report?

This report outlines the procedure followed during the distillation column laboratory and the results and conclusions of the laboratory. Operation of a pilot-plant scale trayed distillation column under total reflux conditions was investigated at various boil-up rates, so as to determine the effect of an increase in boil-up rate upon the minimum number of theoretical stages required to effect a given separation of methanol and 2-propanol and the overall efficiency of operation with regard to product separation. The McCabe-Thiele graphical method, the Fenske equation, and a given equation were employed so as to determine the required minimum number of stages, NT, while this graphical method and a given equation were employed so as to determine the actual number of stages, NA. The overall efficiency, no, was determined according to its definition and a given equation for no.

The operating lines pertaining to each investigated boil-up rate reasonably approximated the 45o reference line, which is indicative of total reflux conditions. According to the Fenske equation and the given equation for NT, an increase in the boil-up rate over the investigated range was seen to decrease the minimum number of theoretical stages required to effect a given separation. The average overall efficiency, on the other hand, was seen to increase with a similar increase in the boil-up rate. The McCabe-Thiele graphical approach quite accurately predicted the actual number of stages, which was known to be eight.

Sincerely,

Abstract

In this laboratory, a pilot-plant scale trayed distillation column was investigated at total reflux conditions, namely with regard to the separation of methanol and 2-propanol at different boil-up rates or different rates of vapor exiting the reboiler within the column. Analysis of the separation of these two species was made possible by varying the power input to the reboiler within the column, which ultimately varied the boil-up rate. Such an analysis involved study of the pressure drop across the column and study of samples of the liquid and vapor and the temperature at all stages within the column, including the reboiler stage, at each investigated power input to the reboiler.

The operating lines pertaining to each of the investigated boil-up rates were seen to be approximately coincident with the 45o reference line, which was theoretically expected, given that the rectifying and stripping operating lines are coincident with this line under conditions of total reflux. Through the use of the given equation for NT, the minimum number of stages required to effect the separation achieved at boil-up rates of 0.270 mL/s, 0.350 mL/s, and 0.410 mL/s were determined to be 1.97, 1.71, and 1.55, respectively. The Fenske equation predicted values of NT of 0.604, 0.555, and 0.396, respectively, with regard to these boil-up rates. It was thus concluded that the required number of such stages decreased as the boil-up rate increased. With regard to these boil-up rates, the average overall efficiencies of operation were determined to be 22.78%, 27.54%, and 29.71%, respectively. Therefore, it was concluded that as the boil-up rate increased, the average overall efficiency of operation, and thus the degree of product separation, increased. Via the McCabe –Thiele graphical method involving consideration of the average Murphree vapor plate efficiency, the actual number of stages was predicted to be 7.76, 6.53, and 7.16, respectively, with regard to the aforementioned boil-up rates. These compared appreciably to the actual number of stages within the column, which was known to be eight.

Introduction

The art of distillation dates back to at least the first century A.D. Distillation was being used in Italy to produce alcoholic beverages by the eleventh century. At this time, it was a batch process based on the use of a single stage, the boiler. The liquid feed to be separated was placed in a vessel to which heat was applied, causing part of the liquid to evaporate. The vapor passed from the heating vessel into another chamber, in which it was cooled via the transfer of heat to water from the chamber wall. The resulting condensate dripped into a product receiver. It was determined by the sixteenth century that the extent of separation could be improved by providing multiple liquid-vapor contacts or stages. The ability of modern distillation to produce almost pure products is derived from the use of multistage contacting.

Multistage distillation is at present the most widely used method for separating liquid mixtures of chemical components. Such distillation is widely used to separate crude oil into petroleum fractions, light hydrocarbons, and aromatic chemicals in petroleum refining. The separation of other organic chemicals, often in the presence of water, is widely practiced in the chemical industry. The fundamentals of distillation are best understood through the study of binary distillation, the separation of a two-component mixture. Such is the basis of this laboratory, in which the separation of a binary mixture of methanol and 2-propanol within a pilot-plant scale trayed distillation column is examined at different boil-up rates under conditions of total reflux. Pilot-plant laboratory studies such as this are often necessary prior to the design of a commercial unit.

