The Reflux Ratio R

The generalized reflux ratio (R ) in a CS is a parameter that fixes the ratio of the liquid stream to the net flow in the CS, defined as 

The general definition given in Equation 3.20 can be written specifically for a simple column rectifying section using Equation 3.11 to give the familiar definition of reflux 

Equation 3.21 is in fact equivalent to the standard definition of a reflux ration used throughout distillation literature. It is not usually common practice to refer to a reflux ratio for a stripping section, but with the general definition it can be defined by incorporating Equation 3.12 

6 PROPERTIES OF COLUMN PROFILE MAPS 3.6.1 The Relationship Between ROMs and CPMs 

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Porter and Momoh have suggested an approximate but simple method of calculating the total vapor rate for a sequence of simple columns. Start by rewriting Eq. (5.3) with the reflux ratio R defined as a proportion relative to the minimum reflux ratio iimin (typically R/ min = 1-D- Defining Rp to be the ratio Eq. (5.3) becomes... 

The two condensate Hquids must be used to provide reflux and distiUate streams. NormaHy, the reflux ratio, r, is chosen so that r = L jD > (j). This requires that the reflux rate be greater than the condensation rate of entrainer-rich phase and that the distiUate rate be correspondingly less than the condensation rate of entrainer-lean phase. This means that the distiUate stream consists of pure entrainer-lean phase, ie, Xj = x, and the reflux stream consists of aU the entrainer-rich phase plus the balance of the entrainer-lean phase. Thus, the overall composition of the reflux stream, Hes on the... 

Any change in the reflux ratio R will therefore modify the slope of the operating line and, as may be seen from Figure 11.15, this will alter the number of plates required for a given separation. If R is known, the top line is most easily drawn by joining point A (xd, Xd) to B (0,Xd/(R + 1)) as shown in Figure 11.17. This method avoids the calculation of the actual flow rates L and Vn, when the number of plates only is to be estimated. 

If the reflux ratio R is assumed to be adjusted continuously to keep the top product at constant quality, then at any moment the reflux ratio is given by R = dLb/dDb. During the course of the distillation, the total reflux liquor flowing down the column is given by ... 

Giluland(30) has given an empirical relation between the reflux ratio R and the number of plates n, in which only the minimum reflux ratio Rm and the number of plates at total reflux nm are required. This is shown in Figure 11.42, where the group [in + 1) — (nm + l)]/(n + 2) is plotted against R — Rm)/(R + 1). 

Avoid saturation of a manipulated variable. A good example of saturation is the level control of a reflux drum in a distillation column that has a very high reflux ratio. Suppose the reflux ratio (R/D) is 20, as shown in Fig. 8.10. Scheme A uses distillate flow rate D to control reflux drum level. If the vapor boilup dropped ouly 5 percent, the distillate flow would go to zero. Any bigger drop in vapor boilup would cause the drum to run dry (unless a low-level override controller were used to pinch back on the reflux valve). Scheme B is preferable for this high reflux-ratio case. 

Determine the number of theoretical stages necessary to achieve the required separation as a function of the reflux ratio R. 

Of these, the feed mixture may or may not vary, but is generally taken as given. The column pressure and the degree of subcooling are normally fairly constant. The main operational variables are the reflux ratio R and the heat input to the reboiler QR and once these are set, the amount of product withdrawal at the bottom or at the top will also be given by the product specifications. An optimum exists for the reflux ratio in terms of operating costs, and normally a number of ratios are tested, and the economics of each scenario is investigated, before a decision is reached. 

In this strategy the feed mixture is charged in the reboiler (at the beginning of the process) to its maximum capacity. For a given condenser vapour load Vc, if the reflux ratio R (which governs the distillate rate, LD, kmol/hr) and the solvent feed rate F (kmol/hr) are not carefully controlled the column will be flooded. To avoid column flooding Tran and Mujtaba (1997) developed the following necessary and sufficient condition ... 

The reflux ratio, R, for a column is the ratio of the liquid we reflux back to the column at the top stage relative to the distillate product flow i.e., R = L/D. where L is the liquid flow in the top section of our column. Suppose we operate our column with a fixed solvent-to-distillate ratio i.e., / , = S/D = constant. If R, and D are fixed, the location of the A point is fixed because... 

We see that we have both an upper bound and a lower bound on the column reflux ratio. Does having an upper bound make intuitive sense We have set the. solvent flow proportional to the distillate product flow i.e., S = RsD. As we increase the reflux ratio R, the ratio of solvent feed flow. RsD, to reflux flow, RD, decreases. This decreases the solvent concentration throughout the column, thus reducing its impact on the liquid activity coefficients that we are using to separate A from B. With an infinite reflux ratio, the. solvent flow reduces to zero, and we have a normal column operating at total reflux which we know cannot separate A from B. 

The ratio of the flowrates can be expressed in terms of the reflux ratio R using (64) ... 

