Reflux ratio, optimum

A trayed tower operating at 1 atm is to be designed to continuously distill 200 kmol/h (55.6 mol/s) of a binary mixture of 60 mol% benzene, 40 mol% toluene. A liquid distillate and a liquid bottoms product of 95 mol% and 5 mol% benzene, respectively, are to be produced. Before entering the column, the feed—originally at 298 K—is flash-vaporized at 1 atm to produce an equimolal vapor/liquid mixture (V F = LJF 

Combining these two balances gives D = 122.2 kmol/h, IV = 77.8 kmol/h. 

The following data were obtained from Perry and Chilton (1973)  

Heat capacities of gases, average in the range 298 to 366 K (Smith et al., 1996) 

Consider now the total condenser. Saturated vapor containing 95 mol% benzene at a dew-point temperature of 355.8 K will enter the condenser at the rate of 293.6 kmol/h (81.6 moles/s). It will leave the condenser as saturated liquid of the same composition and a bubble-point temperature of 354.3 K. An energy balance around the condenser is as follows  

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T.eflux Tatio. Generally, the optimum reflux ratio is below 1.15 and often below 1.05 minimum. At this point, excess reflux is a minor contributor to column inefficiency. When designing for this tolerance, correct vapor—Hquid equiUbrium (VLE) and adequate controls are essential. 

Optimum Reflux Ratio The general effecl of the operating reflux ratio on fixed costs, operating costs, and the sum of these is shown in Fig. 13-39. In ordinary situations, the minimum on the total-cost cui ve wih geueraUy occur at an operating reflux ratio of from 1.1 to 1.5 times the minimum R = Lv + i/D value, with the lower value corresponding to a value of the relative volatility close to 1. 

Optimization As stated previously, optimization studies should include the entire system. Such a study was made by Fair and BoUes [Chem. Eng., 75(9), 156 (1968)], using a hght-hydrocarbon system and with the objective of defining optimum reflux ratio. Coolants used were at —87, —40, and +30°C (—125, —40, and +85°F), corresponding to different pressures of operation and associated different condens-... 

Colburn (chemical engineering lecture notes, University of Delaware, 1943) proposed that the optimum reflux ratio is... 

The effect of utilities costs on optimum operation was noted by Kiguchi and Ridgway [Pet. Refiner,. 35(12), 179 (1956)], who indicated that in petroleum-distillation columns the optimum reflux ratio varies between 1.1 and 1.5 times the minimum reflux ratio. When refrigeration is involved, 1. IRmm < flopt < 1 is used in the condensers, 1.2Rrniii < fLpt < 1 -4Rrn... 

Economically optimum reflux ratio is about 1.2 times the minimum reflux ratio Rm. 

Note Above a reflux ratio of 4 there is little change in the number of stages required, and the optimum reflux ratio will be near this value. 

Consequently, the optimum reflux ratio for an appropriately integrated distillation column will be problem specific and is likely to be quite different from that of a stand-alone column operated from utilities. 

Martin and coworkers described an application of optimization to an existing tower separating propane and propylene. The lighter component (propylene) is more valuable than propane. For example, propylene and propane in the overhead product were both valued at 0.20/lb (a small amount of propane was allowable in the overhead), but propane in the bottoms was worth 0.12/lb and propylene 0.09/lb. The overhead stream had to be at least 95 percent propylene. Based on the data in Table E12.4A, we will determine the optimum reflux ratio for this column using derivations provided by McAvoy (personal communication, 1985). He employed correlations for column performance (operating equations) developed by Eduljee (1975). 

The iterative program incorporating the quadratic interpolation search yielded the results in Table E12.4B. The optimum reflux ratio was 17.06 and the cost,/, was 3870/day. Table E12.4C shows the variation in/ for 10 percent change in R. The profit function changes 100/day or more. 

Optimum Reflux Ratio. The reflux ratio affects the cost of the tower, both in the number of trays and the diameter, as well as the cost of operation which consists of costs of heat and cooling supply and power for the reflux pump. Accordingly, the proper basis for choice of an optimum reflux ratio is an economic balance. The sizing and economic factors are considered in a later section, but reference may be made now to the results of such balances summarized in Table 13.3. The general conclusion may be drawn that the optimum reflux ratio is about 1.2 times the minimum, and also that the number of trays is about 2.0 times the minimum. Although these conclusions are based on studies of systems with nearly ideal vapor-liquid equilibria near atmospheric pressure, they often are applied more generally, sometimes as a starting basis for more detailed analysis of reflux and tray requirements. 

TABLE 13.3. Economic Optimum Reflux Ratio for Typical Petroleum Fraction Distillation near 1 atms... 

The optimum reflux ratio and the minimum batch time for separation task 1 are 3 and 80.62 min (Table 3.1). The separation task 2 could be achieved using 3 different reflux ratio (Table 3.2) but however, / exp = 2 gives the true minimum batch time which is about 40% lower than the batch time that would be required to achieve the same separation with Rexp = 4. 