Test Methods

This laboratory was concerned with the separation at conditions of total reflux of a binary mixture of methanol and 2-propanol within a pilot-plant scale trayed distillation column at various boil-up rates. The boil-up rate was increased by increasing the reboiler power input setting. The laboratory commenced by adjusting this setting to setting one and allowing the separation process within the column to reach steady-state conditions, as indicated by a constant pressure drop over the length of the column and constant temperatures at each of the eight stages within the column. In the meantime, ten 10 mL samples of methanol and 2-propanol were prepared through the use of pipettes of various volumes and working beakers from pure samples of the two species. Beginning with a sample of 0% methanol-100% 2-propanol, each successive sample contained a volume percentage of methanol 10% greater than the previous sample. The refractive index of each sample was determined through the use of a Milton Roy Co. refractive index machine, such that a calibration curve could be created and used to determine the volume percentage of methanol and 2-propanol within a given binary sample of the two species given the refractive index of the sample.

When the column had reached steady-state conditions at this reboiler power input setting, the temperature at each stage within the column and the pressure drop across the length of the column was recorded. While the temperature at a given stage was indicated by a thermometer corresponding to that stage, the pressure drop across the length of the column was indicated by a manometer that housed oil having a specific gravity of 0.826. Beginning with stage one, which corresponded to the uppermost tray within the column, and continuing to stage eight, which corresponded to the reboiler, a liquid and vapor sample were drawn, one at a time, from each stage and were immediately placed into a previously made ice bath. A tube was attached to the labeled liquid or vapor valve at a given stage and the valve was opened, which caused the sample to be drawn from the column. The refractive index of each sample was determined using the aforementioned refractive index machine, such that the composition of each sample could be determined.

The boil-up rate at this reboiler power input was also measured. The liquid downflow, equal to the boil-up rate at total reflux, was measured by noting the time required to collect a given volume of liquid from the downflow. Under normal column operation, the liquid downflow would fall to the reboiler, but the turning of a three-way valve at the base of the column causes the accumulation of this liquid within a graduated section of the column at the base of the column. It is here that the measurement of the time required for collection of a given volume of liquid was determined. This volume is determined by draining the volume to a graduated cylinder by means of the previously mentioned three-way valve. Via this procedure, the boil-up rate at this reboiler power input was determined. This entire procedure was repeated for reboiler power inputs of two and three.

Theory

A feed mixture of two components is separated from a feed mixture of the two components into two or more products in the process of binary distillation or fractionation, including, and often limited to, an overhead distillate and a bottoms. The composition of these products differ from that of the feed. While the feed is most often a liquid or a mixture of liquid and vapor, the bottoms product is almost always a liquid and the distillate may be a liquid, vapor, or a mixture of both. The separation requires that a second phase be formed so that liquid and vapor phases are present and can contact each other on each stage within the separation column, that the components have different volatilities so that they will partition between the two phases to different extents, and that the two phases can be separated by gravity or other mechanical means.

Multistage distillation is the predominant present means of separating binary liquid mixtures of chemical components, due to its ability to produce almost pure products. Stage distillation with reflux may be considered to be a process in which a series of flash-vaporization stages are arranged in a series in such a way that there is a counter-current flow of the liquid and vapor products leaving each stage. While the liquid from a given stage flows to the stage below that stage, the vapor from a given stage flows upward to the stage above that stage. Thus, a vapor stream V and liquid stream L are mixed and equilibrated at each stage and a liquid and vapor stream leave each stage in equilibrium.

The binary feed mixture enters the column somewhere in the middle of the column. The liquid portion of the feed flows down to the nearest tray or stage, while the vapor portion of the feed flows upward to the nearest tray or stage. Considering the tray to which the liquid portion of the feed falls, the entering liquid flows across this tray, while vapor enters the tray from the tray below and bubbles through the liquid on this tray. The vapor and liquid leaving this tray are equilibrated via this process. The vapor leaving this tray flows up to the next tray, where it again contacts a down-flowing liquid. The same procedure occurs with regard to the vapor portion of the feed entering the column. Via this process, the concentration of the more volatile component, or rather the lower-boiling component, is increased in the vapor from stage to stage heading towards the top of the column, while the concentration of this component is decreased in the liquid from stage to stage heading towards the bottom of the column.

