Distillation I: Principles

Definition & Purpose:

Distillation is the most widely used separation process in the chemical industry. It is also known as fractional distillation or fractionation. It is normally used to separate liquid mixtures into two or more vapor or liquid products with different compositions.

Distillation is an equilibrium stage operation. In each stage, a vapor phase is contacted with a liquid phase and mass is from vapor to liquid and from liquid to vapor. The less volatile, "heavy" or "high boiling", components concentrate in the liquid phase; the more volatile, "light", components concentrate in the vapor. By using multiple stages in series with recycle, separation can be accomplished.

Operating Principles:

The feed to a distillation column may be liquid, vapor, or a liquid-vapor mixture. It may enter at any point in the column, although the optimal feed tray location should be determined and used. More than one stream may be fed to the system, and more than one product may be drawn.

A column is divided into a series of stages. These correspond to a cascade of equilibrium stages. Liquid flows down the column from stage to stage and is contacted by vapor flowing upward.

Traditionally, most columns have been built from a set of distinct "trays" or "plates", so these terms end up being essentially interchangeable with "stages". Each tray in a

distillation column is designed to promote contact between the vapor and liquid on the stage. Distillation can be conducted in a packed column (just as absorption can be done in a trayed column), but we will focus on trayed columns for the present.

Stages may be numbered from top down or bottom up. When analyzing a stage, flows and compositions take the number of the stage they leave. The text for this class calls the top tray of the column "Tray 1" and numbers downward - - this is the convention we will use. MSH also denote the streams between the column top and condenser with an "a" subscript and those at the bottom with "b". Personally, I generally prefer to let "Tray 1" be the bottom tray of the column, the reboiler "Tray 0" and number upward (so if you catch me doing this, don't panic). I like this way of numbering because it tends to simplify computer based calculations.

The product leaving the top of the column is called the overhead product, the "overhead", the "top product", the distillate, or "distillate product". Distillate product may be liquid or vapor (or occasionally both) depending on the type of condenser used. Most of the time the distillate flow rate is assigned the symbol D, and the composition xD or yD.

The product leaving the bottom of the column is called the bottom product or "bottoms", and given the symbol B, with composition xB.

In some situations, notably petroleum refining, one or more intermediate or "sidedraw" products may be removed from the column.

Vapor leaving the top of the column passes through a heat exchanger, the condenser, where it is partially or totally condensed. The liquid which results is temporarily held in the "accumulator" or reflux drum. A liquid stream is withdrawn from the drum and returned to the top tray of the column as reflux (R or L) to promote separation.

The portion of the column above the feed tray is called the rectification section. In this section, the vapor is enriched by contact with the reflux.

The portion of the column below the feed tray is called the stripping section. The liquid portion of the feed serves as the reflux for this section.

The operating pressure of the column is typically controlled by adjusting heat removal in the condenser.

The base of the column is typically used as a reservoir to hold liquid leaving the bottom tray. A heat exchanger, the reboiler, is used to boil this liquid. The vapor which results, the "boilup" (V) is returned to the column on one of the bottom three or four trays.

In normal operation, there are five "handles" that can be adjusted to manipulate the behavior of a distillation column -- the feed flow, two product flows, the reflux flow, and the boilup flow (or reboiler heat input).

A normal column has a temperature gradient and a pressure gradient from bottom to top.

Ideal Stages

Stages are built to maximize contact between the incoming vapor and the incoming liquid. During the contact, some of the liqht component in the entering liquid is vaporized and leaves with the vapor; some of the heavy component in the entering vapor condenses and leaves with the liquid.

By definition, an ideal stage is one where the vapor and liquid leave the stage in equilibrium. Consequently, the vapor composition functionally depends on the liquid composition. Ideality is an approximation, but stage efficiencies can be used to account for real cases. A key result of the ideal stage assumption is that liquid streams leaving an ideal stage are assumed to be at their bubble point. Vapor streams leave at their dew point.

When no azeotropes are present, both top and bottom products may be obtained in any desired purity --- if enough stages are provided and enough reflux is available. In practice, there are limits to the number of stages and to the amount of reflux, so not every separation can be accomplished. Theoretical limits on performance are imposed by total reflux (minimum stages) and minimum reflux (infinite number of ideal stages).

Condensers & Reboilers

There are two main categories of condenser, differentiated by the extent of condensation.

In a total condenser, all of the vapor leaving the top of the column is condensed. Consequently, the composition of the vapor leaving the top tray y1 is the same as that of the liquid distillate product and reflux, xD.

In a partial condenser, the vapor is only partially

liquefied. The liquid produced is returned to the column as liquid, and a vapor product stream is removed. The compositions of these three streams (V1, D, and R) are different. Normally, D (composition yD) is in equilibrium with R (composition xD).

A partial condenser functions as an equilibrium separation stage, so columns with a partial condenser effectively have an extra ideal stage.

The "reflux ratio" is an important parameter in column operation. It is normally defined as the ratio of reflux to distillate (L/D), although other formulations (L/L+D, etc.) are occasionally used.

Most reboilers are partial reboilers, that is they only vaporize part of the liquid in the column base. Partial reboilers also provide an ideal separation stage.

