Distillation Column Maintenance, Calibration and...

Distillation Column Maintenance, Calibration and Performance Testing

Bryan Williams October 7, 2002 of 35

October 7, 2002

Bryan WilliamsBlue Team - Distillation ContractorsCollege of Engineering and Computer ScienceUniversity of Tennessee at Chattanooga615 McCallie AvenueChattanooga, TN 37421

To: Dr. Jim Henry, P.E.Professor of EngineeringUniversity of Tennessee at Chattanooga615 McCallie AvenueChattanooga, TN 37421

Dear Dr. Henry:

The following report detailing the investigation into the status and performance of the University’sdistillation column is being submitted for your consideration. The submission of this report marks the firstmilestone for the Blue Team in the Engineering 435 course at the University of Tennessee at Chattanooga.

This report details the objectives, theory, procedures, equipment analysis, findings, and conclusionsobtained during the preliminary investigation of the distillation column. Maintenance, calibrations, heattransfer analysis, and batch distillation performance testing results are discussed herein. References to dataavailable on the Internet are given as an alternative to tabulating all collected data within the report.

If you have any questions, feel free to contact me or one of my team members, David Jolley or ChevalesWard.

Sincerely,

Robert Bryan WilliamsSenior, Chemical Engineering: University of Tennessee at Chattanooga615 McCallie AvenueChattanooga, TN 37403-2598(423) [email protected]




Author: Bryan Williams

Co-Workers: David JolleyChevales Ward

Submitted To: Dr. Jim HenryDr. Frank Jones

Date of Submission: 10-07-2002



I. Abstract

The objective of this investigation was to study the batch distillation process of a binary system byperforming column maintenance, calibration, and performance testing. Calibration of the feed pump,reboiler volume, and computer wattmeter were performed followed by an analysis of the heat transfer in thereboiler, carried out by studying the temperature changes and heat transfer coefficients at constant heatinput. Two batch methanol-water distillations were performed to analyze the correlation of temperature tomixture composition and the connection between reflux and distillate collection. Upon conclusion of theinvestigation, it was concluded that the distillation column apparatus was functioning properly and wasaccurately tuned to produce reliable experimental results. Furthermore, it was found that the heat lost bythe reboiler increased as the temperature in the reboiler increased. Additionally, it was observed that thetemperature at which a liquid mixture boils details the composition of the mixture by weighting itselftoward the boiling point of the component present in the largest amount. It was also observed that thedistillate rate increased with decreasing reflux percentage. Specifically, changing from 80% reflux to 40%reflux decreased the time in which 1 L of distillate was collected from 20 minutes to 15 minutes and at 0%reflux, 1 L of distillate was collected in 26 minutes, all with the same heat going into the reboiler.



II. Table of Contents

Page NumberLetter of Transmittal .....................................................................................................................................................1Title Page ..........................................................................................................................................................................2

I. Abstract................................................................................................................................................................3II. Table of Contents ...............................................................................................................................................4III. Introduction.........................................................................................................................................................5IV. Theory...............................................................................................................................................................6-8V. Equipment......................................................................................................................................................9-10VI. Procedure .................................................................................................................................................... 11-13VII. Results.......................................................................................................................................................... 14-27VIII. Discussion of Results ................................................................................................................................ 28-29IX. Conclusions....................................................................................................................................................... 30X. Recommendations........................................................................................................................................... 31XI. References ......................................................................................................................................................... 32XII. Appendices.................................................................................................................................................. 32-35

Figures1 - Energy Diagram for the Reboiler..........................................................................................................62 - Distillation Column Schematic Diagram.......................................................................................... 103 - Cooling Water Flow Valves Prior to Maintenance........................................................................ 114 - Column Maintenance of Reboiler Surface....................................................................................... 115 - Column Maintenance of Tray Exterior ............................................................................................ 126 - Reboiler Volume and Feed Pump Calibration Process Diagram .............................................. 127 - Feed Pump Calibration Curve ............................................................................................................ 148 - Computer Watt Meter Calibration.................................................................................................... 159 - Heat and Energy Flows Used In Reboiler Analysis ...................................................................... 1610 - Heat and Energy Flows Used In Condenser Analysis .................................................................. 1611 - Process Temperature Data for Distillation Col umn Heat Transfer Analysis........................ 1712 - Process Temperature Data for Distillation Column During Water Boiling........................... 1713 - Reboiler Temperature vs. Time .......................................................................................................... 1814 - UA vs. Reboiler Temperature ............................................................................................................. 2015 - Heat Loss vs. Reboiler Temperature................................................................................................. 2016 - Heat Absorbed by Cooling Water During Boiling ........................................................................ 2117 - Process Temperature Data for 0% Reflux Distillation Performance Test............................. 2218 - Reboiler Boiling Temperature Data for 0% Reflux Distillation Performance Test............. 2319 - Distillate Volume Collected for 0% Reflux Performance Test .................................................. 2320 - Distillate Rate vs. Time for 0% Reflux Performance Test.......................................................... 2421 - Distillate Rate vs. Distillate Volume for 0% Reflux Performance Test................................... 2422 - Heat Absorbed by Cooling Water During Boiling at 0% Reflux .............................................. 2523 - Process Temperature Data for 80% / 40% Reflux Performance Test..................................... 2524 - Distillate Volume Collected for 80% / 40% Reflux Performance Test.................................... 2625 - Distillate Rate vs. Time for 80% / 40% Reflux Performance Test............................................ 2626 - Distillate Rate vs. Distillate Volume for 80% / 40% Reflux Performance Test .................... 2727 - Heat Absorbed by Cooling Water During Boiling at 80% and 40% Reflux.......................... 27

TablesI. Feed Pump Calibration Data............................................................................................................ 14II. Computer Wattmeter Calibration Data........................................................................................ 14III. Temperature Change Over Time Analysis Data................................................................... 18-19IV. Heat Absorbed by Cooling Water................................................................................................... 21V. Distillation Mixture Composition.................................................................................................... 22



III. Introduction

The objective of this investigation was to study the batch distillation process of a binary system byperforming column maintenance, calibration, and performance testing. The first objective was to performnecessary column maintenance to assure that the equipment was functioning at its optimum capacity priorto any calibrations or experimental runs. Following these maintenance steps, the column’s feed pump,computer wattmeter, and reboiler volume were calibrated to assure that the controls were operatingcorrectly and acceptably, and also to make the experimental procedures easier to perform. Aftercompletion of these calibrations, an analysis of the heat loss from the reboiler was performed. This wasfollowed by two methanol-water distillations at different reflux percentages.

