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1. Requires a greater reflux ratio and condenscr duty. The disparity becomes greater as the separation becomes easier.

2. Requires fewer operating trays. The disparity becomes greater as the separation becomes easier.

3. Requires a lower reboiler duty in every case but one. The disparity becomes greater as the separation becomes easier.

4. Requires greater column area with the load tray being in the rectifying section. Thus, if swaging is not practical, the only tower design economy can be effected by reducing tray spacing in the stripping section.

The converse of all the above is true for the case of bubble-point liquid feed.

Based on the above facts, the following conclusions are reached for design cases.

1. The practice of preheating column feed to save reboiler duty requires a greater condenser duty and greater tower area. Thus, the designer must consider utility costs for heating and cooling as well as equipment costs. Generally speaking, more condensing surface is required per unit of heat transferred than is heating surface. This is especially true in the case of fired re-boilers, although alloy requirements for tubes may sometimes offset the apparent savings differential.

2. In economic climates where cooling is expensive due to water shortage or to high ambient air temperatures, e.g., the Middle East, feed preheat by feed-bottoms exchange will almost always result in higher capital and operating costs.

3. Feed preheat should never be practiced in columns having refrigerated condensers. Rather, maximum feasible precooling of the feed is indicated, especially if refrigeration recovery can be effected.

. In difficult separations, minimizing the heat content of the feed will materially reduce reflux requirements and tower area with no significant increase in tray requirements.

For revamps of or additions to existing plants, the problems are not so easily defined as in a design situation. In many cases, systems are first limited by factors other than the tower, such as pumps, condensers, reboilers, external heat exchangers, etc.. then the tower itself. Other factors may come into play such as plot area availability or the limitation to an expensive piece of equipment such as a fired heater. Utilities system limitations may force the designer into a course of action which ordinarily might not be indicated. The following general guidelines are recommended for revamps/expansions.

1. If a reboiler is limiting and the tower is not, capacity can be increased up to the limit of the tower by increasing feed preheat and additional condensing surface.

2. If the tower is limiting, additional capacity may be obtained by reducing the heat content of the feed, thereby decreasing the heat load on the condenser at the expense of increased reboiler duty. A detailed analysis of the internal vapor-liquid traffic is required to optimize this case, and access to a computer can greatly simplify the study.

In many cases, particularly in older plants, towers are operating at conditions far different than those for which they were designed. A study of such towers will often reveal that the owner is getting far more out of the tower than calculations can predict. Unfortunately, test runs are rarely possible in such cases due to various system limitations. If a test run can be made, this is the surest way to define capacity, but, more often than not, the engineer will have to reiy on calculations plus the experience of the owner, both being tempered by judgment.

Example Design Calculations

In this section are presented procedures for calculating every type of distillation process to be found in any refinery gas plant. These are

1. Simple light ends fractionator

2. Whole naphtha stabilizer

3. Whole naphtha splitter

4. Complex fractionator for whole naphtha

5. Reboiled absorber.

Each procedure will be presented as a narrative explaining in detail the required steps. These, together with the others presented in this work, describe design methods for all types of refinery fractionation processes. This work does not consider the absorber since this is very rarely found in the refinery. In addition, the literature is well stocked with absorber design procedures; only new or, at least, previously unpublished work is presented here.

These methods will emphasize "short cut" types of calculations which enable the designer to obtain a close approximation of the answer prior to using more sophisticated techniques if such are indicated to refine the design. There are available at this time many highly developed computer programs for solving distillation problems, but many of these require as input data estimates of temperature, profiles of vapor and liquid traffic, number of trays, etc. The methods presented here can also be used as generators of preliminary data for computer input. An accurate first estimate can often result in significant savings in computer time-which is money—and in actual time which also is money. A second benefit is that supporting hand calculations enable one to analyze computer output much more rapidly and to spot discrepancies much more easily.

Calculation of Simple Discrete-Component Fractionators

This type of column is found in the light ends section of the refinery gas plant and processes only identifiable components. It is also the common type of fractionator found in the distillation section of natural gas liquids recovery facilities or, for that matter, in most chemical plants where the process objective is to make a separation between two components. The design procedure for calculating this type of tower is outlined in the following discussion.

Process Design Basis

As in any engineering design work, the first question to be resolved is "What is it that we are trying to accomplish?" or, in the case of distillation design, "What kind of separation is required by the process?" The designer will generally be guided by criteria such as recovery requirements for certain components, allowable impurity levels in streams, economic values assigned to the various recovered streams and the like, ail being overshadowed by whatever economic factors may exist which are unique to the project under consideration.

At the beginning of the design, the engineer must first set the material balance for the tower. This is most often done on the basis of making a separation between two components whose volatilities, i.e., boiling point or vapor pressure characteristics relative to each other, make them adjacent in the listing of the components in the feed. These two components are called key components and are defined as follows.

