# How To Find Optimum Reflux Ratio

Reflux flow

Figure 3.4 Reflux rate optimization for an existing column. (Reprinted by permission. Copyright © Instrument Society of America, 1978, from P. R, Latour, Instrumentation Technology, July 1978.)

only. For simplicity, the reflux rate can be used instead of S. Further, since the column is existing, there is no capital cost, and all the costs involved are utility costs. Therefore, the total costs curve becomes the utility costs curve. The "net variable value" is the difference between the recovery value (or product value) curve and the utility costs curve, and features an optimum. Not shown on Figure 3.4, but extremely important for existing columns, are constraints on reflux flow. For instance, the boilup is a function of reflux flow; as reflux flow is raised, the reboiler may reach its maximum capacity. This needs to be expressed as a limiting reflux flow, and is shown as a vertical constraint line on Fig. 3.4. Similarly, constraints related to column flooding, condenser capacity, minimum liquid flow, etc., need also to be shown as vertical constraint lines on Fig. 3.4. Often, such constraints may prohibit operation at the optimum.

3.1.4 Application of recovery and separation optimization

The analysis in Sees. 3.1.2 and 3.1.3 is important whenever product specs are not well defined, or whenever there may be an incentive to generate a product better than the specs. The analysis applies both to new and existing columns. In existing columns, this optimization is often incorporated in a computer control strategy and performed online. When computer control is unavailable, the optimization can be performed off-line and translated into operating procedures.

In the above analysis, it was assumed that product prices and the value of products as a function of their impurity content are well defined. Often, this is not so, for example, when one of the products is recycled to a reactor. In this case, the product value needs to be calculated as a function of its impurity content from data on the expected effect of impurity and recycle on the reactor performance. This analysis can become complicated.

One variable not considered in the analysis is fluctuations in feed composition. Such fluctuations may have an effect on product values and on the separation, and need to be considered in the optimization. Where significant fluctuations are expected, it may be worthwhile to work with component recoveries ^DxLK/FzLK) rather than D/F.

The analysis also did not take into account the thermal state of the feed. In most situations, the thermal state can be optimized separately before the product recovery and separation are optimized. If the thermal state optimization leads to the conclusion that preheating or precooling is unjustified, and the thermal state is likely to vary (e.g., feed coming in from a reactor), fluctuations in this thermal state need to be taken into account in the product specs and recovery optimization.

Finally, it should be noted that the optimization described above is of a shortcut nature. The author is yet to encounter a practical situation where the recovery and separation optimization is performed more rigorously. In the majority of new designs experienced by the author, the optimization did not even go that far. Procedures for more rigorous optimization are available (e.g., Ref. 3), but uncertainties in product values, project life, and costs often makes further fine-tuning difficult to justify.

3.1.5 Setting column pressure Raising column pressure

Unfavorable effects

1. Lowers relative volatility and increases separation difficulty. This raises reflux and stage requirements and reboiler and condenser duties.

2. Raises column bottom temperature. This increases chemical degradation, polymerization, and fouling.

3. Above about 100 psig, increases column shell thickness (4,5) and, therefore, capital cost. This is not a significant factor at pressures lower than about 100 psig (4).

4. Raises reboiler temperature, thereby requiring an unavailable or a more expensive heating medium. For the same heating medium, it increases the reboiler area requirement.

5. For superatmospheric separations, it increases leakage, and if process materials are inflammable or toxic, also the hazard potential.

### Favorable effects

1. Increases the distillate boiling point and permits using a cheaper cooling medium. For the same cooling medium it reduces the condenser area requirements.

2. Below 1 atm, reduces the costs of creating and maintaining a vacuum (e.g., ejector energy consumption and capital costs).

3. Increases vapor density and therefore vapor-handling capacity. This leads to major reductions in column diameter and capital costs under vacuum, and to smaller reductions up to pressures of 50 to 150 psia (6).

4. In distillation of liquefied gases, raises boiling points of the column liquid. This allows cheaper construction materials to be used.

5. Reduces the size of vapor pipes and valves.

6. Below 1 atm, reduces air leakage into the system. In case of flammable materials, this also reduces the associated hazards.

Setting the pressure. Either the second or the fourth consideration on the "unfavorable" list is almost always the sole reason for going to vacuum. When chemical degradation, polymerization, or fouling are not significant, and when an adequate heating medium is available, separation is carried out at or above atmospheric pressure. For vacuum separations, it is desirable to set the pressure as high as possible, due to the third, and to a lesser degree also the second, favorable factors. The pressure is therefore set at the highest possible pressure that provides a bubble-point temperature sufficiently low to prevent significant degradation of the bottom materials and to be satisfactorily reboiled with the available heating medium.

