column can be optimized first with two product specifications and two design variables of the total number of stages and feed tray location. One of the product specifications is the selection of the XDl composition by varying the reflux ratio. The other product specification is the bottoms water composition at 0.999 by varying the reboiler duty. 

The total number of trays is a compromise between the total equipment cost and the total utility cost. The optimum total number of trays and the optimum feed-tray location are determined to minimize TAC. The calculation procedure of Douglas is followed with the annual capital charge factor of 1 /3. The utility costs include the steam and cooling water for the operation of reboiler and condenser. The total operating costs include the utility costs and the entrainer makeup cost. The Aspen Plus simulation results for the three entrainers are summarized in Tables 9.10 to 9.12. 

In reactive distillation, chemical reactions are assumed to occur mainly in the liquid phase. Hence the liquid holdup on the trays, or the residence time, is an important design factor for these processes. Other column design considerations, such as number of trays or feed and product tray locations, can be of particular importance in reactive distillation columns. Moreover, because chemical reactions can be exothermic or endothermic, intercoolers or heaters may be required to maintain optimum stage temperatures. Column models of reactive distillation must include chemical reaction equilibrium or kinetic equations along with the material and energy balance equations and the phase equilibrium relations. These models and methods for solving them are discussed in Chapter 13. 

The shortcut column performs Fenske-Underwood shortcut calculations for simple refluxed towers. The Fenske minimum number of trays and the Underwood minimum reflux are calculated. A specified reflux ratio can then be used to calculate the vapor and liquid traffic rates in the enriching and stripping sections, the condenser duty and reboiler duty, the number of ideal trays, and the optimal feed location. The shortcut column is only an estimate of the column performance and is restricted to simple refluxed columns. For more realistic results, the rigorous column operation should be used. This operation can provide initial estimates for most simple columns. 

Viswanathan, J. and I. E. Grossmann. Optimal Feed Locations and Number of Trays for Distillation Columns with Multiple Feeds. Ind Eng Chem Res 32 2942-2949 (1993). 

Note that the total number of plates, the feed plate location and reflux ratio can all be varied during simulation. The array form of the program also allows graphing the axial steady state tray-by-tray concentration profile. Part of the program is shown below. 

Particularly when the number of trays is small, the location of the feed tray has a marked effect on the separation in the column. An estimate of the optimum location can be made with the Under-wood-Fenske equation (13.116), by applying it twice, between the overhead and the feed and between the feed and the bottoms. The ratio of the numbers of rectifying Nr and stripping Ns trays is... 

For more than two species and a reflux ratio set to 1.2 times the minimum, a rule of thumb is to compute the total number of trays required for a total reflux column to produce the separation desired and then double this number as a first guess (Douglas, 1988). The next decision is select the tray on which to feed the column. For multispecies columns, the placement is not obvious. Typically, one must search by placing it on any one of a range of trays using a tray-by-tray simulation, thereby discovering which tray location requires the least reflux to effect the desired separation. 

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