The University of Tennessee at Chattanooga’s distillation column was used to carry out thisinvestigation. The distillation column primarily consists of a liquid storage tank with heating elements,called the reboiler, and a column of distillation trays which serve to allow the liquid and vapor phases tocome into contact and into equilibrium with one another. The vapor that rises from the reboiler iscondensed by cooling water circulating atop the column in a condenser. This condensed vapor can becollected as distillate, sent back through the column to the reboiler as reflux, or a fractional combination ofthe preceding alternatives [1].

This report documents the investigation performed between August 20, 2002 and September 17,2002 and reports the key findings. This report continues in Section IV with a detailed theoreticalbackground which describes the distillation process and presents the fundamental physical andmathematical relationships governing the separation process. Section V provides extensive detail of thedistillation column and supporting equipment, detailing each of the components and depicting a schematicdiagram of the unit. The following Section, VI, outlines the procedures followed during the maintenance,calibration, and experimentation phases so the reader can grasp a full understanding of exactly how thestudy was performed. The results obtained during the course of the investigation follow with tabulated dataand multiple figures depicting the experimental findings. A discussion of these results follows in SectionVIII, with conclusions drawn from the objectives in Section IX. Recommendations for experimentalimprovements follow in Section X, while a list of references, and a detailed collection of appendicesconclude the report.



IV. Theory

A. Overview

Distillation involves the separation of the components of a liquid mixture by boiling the liquid toproduce a vapor that has a higher composition of the more volatile species, identified by a lower boilingpoint [2]. This vapor is then condensed and returned to a receiver as the distillate. Distillation exploitsdifferences in the boiling points of the liquid constituents in order to drive the separation process. As theliquid mixture is heated, the more volatile species evaporates, rises through the trays of the column, andreaches the condenser where it is cooled, condensed, and collected in a receiver. The still, or reboiler,consequently has a composition that is more pure in the heavier, or less volatile components. Oneimportant detail to remember before examining distillation is that the separation is not perfect. Smallamounts of the less volatile species will evaporate as the liquid mixture boils, producing a distillatecomposition that is not pure in the light component. Successive distillations will improve the purity of thedistillate composition [1].

The distillation experiments documented in this report are batch distillations of a binary system.Batch distillation is simply the distillation of a fixed volume of liquid mixture, where there is no feedstream entering the process [1]. A binary system consists of only two components, commonly referred toas the light or volatile component (A) and the heavy or less volatile component (B) [1]. A methanol-watersystem was studied in compliance with management’s direction. The performance tests were also run witha specified percentage of reflux. Reflux is the name of the liquid that is returned through the top traysdown through the column to the reboiler after being condensed [1]. For example, a reflux of 80% translatesto mean that 80% of the liquid that evaporates is condensed and returned to the column in and attempt toincrease the purity of the distillate. The remaining 20% is collected in the distillate receiver.

B. Reboiler Energy Balance

Initially, the focus of the investigation was determining the heat transfer relationships for thereboiler. Selecting a control volume around the reboiler, it can be found that there are principally threeenergy terms to consider. First, there is heat input, provided by the heating elements. Second, there is thechange in temperature of the water due to heating by the elements. Finally, there is a certain amount ofheat loss from the system to the surroundings due to the fact that the system is hotter than the surroundingsand the two shift toward equilibrium with one another. This is illustrated in Figure 1.

Figure 1 - Energy Diagram for the Reboiler

Performing an energy balance on the reboiler will reveal Equation 1, and a more detailed derivation willyield the more useful form of Equation 2. The full derivation is included in Appendix C.

( ) LossinBOHpOH QQTCmdtd ..

, **22

−= (1)

Heat Input,Qin

Heat Loss,QL

Calrod Heaters

LiquidMixture

Reboiler

Water HeatingQabsorbed



( ) ( )[ ]∞−−= TTUAQCmdt

dTBinOHpOH

B.

, 22* (2)

The energy balance states that the change in temperature of the reboiler contents is equal to the heat inputto the system less the heat losses from the system to the surroundings. Since the mass of water is constantfor a batch distillation process with no distillate collection (100% reflux) and the heat capacity of water canbe reasonably assumed constant over the range of operating temperatures, these values can be removedfrom the derivative term [3]. The change in reboiler temperature over time, prior to reaching the boilingtemperature, can be determined from the slope of the line on a reboiler temperature vs. time plot. In theory,the temperature of the solution will remain constant, at the boiling point of the solution, during the boilingprocess, as all energy taken in is used to vaporize the liquid [3]. So, theoretically, the slope would be zeroat these points. Equation 3 allows for the calculation of an instantaneous slope across successive datapoints 1 and 2.

( )( )12

12

ttTT

dtdTb

−−

= (3)

The heat input is constant for these performance tests, and the heat loss can be calculated using Newton’sLaw of cooling where U is the overall heat transfer coefficient, A is the heat transfer surface area, and T∞ isthe ambient room temperature [4].

)( ∞−= TTUAq b (4)

Equation 4 states that as the temperature difference increases, then so does the heat loss. In effect, thetemperature difference drives the heat loss. Measuring the reboiler surface area allows for the calculationof the overall heat transfer coefficient U. The overall heat transfer coefficient can be estimated at between2 and 25 W/(m2K) for this system with free convection of a gas [4]. Anything above 100 W/(m2K) wouldnot make physical sense for the type of heat loss experienced by the system.

The heat input to the system was read from a Valhalla multimeter and the computer voltage signal,Vs, was calibrated from this reading. It was desired to find the proportionality constant, K, between the trueheat input and the voltage signal read by the computer. This voltage signal is produced by an AAC WattTransducer (Model S217) manufactured by American Aerospace Controls. This K is related to the slope ofa plot of Vs versus Watts, and this relationship can be expressed as

sVKW = . (5)

C. Condenser Energy Balance

Another source of heat transfer in the system is the absorption of heat by the condenser coolingwater during the boiling phase. This heat can be expressed as the product of the volumetric flow rate (V)times the density of water (ρ) (which is the mass flow rate cooling water) times the constant pressure heatcapacity (CP) times the change in cooling water temperature (∆TCW ). Mathematically, this is expressed as

CWPCWCW TCVQ ∆= ***..