For pressure separations, the controlling factors are usually the first favorable and first unfavorable effects. The pressure is usually set at the lowest possible pressure that permits satisfactory condensation using cooling water or air. A satisfactory temperature approach between the coolant and distillate is normally 10 to 20°F with cooling water, and 30 to 50°F with air.

For separation of liquefied gases, the critical temperature of the distillate may be lower than the cooling water temperature, and refrigeration is needed. The economic balance is still primarily between the first favorable and first unfavorable effects, but the refrigeration complicates the analysis. Optimization is required for selecting the best pressure, and can be lengthy and tedious if correctly performed. Shortcuts often lead to nonoptimum conclusions. Each case must be considered on its own merits. An example of such an optimization for an ethylene-ethane separation column, as well as of some optimization pitfalls, is described elsewhere (7).

3.1.6 Optimum reflux ratio

As reflux ratio is raised,

■ Condensing and reboiling duties rise. Since these make up the bulk of the column operating costs, operating costs also rise.

■ The number of stages decreases (Fig. 3.5), making the column shorter, but column diameter increases. Near minimum reflux, small increases in reflux ratio considerably shorten the column, but only marginally increase its diameter. Capital cost declines. Upon further increases in reflux, the height reduction slows down while the diameter increases accelerate. Eventually, the savings from the shorter column become less than the cost of increasing Figure 3.5 Stages-reflux relationship for the depropanizer in Example 3.4.

the diameter, and capital costs begin to escalate as reflux ratio is raised.

Figure 3.6a shows how costs for a new distillation system vary with the reflux ratio. It expresses the capital cost as an annual cost. This can be achieved by dividing the capital cost by the expected payout period. A discounted cash flow (DCF) analysis is used for estimating this payout period. The capital cost should include the costs of auxiliaries (reboiler, condenser, vacuum equipment, pumps, piping; in many cases, costs of vent systems, coolant, and heating medium handling equipment are also affected). The operating costs should include reboiler Capital cost

Operating cost

Total cost

Rop+ Reflux ratio

Capital cost

Operating cost

### Total cost

Figure 3.6 Optimum reflux ratio. (a) Capital and operating cost curves; (6) effect of using expensive materials of construction on the optimum; (c) effect of high energy costs on the optimum; id) optimum reflux, toluene-benzene separation, show a flat total cost curve near the optimum. (Part <f reprinted with permission from W. R. Fisher, M, F. Doherty, and J. M. Douglas, Ind. Eng. and Chem. Proc. Des. and Devel.. Vol. 24, p. 955, Copyright © (1985) American Chemical Society).

Rop+ Reflux ratio la)

heat, coolant, reflux pumping, and utility pumping. In most water-cooled and air-cooled columns, the cost of reboiler heat is the dominant operating cost.

Figure 3.6a shows that there is an optimum reflux ratio. Using expensive materials of construction (ALLOY curves in Fig. 3.66) shifts the optimum to the right, and favors high-reflux designs. High energy cost (HEC curves in Fig. 3.6c) shifts the optimum to the left, favoring operation closer to minimum reflux.

With energy-saving designs, optimum reflux is often near minimum reflux. Here small errors in relative volatilities and enthalpies lead to large errors in the number of trays. In addition, any maldistribution will cause part of the column to operate below minimum reflux, and the separation will not be achieved. It is customary to leave a safety margin from minimum reflux. An excellent alternative practice for towers whose optimum reflux is close to minimum is (8) to leave this safety margin only in the design of the reflux system and utilities. The number of trays is designed to the optimum reflux. This practice permits approaching minimum reflux while safeguarding against potential disasters arising from volatility and enthalpy errors or maldistribution near minimum reflux.

The total cost curve tends to flatten near the optimum. Figure 3.6d, based on a benzene-toluene separation case study (2), shows a total cost within 2 percent of the optimum for reflux ranging from 1.15 to 1.5 times the minimum. King (9) reached an identical conclusion and demonstrates it with an entirely different case study. The author observed this flatness in many actual designs.

Rules of thumb are often used by designers to shortcut reflux opti-

/ Total cost, alloy

Total cost, base

Operating cost (both base arid alloy)

/ Total cost, alloy

Total cost, base

Operating cost (both base arid alloy) Reflux ratio -(b) Legend:

HEC = high energy cost

Capital cost base and HEC

Total cost, base

Operating cost, base

Legend:

HEC = high energy cost

Capital cost base and HEC

^min Ropt> HEC Ropt, base Reflux ratio <c>

Figure 3.6 {Continued) Optimum reflux ratio, (6) effect of using expensive materials of construction on the optimum; (c) effect of high energy costs on the optimum;

mization. Due to the flatness of the total cost curves near the optimum, this shortcut usually incurs no more than a minor economic penalty. The rules of thumb are expressed as the optimum ratio of reflux to minimum reflux i^opt/Rmin-

During the 1960s, when energy was cheap, i?optARmiri ratios were high. An extensive survey by King (9), however, shows that even with cheap energy, these "high" ratios were generally very close (1.1 to Figure 3.6 (Continued) Optimum reflux ratio, id) optimum reflux, toluene-benzene separation, showing a flat total cost curve near the optimum. (Part d reprinted with permission from W. R. Fisher, M. F. Doherty, and J. M. Douglas, Ind. Eng. and Cketn. Proc. Des. and Devel., Vol. 24, p. 955, Copyright © (1985) American Chemical Society).

