Fenske minimum trays

Minimum Trays at Total Reflux Fenske Equation ... 

Minimum Trays. This is found with the Fenske-Underwood equation,... 

The shortcut methods can also be used for approximate analysis of the performance of an existing column. Here, the number of trays, N, is fixed, and the objective is to determine the reflux ratio required to meet a specifled separation. The Fenske and Underwood methods (Equations 12.17, 12.29, and 12.30) are used to calculate the minimum trays and minimum reflux ratio, and R. The operating reflux ratio corresponding to the given number of trays is then read from the Gilliland chart (Figure 12.4). The internal vapor and liquid rates are calculated from the reflux ratio and product rates. A check must be made to determine if the existing column can handle the calculated vapor and liquid traffic. 

Next, the relative volatilities, a, are determined as averages of estimated s obtained from T-value calculations at overhead and bottoms conditions. These conditions include the operating pressure, the estimated overhead and bottoms compositions, and the estimated dew point and bubble point temperatures. With a starting set of relative volatihties, the minimum trays, N , and the overhead and bottoms compositions at total reflux are calculated by the Fenske method (Equations 12.17 and 12.17a) for the specified separation. The new compositions may be used to recalculate more accurately the temperatures, pressures, and relative volatihties. The process is repeated until the a s stabilize. 

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. 

Fenske Equation Overall Minimum Total Trays with Total Condenser... 

Because the feed tray is essentially non-effective it is suggested that an additional theoretical tray be added to allow for this. This can be conveniently solved by the nomographs [21] of Figures 8-16 and 17. If the minimum number of trays in the rectifying section are needed, the)t can be calculated by the Fenske equation substituting the limits of xpi for x jj and x i, and the stripping section can be calculated by difference. 

Assume xi values of bottoms compositions of light key for approximate equal increments from final bottoms to initial feed charge. Calculate L/V values corresponding to the assmned xi values by inserting the various xi values in the Fenske equation for minimum reflux ratio of l-(d). The xi values replace the x b of this relation as the various assumptions are calculated. The actual (L/D) are calculated as in l-(d) keeping the minimmn number of trays constant. Complete the table values. 

The minimum theoretical trays at total reflux can be determined by the Fenske relation as previously given... 

Calculate the minimum number of trays using the Fenske Equation. 

The minimum reflux ratio can be evaluated for this two component distillation by using the Fenske-Underwood-Gilliland method and then determining what ratio factor to use to obtain the desired separation using 94 theoretical trays. This approach uses Eq. (15-1), (15-2), (15-3) and (15-4). If this approach is used, Nmm = 21.2 stages and Raun = 2.62. A trial and error calculation with Eq. (15-4) where R is unknown, establishes that a value of 2.75 for R is required to obtain 94 theoretical trays. Thus R = (1.05X2.62) or 2.75 for this colunm. This is reasonable since the ratio ctor for low tonperatures distillation columns is generally between 1.05 and 1.10. 

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. 

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