Through the use of a condenser, the final product exiting the top of the column is condensed and a portion of the liquid product, termed the distillate, is removed. This distillate will contain a high concentration of the more volatile component. The remainder of the liquid from the condenser is refluxed, or returned, to the top tray of the column. A reboiler is used so as to partially vaporize the liquid leaving the bottom tray of the column. The remaining liquid, lean in the more-volatile component and rich in the less-volatile component, is withdrawn as a liquid bottoms product. The vapor exiting the reboiler is routed back to the bottom tray of the column. The reboiler is often considered as a theoretical tray or stage.

The goal of distillation is to produce from the feed a distillate rich in the light key, or more-volatile component, and a bottoms product rich in the heavy key, or less-volatile component. The ease with which this separation can be achieved is dependent upon the relative volatility of the two components, where

1,2 = K1/K2 1)

From the definition of the K-value as

Ki= xi/yi 2)

The relative volatility can be expressed in terms of equilibrium liquid and vapor compositions. For a binary mixture,

1,2 = (y1/x1)/(y2/x2)= y1(1-x1)/(x1(1- y1)) 3)

This equation ultimately describes the equilibrium curve for a given binary mixture of components. The equilibrium curve may be created via this equation or through the use of given liquid-vapor equilibrium data. The temperature change over the column is small and 1,2 is almost constant for ideal binary mixtures of components with close boiling points. The higher the value of 1,2, the easier it is to achieve the desired separation.

In 1925, McCabe and Thiele proposed an approximate graphical method that combined the equilibrium curve with the operating lines for a given separation process to estimate, for a given column operating pressure and binary feed mixture, the minimum required number of theoretical stages and the amount of reflux required for a given degree of separation of the feed. This method involves a 45o reference line, separate operating lines for the upper rectifying section of the column and the lower stripping section of the column, and a feed line corresponding to the phase or thermal condition of the feed. All such lines lie on a plot of the vapor mole fraction of the light key versus the liquid mole fraction of the light key. The rectifying section of equilibrium stages extends from the top stage, stage one, of the column to just above the feed stage. The liquid entering the top stage is the external reflux rate, Lo, and its ratio to the distillate rate, D, is termed the reflux ratio, R. The stripping section of equilibrium stages extends from the feed stage to the bottom stage. The rate of vapor leaving the reboiler at the bottom of the column is termed the boil-up, VN+1 , and its ratio to the bottoms product rate, B, is the boil-up ratio, VB.

For a given specification, a reflux ratio can be selected anywhere from a minimum value to an infinite value. While a minimum reflux ratio corresponds to the need for an infinite number of equilibrium stages, an infinite reflux ratio corresponds to the need for a minimum number of equilibrium stages. The slope of the rectifying section operating line increases to a limiting value of one as the reflux ratio is increased, while the slope of the stripping section operating line decreases to a limiting value of one. At this limiting condition of total reflux, both the rectifying and stripping operating lines coincide with the 45o reference line and neither the feed composition or the feed line influence the determination of the minimum number of theoretical stages via the McCabe-Thiele graphical method. In this situation, L=V, D=B=0, and the total condensed overhead is returned to the column from the total condenser as reflux. All liquid leaving the bottom stage is vaporized via a total reboiler and is returned as boilup to the column. The feed to the column is zero, given that the distillate and bottoms flowrates are zero.

Such an operation is convenient for measuring tray efficiencies, as a steady-state condition is readily achieved. This method of McCabe and Thiele assumes that the two phases leaving each stage are in thermodynamic equilibrium. However, it is not always practical to use industrial, counter-current, multistage equipment in which such a state of equilibrium at each stage is closely approached. Therefore, concentration changes for a given stage are often less than those predicted by equilibrium. The Murphree vapor efficiency is a stage efficiency that is frequently used to describe individual tray performance for individual components. This efficiency is equal to the change in actual composition in the vapor phase, divided by the predicted that predicted by equilibrium for a given component,

nM= (yn-yn+1)/(yn*-yn+1) 4)

This equation yields the Murphree vapor efficiency at stage n, where n+1 is the stage below and yn* is the composition in the vapor phase in equilibrium with the liquid composition leaving stage n.