"The Light Key Component is the heaviest component whose percent recovery is greater in the distillate than in the bottoms. Conversely, the Heavy Key Component is the lightest component whose percent recovery is greater in the bottoms than in the distillate.

Obviously, key component recovery can never be 100 percent. If it were, another component would be the key component.

In a typical case, the tower could be a depropanizer making a separation between propane and isobutane. Purity specifications on the butane product from the base of the tower allow a relatively large concentration of propane. Isobutane level in the recovered propane would be estimated by what separation would occur in a deethanizer which would further fractionate the depropanizer distillate into an ethane-rich fuel gas overhead and a propane product bottoms. The preceding knowledge is not required in order to perform actual calculations but is included here to show the relationships that come into play in setting up a design.

Having defined the key components and their required recoveries, one can now establish the preliminary material balance for the design. Ordinarily, one can assume that all components lighter than the light key will appear completely recovered in the distillate and that all components heavier than the heavy key will be completely recovered with the bottoms. In the case where the separation is to be between components which have isomers, such as between propane and the butanes, isobutane being the heavy key, a portion of the non-key isomer will follow along with the key. In the preliminary estimate of the material balance, the designer should guess the non-key component distribution because the presence of these components may materially affect the temperatures and pressures within the system. These assumptions will be checked later and then adjusted for the final calculations.

Occasionally, a situation will arise where the key components are not adjacent when ranked according to volatility. In this case, components lying between the keys will appear in substantial quantities in both product streams and, for this reason, are called distributed components. In setting up the preliminary material balance, the designer must estimate the quantitative presence of these components in the products. This preliminary assumption will later be checked by the techniques described in a later portion of this procedure.

Operating Temperatures and Pressures

The operating conditions at key points in the system are established in the following sequence.

Reflux Drum Conditions. By definition of the process requirements, it is usually known that the distillate must be either a vapor or a liquid. From this knowledge, the reflux drum conditions are set as a function of the available cooling media.

If cooling water is to be used in the condenser, set the temperature in the reflux drum at the maximum allowable temperature of the outlet cooling water. For example, cooling water is available at 85 degrees F, and its return temperature shall not exceed 120 degrees F. Therefore, set the reflux drum temperature at 120 degrees F.

In systems which are inherently high pressure, the operating pressure level may be significantly reduced by taking an approach of 15 degrees F at the cold end of the condenser and a 15 degree F rise on the cooling water. For the conditions stated previously, the reflux drum would mi operate at 100 degrees F, and the cooling water temperature range would be 85 to 100 degrees F.

If the condenser is to be cooled by air, set the temperature in the reflux drum no closer than 40 degrees F to the available summer dry bulb temperature. For example, air is available at 90 degrees F dry bulb. This will result in a minimum reflux drum temperature of 130 degrees F.

In the case where the condenser duties are large and where there is a genuine need to reduce tower pressure by cooling the overhead to the minimum feasible temperature, the condenser function may be satisfied by a combination of air and water cooling provided that the temperature of the vapor leaving the top tray is sufficiently high. For example, vapor could be cooled-condensed from 200 to 130 degrees F, using 90 degrees F air, and from 130 to 100 degrees F, using water from 85 to 100 degrees F. This technique minimizes cooling water consumption, at the same time maintaining reasonable equipment sizes. Having established the temperature in the reflux d rum, the pressure is calculated by bubble-pointing in the case of liquids or dew-pointing in the case of vapor distillates.

Top Tray Temperature. For the case of a liquid distillate, the composition of the vapor leaving the top tray is the same as that of the distillate product. Thus, the top tray temperature is determined by making a dew point calculation on the distillate composition after taking a pressure increase of 5 to 10 psi above that in the reflux drum. For the case of a vapor distillate, the condenser is the top separation stage, and its temperature is already known. Later, after the reflux requirements have been determined, the top tray temperature is calculated by adding the reflux to the vapor distillate and dew-pointing the resultant mixture after taking the necessary pressure increase. For vapor distillate systems, this is necessary only to specify the condenser and is not required for the distillation analysis.

Bottoms Temperature. The bottoms temperature is its bubble point after taking a pressure increase of 5 to 10 psi across the trays. In the case of relatively low pressure operation, the actual pressure which can be obtained and which becomes known only after the equipment design is complete may necessitate a réévaluation of the assumed pressure profile. This is seldom critical in towers operating above 100 psia. A design criterion that must be satisfied at this point is that the base temperature should not approach the pseudocritical temperature of the bottoms product by any closer than 25 degrees F. If this situation arises, two alternatives are normally open. First, consider producing the distillate as a vapor using the conventional condenser coolant. This will result in operating the reflux drum at the same temperature as before but at the dew-point pressure.