Figure 3.6 (Continued) Optimum reflux ratio, id) optimum reflux, toluene-benzene separation, showing a flat total cost curve near the optimum. (Part d reprinted with permission from W. R. Fisher, M. F. Doherty, and J. M. Douglas, Ind. Eng. and Cketn. Proc. Des. and Devel., Vol. 24, p. 955, Copyright © (1985) American Chemical Society).

1.25 times) to the minimum. The optimum ratio dropped when the cost of energy sharply escalated in 1973. Although energy prices have declined since, the awareness of the high cost of energy remained, and so has the practice of using low i?opt//?min ratios. Pre-1973 rules of thumb for optimum reflux are therefore not recommended. Rules of thumb proposed for Ropi/Rmin in recent years are summarized in Table 3.2.

### 3.1.7 Feed stage optimization by computer

The ideal feed point can be determined by graphical (Sec. 2.3.7), shortcut (Sec. 3.2.6), or rigorous techniques. Commercial simulations often incorporate search techniques (e.g., Ref. 15) for seeking the optimum table 3.2 Rules of Thumb for fl^/f?^ Ratio

RopJRm^ Ref. Note

Water-cooled or air-cooled condensers 1.2-1.3 10,11

High-level refrigeration condensers 1.1-1.2 10,13,14 (Note 1) < 1.1 9

Low-level refrigeration condensers 1.05-1.1 10,13 1,4

'Presumably, the rules are based on carbon and stainless steet. For columns constructed out of more expensive materials, R„vJRmtn is higher (Fig. 3.66).

'Presumably, these rules are based on steam, hot oil, or a similar heating medium. For columns reboiled with waste heat, RapliRm,n ratios as high as 1.4 to 1.5, and even larger, are often optimum. 3 Author of this rule presents a thorough survey to back it up, ■"Due to uncertainty in the vicinity of minimum reflux (see text), the author does not recommend designing for R^R^^ lower thari 1.1.

feed stage. These are usually based on minimizing an objective function. Small variations are introduced to the feed point, and their effect on top and bottom compositions is estimated by a rigorous or shortcut method. The results are substituted into the objective function, and the next trial begins with the feed entering a stage for which the objective function is lower.

Alternatively, results from a computer simulation can be plotted to determine the optimum feed stage. Simulation runs are performed at several different feed points, keeping the material balance, reflux ratio, and total number of stages constant. Key component concentrations in the product streams are plotted against the feed stage number (Fig. 3.7). The minimum is at the optimum feed stage.

Generally, the ratio of optimum feed stage to total number of stages is independent of the number of stages. This is predicted from Fenske's feed point relationship (Sec. 3.2.6). In Fig. 3.7a, optimum NSJ N is between 0.44 and 0.47 for N between 15 and 25. On the other hand, the optimum Ns/N is a strong function of the material balance (Fig. 3.76). Reducing the distillate rate shifts the ideal feed stage down the column, while reducing the bottoms rate shifts it up the column. In Fig. 3.76, a product rate shift of less than 2 percent shifts the optimum feed by more than 3 stages out of 20.

The minima are usually flat, but steepen as a pinch or as minimum reflux is approached. They appear quite flat in Fig. 3.7 even though reflux declines from 2.6 times to 1.2 times the minimum (as the number of stages rises from 15 to 25). The steepening of the minima as reflux is lowered would have been apparent had the x-axis of Fig. 3.7a been the ratio of rectifying (or stripping) stages to total stages. Figure 3.7 Feed point optimization by plotting results of computer simulation, depropaniier in Example 3.4, (a) Effect of the total number of stages F = 100, D = 59.9

Figure 3.7 Feed point optimization by plotting results of computer simulation, depropaniier in Example 3.4, (a) Effect of the total number of stages F = 100, D = 59.9

### 3.1.8 Minimum reflux by computer

Minimum reflux can be determined by graphical (Sees. 2.3.5, 2.4.1), shortcut (Sees. 3.2.2 to 3.2.4), or rigorous techniques. Most graphical and shortcut methods give good results either when constant molar overflow (Sec. 2.2.2) applies, or when the method is corrected for energy balance. Unfortunately, shortcut methods in most commercial simulations apply no energy balance correction, and wild minimum reflux predictions are not uncommon.