The minimum number of theoretical stages required to achieve a given separation with regard to a binary mixture may be determined via a number of methods, including the McCabe-Thiele graphical method, the Fenske equation, and through the use of a given equation for NT, the minimum number of theoretical stages required. Via the former method, the stages are stepped off graphically between the equilibrium curve and the operating lines for the separation of interest. At total reflux, which is the operating condition with regard to this laboratory, a mass balance over the length of the column yields an operating line having the following equation,

yn= (L/V)*xn+1= xn+1 5)

Beginning at xD, the mole fraction of the light-key component in the liquid refluxed back to the column from the total condenser, stages are stepped off graphically by drawing a straight line from the operating line across to the equilibrium curve, then back down to the operating line, and so on. This procedure is stopped at xB, the mole fraction of the light-key component in the vapor sent back to the column from the total reboiler (see Figures Three, Four, and Five). If the relative volatility of the binary mixture of the binary mixture is approximately constant, the Fenske equation can be used to calculate NT, when a total condenser is used,

NT= [log (xD/(1-xD)*(1-xB)/xB)] / [log (av)] 6)

where av= (stage 1 *stage N)^(0.5) 7)

The given equation for NT, which is valid for a straight equilibrium line over the range of the operating line and a straight operating line, is expressed as follows,

NT= [log ((yA*-yA)/(yB*-yB))] / [log((yA*-yB*)/(yA-yB))] 8)

where the subscripts a and b denote the first or uppermost stage and the reboiler or lowest stage, respectively.

The actual number of stages with regard to a given separation may also be determined by the McCabe-Thiele graphical method and through the use of a given equation for NA, the actual number of stages. The Murphree vapor efficiency can be used to dictate the percentage of the vertical distance considered from the operating line to the equilibrium line in the determination of NA via the former method. Only nM of the total vertical path is considered with regard to the determination of NA in such a manner. The same procedure followed for the determination of NT by this method is again followed, but in this case, the actual equilibrium curve is replaced by a new equilibrium curve that accounts for the average Murphree vapor efficiency. If nM is uniform from stage to stage, the value of NA may also be determined by the following equation,

NA= [log ((yA+ nM(yA*-yA))/(yB+ nM(yB*-yB)))]

/ [log ((yA+ nM((yA*-yA)-(yB*-yB))-yB)/yA-yB))] 9)

The overall efficiency of operation is defined as the ratio of the minimum number of required theoretical stages to the actual number of stages. It may, however, also be determined by the following given equation, given that the equilibrium line is straight over the range of the operating line, that the operating line is straight, and that nM is uniform over the length of the column,

no= [log (1+nM(mV/L-1))] / [log (mV/L)] 10)

where V=L and m is the slope of the equilibrium line over the range of the operating line for a given separation.

Presentation of Results

Table Nine: Calcualted Number of Theoretical Plates, Number of Actual Plates, and Overall Efficiency
	Nt (McCabe-Thiele)	Nt (Fenske)	Nt (Given equation)
Level One Heat Input	1.62	0.604	1.97
to the Reboiler
Level Two Heat Input	1.78	0.555	1.71
to the Reboiler
Level Three Heat Input	1.48	0.396	1.55
to the Reboiler
	Na (McCabe-Thiele)	Na (Given equation)	no (%, Given equation)
Level One Heat Input	7.76	26.57	12.96
to the Reboiler
Level Two Heat Input	6.53	15.01	21.18
to the Reboiler
Level Three Heat Input	7.16	2.97	18.33
to the Reboiler
	no,avg (%)
Level One Heat Input	22.78
to the Reboiler
Level Two Heat Input	27.54
to the Reboiler
Level Three Heat Input	29.71
to the Reboiler

Discussion of Results

This laboratory allowed for the investigation of the separation of a binary mixture of methanol and 2-propanol in a pilot-plant scale trayed distillation column at different boil-up rates under total reflux conditions. The boil-up rates corresponding to the investigated reboiler power inputs of one, two, and three were determined to be 0.270 mL/s, 0.350 mL/s, and 0.410 mL/s, respectively. The operating lines corresponding to each of these boil-up rates very closely approximated the 45o reference line. At total reflux, R is equal to an infinitely large value and the slope of the rectifying operating line , given by m= R/(R+1), increases to a limiting value of one. Correspondingly, the boil-up ratio increases, and the slope of the stripping operating line, given by m= (VB+1)/VB, decreases to a limiting value of one. Therefore, at this limiting condition of total reflux, both the operating lines should theoretically coincide with the 45o reference line.