Note in this description the words reflux rate and reflux ratio. They are different, and you need to be careful to use the right one, since using too small a reflux rate could make your column not work. Finally, you use the Eduljee version (Eduljee, 1975) of the Gilliland correlation (Gilliland, 1940) [Eq. (6.6)] to find the actual number of stages. This equation correlates data on roughly one-hundred distillation columns. You must specify either the reflux ratio (R) or number of stages (S) in order to use this equation. 

From the equations listed, McCormick s gives a good agreement in the normal operating range of real towers. The reflux ratio, R, is calculated as a multiple of the minimum reflux ratio, R . 

The Fenske-Underwood-Gilliland methods are again applied to the distillate composition, X (assumed constant), the current reboiler composition, X y+j and the number of trays, N, to determine r and hence the reflux ratio, R. The procedure is repeated by further incrementing the reference component composition for each time step until a target composition X y is reached. 

The liquid entering the top stage is the external reflux rate, L0, and its ratio to the distillate rate, LQ/D, is the reflux ratio, R. For the case of a total condenser, with reflux returned to the column at its bubble point, L0 = L and R = LID, a constant in the rectifying section. Since V = L + D,... 

If the reflux ratio R or distillate rate D is fixed, instantaneous distillate and bottoms compositions vary with time. For a total condenser, negligible holdup of vapor and liquid in the condenser and the column, equilibrium stages, and constant molar overflow, the Rayleigh equation can now be written as... 

DisWISte Addition Before discussing the experimental setup, it is important to first interpret the underlying mathematics of Equation 4.3. Through the variable transformations used to obtain Equation 4.3, it can be shown that the reflux ratio r and the distillate flowrate D can be related to each other as follows ... 

FIGURE 4.4 Experimental validation of column profiles for the acetone/ethanol/methanol system with the reflux ratio r = = 1 and Xd = = [0.54,0.11]. Theoretical profiles were... 

FIGURE 4.6 Experimental validation of rectifying column profiles for the benzene/diethyl ether/methanol system with the reflux ratio r== 3 and x/> = X d = [0.694, 0.066] using the NRTL thermodynamic model at P=0.825 atm. 

FIGURE 4.10 Experimental validation of stripping column profiles for the acetone/ ethanol/methanol system with the reflux ratios R/ = 3 and 5, and X b = [0.05, 0.80]. Theoretical profiles were generated using the NRTL model at 0.825 atm. 

However, it was shown that for the above conditions the multiplicity regions in the space of the adjustable operating parameters are fairly small for the MTBE process ]73]. This is illustrated in Fig. 10.13 for the pilot plant column treated in ]72, 73]. The bifurcation parameters are the heating rate Q and the reflux ratio R, which can be directly adjusted at the real plant. The parameter range is further decreased if a finite mass transfer between the vapor and the hquid phase is taken into account as shown in ]5, 40] for the column configuration of Jacobs and Krishna ]45]. Moreover, the multiplicity regions even seem to disappear entirely, when finite transport processes are taken additionally into account inside the catalyst [39]. Hence, practical relevance seems to be low. 

The split of the overhead condensate is often referred to in terms of the reflux ratio, R = L/D. Then we have... 

The separation power base in the classic McCabe-Thiele graphical model of a binary distillation column is established by the reflux ratio, R/D, which is the ratio of the reflux flow rate divided by the distillate flow rate. For example, with a distillation column that is fed 1,000 kg/h of feed that produces 85 kg/h of distillate with 425 kg/h of reflux, the reflux ratio is 425/85 = 5. A minimum reflux ratio is required to achieve the desired separation with an infinite number of theoretical stages. The maximum reflux ratio, called total reflux, with zero distillate flow rate can be used in design calculations to determine the minimum number of theoretical stages required to achieve a desired separation. 

Other factors affecting the design and performance of a distillation column are (a) the feed composition, (b) the specifications of the top and bottom products, (c) the number of stages in the column, and (d) the reflux ratio R. This ratio is the amount of reflux to the amount of distillate (top product). Both quantities are generally expressed in units of moles per unit time and therefore the reflux ratio is dimensionless. 

The feed composition, its temperature and whether it is liquid or vapour, are all important. A column designed for a liquid feed is unlikely to perform satisfactorily if the feed were to be all vapour. For given feed conditions and product quality there is a trade-off between the reflux ratio R and the number of stages N. However, there is both a minimum reflux ratio and a minimum number of stages and the next two sections will explain, with respect to binary mixtures, the origin of these minima. 

Defining the reflux ratio R as the ratio of the amount of liquid returned to the amount of top product withdrawn, that is T = RD, equation (6.4) can be written as ... 

The conditions around a simple distillation column are shown in Fig. 6.15. Products D and W leave the top and bottom of the column respectively and feed F is introduced at some intermediate point. A liquid stream L is returned to the top of the column and a vapor stream V to the bottom. The stream L is the reflux and LjD is the reflux ratio R. The number of plates or stages in the column is N. Heating and cooling services are provided by a reboiler and condenser. 

The method as shown assumes total reflux, i.e. no overhead product is drawn. The reflux ratio (R/D) is therefore infinite. It therefore gives us the minimum number of theoretical trays. 

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