If, however, the production of a liquid distillate is mandatory, set the base temperature at 25 degrees F less than the pseudocritical temperature of the bottoms and establish the pressure levels in the system. After calculating the temperature required in the reflux drum, select a refrigerant temperature level to give a cold end temperature difference at the condenser of 15 to 25 degrees F.

A third alternate is to yield the overhead product as two phases, their composition being determined by making a flash calculation at the appropriate temperature dictated by the available cooling media at this maximum operating pressure level.

A second criterion that must be observed is that the pressure in the reflux drum must not fall below 5 psig. This may necessitate operating the reflux drum at a temperature higher than that normally attainable with the available cooling media. This practice is limited to systems whose distillate product is hexanes or heavier, i.e., whose atmospheric pressure boiling points exceed 120 degrees F.

Checking the Preliminary Materia! Balance

The original assumptions as to the distribution of non-key components are now checked by employing Hengste-beck's (16) technique which postulates that all components in a distillation are distributed according to the relationship, log (D/W) = f (log a)

This is used in the following sequence.

1. Calculate the arithmetic average temperature and pressure of the tower based on the vapor from the top stage and the liquid from the bottom stage.

2. At this condition, tabulate the vapor-liquid equilibrium coefficient, the K value, for each component in the system. Then, calculate their volatilities relative to the heavy key component.

3. For the key components only, calculate D/W, which is their ratio of distribution between distillate and bottoms.

4. On log-log paper, plot the points, (a, D/W), for the two keys and draw a straight line between them. The ratio of distribution for all components in the system will lie on this line. At any given value of a, the corresponding value of D/W for that component is found which, for the purpose of this illustration, will be designated as z.

D/W = z, which reduces to D = zW = z(F - D) D = F(Z/(l+z)]

5. If revisions are required to the assumed material balance, the temperatures and pressures within the system must be checked for the new balance and revised where necessary. Unless a serious error is made in the original assumptions, more than one iteration will seldom be required. This procedure is particularly useful in systems having distributed components.

Thermal Condition of the Feed

The thermal condition of the feed to the tower is generally not treated as a design variable except in a revamp situation where one might attempt to control vapor or liquid loadings in the tower by controlling the feed flash. Since feed comes to the tower system from another system, its thermal condition upon entering the environment of the tower is a function of its temperature and pressure level into which the feed enters. The thermal content of the feed can be altered by heat exchange against other streams, by heating or by cooling utilizing plant utilities. The implications to design of the thermal condition of the feed have been treated in detail earlier in this chapter. For the purpose of final design involving any feed heat exchange, one can calculate the feed bubble point and dew point at tower pressure and then a flash at some intermediate temperature for the purpose of drawing a healing curve.

Average Relative Volatility

The average relative volatility for the light key-heavy key pseudobinary system is determined by calculating these values at the conditions of dew-point vapor leaving the top stage and bubble-point liquid leaving the bottom stage and then using the lesser of geometric and arithmetic mean values. The geometric mean will usually be the smaller value and the one to use.

The average relative volatility will be used in all calculations involving the determination of tray and reflux requirements.

Minimum Number of Stages at Total Reflux

The minimum number of separation stages required to attain the specified separation at conditions of total reflux is calculated by Fenske's (11) equation.

N^ = (log (light key in distillate x heavy key in bottoms) I (light key in bottoms x heavy key in distillate)] + log a.

An alternate method is that of Winn ( 12), which can be used as a check. The two methods agree within reasonable tolerances, but Winn's method is a little more time consuming to use.

Minimum and Operating Reflux Ratios

The literature is full of methods and procedures for calculating the minimum reflux required to effect a specified separation. Most are complex and require a good deal of time, quite often involving triafand-error. Of all those known to this author, Underwood's (10) procedure is the simplest to use for manual calculations.

The method recommended here is an analytical solution for the reflux-to-distillate ratio which has been found to check very closely the values obtained from other more sophisticated calculation procedures. It has been of particular value in setting up and analyzing distillation problems on the computer. It involves a three-step procedure correlating key component vapor-liquid equilibrium at the feed point and the purity of the reflux liquid.

A stepwise illustration for the case of bubble-point feed is as follows. In this discussion, note that the x and y values refer to the light key mole fractions in a pseudo-binary system consisting only of the keys. These concentration values are xr = mole fraction in reflux xp = mole fraction in total feed xpy - mole fraction in feed point equilibrium liquid ypy = mole fraction in feed point equilibrium vapor

1. Calculate the light key concentration in the vapor phase which is in equilibrium with the bubble point feed. This quantity is yFV = (axF)/ [1 + (a - 1) x F]

2. Calculate the following quantity m = (xR - ypy) / (xR - xF)

3. Calculate the minimum reflux-to-distillate ratio as

R-DM = ml (1 — m), moles keys in reflux/rnoles keys in distillate.

A similar treatment for dew point vapor feed yields these sequential equations.

iv I

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