Reboilers take several forms: they may be "thermosiphon" types that rely on the thermal effects on density to draw liquid through the heat exchanger, "forced circulation" types that use a pump to force liquid through, or even "stab-in" types that come through the side of the column into the liquid reservoir.

In large, complex columns, sidestream reboilers can be used. These draw liquid off a tray, heat it, and then return the vapor liquid mixture to the same or a similar trays.

Feed Condition

The thermal condition of the feed determines the column internal flows.

If the feed is below its bubble point, heat is needed to raise it to where it can be vaporized. This heat must be obtained by condensing vapor rising through the column, so the liquid flow moving down the column increases by the entire amount of the feed plus the condensed material and the vapor flow upward is decreased.

If the feed enters as superheated vapor, it will vaporize some of the liquid to equalize the enthalpy. In this case, the liquid flow down the column drops and the vapor flow up is increased by the entire amount of the feed plus the vaporized material.

If the feed is saturated (liquid or vapor), no additional heat must be added or subtracted, and the feed adds directly to the liquid or vapor flow.

Feed effects are important enough that a variable, q is assigned as a descriptor.

Subcooled Liquidq>1q=1+cpL(Tbp-Tf)/lambda

Saturated Liquid (bubble point feed)q=1

Partially Vaporized0 < q < 1 q is the fraction of the feed that is liquid. It can be found by doing a flash calculation and then q=(L/F)=(1-V/F)

Saturated Vapor (dew point feed)q=0

Superheated Vaporq<0 q=(-cpV*(Tf-Tdp)/lambda)

Distillation II: Modeling Some equations in this document are being displayed using MINSE, a browser independent approach to

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When modeling a distillation column, one can draw balances on the entire system, the column base, the accumulator, each tray (or a group of trays). Mass and component balances are always required. In special cases, the energy balances can be neglected.

The overall material balance on a distillation column with NT trays is: where F,D, and B are mass flow rates, MB is the mass in the column base, MD the mass in

the accumulator, and Mn the mass on tray n. Often, the mass of the vapor in the column is much smaller than the mass of the liquid in the column; in such cases, it is often a reasonable approximation to write the mass accumulation terms for the liquid phase only.

The overall component balance is: This can also be written with accumulation terms representing the liquid alone, if the

appropriate assumptions are made. The balances required for the accumulator are: where V1 is the vapor flow off the top tray to the condenser, and for a total condenser or for a partial condenser with a vapor product. The base and reboiler balances are for a partial reboiler with boilup rate VB (LNT is the liquid flow off the bottom tray of the

column), and Don't forget that xB and yB are in equilibrium with each other. For each tray, we can write:

in a general form that allows one feed (Fn) and one liquid product (Pn) on each tray. Usually, only one tray will have a feed stream, and there will be only a few, if any sidedraw products. You can also have vapor products, which will require replacing Pnxn in the component balance with Pnyn.

Steady-State Model The column mass and component balances in their steady state forms are:

These are equivalent to Equations 21.3 and 21.4 in McCabe, Smith, & Harriott. These two equations can be solved simultaneously to eliminate any one variable. For

example:

Similar rearrangements yield: and

Some authors like to use these ratios in their calculations. I usually find it makes more sense to work directly from the balance equations.

Feed Tray It also may be useful to examine the steady state balances on a feed tray. The total

material balance on feed tray n is To capture all necessary detail, one must recall that the feed can be both vapor and liquid.

As described by the feed variable q, the fraction liquid is Fq, so the vapor rate above the feed tray and the liquid rate below the feed tray will change. The new values will be

An equivalent analysis can be made for draw trays. It will be necessary to specify whether the draw is made from the liquid space or vapor space on the tray. This defines a q value for the draw. The equations will then be essentially the same, but keep in mind that the effect of a draw is to reduce the traffic in the column while a feed increases traffic.

For a binary system, we can make a plot of the stage vapor composition vs. stage liquid composition, yn vs. xn. If the points for all the stages are joined, the plot represents the operating path of the system. If the liquid and vapor rates are constant through a section of the column, the operating curve will be a straight line.

In the following analysis, we will assume our column has a single feed and no sidedraw products, but the equations are easily adjusted should this change.

Rectifying Section Writing steady state balances over the entire rectifying section, including the accumulator

produces:

The latter can be rearranged: and the total mass balance used to eliminate the vapor rate: This equation is the operating equation for the rectifying section of the column. Some

authors prefer to call this the material balance equation. Stripping Section Next, follow a similar procedure for the stripping section, including the reboiler:

and you have the operating equation for the stripping section. Equimolal Overflow Calculations using these equations are much more convenient if the two operating

equations are lines. This is true only if the liquid and vapor flows do not change in a given section of the column. What is required for them to be constant?

Constant Molal Overflow (also called equimolal overflow) is what is needed. This occurs when the molar heat of vaporization of the liquid phase is essentially equal to that of the vapor phase. That is, the heat needed to vaporize one mole of liquid is roughly the same as the heat released when one mole of vapor is condensed. Consequently, any

condensation on a stage is balanced out by vaporization and flow rates within the column are changed solely by feed or product streams.

The quickest way to check the validity of an assumption of equimolal overflow is to compare the heats of vaporization of the components. If their ratio is roughly 1:1, the assumption is probably acceptable.

