Computer minimum reflux

Gilliland (45) used the Fenske method (Sec. 3.2.1) to compute minimum stages, and his own method for computing minimum reflux. However, it was shown (11,48) that the Underwood method (Sec. 3.2.2) for minimum reflux can also be used. 

Use of Underwood s Method. Table III presents an example that illustrates a computation we might do to compute the minimum reflux flows for a column. In this example, species C distributes between the top and bottom product in the column. Underwood s method permits us to compute how it distributes. The approach for using Underwood s equations to compute minimum reflux is as follows ... 

An approach to setting the reflux ratio often involves computing a minimum reflux ratio, a topic we have discussed several times in this article with respect to pinch points. Considerable work has been done on computing minimum reflux ratios tor columns. Koehler (1991) reviews this work. As a rule of thumb, one sets the reflux ratio to be 20-100% or so above the minimum, a number that experience shows trades off the number of trays with column diameter in a near cost-optimal way. 

However, the total number of equilibrium stages N, N/N,n, or the external-reflux ratio can be substituted for one of these three specifications. It should be noted that the feed location is automatically specified as the optimum one this is assumed in the Underwood equations. The assumption of saturated reflux is also inherent in the Fenske and Underwood equations. An important limitation on the Underwood equations is the assumption of constant molar overflow. As discussed by Henley and Seader (op. cit.), this assumption can lead to a prediction of the minimum reflux that is considerably lower than the actual value. No such assumption is inherent in the Fenske equation. An exact calculational technique for minimum reflux is given by Tavana and Hansen [Jnd. E/ig. Chem. Process Des. Dev., 18, 154 (1979)]. A computer program for the FUG method is given by Chang [Hydrocarbon Process., 60(8), 79 (1980)]. The method is best applied to mixtures that form ideal or nearly ideal solutions. 

Binary minimum reflux so calculated implies feed enthalpy just equal to the above started vapor V and liquid L. Any increase or decrease in that enthalpy must be matehed by inerease or decrease in total heat content of overhead reflux. Note that the Underwood" binary reflux equation essentially computes the flash versus specifi-eation composition relationship along with enthalpy correction. 

Design procedure. The minimum refluxes computed for each section are compared with each other. The highest value is the minimum reflux for the column. From Eq. (2.35) the corresponding minimum liquid flow in the section is calculated. This flow can be multiplied hy a certain factor, commonly between 1.05 and 1.3 to give the optimum flow. Guidelines for selecting factors are given in Sec, 3.1,6, The liquid flow can now be resubstituted into Eq. (2.35) and the actual reflux ratio calculated. 

Figure 3.e Calculating minimum reflux and minimum stages by extrapolating the reflux stages curve obtained by computer simulation. Depropanizer In Example 3.4. D = 59.9 lb-mole/h. 

It is common to design and operate reasonably close to the minimum reflux or minimum boilup (Sec. 3.1.4). A computer solution at such low reflux ratios can be unstable and fail. A solution may only be reached if very good initial values are available. The technique of "sneaking up on an answer" is powerful in these cases. Initially, the column is solved at a higher reflux ratio. This solution is used as the initial value for the subsequent calculation, in which the reflux ratio is slightly lowered. This process is continued until the desired reflux ratio is reached. Other examples of how to use the solution of one simulation to initialize another simulation are described by Brierley and Smith (106). The "sneaking-up technique is part of the basis of the homotopy methods (Sec. 4.2.12) and these and other forcing techniques may also be used. 

Equation-Based Design Methods Exact design equations have been developed for mixtures with constant relative volatility. Minimum stages can be computed with the Fenske equation, minimum reflux from the Underwood equation, and the total number of stages in each section of the column from either the Smoker equation (Trans. Am. Inst. Chem. Eng., 34, 165 (1938) the derivation of the equation is shown, and its use is illustrated by Smith, op. cit.), or Underwoods method. A detailed treatment of these approaches is given in Doherty and Malone (op. cit., chap. 3). Equation-based methods have also been developed for nonconstant relative volatility mixtures (including nonideal and azeotropic mixtures) by Julka and Doherty [Chem. Eng. Set., 45,1801 (1990) Chem. Eng. Sci., 48,1367 (1993)], and Fidkowski et al. [AIChE /., 37, 1761 (1991)]. Also see Doherty and Malone (op. cit., chap. 4). 