A series of minimum time problems (Chapter 5) were solved at different values of q with increasing holdup for each case. Figures 3.18a and 3.18b show the minimum time solution vs. percent total holdup in the column for different mixtures at different q and Figures 3.19a and 3.19b show the corresponding optimum reflux ratio (required to get the separation in minimum time) vs. percent total holdup of the column. The results are summarized in Table 3.3 which shows, for each given separation, the optimum value of holdup to achieve the best performance out of the given column. The corresponding best minimum batch time and the optimum reflux ratio to achieve that are also presented in the table for each case. 

Figure 3.19a. Optimum Reflux Ratio vs Column Holdup at different qe...

For single separation duty, Al-Tuwaim and Luyben (1991) proposed a shortcut method to design and operate multicomponent batch distillation columns. Their method, however, required a great number of simulations, which must be computationally very expensive, before they could arrive at an optimum design and find an optimum reflux ratio. Further details are in Chapter 7. 

Determine the optimum reflux ratio for the whole operation that will maximise the CAP... 

Mayur et al. (1970) formulated a two level dynamic optimisation problem to obtain optimal amount and composition of the off-cut recycle for the quasi-steady state operation which would minimise the overall distillation time for the whole cycle. For a particular choice of the amount of off-cut and its composition (Rl, xRI) (Figure 8.1) they obtained a solution for the two distillation tasks which minimises the distillation time of the individual tasks by selecting an optimal reflux policy. The optimum reflux ratio policy is described by a function rft) during Task 1 when a mixed charge (BC, xBC) is separated into a distillate (Dl, x DI) and a residue (Bl, xBi), followed by a function r2(t) during Task 2, when the residue is separated into an off-cut (Rl, xR2) and a bottom product (B2, x B2)- Both r2(t)and r2(t) are chosen to minimise the time for the respective task. However, these conditions are not sufficient to completely define the operation, because Rl and xRI can take many feasible values. Therefore the authors used a sequential simplex method to obtain the optimal values of Rl and xR which minimise the overall distillation time. The authors showed for one example that the inclusion of a recycled off-cut reduced the batch time by 5% compared to the minimum time for a distillation without recycled off-cut. 

Maximum Conversion C = gift) Optimum Amount of Distillate Dj = g2(t) Optimum Reflux Ratio r = g3(t) Total Reboiler Heat Load QR = g4(t)... 

For each operation, the amount of distillate ( >, kmol) achieved and the optimum reflux ratio profile are also presented in Table 10.2. Note in all cases the constraints on the distillate amount and purity are satisfied. Table 10.2 dearly shows that tTi decreases and P increases with F. Equation 10.8 shows that for a given recovery, feed composition and distillate purity D, is directly proportional to B0-... 

For different values of F, Rmax, optimum reflux ratio (/ 2)> minimum operation time, productivity are shown in Table 10.4. In all cases the total amount of distillate is 3.95 kmol with 95% purity in Heptane. The productivity (Prod) is calculated using total operation time (rwfo/) which includes 2 hrs of total reflux operation time in STEP 1. 

Key R2, t2 = optimum reflux ratio, minimum time for STEP 2... 

The steady state optimisation problem is solved for different feed flow rates. The maximum achievable distillate rate, optimum reflux ratio (internal), total amount of distillate, pass time and recovery of key component (e.g. component 1) for the first pass are summarised in Table 11.2. For any pass p, the pass time (tp, hr), total amount of distillate (Dp, kmol) and recovery of key component (Rep) are calculated using ... 

Here the feed rate is maximised while the reflux ratio is optimised. The bottom product composition imposes an additional constraint to the problem. The results are summarised in Table 11.8 which gives the maximum feed rate, minimum batch time, optimum reflux ratio, and total number of batches for each mixture and total yearly profit. 

Discrete reflux ratio used in most pilot plant batch distillation columns, including those used in industrial R D Departments (Jenkins, 2000 Greaves, 2003), does not allow a direct implementation of the optimum reflux ratio (treated as a continuous variable) obtained using a model based technique (as presented in earlier chapters of this book). In Greaves et al. (2001), a relationship between the continuous and the discrete reflux ratio is developed. This allows easy communication between the model and the process and comparison on a common basis. 

Many industrial users of batch distillation (Chen, 1998 Greaves, 2003) find it difficult to implement the optimum reflux ratio profiles, obtained using rigorous mathematical methods, in their pilot plants. This is due to the fact that most models for batch distillation available in the literature treat the reflux ratio as a continuous variable (either constant or variable) while most pilot plants use an on-off type (switch between total reflux and total distillate operation) reflux ratio controller. In Greaves et al. 2001) a relationship between the continuous reflux ratio used in a model and the discrete reflux ratio used in the pilot plant is developed. This allows easy comparison between the model and the plant on a common basis. 

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