When equimolal overflow is present, and for any given section of the column. (Remember: the only things causing L and V to change are feeds and products). L/V, D/V, and B/V are all constants within a section, so the operating equations are lines:

which can be expressed in terms of the reflux ratio

If you examine the equations, you see that when x=xD that y=xD as well (prove it by substituting xD into the equation). This means that the point (xD, xD) lies on the rectifying line. Thus, if we assume equimolal overflow, the rectifying operating line can be drawn using only this point and the slope.

Similarly, the stripping operating line runs through the point (xB, xB). If there is a secondary feed or a sidestream product, there are more than two regions in

the column; consequently, an additional operating line is required for each sidestream. The forms of the the equations don't change, but the numerical values do. The slope of line through the region will be the (L/V) ratio for that region.

Feed Line It would be nice to know where the rectifying line and the stripping line intersect. The vapor and liquid flow rates will be different in the different sections, so (still

assuming equimolal overflow!) the rectifying and stripping section steady state balances are:

Subtracting the stripping balance from the rectifying balance yields In order to rearrange this to a convenient form, refer to the steady state model for the feed

tray, where we showed how the flow rates were changed by the feed:

These can be rearranged to get the flow difference terms we'd like to replace:

and we can substitute them back into the balance equation to get Similarly, we can substitute the column overall material balance to obtain

This is a third operating equation. The feed variable q and the feed composition xF are constants so this equation is called the feed line. It can be plotted from xF and q alone. It intersects the diagonal at x=xF.

The slope and position of the feed line depend upon the thermal condition of the feed as described by the parameter q. The line will have positive slope and lie to the right of the

vertical for cold feed. The line will be vertical for saturated liquid and horizontal for saturated vapor. For a mixed vapor-liquid feed, it will lie between the horizontal and vertical (negative slope). Superheated feed will produce a line below the horizontal.

The rectifying and stripping lines intersect on the feed line. If the column has an intermediate feed or product, the same rules apply. A feed/product

line, depending only on the composition of the stream and its thermal condition, can be constructed to serve as the set of possible intersections of the operating equations for the regions above and below the sidestream.

Distillation IV: Calculations

Before beginning most distillation calculations, a decision must be reached: does equimolal overflow apply? If so, the operating equations are lines and you have one set of options -- notably the McCabe-Thiele method. If not, energy balances must be explicitly considered.

There are several ways of incorporating the energy effects. The Ponchon-Savarit method is a graphical approach that does not require an assumption of equimolal overflow. Graphical construction is done on the enthalpy composition diagram. Your text does not include this method, but it may be useful.

In all cases, one can use a "stepping" approach. Starting from one end of the column, the component, material, and energy balances can be solved simultaneously. After a stage is determined, you step up (or down) to the next and calculate that stage. Depending on what information is known, the form of the equilibrium relation, etc., this approach may require an iterative solution.

McCabe-Thiele Method

The graphical McCabe-Thiele Method can be used to determine the number of ideal stages and feed tray location. To do this, you make a plot showing the equilibrium curve, feed line, and operating lines for the rectifying and stripping sections (all on the same axes), and then find answers by graphical construction.

A standard (beginner) distillation problem provides you with xF, q, xD, xB, and RD; although not necessarily directly. You may need to use the overall material balances to find some of the compositions; to calculate the q factor from temperature and composition data; and/or determine the reflux ratio based on the limiting minimum value. Once you have these values, the solution procedure is:

1. Plot the equilibrium curve. 2. Calculate the slope q/(q-1) of the feed line. 3. Plot the feed line using x=xF and the slope. 4. Calculate the y-intercept of the rectifying line xD/(RD+1). 5. Plot the rectifying line using (xd,xd) and the intercept. 6. Draw the stripping line connecting the intersection of the rectifying and feed lines and the point

(xb,xb).

7. Correct for stage efficiency by drawing the "effective" equilibrium curve between the equilibrium curve and the operating lines.

8. "Step off" equilbrium stages.

The number of stages is found graphically by constructing triangles on the diagram. You can start from either the top or the bottom. From a product composition on the operating line (either (xd,xd) or (xb,xb)) move horizontally to the equilibrium curve, then vertically back to the operating line, horizontally to the equilibrium curve, etc., constructing triangles along the way. Always make the steps between the equilibrium curve and the lower of the two operating lines (the rectifying line in the top half of the column, the stripping line in the bottom half -- if you're looking for the bottom line, the switchover point will be clear). The number of triangles you draw is the number of stages in your column. If you are using the equilibrium curve to step from, you are determining ideal stages.

If you don't want to draw, you can do the same thing, iteratively solving for the various equation intersections. You'll need to be pretty careful with your "bookkeeping" if you try this.

To apply Murphree tray efficiencies, construct an effective equilibrium curve between the equilibrium and operating curves, and step using the effective curve to determine actual separation stages. Remember that a partial reboiler or partial condenser is by definition an ideal stage, so you use the ideal equilibrium curve (not the effective) for these stages.

The optimum feed tray is the triangle with one corner on the rectifying line and one on the stripping line. Putting the feed anywhere else increases the number of stages needed to make the separation. To visualize this, notice that the closer the operating line is to the equilibrium curve, the smaller the stepping triangles become. Introducing the feed at the intersection of the rectifying and stripping lines maximizes the size of the triangles and so leads to the fewest steps.