As the reboiler power input, and thus the boil-up rate, was increased over the course of the laboratory, the minimum number of theoretical stages required to accomplish the given separation was seen to decreases according to the Fenske equation and the given for NT. The Fenske equation predicted a decrease in the minimum required number of theoretical stages from 0.604 stages at a boil-up rate of 0.270 mL/s to 0.396 stages at a boil-up rate of 0.410 mL/s (see Sample Calculations). Similarly, the given equation for the determination of NT predicted an decrease from 1.97 stages to 1.55 stages, respectively, with regard to these two boil-up rates (see Sample Calculations).

With regard to a consideration of the power input to the reboiler, theory predicted similar results. As the power input to the reboiler was increased over the course of the laboratory, the boil-up rate within the column was effectively increased. The greater the boil-up rate, the greater is the flow of vapor upwards through the column, and thus the greater the flow of liquid down through the column, given that L=V at total reflux conditions. Since more liquid is falling onto the trays within the column and more vapor is flowing upwards through these trays and effectively impeding the passing of the liquid through the trays, one would expect to see a greater level of liquid on every tray within the column as the boil-up rate increased. The degree of component separation when considering a given tray increases as the level of liquid upon that tray increases, as the effective degree of contact between phases will increase with an increase in tray liquid level. The minimum number of theoretical stages required to effect a given separation decreases as the degree of separation within the column increases. Thus, as the boil-up rate increases at total reflux, one would expect the minimum number of theoretical stages required to effect a given separation to decrease.

At a given boil-up rate, however, this trend will reverse and the minimum number of theoretical stages required to effect a given separation will begin to increase. Such is based upon the contact time between the liquid and vapor phases within the column at each stage. The residence time of the liquid and vapor phases at a given tray is dictated by the flows L and V. The greater the flowrates, the shorter the residence time of the liquid and vapor phases at this tray. This ultimately leads to a decreased contact time between phases and thus a decreased degree of separation with regard to the components of interest. If the boil-up rate is increase only marginally, as is done through the course of this laboratory, it is the heightened liquid level on the trays within the investigated column, as opposed to the liquid and vapor flowrates, that will ultimately dictate the value of NT. However, as the boil-up rate is increased to an appreciable extent, beyond the range investigated within this laboratory, the increased liquid and vapor flowrates ultimately dictate the value of NT.

Given that the degree of component separation increases as the boil-up rate increases, the values of xD and xB in the Fenske equation the values of yA (yD) and yB in the given equation for NT will differ to a greater extent as the boil-up rate is increased through the course of the laboratory. The greater the difference between these values, the smaller the values of NT predicted by either equation. The McCabe-Thiele graphical method used to determine the minimum number of theoretical stages required indicated that an increase in the boil-up rate at total reflux conditions led to an increase in NT with regard to the first two investigated boil-up rates, but indicated an opposite trend with regard to the latter two investigated boil-up rates. The sources of error encountered within the laboratory account for this former trend (see Figures Three, Four, and Five and Sample Calculations).

The distillation column under investigation was known to have eight stages, including seven trays and the total reboiler. While the McCabe-Thiele graphical method in which Murphree vapor efficiency is considered predicted the number of actual stages to a high degree of accuracy, the given equation for NA, the actual number of stages, predicted values of NA substantially different than the known value of eight. The McCabe-Thiele graphical method predicted values of NA of 7.76, 6.53, and 7.16 stages, with regard to boil-up rates of 0.270, 0.350, and 0.410 mL/s. The given equation for NA yielded values of NA of 26.57, 15.01, and 2.97, respectively, with regard to these boil-up rates. The sources of error encountered within the laboratory ultimately led to the poor results for NA predicted by the given equation for NA (see Sources of Error).

The calculated Murphree vapor efficiencies corresponding to each stage within the column differed substantially from one stage to the next. In theory, their magnitude should have been uniform over the length of the column for a given boil-up rate at steady-state conditions. If the conditions within the column, namely the stage temperatures, the pressure drop across the column, and the liquid and vapor flowrates, remain constant, as they should at steady-state conditions, the Murphree vapor efficiencies should ideally be constant from stage to stage if all the trays were fabricated in an identical fashion. Again, the sources of error present during the laboratory led to the Murphree vapor efficiencies being substantially different from stage to stage.