ρ . (6)

D. Distillation Mixture Composition

In the performance testing phase of the investigation, it was necessary to calculate molarpercentages of the two components in a binary system. Knowing the volumes (Vi) of each pure substancein the mixture, the densities (ρι) of each component can be used to determine the mass (mi) of eachcomponent in the mixture [5].



iii Vm ρ*= (7)

Then, the number of moles of each species (ni) can be found by dividing the mass by the molecular weight(MWi) of each substance.

i

ii MW

mn = (8)

Finally, the mole percentage of each component can be computed as outlined in Equation 9.

100*(%)∑

=i

i

nn

n (9)

In analyzing the temperature data collected during the distillations, it is important to note theboiling point of the solution and its difference from the individual species’ pure boiling points.Theoretically, if a solution has a higher composition of one component, then the boiling point of thesolution should be closer to the pure species boiling point of that component. Furthermore, as the morevolatile component boils, it should be seen that the reboiler temperature will rise and approach the boilingpoint of the pure heavy component, assuming that the light component is in the vapor phase or collected asdistillate.

In analyzing the distillate volume collected, it is important to look for any impact of distillate ratecaused by changes in reflux percentage.



V. Equipment

The distillation column used in this experiment is depicted in Figure 2. It consists of a reboiler,which is a clear glass cylinder with calrod heaters partially occupying the bottom half of the container. Theapproximate area of the reboiler’s external surface is 0.42 m2. The liquid mixture is housed in the reboilerwhere the calrod heaters apply heat input to bring the mixture to a boil. Temperature, pressure, and levelsensors monitor the conditions in the reboiler, and a reboiler pump allows for draining the heavy liquidproduct at the conclusion of an experiment. This product is typically pumped to a large storage tank forproper use afterward. Feed is supplied to the reboiler through a feed pump, which draws from a feed linethat can be connected to graduated cylinders, the feed tank, or any other liquid container. The feed line hasa volume of approximately 0.5 L, and this volume must be taken into account when filling the reboiler.The feed enters the column in the feed section shown in Figure 2, and falls through the lower trays into thereboiler. A measurement of the feed temperature is collected where shown. As the liquid in the reboilerboils and vapor is produced, it ascends the column, through each tray from twelve to one. Temperaturemeasurements are made at each level. An electromagnetic reflux control is situated atop the distillationcolumn trays, where condensed liquid may be redirected down the column if the reflux is turned on. As thevapor rises through the condenser, the cooling water absorbs heat from the vapor and condenses the vaporto a liquid. Temperature indicators record the temperature of the cooling water supply and return lines, aswell as the condenser vapor. The cooling water flow rate can be adjusted by adjusting the solenoid valvesor manual valves in the water supply line and is measured via a paddlewheel flow meter. The distillate thatis not sent back through the column is directed through a cooler and into the distillate receiver. The levelindicator at the distillate receiver does not function correctly, so volume and time readings must be taken tomeasure the amount of distillate collected and calculate the rate. When the receiver becomes full, it may bedrained using the distillate pump, which pumps the collected distillate to the product tank or othercollection vessel. The entire process is controlled using a LabView control interface on the computer.



Reboiler Pump

Calrod HeatersLiquid Mixture

Reboiler

Feed /Product

Tank

TI PI

LI

Tray 12

Tray 11

Tray 10

Tray 9

Tray 8

Tray 7

TI

TI

TI

TI

TI

TI

Feed

Tray 6

Tray 5

Tray 4

Tray 3

Tray 2

Tray 1

LI

TI

TI

TI

TI

TI

Feed Pump

Reflux

TI

TI

CondenserTI

TI

Supply

Return

Cooling WaterTI

Cooler DistillateReceiver

DistillatePump

F

Heat Loss vs. Reboiler Temperature

0

200

400

600

800

1000

1200

1400

2 0 30 40 50 6 0 70 80 90 100

Reboiler Temperature (°C)

Hea

t L

oss

(W

)

ComputerController

CoolingWater Flow

Valves

Figure 2 -Distillation ColumnSchematic Diagram

Cooling Water



VI. Procedure

A. Distillation Column Maintenance and Calibration

First, column maintenance and calibrations were performed to assure that the equipment wasprepared for the experimental tests. First, the solenoid cooling water supply valves and the manual coolingwater supply valves were reversed so the solenoid valves would function properly. The solenoid valvemust have a certain amount of pressure to operate correctly, and if the manual valves were partially closed,then the solenoid valve would not have the necessary pressure to function. Therefore, using some pipewrenches, square wrenches, a vice, and Teflon tape, we interchanged the two valves so that the solenoidvalve could function properly. Figure 3 shows the two valves in the incorrect position, since water entersthe system from below. No picture is available showing the valves in the reversed positions.

Figure 3 - Cooling Water Flow Valves Prior to Maintenance

Another column problem that was inherited was a burned and baked reboiler, the exterior of which wascharred from burned insulation and overheating. The outside of the container was scraped with ascrewdriver to remove the residue. Figure 4 depicts this process.

Figure 4 - Column Maintenance of Reboiler Surface

Finally, the column itself, specifically the outside of the trays, was cleaned for good measure. Figure 5depicts this cleaning process.



Figure 5 - Column Maintenance of Tray Exterior

In the next step of the process, the reboiler volume, feed pump flow, and computer wattmeter werecalibrated. The reboiler volume was calibrated by measuring out increments of 1 L of water and pumpingthem into the reboiler via the feed pump. Once one liter was pumped into the system, a graduated markwas made on the reboiler surface to provide a tool to visually measure the reboiler volume. A total of 15 Lwere pumped into the reboiler, and 1 L graduations were made on the reboiler up to a 15 L mark. Carefulattention was paid to not run air in the feed lines to avoid any error in liquid volume that was fed.

Next, the feed pump calibration was performed. To perform this calibration, the feed pump wasset at variable speeds (2, 4, 6, 8, and 10) and the volume of water that was pumped from the feed cylinderin one minute was recorded. Therefore, this calibration produced a chart of volumetric flow ratescorresponding to computer pump settings. Figure 6 depicts this experimental setup for both calibrations.