When analyzing existing distillation systems, the actual feed entry point may not be at the optimum (the tray where the operating lines intersect). In this case, the tray stepping should switch from the rectifying line to the operating line at the actual feed tray location.

An example of McCabe-Thiele analysis has been prepared. It is available for download as a Mathcad 5.0+ file.

Limiting Cases

Frequently, when analyzing or designing a process, it is useful to look at limiting cases to assess the possible values of process parameters. In distillation analysis, separation of a pair of components can be improved by increasing the number of stages while holding reflux constant, or by increasing the reflux flow for a given number of stages. This tradeoff sets up two limiting cases:

1. Total Reflux (minimum ideal stages) 2. Minimum Reflux (infinite ideal stages)

The design tradeoff between reflux and stages is the standard economic optimization problem chemical engineers always face -- balancing capital costs (the number of trays to be built) vs. the operating cost (the amount of reflux to be recirculated). A good design will operate near a cost optimum reflux ratio.

Total Reflux

The total reflux condition represents operation with no product removal. All the overhead vapor is condensed and returned as reflux. Consequently, the reflux ratio (L/D) is infinite. This, in turn, makes the operating lines the 45 degree line (prove it to yourself by setting D=0, and noticing that consequently L=V). With the operating lines on the diagonal, they are as far as they can get from the equilibrium curve, so if the number of plates are stepped off using the diagonal and the equilibrium curve, the number of theoretical stages will be a minimum.

Often, columns are operated at total reflux during their initial startup, and product is not withdrawn until a separation close to that desired is achieved.

The Fenske Equation is another method for determining the minimum number of trays required for a given separation. It is an example of a "shortcut" distillation method. There are a number of these approximate methods available to get initial estimates of distillation requirements.

The Fenske equation applies to distillation systems with constant relative volatility. Note that the form of the Fenske equation shown calculates the minimum number of plates; it does not include the reboiler (hence the -1 on the right hand side). Other texts may use a form for the minimum number of stages and not subtract the reboiler.

If the relative volatility varies through a column because of temperature effects, it is possible to use a geometric mean value of the relative volatility (as is done for multicomponent distillation) and the Fenske equation to get an approximate value for the number of stages.

Pinch Points

The intersection of an operating line and the equilibrium curve is called a pinch point. A simple column will have two pinch points (because there are two operating lines). The points change when the operating lines do. An existing column can "pinch" if its operating line is too close to its equilibrium curve. This means that there are several stages doing very little separation and wasting resources.

To cure a pinch, the most direct solution is to move the feed entry point. This is often an expensive proposition. In such cases, the reflux and boilup ratios can be increased to change the operating lines. This will increase operating costs and energy consumption, but may be the only realistic option.

A pinch at the intersection of the feed line and the equilibrium curve indicates that the column is operating at minimum reflux.

Minimum Reflux

The minimum reflux condition represents the theoretical opposite of total reflux -- an infinite number of ideal separation stages. In this case, the intersection of the operating lines lies on the equilibrium curve itself. Thus, the distance between the equilibrium curve and the operating lines is at its minimum, the stepping triangles become very small, there is no gap between the equilibrium curve and the intersection point, so you cannot step past the feed point.

The minimum reflux rate can be determined mathematically from the endpoints of the rectifying line at minimum reflux -- the overhead product composition point (xD,xD) and the point of intersection of the feed line and equilibrium curve (x', y').

The derivation of this formula is given later. One important thing to realize: the formula only applies when the feed line is the breakpoint for the operating curve in the top portion of the column. If there are intermediate product draws between the reflux and the feed, the formula does not apply. In this case, you must calculate the liquid flow down the column at the pinch point, and then work it back up the column to find the reflux flow at minimum reflux conditions.

If the equilibrium curve has an inflection point, it may not be possible to construct a line between the overhead product point and the feed/equilibrium intersection without passing outside the equilibrium envelope. Operating curves must always intersect within the equilibrium envelope and cannot cross outside (in either half of the column). In this case, minimum reflux occurs at a tangent pinch and the operating line is tangent to the equilibrium curve. Calculations are based upon the intersection of the tangent operating line and the feed point.

When designing columns, it is common to define the design reflux ratio as some multiple of the theoretical minimum reflux. The cost optimum reflux ratio is typically in the 1.1 to 1.5 range depending on energy costs, condenser coolant, and materials of construction. The rule of thumb reported most often suggests that a reflux ratio of about 1.2 times the minimum is a good design value.

It may also be necessary to distinguish between returned reflux (the reflux stream flowing from the accumulator to the column) and the effective reflux flowing down the column. This is a concern if the reflux is subcooled. In this case, the effective reflux will consist of the returned reflux plus whatever additional liquid is condensed when the cold liquid contacts vapor on the reflux tray. It is probably best to use effective reflux in minumum reflux calculations.

Derivation of Minimum Reflux Formula

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Minimum reflux corresponds to a pinch at the intersection of the feed line and the equilibrium curve. From its formula, the rectifying line has slope and will connect the intersection point (xint, yint) and (xD, xD). Consequently, we can express the slope in terms of "rise over run", or

Algebraic rearrangement gives the desired formula:

Clearly, this formula doesn't apply if there are more than two operating regions. In these cases, it is probably smarter to calculate the reflux ratio from the ratio of the liquid and vapor flow rates.