The overall efficiency was determined according to its definition, no= NT/NA, where NT and NA may be either of the aforementioned calculated and known values, and according to the given equation for no. Theoretically, it was expected that this parameter would increase with an increase in boil-up rate over the range of boil-up rate analyzed through the course of this laboratory. Such is explained by the fact that the degree of component separation increases as the boil-up rate is increased over this range. While the transition from the first investigated boil-up rate to the second investigated boil-up rate led to an increase in no according to the given equation for no, the transition from the second investigated boil-up rate to the final investigated boil-up rate led to a decrease in no according to this equation. Like all unexpected occurrences, this is explained by the aforementioned sources of error (see Sources of Error). Since the value of no can be determined by the equation no= NT/NA by so many means, due to the many calculated and known values of NT and NA, it is too difficult to examine the effect of an increase in boil-up rate on the value of no predicted by this equation. The average overall efficiency at a given boil-up rate was calculated as the average all overall efficiency values calculated by the aforementioned equations. The average overall efficiency with regard to each boil-up rate was seen to increase with an increase in the boil-up rate. It increased from a value of 22.78% at a boil-up rate of 0.270 mL/s to a value of 29.71% at a boil-up rate of 0.410 mL/s. Such was theoretically expected, given that the degree of component separation increased as the boil-up rate was increased over the investigated boil-up rate range investigated in the laboratory.

Sources of Error

A number of sources of error were encountered through the course of this laboratory. The primary error was the fact that liquid and vapor samples were not taken from all stages within the column at each investigated boil-up rate. Inexperience with regard to distillation column operation led to this error. The end result of this error was the creation of operating lines whose equations contained error, and calculated values of NT, NA, and no that contained error. These operating lines ultimately led to inaccurate values of NT and NA predicted by the McCabe-Thiele graphical method. The given equations for NT and NA and the Fenske equation, which called for compositions at the uppermost and lowest stages, therefore predicted values of NT and NA that contained error, as the compositions at the nearest investigated tray or stage had to be used.

A second significant error pertained to the calculated values of NT, NA, and no via the given equations for these parameters. This equation for NT assumed a straight equilibrium line over the range of the operating line and a straight operating line for a given boil-up rate. At each investigated boil-up rate, it was seen that the operating line did not coincide exactly with the 45o reference line and that it was not perfectly straight, as is indicated by the R2 value pertaining to this line (see Figures Three, Four, and Five). For a straight line, R2=1 for that line. Via the same analysis, it was seen that the equilibrium line was not perfectly straight over the range of the operating line corresponding to each analyzed boil-up rate. This ultimately led to error within the values of NT calculated using the given equation for NT. This also led to error within the calculated values of no predicted by the given equation for no, as this equation called for a straight operating line and a straight equilibrium line over the range of the operating line. The given equation for NA called for a uniform Murphree vapor efficiency from stage to stage, as did the given equation for no. The fact that nM differed from stage to stage thus led to the introduction of error into the values of NA and no calculated in this manner t each investigated boil-up rate.

Poor mixing from stage to stage is likely the cause of the variation in the values of nM from stage to stage within the column. The liquid sample will only be accurate for plate n if perfect mixing occurs at plate n. Since the liquid sample port is directly beneath the downcomer from the tray above tray n, the liquid sample at tray n will be more representative of what has occurred at the tray above tray n if poor mixing is occurring. Via the same analysis, the vapor sample at tray n will be more representative of what has occurred on the tray below tray n if poor mixing is occurring. Given that the calculation of Murphree vapor efficiencies and the construction of the operating line at a given boil-up rate is dependent upon the concentration of the liquid and vapor samples drawn from each stage within the column, poor mixing at given stages will ultimately lead to error with regard to these efficiencies and the equation of these operating lines. This is turn will introduce error into the values of NT and NA predicted by the McCabe-Thiele graphical method and explains why the constructed operating lines do not coincide perfectly with the 45o reference line.

Other sources of error encountered within this laboratory include the loss of heat from the column through the column insulation and measurement error. The column was not perfectly insulated, as the insulation covering the length of the column sat quite loosely against the column and did not cover the entire column. Thus, heat was lost from the column on a continuous basis. Heat loss from the column also occurred when samples were drawn from a given stage. The loss of heat ultimately led to temperature drops over the length of the column, and thus temperatures that were not representative of the power input to the reboiler. This in turn led to sample compositions at a given stage that were also not representative of this power input, as they are dependent on the temperature at that stage. The loss of heat from the column thus introduced error into the equation of the aforementioned operating lines, and thus the values of NT and NA predicted by the McCabe-Thiele graphical method, the calculated values of Murphree vapor efficiency, the values of NT calculated via the Fenske equation, and the values of NT, NA, and no calculated through the use of given equations for these parameters.