Rigorous procedures (e.g., Refs. 15 to 20) accurately predict minimum reflux. Since convergence of rigorous calculations near minimum reflux is extremely difficult, these methods often fail to converge. Bolles (21) reported that Chien's rigorous method (20) works extremely well for practically all systems, even the highly nonideal, Figure 3.7 [ContinuecDFeed point optimisation by plotting results of computer simulation, depropanizer in Example 3.4. (6) effect of column material balance JV = 20.

Figure 3.7 [ContinuecDFeed point optimisation by plotting results of computer simulation, depropanizer in Example 3.4. (6) effect of column material balance JV = 20.

with no convergence difficulties. Chien (20) stated that his method experiences convergence problems only when a tangent pinch is encountered (Fig. 2.12). Chien's method is incorporated in Monsanto's FLOWTRAN simulator.

A simple method (22) which rigorously calculates minimum reflux without convergence problems is extrapolation of the reflux-stages plot (Fig. 3.8). Simulation runs are performed at different numbers of stages, keeping the material balance, product compositions, and Ng/N constant, while letting reflux rate vary. For each run, the number of stages is plotted against reflux, and the curve is extrapolated asymptotically to an infinite number of stages.

An alternative method proposed by Rose (23) is to plot 1/R versus 1/N, extrapolating to UN of zero to obtain minimum reflux. The author found this extrapolation to be far more difficult, and also this plot to be a curve and not the straight line shown by Rose (23). Figure 3.8 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,

Figure 3.8 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,

### 3.1.9 Minimum stages by computer

Minimum stages can be determined by graphical (Sec. 2.2.8), shortcut (Sec. 3.2.1), or rigorous techniques. Usually, shortcut techniques are satisfactory, providing a good approximation is applied for relative volatility. For systems where relative volatility varies widely from column top to bottom, a more rigorous method may be desired. Chien (24) presented such a method, and Bolles (21) reported favorable experiences with it. Alternatively, extrapolation of a reflux-stages plot (Fig. 3.8) to infinite reflux gives a rigorous approximation of the minimum number of stages, as outlined in Sec. 3.1.8.

3.1.10 Process design procedure

Process design proceeds in the following steps:

1. Specify separation. If product composition or product flow requirements are not defined, determine them by material and energy balance optimization.

2. Set column pressure.

3. Determine the minimum reflux and minimum number of stages.

### 4. Find the optimum feed stage.

5. Select three ratios of actual to minimum reflux. For each, calculate a number of stages and size the column and auxiliaries. Determine which is the most economical. This optimization procedure can be bypassed by selecting a single ratio of reflux to minimum reflux.

6. The calculations so far can be shortcut or rigorous. If a rigorous (tray-by-tray) calculation has not been performed yet, now is the time.

7. Reexamine steps 3 and 4, refining earlier estimates as necessary. If the refinements are large, steps 5 and 6 may need repeating.

8. Analyze the design graphically (Sec. 2.4) to ensure optimum design and absence of pinched regions.

3.2 Reflux and Stages: Shortcut Methods 3.2.1 Minimum stages

The minimum number of stages is given by Fenske's equation (25)

Nmia = In S/ln («lk/hk^v (3.4) where S was given earlier by Eq. (3.3)

S = (W*HK)D (W*LK)B (3.5) The Fenske equation was shown to be rigorous (25) if

(aLK/HK)sv ~ \Z<*LK/HK,laLK/HK,2 • • '«LK/HKJi (3.6)

However, («LK,HK)av is usually obtained from one of the following approximations:

5. aav = VtttopOmid^bot

Method 1 was recommended by Maddox (26,27); method 2 was recommended by Van Winkle (28), method 4 or 5 was recommended by Fair (29), Seader and Kurtyka (30), and McCormick and Roche (13), method 3 or 4 was preferred by King (9), while method 4 was preferred by a number of designers (11,31-33). Douglas (34) proposed a criterion for testing the relative volatility approximation.

When the above inequality is obeyed, relative volatility is reasonably constant throughout the column, and the simpler approximations such as 2 or 4 are appropriate.

The Fenske equation applies not only to the light key and heavy key components. It can also be applied to any pair of components.

Winn's modification. In an attempt to account for temperature variation of the relative volatility, Winn (35) proposed the equation

_xlKJt\XMKJ)j plk/hk

Plk/hk ©lk are constants at a fixed pressure, evaluated from the K-values for the light key and heavy key at the top and bottom temperatures. Plk/hk and 9lk related to each other by (35)

The Winn equation reduces to Fenske's equation when 6LK = 1.0 and plk/hk = alk/hk'

Example 3.1 Evaluate the minimum number of stages for the depropanizer in Example 2.4 using each of the methods described above. Use the following data:

Example 3.1 Evaluate the minimum number of stages for the depropanizer in Example 2.4 using each of the methods described above. Use the following data: