Examples operating reflux ratio

McCabe-Thie/e Example. Assume a binary system E—H that has ideal vapor—Hquid equiHbria and a relative volatiHty of 2.0. The feed is 100 mol of = 0.6 the required distillate is x = 0.95, and the bottoms x = 0.05, with the compositions identified and the lighter component E. The feed is at the boiling point. To calculate the minimum reflux ratio, the minimum number of theoretical stages, the operating reflux ratio, and the number of theoretical stages, assume the operating reflux ratio is 1.5 times the minimum reflux ratio and there is no subcooling of the reflux stream, then ... 

Example 8-25 Scheibel-Montross Minimum Reflux, 80 Minimum Number of Trays Total Reflux — Constant Volatility, 80 Chou and Yaws Method, 81 Example 8-26 Distillation with Two Sidestream Feeds, 82 Theoretical Trays at Operating Reflux, 83 Example 8-27 Operating Reflux Ratio, 84 Estimating Multicomponent Recoveries,... 

To employ statistics, the first step is to develop a mathematical model for the unit or process. With a well-established process that has been operating for a considerable period of time, a mathematical model that is highly fundamental based on well-determined steps or reactions can often be developed. For example, Hougen and Watson [16] many years ago showed how the numerous steps in catalytic reactions can be modeled in a relatively fundamental manner. For distillation units, relatively fundamental models can generally be developed to indicate how changes of the following affect operations reflux ratio, process conditions, cost of feed streams, product and feed compositions, demand for product, etc. 

EXAMPLE 11.7-3. Minimum Reflux Ratio and Number of Stages at Operating Reflux Ratio... 

In the example, the minimum reflux ratio and minimum number of theoretical plates decreased 14- to 33-fold, respectively, when the relative volatiHty increased from 1.1 to 4. Other distillation systems would have different specific reflux ratios and numbers of theoretical plates, but the trend would be the same. As the relative volatiHty approaches unity, distillation separations rapidly become more cosdy in terms of both capital and operating costs. The relative volatiHty can sometimes be improved through the use of an extraneous solvent that modifies the VLE. Binary azeotropic systems are impossible to separate into pure components in a single column, but the azeotrope can often be broken by an extraneous entrainer (see Distillation, A7EOTROPTC AND EXTRACTIVE). 

While process design and equipment specification are usually performed prior to the implementation of the process, optimization of operating conditions is carried out monthly, weekly, daily, hourly, or even eveiy minute. Optimization of plant operations determines the set points for each unit at the temperatures, pressures, and flow rates that are the best in some sense. For example, the selection of the percentage of excess air in a process heater is quite critical and involves a balance on the fuel-air ratio to assure complete combustion and at the same time make the maximum use of the Heating potential of the fuel. Typical day-to-day optimization in a plant minimizes steam consumption or cooling water consumption, optimizes the reflux ratio in a distillation column, or allocates raw materials on an economic basis [Latour, Hydro Proc., 58(6), 73, 1979, and Hydro. Proc., 58(7), 219, 1979]. 

In the distillation column example, the manipulated variables correspond to all the process parameters that affect its dynamic behavior and they are normally set by the operator, for example, reflux ratio, column pressure, feed rate, etc. These variables could be constant or time varying. In both cases however, it is assumed that their values are known precisely. 

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). 

An alternative method of operation is to work with a constant reflux ratio and allow the composition of the top product to fall. For example, if a product of composition 0.9 with respect to the more volatile component is required, the composition initially obtained may be 0.95, and distillation is allowed to continue until the composition has fallen to some value below 0.9, say 0.82. The total product obtained will then have the required composition, provided the amounts of a given purity are correctly chosen. 

Hence the reflux ratio, the amount of distillate, and the bottoms composition can be related to the fractional distillation time. This is done in Example 13.4, which studies batch distillations at constant overhead composition and also finds the suitable constant reflux ratio that enables meeting required overhead and residue specifications. Although the variable reflux operation is slightly more difficult to control, this example shows that it is substantially more efficient thermally—the average reflux ratio is much lower—than the other type of operation. 

The batch distillation operation can be schematically represented as a State Task Network (STN). A state (denoted by a circle) represents a specified material, and a task (rectangular box) represents the operational task (distillation) which transforms the input state(s) into the output state(s) (Kondili et al., 1988 Mujtaba and Macchietto, 1993). For example, Figure 3.1 shows a single distillation task producing a main-cut 1 (Di) and a bottom residue product (Bj) from an initial charge (B0). States are characterized by the amount and composition of the mixture residing in them. Tasks are characterized by operational attributes such as then-duration, the reflux ratio profile used during the task, etc. 

This example is taken from Mujtaba and Macchietto (1996). The problem is to design a column for 2 binary separation duties. One of the separations is very easy compared to the other one. The fraction of production time for each duty is specified together with the still capacity (B0) and the vapour load (V). Each binary mixture produces only one main distillate product and a bottom residue (states MPf= Dl, Bfl] and MP2=[D2, Bf2]) from feed states EFt= Fl and EF2= F2], respectively, with only one distillation task in each separation duty. Desired purities are specified for the two main-cuts (x Di and xID2). Also obtain the optimal operating policies in terms of reflux ratio for the separations. 

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. 

The minimum batch times for the individual cuts and for the whole multiperiod operation are presented in Table 8.8 together with the optimal amount of recycle and its composition for each cut. The percentage time savings using recycle policies are also shown for the individual cuts and also for the whole operation. Figure 8.18 shows the accumulated distillate and composition profile with and without recycle case for the operation. These also show the optimal reflux ratio profiles. Please see Mujtaba (1989) for the solution statistics for this example problem. 

Here, the same mixture used for example 1 is considered. Semi-continuous solvent feeding mode with full charge strategy is opted in this example. The objective is to maximise the productivity of Task 1 of the STN shown in Figure 10.6. The specification on the distillate composition is 0.95 molefraction in Heptane. The optimisation problem (OP1) is considered and both the reflux ratio and solvent rate profiles are optimised. Again two time intervals are used for the entire operation period (Task 1). In each interval, constant reflux ratio and solvent feed rate are used, the values of which are optimised. The input data are the same as those in Table 10.1 except that the maximum reboiler capacity is 25 kmol. The solvent is introduced in plate 6 (Nf). 

Example 2.4 A material balance for the column is shown in Table 2.7. Tbe column operates at a pressure of 315 peia. The feed is 66 percent vapor at the column inlet- Tlie relative volatilities of the components at 206°F (feed plate temperature) are shown in Table 2.3. The column is equipped with a partial condenser, and the reflux ratio is 1.5. It is required to determine the number of theoretical stages. 

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. 

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 ... 

As an example, consider a batch rectifier fed with a 1 1 mixture of ethanol and n-propanol. The rectifier has eight theoretical stages in the column and is operated at a reflux ratio of 19. The distillate and pot compositions are shown in Fig. 13-127 for various values of the holdups. 

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