Condenser & Reboiler Loads

The heating and cooling loads in the condenser and reboiler can be calculated from straighforward energy balances. The chief difficulty is in getting good values for the heats of vaporization -- an enthalpy-concentration diagram is very useful!

For the reboiler, energy must be added equal to the sum of the sensible heat needed to raise the liquid to its boiling point and the latent heat of vaporization. The steady-state energy balance on the process side of the reboiler is then:

This equation is expressed in terms of average heat capacities and an average latent heat and depends on the vapor boilup rate. Usually, the sensible heat transfer in a reboiler is relatively small, so that the heat load can be calculated from

The heating medium requirements can be calculated from an energy balance on the heating side of the reboiler. If saturated steam is the heating medium, then

so that (neglecting thermal capacitance in the reboiler and heat losses) the steam rate can be obtained from Similarly, if a liquid heat transfer fluid (hot oil, etc.) is used, the equations (htfs = heat transfer fluid supply, htfr = heat transfer fluid return) or may be used.

A similar analysis provides the condenser load as

(neglecting any subcooling of reflux), so that when cooling water is used in the condenser (cws = cooling water source, cwr = cooling water return) and since the specific heat of water is 1.0 for common units When calculating cooling loads, you may need to adjust the vapor rate or condenser duty to account for vapor condensed by direct contact with cold reflux on the reflux return tray. Watch for this whenever the condenser temperature is significantly below the expected tray temperature.

It is possible to imagine a case where ; that is, when . The case when the vapor rates at the top and bottom of the column are most likely to be the same occurs when the feed is at its bubble point, and . In this situation, the condenser and reboiler loads will be approximately equal.

Stage Efficiencies

Mass transfer limitations prevent the vapor leaving a tray from truly being in precise equilibrium with the liquid on the tray; consequently, the assumption of ideal stages is only an approximation.

An efficiency is used to represent the deviation from equilibrium. There are three types of efficiencies we will consider:

1. Overall efficiency 2. Local efficiency 3. Murphree efficiency

An overall efficiency is the simplest choice. It is the ratio of the number of ideal stages to the number of actual stages.

A single efficiency can thus be used for the entire column, but is only accurate enough for prelimary design. Some improvement can be achieved by using separate efficiencies for each section of the column. Accuracy is limited because effectiveness of mass transfer is constrained by geometry and design of the trays, flowrates and paths of all streams, compositions, etc. The problem is really too complex to lump into a single parameter, so when overall efficiencies are used they should be based on performance data from similar columns or laboratory tests.

The local efficiency is the most accurate option, but also the most difficult to use. It is defined at only a single point on a specific tray.

It is most necessary on large diameter columns where position dependence is significant.

A Murphree efficiency is probably the most common choice, since it represents a workable compromise between accuracy and ease of use. It has the same form as a local efficiency but is based on tray average compositions.

Values between 0.6 and 0.75 are common for sieve trays. We know that the liquid leaving a tray is not really the same as the tray average, so a Murphree efficiency effectively assumes perfect mixing on the tray. In practice, we normally measure the liquid composition and get the vapor composition from an equilibrium calculation or diagram. In the case of multicomponent systems, the efficiencies are different for each component.

The overall efficiency and the Murphree efficiency are not directly related. You cannot use an average Murphree efficiency in place of an overall value.

To use a local or Murphree efficiency with a graphical method, the true equilibrium curve is replaced with an effective equilibrium curve located between the true curve and the operating curves. The effective curve is used to count stages. Note, however, that the efficiency doesn't apply to the reboiler, so the true equilibrium curve should be used for the last stage of the stripping section.

To construct an effective equilibrium curve is not difficult. The effective curve is given by:

where y represents the operating curve. A plot of yeff will produce an interior line on the equilbrium diagram construction.

Distillation V: Enthalpy Balances

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Variations in internal vapor and liquid flows inside a distillation column depend on the enthalpies of the mixtures. Equimolal overflow assumes the rates are independent of the energy balance. To remove the assumption we must consider the enthalpy balances explicitly.

The overall enthalpy balance on a distillation column with NT trays is:

where the Q terms are the condenser and reboiler loads. This equation reduces at steady-state to:

For a given feed and products, only one of QC and QR may be independently set. Normally, QC is chosen to get the desired operating pressure, product and reflux rates, and QR found by balance. In operation, however, the reboiler duty is usually varied to control an inventory or product composition.

Rectifying Section

Balances on the rectifying section are:

These can be combined with the steady state balance on the accumulator: to eliminate the condenser duty:

In cases where constant molar overflow is not valid, this equation may be used to calculate vapor flowrates.

Stripping Section

The balance for the stripping section:

is combined with the steady state balance on the reboiler: in order to obtain:

Calculations

In order to solve problems when constant molar overflow does not apply, one must simultaneously solve the set of equations consisting of:

Component Balance Overall Balance Enthalpy Balance Thermodynamic Property Equations

Equilbrium Equations

These equations are linked with enough complications, that an iterative solution is typically required.

