Reflux, distillation optimum, ratio

An efficient optimization approach for reactive batch distillation using polynomial curve fitting techniques was presented by [55]. After finding the optimal solution of the maximum conversion problem, polynomial curve fitting techniques were applied over these solutions, resulting in a nonlinear algebraic maximum profit problem that can be efficiently solved by a standard NLP technique. Four parameters in the profit function, which are maximum conversion, optimum distillate, optimum reflux ratio, and total reboiler heat load, were then represented by polynomials in terms of batch time. This algebraic representation of the optimal solution can be used for online optimization of batch distillation. 

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... 

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. 

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

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. 

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. 

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 ... 

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. 

In this study it was shown that propane or mixtures of propane and butane may be used as supercritical solvents to fractionate mixtures of high molecular weight alkanes. By using an optimum reflux ratio, selectivities better than that of molecular distillation can be obtained. It was also found that for the system in this study, the operating costs of a supercritical extraction unit may be marginally lower than that of a molecular distillation unit. 

Supercritical fractionation of high molecular weight alkane mixtures with propane or LPG may be used to produce products with lower polydispersity that that of molecular distillation. Operating temperatures just above the cloud point of the mixtures can be used compared to the high temperatures needed in molecular distillation. It was also shown that an optimum reflux ratio exists for every set of operating conditions. For this system it was also found that the operating costs of a supercritical fraction unit is marginally less than that of a molecular distillation unit. 

As indicated in Fig. 11-7, the optimum reflux ratio occurs at the point where the sum of fixed charges and operating costs is a minimum. As a rough approximation, the optimum reflux mho usually falls in the range of 1.1 to 1.3 times the minimum reflux ratio. The following example illustrates the general method for determining the optimum reflux ratio in distillation operations. 

Example 6 Determination of optimum reflux ratio. A sieve-plate distillation column is being designed to handle 700 lb mol (318 kg mol) of feed per hour. The unit is to operate continuously at a total pressure of 1 atm. The feed contains 45 mol% benzene and 55 mol% toluene, and the feed enters at its boiling temperature. The overhead product from the distillation tower must contain 92 mol% benzene, and the bottoms must contain 95 mol% toluene. Determine the following ... 

There are other mles-of-thumb based on economic experience, which the reader will recognize, such as the optimum reflux ratio in distillation and the optimum liquid to gas ratio in gas absorption. You may also specify recoveries of key conq)onents or their concentrations in an exit stream for separators. When we use any of these rules, the assim tion is that the calculated separator size will be of reasonable cost, approximating the optimum-size separator. Similarly, for chemical reactors we may specify conversion of a desirable con jound, its exit composition or an approach temperature difference. For chemical reactors, the approach temperature difference is the difference between the actual temperature and the chemical-equilibrium ten5)erature. Again, we assume that a reactor that approximates the optimum-size reactor will result when using this rule. 

Distillation towers feed-tray location for, 10 optimum reflux ratio for, 371-376 specifications for, 16 (See also Bubble-cap contactors, Packed towers. Sieve trays, and Valve trays) Distribution costs, 194, 196, 207, 211 Distribution in statistical analyses, 745-746 Dividends, tax exemptions for, 259 Documentation, 137-149,452-476 Double-entry bookkeeping, 143-144 Downcomers in tray columns, 684-686 Drives, cost of 532-533 Dryers, cost of 713-716... 

The easiest way to use a shortcut distillation model is to start by estimating the minimum reflux and number of stages. The optimum reflux ratio is usually between 1.05 and 1.25 times the minimum reflux ratio, Rmm, so 1.15 x Rmin is often used as an initial estimate. Once the reflux ratio is specified, the number of stages and optimum feed stage can be determined. The shortcut model results can then be used to set up and initialize a rigorous distillation simulation. 

A distillation process has been set up to separate an ethylene-ethane mixture as shown in Fig. P4.94. The product stream will consist of 98% ethylene and it is desired to recover 97% of the ethylene in the feed. The feed, 1000 lb per hour of 35% ethylene, enters the preheater as a subcooled liquid (temperature = — 100 F, pressure = 250 psia). The feed experiences a 20 F temperature rise before it enters the still. The heat capacity of liquid ethane may be considered to be constant and equal to 0.65 Btu/(lb)(°F) and the heat capacity of ethylene may be considered to be constant and equal to 0.55 Btu/(lb)("F). Heat capacities and saturation temperatures of mixtures may be determined on a weight fraction basis. An optimum reflux ratio of 6.1 lb reflux/lb product has been previously determined and will be used. Operating pressure in the still will be 250 psia. Additional data are as follows ... 

In the calculation of the plate number for batch distillation Zuiderweg [158] takes into account the influence of the total hold-up and the magnitude of the transition fraction. Mixtures having ix-values from 1.07 to 2.42 were used to study the dependence of separation sharpness on relative total hold-up, reflux ratio and plate number. By means of the pole height S the optimum reflux ratio can be determined. The method corresponds to the determination after McCabe-Thiele with a final state. cs = 5 mol%. 

The analysis of the minimum reflux mode is used at the stage of sequence selection, as well as at the stage of determination of optimum reflux ratios and the quantity of column trays. The geometric theory of distillation makes it possible to develop the general methods of calculation of minimum and more reflux mode. 

Figure 3.3.17 Principle of the method used to determine the cost optimum reflux ratio of a distillation.

Optimum Reflux Ratio Example. The following estimates illustrate these factors for the fractional distillation of a methanol-water mixture to produce 250 gal. of methanol per hour. In making the calculations, it was assumed that the heat-transfer surface required was proportional to the vapor rate which is equal to... 

FIGURE 7.7 Optimum reflux ratio for distillation column. 

This will be possible for only a few practical design problems. The technique is illustrated in Example 1.1, and in the derivation of the formula for optimum pipe diameter in Chapter 5. The determination of the economic reflux ratio for a distillation column, which is discussed in Volume 2, Chapter 11, is an example of the use of a graphical procedure to find the optimum value. 

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