Figure 6 - Reboiler Volume and Feed Pump Calibration Process Diagram



Finally, the computer wattmeter was calibrated. This was accomplished by connecting a Valhallamultimeter to the distillation column to measure the true wattage and amps supplied to the reboiler heaters.At discrete values of amperage (5, 10, and 15 Amps) the wattage was read from the multimeter and thecomputer voltage signal was read from the LabView display. The voltage signal is from the power-transmitter that is located on the column. It has a 0-5 kW rating on 220V AC and is connected alongsidethe main power supply box. A plot of computer voltage signal versus true wattage was plotted, and theproportionality constant, or the slope of the line given by the plotted points was calculated. Equation 5 wasused to find this constant, K. This calibration produced a constant by which the voltage signal can bemultiplied to yield the true wattage input to the system.

B. Performance Testing and Energy Analysis

Upon completion of the maintenance and calibration steps, performance tests were run on thecolumn to assure that it was working correctly and to report upon the batch distillation of the binarymethanol-water system. The first test run was run with 14 liters of water and was aimed at determining theheat transfer relationships in the column and reboiler. First, 14 liters of pure water were pumped into thereboiler by setting the feed pump to 10 and connecting the supply line to a series of graduated cylinderswith precisely measured volumes of water in them, totaling 14 liters. With the water in the reboiler, theamperage was set to 15 amps, and 2487 Watts of constant power were supplied to the system via the calrodheaters in the reboiler. Reflux was set to 100% such that no distillate would be collected and all evaporatedvapor would be returned to the column. The process temperatures and pressures were measured as thewater heated toward its boiling point. When vigorous boiling occurred, the heat was left on for anadditional 10 minutes and then the heat input was set to 0 Amps and, accordingly, 0 Watts. Additionaltemperature data was recorded as the system gave off heat in order to reach equilibrium with itssurroundings. Following the data collection, the energy balance and analysis prescribed in the theory ofthis report, Equations 1-4 and 6, was performed on the raw data to find the change in temperature overtime, the overall heat transfer coefficient, the heat losses from the system, and the heat absorbed by thecooling water during condensation.

Upon analysis of the heat losses from the system, a methanol-water distillation was performed at0% reflux. A solution consisting of 14 L of water and 1 L of methanol was pumped into the reboiler asprescribed above, and 2487 W of power at 15 amps were supplied to the system. Mole percentages of eachcomponent were calculated from the volumes using Equations 7-9. Again, process temperatures wererecorded throughout the run time. As the solution reached the mixture’s boiling point, distillate wascollected in the receiver. Due to the fact that the distillate level indicator does not function properly, thechange in distillate receiver volume over time was measured and recorded. A plot of the distillate volumecollected versus time was constructed so as to interpret the rate at which the distillate was collected and toobserve any discrepancies therein. Because the distillate receiver has a maximum volume of 1 L and 3 L ofdistillate were collected, the distillate pump was turned on and set to 10 during times when the receiver wasalmost full. This took approximately 2 to 3 minutes to drain the distillate receiver, and as a consequencethree data points were lost due to this necessity.

In the next performance test, an identical liquid mixture was used, except that the reflux was set to80% and later changed to 40%. Upon heating and vaporizing part of the liquid mixture, the distillatereceiver began to collect product. The reflux was kept on 80% until exactly 0.5 L of distillate wascollected. At that point, the reflux was reset to 40% and the corresponding change in the distillate flow ratewas observed. After an appreciable amount of time the heat input was removed and the system was slowlycooled to ambient temperature.



VII. Results

A. Distillation Column Maintenance and Calibration

The feed pump calibration was performed at settings 2, 4, 6, 8, and 10. The recorded change involume over the one-minute interval at each of these settings is given as Table I. Figure 7 presents thecalibration curve for the feed pump.

Table I. Feed Pump Calibration Data

Pump Setting Feed Flow Rate (mL/min)0 02 1004 2756 4808 60010 630

Feed Pump Calibrations

0

100

200

300

400

500

600

700

0 2 4 6 8 10

Pump Setting

Flo

w R

ate

(mL

/min

)

Figure 7 - Feed Pump Calibration Curve

The computer Wattmeter was calibrated by comparing the wattage and amps recorded by thecomputer to the standard displayed on the Valhalla multimeter and the control box meter. The computerreceives a voltage signal from the system that it represents as a wattage reading. The voltage signal read bythe computer and the wattage measurement from the multimeter at three distinct amperage settings arereported in Table II.

Table II. Computer Wattmeter Calibration Data

Control Box Meter (A) Valhalla (A) Valhalla (W) Computer Vs (W)4.75 5.77 377 0.28110 9.39 976 0.87915 14.91 2487 2.398



Graphing the computer voltage signal versus the Valhalla wattage reading and determining the slope of thelinear line produced proportionality constant, or calibration parameter, between the two readings. Figure 8shows the calibration curve for the computer wattmeter and reports the proportionality constant as 0.001.Therefore, the CPU meter accurately measures kilowatts directly. Alternately, the Voltage signal (Vs)multiplied by 1000 produces the true reboiler wattage (W), or

sVW 1000= . (10)

Computer Watt Meter Calibration

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 500 1000 1500 2000 2500 3000

Valhalla (W)

CP

U S

igna

l (V s

)

Reboiler Watts = 1000Vs

Vs = 0.001W

Figure 8 - Computer Watt Meter Calibration

B. Energy Analysis

Armed with the true wattage input at 15 amps, analysis of heat transfer in the reboiler wasperformed. A volume of 14 L of water was used for this analysis with 100% reflux. This volume isaccurate in that the volume of the feed line, which is important in terms of delay time for feed compositionchanges, was also taken into account. The volume of the feed line was determined to be approximately 500mL, which consists of 15 feet of 0.125 inch radius feed line and 375 mL of feed in the pieces of equipmentin the feed pathway. For heat loss calculations, a reboiler volume of 0.42 m2 was used, approximating thereboiler as a cylinder with a 20 inch length, and two 4.3 inch radius circular end caps. Figures 9 and 10show the heat and energy flows used in the analysis. Figure 9 shows a constant heat input to the reboilerand the corresponding heat losses to the surroundings and heat absorbed by the reboiler mixture. Figure 10shows the heat transferred from the inlet vapor to the cooling water (which leaves with an increasedtemperature relative to supply) and the corresponding condensed liquid which re-enters the column.



Figure 9 - Heat and Energy Flows Used In Reboiler Analysis

Figure 10 - Heat and Energy Flows Used In Condenser Analysis

Process data was recorded using the LabView interface. This data is available on the Internet asdetailed in reference [6]. Figure 11 presents all of the process temperature data for this experimental run,with particular interest being paid to the heating range (0min-40min), boiling range (40min-55min), andcooling range (t>55min). It is important to note that the reboiler temperature is not uniform, particularlyduring heating. The water below the heaters is relatively cool while the water in direct contact with theheaters is very hot. Then, during the boiling phase, it was observed that the rigorous mixing helped to moreevenly distribute the temperature within the reboiler. The pure water mixture begins to boil atapproximately 99.5 °C, as literature references would attest to [5]. It is also interesting to note that thereboiler temperature remains constant during the boiling phase. This phenomenon is characteristic of apure species, but a distinction will be made later on in this report regarding this pure species behavior andthe behavior of a mixture. Temperatures above 100 °C were recorded in some of the trays, which is topicfor controversy, but they are due to instrumental errors in the measurements. Figure 12 depicts a zoomedin region of the graph during the boiling process, so that the constant reboiler temperature can be noted.

Heat Input,Qin

Heat Loss,QL

Calrod Heaters

LiquidMixture

Reboiler

Water HeatingQabsorbed

Supply -Cool

Return -Hot

Cooling Water

Condenser

Inlet Gas

Condensed Vapor -Cool

∆Q Transfer



Process Temperature Data

2030405060708090

100110

0 50 100 150

Time (min)

Tem

per

atu

re (

°C)

Tray 1 T (C)

Tray 2 T (C)

Tray 3 T (C)

Tray 4 T (C)

Tray 5 T (C)

Tray 6 T (C)

Tray 7 T (C)

Tray 8 T (C)

Tray 9 T (C)

Tray 10 T (C)

Tray 11 T (C)

Tray 12 T (C)

Reflux T (C)

Reboiler T (C)

Figure 11 - Process Temperature Data for Distillation Column Heat Transfer Analysis


90

100

110

25 35 45 55 65 75

Time (min)

Tem

per

atu

re (

°C)

Tray 1 T (C)

Tray 2 T (C)

Tray 3 T (C)

Tray 4 T (C)

Tray 5 T (C)

Tray 6 T (C)

Tray 7 T (C)

Tray 8 T (C)

Tray 9 T (C)

Tray 10 T (C)

Tray 11 T (C)

Tray 12 T (C)

Reflux T (C)

Reboiler T (C)

Figure 12 - Process Temperature Data for Distillation Column During Water Boiling

Specifically, the change in reboiler temperature over time was of particular interest. Analysis ofthis temperature change was performed as the reboiler liquid was heated to a boil and then after the heatinput was removed and the system slowly reached thermal equilibrium with its surroundings. This isdepicted in Figure 13.

ConstantReboilerTemperature



Reboiler Temperature vs. Time

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300

Time (min)

Tem

per

atu

re (

°C)

Figure 13 - Reboiler Temperature vs. Time

An instantaneous slope across each data pair collected was calculated using Equation 3 (A samplecalculation appears in Appendix II of this report). Five-minute averages of the temperature and slope werecalculated to be used along with the unsteady-state energy balance to analyze the heat transfer in thereboiler. From this energy balance, the overall heat transfer coefficient was determined by solvingEquation 1 for the product UA and then dividing by the reboiler area, 0.42 m2. Finally, the total heat losswas calculated from Newton’s Law of Cooling. Table III presents this energy balance data.

Table III. Temperature Change Over Time Analysis Data

T (°C) dT/dt (°C/min) UA (W/°C) U (W/(m2 °C)) Qloss (W)35.0 2.5 4.9 11.6 63.747.3 2.4 7.4 17.5 187.058.5 2.2 9.4 22.1 341.269.5 2.1 9.8 23.1 464.579.2 1.9 11.3 26.8 648.388.0 1.7 12.5 29.6 826.095.8 1.1 18.8 44.3 1384.097.6 0.3 4.2 10.0 318.495.8 0.3 4.2 9.9 310.594.0 0.3 4.2 9.9 300.692.2 0.3 4.3 10.2 304.490.5 0.3 4.3 10.2 295.888.8 0.3 4.5 10.6 298.387.2 0.3 4.3 10.2 280.785.6 0.3 4.3 10.3 276.384.0 0.3 4.5 10.7 281.682.5 0.3 4.4 10.5 269.181.1 0.3 4.3 10.1 252.179.6 0.3 4.3 10.3 250.678.2 0.2 4.3 10.3 244.276.8 0.2 4.2 9.9 229.1



75.5 0.2 4.3 10.3 232.274.2 0.2 4.3 10.2 226.273.0 0.2 4.3 10.2 218.871.7 0.2 4.2 9.9 207.570.6 0.2 4.0 9.5 194.969.4 0.2 4.2 9.8 197.568.3 0.2 4.1 9.7 190.067.1 0.2 4.2 9.9 188.766.1 0.2 4.0 9.4 176.165.0 0.2 4.2 9.9 179.564.0 0.2 4.1 9.8 173.463.1 0.2 4.0 9.6 166.262.1 0.2 3.8 9.0 153.661.3 0.2 4.0 9.3 155.160.4 0.2 4.1 9.7 157.059.5 0.1 3.9 9.2 145.958.7 0.1 3.8 9.0 139.357.9 0.1 3.8 8.9 134.957.0 0.1 3.9 9.2 136.556.3 0.1 3.5 8.3 121.155.6 0.1 3.9 9.2 130.854.8 0.1 3.7 8.8 121.754.2 0.1 3.7 8.8 119.5

At room temperature, the slope (dT/dt) was found to be 2.7 °C/min. Using Equation 6 to solve forthe heat input at room temperature, where losses should be negligible, the value found was approximately2.6 kW, very close to the true 2.5 kW input detected from the wattmeter.

Figure 14 depicts a plot of UA vs. Temperature for periods of reboiler heating and cooling. Sincethe area is constant, the trends shown in these figures are also for the heat transfer coefficient. Namely,with heat input, UA increases with increasing temperature. Without heat input, UA remains constant withtemperature. Figure 14 clearly shows how much heat is lost at a given reboiler temperature, for heating andcooling. Heat loss with constant heat input increases at an increasing rate as the system temperature rises.Heat loss without heat input increases at a steady rate of 50 W/ °C as the temperature rises. The heat lossesincurred for a system with heat input are much larger than those without heat input, as Figure 15 shows.