Distillation VI: Enthalpy-Concentration Methods

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Distillation calculations can be performed graphically on an enthalpy-concentration (Hx) diagram. This approach is sometimes called the Ponchon-Savarit Method. Working on the Hx diagram is more general than a McCabe-Thiele construction, because it takes direct account of the thermal effects and does not require an assumption of equimolal overflow.

The very shape of the Hx diagram provides a clue as to the importance of the energy balances. If the dew point and bubble point lines are more or less straight and roughly parallel, it indicates that the latent heat of vaporization is basically constant with respect to composition. This is the prerequisite for assuming equimolar overflow, and so the energy balances may be neglected. If the saturation curves show significant changes in curvature or separation, it suggests that to assume equimolar overflow will introduce error.

Points for the feed and product can be located on the Hx diagram; for our purposes we'll call them the F, D, and B points. The coordinates are their composition and enthalpy. If the products are saturated liquid, as is the case for total condensers without subcooling and for partial reboilers, these points will lie on the bubble point curve on the Hx diagram.

Overall Enthalpy Balance

The steady-state enthalpy balance for a distillation column is:

One of the tools of graphical solution is the notion of colinearity. This has been used before if you have used lever arm principles. For an adiabatic process, the feed and products will be colinear on an Hx diagram. Thus, it is useful to redefine our distillation system to be adiabatic, by bringing the condenser and reboiler inside the system boundary. Rearranging the enthalpy balance gives:

If we then define:

The enthalpy balance becomes: Substituting from the overall material balance:

After this modification, the system is adiabatic, so a line can be drawn through the feed point, F, and the points (xD, hDp) and (xB, hBp). This line represents the system enthalpy balance, and so is called the overall enthalpy line. Remember: for a given separation only one of the reboiler and condenser duties is independent. So, you will probably want to pick one duty and then construct the line through the feed point to determine the other duty.

Reflux Ratio

As before, the reflux ratio can be determined from the L/V ratio, and for this formulation is given by:

where hD is the enthalpy of the overhead product, Hy1 the enthalpy of the vapor entering the condenser, and hDp the adjusted enthalpy of the overhead. Notice that this represents the ratio of distances on the Hx diagram: the numerator is the vertical distance between the hDp point and the dew point saturation curve, while the denominator is the distance between the saturation curves.

A calculation often begins by using the overhead product composition and temperature to obtain hDand Hy1. These in turn are used with the reflux ratio to get hDp. Then the overall enthalpy line is drawn from hDp through the feed point, and the intersection with xB gives hBp.

Stepping Off Stages

In the McCabe-Thiele procedure, operating curves were constructed to represent the component balances for the column and to relate the liquid composition on a stage to the composition of the entering vapor. These were then paired with the equilibrium curve, which relates the composition of liquid on a stage to the vapor leaving the stage.

A similar procedure can be followed on an Hx diagram, except instead of using component balances, enthalpy balances are used. The equilibrium data is represented by the equilibrium tie lines on the Hx diagram.

The operating lines are developed from enthalpy balances on the rectifying and stripping sections (just as in the McCabe-Thiele approach operating equations were developed from the equivalent component balances). The operating lines will connect the point representing the liquid on a stage (with coordinates xn, hn) to the point representing the adjusted enthalpy at the appropriate end of the column. It will cross the saturated vapor line on the Hx diagram at the point corresponding to the vapor leaving the stage (coordinates yn+1, Hn+1).

Summary of Procedure

1. Obtain enthalpy-composition diagram 2. Fix the feed point F, and product points D and B using stream compositions and enthalpies 3. Use the overhead product enthalpy and the reflux ratio to find the adjusted enthalpy of the

overhead. Plot it as point D', on a vertical line with point D. 4. Construct the overall enthalpy line from point D' through the feed point. It intersects a vertical

line drawn through point B at point B'. 5. Plot point V1. For a total condenser, the composition entering the condenser is the same as the

overhead product, so this point will be vertically above point D on the saturated vapor curve. 6. Follow the tie line from point V1 to the saturated liquid curve. This intersection will be point L1. 7. Construct an operating line connecting points D' and L1. The intersection of the operating line

with the saturated vapor curve will be point V2. 8. Repeat the two preceding steps until one of the V or L points is to the left of the overall enthalpy

line. Once it is crossed, construct operating lines using points Li and B'. 9. When xi is less than xB, construction is finished.

The number of stages can be read as the number of complete triangles.

Limiting Conditions

At total reflux, operating lines are vertical (infinite slope). This can be used to determine the minimum number of stages. Not that operating curves are not required to do this -- only the endpoint compositions.

While doing constructions on the yx diagram, a "pinch" was defined as the intersection point between the equilibrium curve and the operating curve. On an Hx diagram, there isn't an equilibrium curve -- it has expanded to a region, and each point from the xy equilibrium curve is represented by a tie line. The "pinch point" also expands, resulting in a single line where the operating and tie lines overlap.

Minimum reflux still corresponds to a pinch at the feed conditions, so to determine the minimum reflux a line must be constructed so that the overall enthalpy line coincides with the tie line that runs through the feed point.

Example

A feed containing 40 mole percent n-hexane and 60 percent n-octane is fed to a distillation column. A reflux ratio of 1.2 is maintained. The overhead product is 95 percent hexane and the bottoms 10 percent hexane. Find the number of theoretical stages and the optimum feed stage. Assume that a total condenser is used. The column is to operate at 1 atm.