Measurement error during the laboratory introduced error into the calculated values of NT, NA, no, and VB, the boil-up rate. Such error was introduced during the determination of NT and NA via the McCabe-Thiele graphical method, during the preparation of 10 mL samples of methanol and 2-propanol, and during the determination of the various boil-up rates. In the former situation, error is introduced during measurements with regard to the graph. Error is introduced during sample preparation when volumes are read from graduated pieces of equipment, whether it be a graduated cylinder or a pipette, and when refractive indices of samples are read from the refractive index machine. In the latter case, error is introduced when volumes are read from the graduated section of the column at the base of the column and a graduated cylinder.

Conclusions

1. The operating lines corresponding to the different investigated boil-up rates approximated the 45o reference line to an appreciable degree, as was theoretically expected, given that operation of the pilot-plant scale trayed distillation column was at all times conducted under total reflux conditions.

2. The required minimum number of theoretical stages to effect a given separation was seen to decrease with an increase in the boil-up rate, according to the given equation for NT and the Fenske equation. While the former equation indicated an decrease in NT from 0.604 to 0.396 stages with regard to an increase in the boil-up rate from 0.270 to 0.410 mL/s, the latter equation indicated a decrease in NT from 1.97 to 1.55 stages under the same conditions. This was theoretically expected, as an increase in the boil-up rate over the range investigated in the laboratory leads to greater separation within the column and thus the requirement for a smaller minimum number of theoretical stages to effect a given separation.

3. The McCabe-Thiele graphical method approximated quite accurately the actual number of stages within the investigated column, which was known to be eight. This method predicted values of NA of 7.76, 6.53, and 7.16 stages, respectively, with regard to boil-up rates of 0.270, 0.350, and 0.410 mL/s, respectively.

4. The average overall efficiency with regard to column operation at total reflux was seen to increase with an increase in the boil-up rate. This parameter increased from a value of 22.78% at a boil-up rate of 0.270 mL/s to a value of 29.71% at a boil-up rate of 0.410 mL/s. This was also theoretically expected, given that an increase in boil-up rate over the range investigated in the laboratory will ultimately lead to greater separation within the column or a greater overall column efficiency.

Recommendations

1. Liquid and vapor samples should have been drawn from stages one through eight. However, due to inexperience with regard to the operation of the investigated distillation column, this was not always done. The failure to take liquid and vapor samples from all stages ultimately led to error in the constructed operating lines and the values of NT, NA, and no calculated by all investigated methods.

2. The column should be insulated in a better fashion so as to prevent the loss of heat from the column. This will lead to samples from stage to stage that are much more representative of the power input to the reboiler and the corresponding boil-up rate. The introduction of further error into the equation of the created operating lines and the values of NT, NA, and no calculated by all investigated methods will thus be prevented by this procedure.

Acknowledgments

Special thanks are to be given to Mr. David Tracey and Dr. Mladen Eic for their time and aid with regards to this laboratory.

Nomenclature

1,2 – relative volatility of component one with regard to component two (dimensionless)

K1- K-value of component one (dimensionless)

x1- liquid mole fraction of component one (dimensionless)

xD- liquid mole fraction at stage one (dimensionless)

y1- vapor mole fraction of component one (dimensionless)

yB- vapor mole fraction at stage N, the reboiler (dimensionless)

y1*- vapor in equilibrium with liquid leaving a given tray with reagrd to component one (dimensionless)

a- denotes uppermost stage, stage one

b- denotes lowest stage, stage N, the reboiler

L- molar flow of liquid phase (mol/s)

V- molar flow of vapor phase (mol/s)

D- molar flow of overhead distillate (mol/s)

B- molar flow of bottoms product (mol/s)

R- reflux ratio (dimensionless)

VB- boil-up ratio (dimensionless)

NT- required minimum number of theoretical trays or stages to effect a given separation

NA- actual number of trays or stages

nM- Murphree vapor efficiency (%)

no- overall efficiency (%)

References

1. Geankoplis, Christie J., Transport Processes and Unit Operations, Third Edition, Prentice Hall P T R, Englewood Cliffs, 1993.

2. Seader, J.D. and Henley, Ernest, J., Separation Process Principles, John Wiley and Sons, Inc., New York, 1998.