E.xample problems are included to highlight the need to estimate the entire set of products that can be reached for a given feed when using a particular type of separation unit. We show that readily computed distillation curves and pinch point cur es allow us to identify the entire reachable region for simple and e.xtractive distillation for ternary mixtures. This analysis proves that finite reflux often permits increased separation we can compute exactly how far we can cross so-called distillation boundaries. For extractive distillation, we illustrate how to find minimum. solvent rates, minimum reflux ratios, and, interestingly, ma.xinnim reflux ratios. 

Step 2) Once we have 6, we can compute the minimum reflux ratio from... 

Equation 7-117 shows the relationship for the feed, where q is the fraction of feed that is liquid at the feed tray temperature and pressure. For a bubble point feed, q = 1, and for a dew point feed, q = 0. The minimum reflux ratio is determined from Equation 7-117 by substituting into Equation 7-116. Coker [41] developed a numerical method for computing 6 and respectively. However, other methods should be tried, if R in gives a negative value. Also, it may be that the separation between the feed and the overhead can be accomplished in less than one equilibrium stage. 

The minimum reflux is computed directly from Equation 12.29, using the over-... 

First, the minimum number of stages is computed by the Fenske method. Then, the minimum reflux ratio is computed by the Underwood method. Next, the design (operating) reflux ratio is chosen as some multiple of the minimum reflux ratio, e.g., 1.15 x R. (The optimum multiple is in the... 

When the key components upon which the specifications are made are not adjacent in relative volatility, the total distillate rate D and the d-s for the split keys (the components having a values lying between those of the keys) are unknown. To determine the minimum reflux ratio, it is necessary to make use of the fact that all of the roots of the function Clf lying between a, and ah (afc < k+1 < afc+ j < < fl < a,) satisfy the functions Qr and Qs. Murdoch and Holland10 developed the following formulas for computing the minimum reflux ratio, the distillate rate D, and the dt s of the split key components... 

Compute the minimum reflux ratio (Lr/D), the distillate rate D, and the flow rate of dk for each split key component for the following mixture... 

NUMBER OF IDEAL PLATES AT OPERATING REFLUX. Although the precise calculation of the number of plates in multicomponent distillation is best accomplished by computer, a simple empirical method due to Gilliland is much used for preliminary estimates. The correlation requires knowledge only of the minimum number of plates at total reflux and the minimum reflux ratio. The correlation is given in Fig. 19,5 and is self-explanatory. An alternate method devised by Erbar and Maddox is especially useful when the feed temperature is between the bubble point and dew point. 

Even when (12-27) is invalid, it is useful because, as shown by Gilliland, the minimum reflux ratio computed by assuming a Class 1 sepmation is equal to or greater than the true minimum. This is because the presence of distributing nonkey components in the pinch-point zones increases the difficulty of the separation, thus increasing the reflux requirement. 

The distillate rate for nCj is very close to the value of 2.63 computed in Example 12.4, if we assume a Class 1 separation. The internal minimum reflux ratio at the rectifying pinch point is considerably less than the value of 389 computed in Example 12.4 and is also much less than the true internal value of 298 reported by Bachelor. The main reason for the discrepancy between the value of 219.8 and the true value of 298 is the invalidity of the assumption of constant molal overflow. Bachelor computed the pinch-point region flow rates and temperatures shown in Fig. 12.9. The average temperature of the region between the two pinch regions is 152°F (66.7°C), which is appreciably lower than the... 

For the conditions of Problem 12.7, compute the minimum external reflux rate and the distribution of the nonkey components at minimum reflux by the Underwood equation if the feed is a bubble-point liquid at column pressure. 

For Class 2 separations, (12-23) to (12-26) still apply. However, (12-26) cannot be used directly to compute the internal minimum reflux ratio because values of x,> are not simply related to feed composition for Class 2 separations. Underwood devised an ingenious algebraic procedure to overcome this difficulty. For the rectifying section, he defined a quantity <1> by... 

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