UA vs. Reboiler Temperature

02468

101214161820

20 30 40 50 60 70 80 90 100


UA

(W

/°C

)

Figure 14 - UA vs. Reboiler Temperature

Heat Loss vs. Reboiler Temperature

0

200

400

600

800

1000

1200

1400

20 30 40 50 60 70 80 90 100


Hea

t Lo

ss (

W)

Figure 15 - Heat Loss vs. Reboiler Temperature

Another method of heat transfer in the system is the heat absorbed by the condenser cooling waterduring the boiling and vaporization phase. The heat absorbed is shown graphically as a function of thereflux temperature in Figure 16. The heat-absorbed data is presented as Table IV.

Constant Heat Input

No Heat Input

Constant Heat Input

No Heat Input



Heat Absorbed by Cooling Water During Boiling

0

200

400

600

800

1000

1200

1400

1600

1800

2000

98 99 100 101 102 103 104 105

Reflux Temperature (°C)

Hea

t A

bsor

bed

by W

ater

(W

)

Figure 16 - Heat Absorbed by Cooling Water During Boiling

Table IV. Heat Absorbed by Cooling Water

Time (min) Reflux T (°C)Cooling

Water Flow(gpm)

CoolingWater Supply

T (°C)

CoolingWater Return

T (°C)

HeatAbsorbed by

CoolingWater (W)

48.40 98.54 0.68 28.80 32.03 58048.89 100.44 0.68 28.80 34.32 99149.36 101.47 0.68 28.78 36.06 130749.82 102.11 0.68 28.77 37.24 152150.30 102.58 0.69 28.79 37.77 163650.78 103.07 0.67 28.77 38.13 165651.26 103.48 0.68 28.78 38.70 178151.72 103.94 0.66 28.74 39.37 185252.20 104.27 0.68 28.78 39.17 186552.69 104.44 0.68 28.73 38.43 174153.14 104.52 0.68 28.74 38.57 176553.63 104.04 0.67 28.77 38.89 1790

At constant reboiler temperature, the heat into the system should be approximately equal to the heatremoved by the condenser. From the last points in Table IV at 104 degrees C, the heat removed isapproximately 1.8 kW, comparable to the 2.5 kW supplied less some losses to the surroundings at thistemperature.

C. Performance Testing

After analysis of the heat transfer relationships in the distillation column, two performance testswere run on the methanol-water binary system. In the first experiment, a solution consisting of 14 L of



water and 1 L of methanol was prepared for batch distillation with 0% reflux. Mole percentages of themixture constituents were calculated using Equation 10 and are tabulated in Table V.

Table V. Distillation Mixture Composition

Volume Methanol (L) Volume Water (L) Mole % Methanol Mole % Water1 14 3.1 96.9

As before, process temperature data was recorded during the distillation process. Notably, the temperatureat which the liquid boils is around 95 °C, lower than that of pure water. This data is available on theInternet and is presented as Figure 17 [7].


2030405060708090

100110

0 50 100 150 200 250 300 350

Time (min)

Tem

per

atu

re (

°C)

Tray 1 T (C)

Tray 2 T (C)

Tray 3 T (C)

Tray 4 T (C)

Tray 5 T (C)

Tray 6 T (C)

Tray 7 T (C)

Tray 8 T (C)

Tray 9 T (C)

Tray 10 T (C)

Tray 11 T (C)

Tray 12 T (C)

Reflux T (C)

Reboiler T (C)

Figure 17 - Process Temperature Data for 0% Reflux Distillation Performance Test

It is interesting to note that the reflux temperature was approximately 95 °C when the solution came to arigorous boil. The reflux temperature then increased as boiling and evaporation continued. Figure 18details this area. This will be addressed in the discussion of results section to follow.




90

100

110

0 50 100 150 200

Time (min)

Tem

per

atu

re (

°C)

Tray 1 T (C)

Tray 2 T (C)

Tray 3 T (C)

Tray 4 T (C)

Tray 5 T (C)

Tray 6 T (C)

Tray 7 T (C)

Tray 8 T (C)

Tray 9 T (C)

Tray 10 T (C)

Tray 11 T (C)

Tray 12 T (C)

Reflux T (C)

Reboiler T (C)

Figure 18 - Reboiler Boiling Temperature Data for 0% Reflux Distillation Performance Test

The volume of distillate collected over time was also monitored, and Figure 19 depicts this data.

Distillate Volume vs. Time

0

500

1000

1500

2000

2500

3000

3500

50 60 70 80 90 100 110 120 130 140 150 160 170

Time (minutes)

Dis

tilla

te V

olu

me

(mL

)

Figure 19 - Distillate Volume Collected for 0% Reflux Performance Test

Figures 20 and 21 depict plots of distillate rate versus time and distillate rate versus distillate volume.

Increasing Reboiler Temperature



Distillate Rate vs. Time

0

10

20

30

40

50

0 50 100 150 200

Time (min)

Dis

tilla

te R

ate

(mL/

min

)

Figure 20 - Distillate Rate vs. Time for 0% Reflux Performance Test

Distillate Rate vs. Distillate Volume

0

10

20

30

40

50

0 1000 2000 3000 4000

Distillate Volume (mL)

Dis

tilla

te R

ate

(mL/

min

)

Figure 21 - Distillate Rate vs. Distillate Volume for 0% Reflux Performance Test

Also during this time, heat was removed by the condenser, as Figure 22 shows. During the boiling process,the amount of heat removed was fairly constant, as the plotted points show.




0

200

400

600

800

1000

1200

1400

1600

1800

0 20 40 60 80 100 120


Hea

t A

bsor

bed

by W

ater

(W

)

Figure 22 - Heat Absorbed by Cooling Water During Boiling at 0% Reflux

In the second performance test, the same composition of methanol-water solution was used but the refluxwas set at 80% and then changed to 40% during the experiment. The process temperatures were againmonitored and are presented in Figure 23. The data is available on the Internet [8].


2030405060708090

100110

0 200 400 600 800 1000 1200

Time (min)

Tem

per

atu

re (

°C)

Tray 1 T (C)

Tray 2 T (C)

Tray 3 T (C)

Tray 4 T (C)

Tray 5 T (C)

Tray 6 T (C)

Tray 7 T (C)

Tray 8 T (C)

Tray 9 T (C)

Tray 10 T (C)

Tray 11 T (C)

Tray 12 T (C)

Reflux T (C)

Reboiler T (C)

Figure 23 - Process Temperature Data for 80% / 40% Reflux Performance Test

As before, the distillate volume was recorded over time and this data is presented as Figure 24. Also,additional plots of distillate rate versus time and distillate rate versus distillate volume are presented asFigures 25 and 26, respectively.