Step 1: Equilibrium data is collected.

VLE Data, Mole Fraction Hexane, 1 atmx (liquid) 0.0 0.1 0.3 0.5 0.55 0.7 1.0y (vapor) 0.0 0.36 0.70 0.85 0.90 0.95 1.0

Enthalpy-Concentration DataMole Fraction Hexane Enthalpy cal/gmol

Sat. Liquid Sat. Vapor0.0 7000 15,7000.1 6300 15,4000.3 5000 14,7000.5 4100 13,9000.7 3400 12,9000.9 3100 11,6001.0 3000 10,000

This information can be used to create enthalpy-concentration and equilibrium diagrams.

Step 2: Plot the feed and product points. All three will lie on the saturated liquid line, B at xB=0.1, F at xF=0.4, and D at xD=0.95.

Step 3: From the data tables (or from the Hx diagram) find the enthalpy of the distillate, hD=3050 cal/gmol. Because a total condenser is used, the vapor leaving the top stage will have concentration y1=0.95. Consequently, it will have enthalpy HD=10,800. These values and the reflux ratio can be used to find the enthalpy coordinate for the D' point, HDp.

and so HDp=20,100. The D' point on the Hx diagram can then be placed at (0.95,20100).

Step 4: The overall enthalpy line is then drawn from D', through F. Its intersection with the line x=0.1 is the point B'.

Step 5: Because of the total condenser, the V1 point will lie on the saturated vapor curve at x=xD.

Step 6: Follow the tie line that passes through the V1 point back to the saturated liquid curve. The intersection is the point L1 (liquid on tray 1). If tie lines are not available, they may be constructed using the xy diagram.

Step 7: Construct an operating line through both the L1 point and the D' point. Its intersection with the saturated vapor curve will be the point V2.

Step 8: Continue the construction, alternating between tie lines and and operating lines until you have moved to the left of the overall enthalpy line at point L3.

Once the overall enthalpy line is crossed, construction continues, but operating lines are now drawn between the Li point and the B' point (instead of the D' point). Construction continues until L5 which is almost directly on top of xB.

Consequently, there are 5 ideal stages required for this separation -- with a partial reboiler, that means 4 ideal trays. The optimum feed tray is number 3.

Distillation VII: Equipment and Column Sizing

In order to have stable operation in a distillation column, the vapor and liquid flows must be managed. Requirements are:

vapor should flow only through the open regions of the tray between the downcomers liquid should flow only through the downcomers liquid should not weep through tray perforations liquid should not be carried up the column entrained in the vapor

vapor should not be carried down the column in the liquid vapor should not bubble up through the downcomers

These requirements can be met if the column is properly sized and the tray layouts correctly determined.

Tray layout and column internal design is quite specialized, so final designs are usually done by specialists; however, it is common for preliminary designs to be done by ordinarily superhuman process engineers. These notes are intended to give you an overview of how this can be done, so that it won't be a complete mystery when you have to do it for your design project.

Basically in order to get a preliminary sizing for you column, you need to obtain values for

the tray efficiency the column diameter the pressure drop the column height

Tray Construction & Hydraulics

Three main types of trays are to be discussed:

Bubble Cap Trays Sieve Trays Valve Trays

Typically, the liquid flow between trays is governed by a weir on each tray. The flow depends on the length of the weir and how high the liquid level on the tray is above the weir. The Francis weir equation is one example of how the flow off a tray may be modeled.

Tray Efficiency

Ideally, tray efficiencies are determined by measurements of the performance of actual trays separating the materials of interest; however, this is usually not practical in the early phases of a design. Consequently, some form of estimation is required. Estimates can be based on theory or on data collected from other columns.

The O'Connell correlation is based on data collected from actual columns. It is based on bubble cap trays and is conservative for sieve and valve trays. It correlates the

overall efficiency of the column with the product of the feed viscosity and the relative volatility

of the key component in the mixture. These properties should be determined at the arithmetic mean of the column top and bottom temperatures. A fit of the data has been determined:

This, or a similar data set, can be used to get preliminary estimates of efficiency numbers.

Column Diameter

Column diameter is found based on the constraints imposed by flooding. The number of ideal stages isn't needed to find the diameter -- only the vapor and liquid loads. You do need the number of actual stages to get the column height.

Before beginning a diameter calculation, you want to know the vapor and liquid rates throughout the column. You then do a diameter calculation for each point where the loading might be an extreme: the top and bottom trays; above and below feeds, sidedraws, or heat addition or removal; and any other places where you suspect peak loads.

Once you've calculated these diameters, you select one to use for the column, then check it to make sure it will work. Some columns will have two sections with different diameters -- consider this possibility if you end up with regions where the estimated diameter varies by 20% or more, but realize it will be more expensive than a column that is the same all the way up.

One issue that ought to be considered is the validity of your design numbers. If you are following the "traditional" approach, you've probably designed your column for reflux rates in the range of 1.1 to 1.2 times the minimum. This may not give you a column that can handle "upsets" well, so you may want to design for a capacity slightly greater than that -- increasing the flows by about 20% might be wise.

Flooding

Downcomer flooding occurs when liquid backs up on a tray because the downcomer area is two small. This is not usually a problem. More worrisome is entrainment flooding, caused by too much liquid being carried up the column by the vapor stream.

A number of correlations and techniques exist for calculating the flooding velocity; from this, the active area of the column is calculated so that the actual velocity can be kept to no more than 80-85% of flood; values down to 60% are sometimes used.

A force balance can be made on droplets entrained by the vapor stream (which can lead to entrainment flooding). This balance yields an expression relating the vapor and liquid densities and a capacity factor (C, with velocity units) to the flooding velocity:

Capacity Factors

The capacity factor can be determined from theory (it depends on droplet diameter, drag coefficient, etc.), but is usually obtained from correlations based on experimental data from distillation tray tests. Depending on the correlation used, C may include the effects of surface tension, tendency to foam, and other parameters.

A common correlation is one proposed by Fair in the late 50s - early 60s. The version for sieve trays is available in a wide range of sources (including Figure 21.28 of MSH). The correlation takes the form of a plot of a capacity factor (which must be corrected for surface tension) vs. a functional group based on the liquid to vapor mass ratio:

Enter the plot from the bottom with this number, and then read the capacity factor from the left. This capacity factor applies to nonfoaming systems and trays meeting certain hole and weir size restrictions. It will need to be corrected for surface tension:

where the surface tension is in dynes/cm.

Other correlations for the capacity factor are also available. Several are based on more recent information, and may well be more accurate than the Fair plot; however, they also tend to be less broadly known and often require more a priori information on the system. You should use a correlation that is acceptable for your problem.

Diameter

Once you have the capacity factor, you can readily solve for the flooding velocity:

(this solution is for the Fair correlation, and adds the surface tension correction).

We know that flow=velocity*area, so we can calculate the flow area from the known vapor flow rate and the desired velocity (a fraction of flood). This area needs to be increased to account for the downcomer area which is unavailable for mass transfer. The resulting tray area can then be used to calculate the column diameter. So, with everything lumped together, we have:

The only "new" term is the ratio of downcomer area to tray area. This should probably never be less than 0.1, and probably seldom will be greater than 0.2.

Trays probably aren't a good idea for columns less than about 1.5 ft in diameter (you can't work on them) -- these are normally packed. Packing is less desirable for large diameter columns (over about 5 ft in diameter).

Pressure Drop

There is a pressure gradient through the column -- otherwise the vapor wouldn't flow. This gradient is normally expressed in terms of a pressure drop per tray, usually on the order of 0.10 psi.

The best source of pressure drop information is to measure the actual drop between trays, but this isn't always feasible at the beginning of a design. Detailed calculations are possible, but these depend so much on the actual tray specifications that final values are usually obtained from experts, but approximate methods can be used to get values to put in your design basis.

There are two main components to the pressure drop: the "dry tray" drop caused by restrictions to vapor flow imposed by the holes and slots in the trays and the head of the liquid that the vapor must flow through.

Dry Tray Losses

The dry tray head loss can be related to an orifice flow equation:

This equation determines the dry tray drop in inches of fluid (your text has a similar equation in SI units). The constant 0.186 takes care of the units and is appropriate for sieve trays. The orifice size coefficient

Co depends on the tray configuration and will usually fall between 0.65 and 0.85. The hole velocity can be obtained by dividing the vapor flow rate by the total hole area of the tray.

Liquid Losses

The liquid head pressure drop includes the effects of surface tension and of the frothing on the tray. It is typically represented as the product of an aeration factor and the height of liquid on the tray:

Correlations are available for the aeration factor (beta); a value of 0.6 is good for a wide variety of situations.

The height of liquid on the tray is the sum of the weir height and the height of liquid over the weir. The total height can be calculated directly from the volume of liquid on the tray and its active area. Another approach is to back the height out of a version of the Francis weir equation (which relates flow off a tray to liquid height and weir length). One version, for a straight weir, in units of inches and gal/min is:

Realize that these equations depend on the size and shape of the weir.

Column Height

The height of a trayed column is calculated by multiplying the number of (actual) stages by the tray separation. Tray spacing can be determined as a cost optimum, but is usually set by mechanical factors. The most common tray spacing in 24 inches -- it allows enough space to work on the trays whenever the column is big enough around (>5 ft diameter) that workers must crawl inside. Smaller diameter columns may be able to get by with 18 inch tray spacings.

In addition to the space occupied by the trays, height is needed at the top and bottom of the column. Space at the top -- typically an additional 5 to 10 ft -- is needed to allow for disengaging space.

The bottom of the tower must be tall enough to serve as a liquid reservoir. Depending on your boss's feelings about keeping inventory in the column, you will probably design the base for about 5 minutes of holdup, so that the total material entering the base can be contained for at least 5 minutes before reaching the bottom tray.

The total of height added to the top and bottom will usually amount to about 15% or so added to that required by the trays.

You rarely will see a real tower that is more than about 175 ft. tall. Tall, skinny towers are not a good idea, so watch the height/diameter ratio. You generally want to keep it less than 20 or 30. If your tower ends up exceeding these values, you probably want to look at a redesign, maybe by reducing the tray spacing, or splitting the tower into two parts.

Quattro Pro 6.0 Example -- Distillation Sizing