Distillate Volume vs. Time

0

200

400

600

800

1000

1200

1400

1600

70 80 90 100 110 120 130 140

Time (min)

Dis

tilla

te V

olu

me

(mL

)

Figure 24 - Distillate Volume Collected for 80% / 40% Reflux Performance Test

Distillate Rate vs. Time

05

10152025303540

80 90 100 110 120 130 140

Time (min)

Dis

tilla

te R

ate

(mL

/min

)

Figure 25 - Distillate Rate vs. Time for 80% / 40% Reflux Performance Test

80% Reflux 40% Reflux

80% Reflux

40% Reflux



Distillate Rate vs. Distillate Volume

05

10152025303540

80 280 480 680 880 1080 1280 1480 1680

Distillate Volume (mL)

Dis

tilla

te R

ate

(mL

/min

)

Figure 26 - Distillate Rate vs. Distillate Volume for 80% / 40% Reflux Performance Test

Figure 27 details the constant heat absorbed by cooling water during boiling at 80% and 40% reflux.


0

500

1000

1500

2000

2500

70 75 80 85 90 95 100 105


Hea

t A

bsor

bed

by W

ater

(W

)

Figure 27 - Heat Absorbed by Cooling Water During Boiling at 80% and 40% Reflux

80% Reflux

40% Reflux



VIII. Discussion of Results

A. Maintenance and Calibration Results

The maintenance performed on the column served its purpose and assured that the system was inpeak operating conditions. The cleaning and cooling water valve switching prepared the unit to functionappropriately for the test runs. The feed flow meter calibration produced a curve translating the feed pumpsettings into feed flow rates. For continuous distillation processes, this calibration curve allows the user toadjust the pump setting to produce the desired flow rate. The pump flow rate levels out from setting 8 to10, only increasing in flow rate by about 30 mL/min between the settings, unlike the more noticeableincrease seen in the lower settings, for example 175 mL/min going from 2 to 4.

The computer wattmeter calibration provided a proportionality constant of 1000, which is thefactor by which the voltage signal can be multiplied to produce the true wattage measured. With this factorand the linear relationship it describes, a formula can be created in LabView to display the correct wattageon the screen for the benefit of future users. Similarly, the graduations marked on the reboiler offer a quickand convenient way for future users to determine the volume of liquid in the reboiler with a simple glance.

B. Heat Transfer Analysis Results

The heat transfer analysis performed on the distillation column offered valuable insight into thethermal behavior of the system. Figure 13 shows that as the water was heated at constant power equal to2487 W, the reboiler temperature increased at a decreasing rate. Initial slopes were as high as 2.5 °C/minand faded to 1.1 °C/min as the boiling point was reached. The temperature of the water was constantduring the boiling process, as shown in Figure 11 during the 40 min to 55 min time range, as all the energywas being used to vaporize the liquid, thus validating the theory of this report. When the supply of heatwas turned off, boiling ceased, and the liquid began to cool, coming to equilibrium with its surroundings. Itcooled faster, some 0.3 °C/min, when the temperature was in the higher ranges of approximately greaterthan 80 °C, while this rate diminished to 0.1 °C/min as the mixture began to reach room temperature.Again, Figure 13 depicts this reported trend. The overall heat transfer coefficient was found to beapproximately 10 W/(m2K) during the cooling of the reboiler back to room temperature. The heat transfercoefficient ranged from about 10 to 45 W/(m2K) during the heating process, with higher heat transfercoefficients seen during boiling. These low heat transfer coefficients agreed with the theoretical range of Uvalues for the free convection of gases [4]. These heat transfer coefficient trends for heating and coolingare shown in Figure 14. Figure 15 depicts a general trend for heat loss as a function of temperature. Bothgraphs show that as the temperature is increased, the heat losses from the system increase. It should benoted that the losses are higher with heat input to the system than they are without heat input to the system.At 80 °C, the heat loss in the heated system is 675 W, while in the cooling system it is only 250 W at thesame temperature. This temperature dependence of heat loss was expected from theory, as Equation 4states mathematically that as the temperature difference or driving force increases, then the heat loss willalso increase. Figure 16 revealed a final interesting point about the heat losses from the system. As thereflux temperature increased, the amount of heat absorbed by the cooling water increased. In one case, theheat absorbed by the cooling water was 1865 W, 75% of the entire 2476 W input to the system. Thequantity of heat absorbed by the cooling water in the boiling process offered another additional conclusion.From Equation 6, if the volumetric flow rate of the water was lessened then the temperature increase seenin the cooling water would have been greater. However, the quantity of heat absorbed would have been thesame as long as sufficient flow was provided to carry away 1865 W of heat.

C. Performance Testing

In the next phase of the investigation, the two distillations produced some noteworthy results. Inthe first distillation, at 0% reflux, the process temperature graph, Figure 17, offered some insight into thepurity of the mixture. Pure methanol boils at 64.7 °C, while pure water boils at 100.0 °C [5]. For thedistillation of 3.1 mol % methanol and 96.9 mol % water, the reboiler temperature was 95 °C when boilingbegan to occur. The reflux temperature spiked to 95 °C almost instantly when the boiling process began.This temperature lies between the boiling points of the two liquid constituents, more heavily weighted



toward water, the component present in larger proportion. Likewise, reviewing the data for the pure waterrun and the heat transfer analysis, the reboiler temperature reached 99.5 °C before rigorous boiling began tooccur. So the boiling point of the mixture offers some insight as to the relative composition of each speciesin the mixture. Also, we see in Figure 17 that as boiling continues the reboiler temperature increases. Thissuggests that the lower boiling methanol is being removed from the mixture, and the temperature increasesto boil the now almost pure water. The distillate volume collected, Figure 19, showed that the volumecollected was approximately equal to 2000 mL. Clearly since only 1 L of methanol was present in themixture, water was present in the distillate. After about 2 L had been removed, the rate at which thedistillate was being collected diminished, as the graph shows, from about 28 minutes for 1 liter for the first2 liters to about 40 minutes for 1 liter following. Here it is suggested that the water is being heated to itspure boiling point since most of the methanol is assumed to be removed from the liquid.

The next distillation at 80% and 40% reflux also validated the boiling temperature and puritycorrelation, but the change in reflux after 0.5 L of distillate was collected was particularly noticed in thedistillate volume plot, Figure 24. The first half-liter of distillate was removed in about 20 minutes, whilethe next half-liter of distillate was removed in about 15 minutes. The increase in this distillate collectionrate is directly attributable to the reduction in the reflux rate. As less condensed vapor is redirected throughthe column at the lower reflux rate, distillate is collected in the receiver at a faster rate as is expected fromtheory. The experimental results validated this theoretical behavior.

In both distillation trials, the heat removed by the condenser cooling water was constant.



IX. Conclusions

Upon completion of the experiment, it was largely concluded that the objectives set forth weremet. Column maintenance performed during this investigation corrected an operational problem with thesolenoid flow valves in the cooling water line and beautified the work area. The calibration of thecomputer wattmeter, reboiler tank volume, and feed flow meter provided basis measurements forexperiments to follow.

Analysis of the heat transfer in the reboiler revealed the trend that as the temperature of thereboiler increases then the heat lost to the surroundings increases. Quantitative measurements of the heattransfer coefficient describing the heat loss to the surroundings were made, and reliable logical values werecalculated. It was determined that the condenser cooling water can absorb a large percentage of the heatinput during boiling, up to around 75%.

Distillation of the methanol-water system revealed that the initial boiling point of the mixturecould offer insight into the composition of the mixture by weighting itself toward the boiling point of theliquid present in the largest amount. Furthermore, the reboiler temperature increases during the boilingphase as the light component is vaporized and the mixture heats up to the boiling point of the heavycomponent. Finally, it was observed that a higher reflux percentage produced a lower distillate flow rate.



X. Recommendations

In future experiments, it would be desirable to locate a large volumetric container from which feedmay be supplied. The largest containers available were 1 L containers, and these had to be frequentlyrefilled so as the pump would not be pumping dry. It would be better to measure out a large quantity offeed from smaller containers, and then dump them into a larger container for a continuous feed. Thiswould cut out some of the manual labor and the risk of decreasing the pump’s life and well-being.

It is also desired to find a way to determine the composition of the distillate at varying levels ofreflux. It is known that higher reflux yields a more pure product, and it is desirable to quantify such astatement and validate it experimentally [1].



XI. References

[1] Unit Operations of Chemical Engineering, 6th Ed., Warren L. McCabe, Julian C. Smith andPeter Harriott, McGraw-Hill, Boston, 2001.

[2] Perry’s Chemical Engineers’ Handbook, 7th Ed., Robert H. Perry and Don W. Green, McGraw-Hill, New York, 1997.

[3] Thermodynamics: An Engineering Approach, 3rd Ed., Yunus A. Cengel and Michael A. Boles,McGraw-Hill, Boston, 1998.

[4] Fundamentals of Heat and Mass Transfer, 4th Ed., Frank P. Incropera and David P. DeWitt, JohnWiley & Sons, Inc., New York, 1996.

[5] Elementary Principles of Chemical Processes , 3rd Ed., Richard M. Felder and Ronald W.Rousseau, John Wiley & Sons, Inc., New York, 2000.

[6] UTC Engineering Controls Lab Online. University of Tennessee at Chattanooga. 28 August2002 http://chem.engr.utc.edu/Student-Files/2002/435/Distillation/8-28-2002--4-26-PM-/8-28-2002--4-26-PM-.txt

[7] UTC Engineering Controls Lab Online. University of Tennessee at Chattanooga. 3 September2002 http://chem.engr.utc.edu/Student-Files/2002/435/Distillation/9-3-2002--2-13-PM-/9-3-2002--2-13-PM-.txt

[8] UTC Engineering Controls Lab Online. University of Tennessee at Chattanooga. 10 September2002 http://distillation.engr.utc.edu/data.htm



XII. Appendices

A. Raw Data

The raw data collected in the laboratory may be accessed through the Internet at the referencesprovided in the preceding section.

B. Sample Calculations

( ) ( )[ ]∞−−= TTUAQCmdt

dTBinOHpOH

B.

, 22* (2)

( )( )∞−

−=

TT

Cmdt

dTQ

UAB

OHpOHB

in 22 ,

.

*

( )

( )CC

JWs

calJ

Cgcal

Lg

LC

W

UA°−°

°

°

−

=225.69

sec60min1868.411000

14min1.2

2487

CW

UA°

= 8.9

( ) ( )[ ]∞−−= TTUAQCmdt

dTBinOHpOH

B.

, 22* (2)

( )( )∞−

−=

TTA

CVdt

dTQ

UB

OHpOHB

in 22 ,

.

*ρ

( )

( )( )242.0225.69

sec60min1868.411000

14min1.2

2487

mCC

JWs

calJ

Cgcal

Lg

LC

W

U°−°

°

°

−

=

KmW

U2

1.23=

( )( )12

12

ttTT

dtdTb

−−

= (3)

( )( )min77.1223.13

37.4742.48−

°−=

Cdt

dTb

min28.2

Cdt

dTb °=



)( ∞−= TTUAq b (4)

( ) CmKmW

q °−

= )225.69(42.0

1.23 22

Wq 5.464=

CWPCWCW TCVQ ∆= ***..

ρ . (6)

( ) CJ

Wsg

molKmol

Jgal

mLmL

ggalQCW °−

= 8.2803.32*

sec60min

18327.75

*4.37851

*min68.0.

WQCW 580.

=

iii Vm ρ*= (7)

=

Lg

Lm OH

100014

2

gm OH 140002

=

i

ii MW

mn = (8)

=

molg

gn OH 18

140002

moln OH 7782

=

100*(%)∑

=i

i

nn

n (9)

100*25778

778(%)

2 molmolmol

n OH +=

%97(%)2

=OHn

C. Derivations

1. Derivation of Unsteady State Energy Balance



Unsteady State Energy Balance

( ) LossinBOHpOH QQTCmdtd ..

, **22

−= (1)

Remove Constants from Derivative Term

( ) LossinOHpOHB QQCm

dtdT ..

, 22* −=

Apply Newton’s Law of Cooling, Equation 4, to Express Energy Loss Term

( ) ( )[ ]∞−−= TTUAQCmdt

dTBinOHpOH

B.

, 22* (2)

Solve For Unknown Term, UA

( )( )∞−

−=

TT

Cmdt

dTQ

UAB

OHpOHB

in 22 ,

.

*

Solve for U and Express Mass in terms of measured Volume and Density

( )( )∞−

−=

TTA

CVdt

dTQ

UB

OHpOHB

in 22 ,

.

*ρ

Distillation Column Maintenance, Calibration and...

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