CHE 415 -Rayleigh’s Equation Final Report 2007

(Data Reporter) (Leader) (Inspector) Experiment #5, Rayleigh’s Equation October 9th, 2007 Section #1, Group #5 (Data Reporter) (Leader) (Inspector) Experiment #5, Rayleigh’s Equation October 9th, 2007 Section #1, Group #5 (Data Reporter) (Leader) (Inspector) Experiment #5, Rayleigh’s Equation October 9th, 2007 Section #1, Group #5 Ryerson University Department of Chemical Engineering CHE 415 Unit Operations II Lab Report Experiment #5: Rayleigh’s Equation Experiment Performed on October 9th, 2007 Report Submitted to Dr. 1. /Leader By Group # 5 Section # 1 2. / Data Reporter 3. /Inspector October 9nd, 2007 Date Report Submitted Marking Scheme Formatting Answered all 6 questions in each Report Section / 10 General Appearance; Grammar and Spelling / 5 Complete and Informative Tables and Graphs / 15 Contents Accuracy and Precision of Results / 20 Comparison with Literature Data / 10 Discussion on Influence of Procedural Design on Results / 10 Logic of Argumentation / 20 Sample Calculations / 10 _____ Total: / 100 Abstract Binary distillation is the process of separating a mixture of two components into two phases, where the most volatile component (the lower boiling point) is rich in the vapour phase and the other component is rich in the liquid phase. Rayleigh’s equation correlates the mole fraction in the vapour and liquid phase to the total initial and final amount of moles in a vessel. The objective of this experiment was to verify the applicability of Rayleigh’s equation and to determine the efficiency of a simple batch and rectification distillation unit. It was achieved by mixing a methanol and water solution together. In the batch distillation, the solution was heated in a heating kettle over time. The vapours were condensed and collected. The density of the residue and distillate were measured with a pycnometer. In the rectification distillation unit, the solution was heated in a flask vessel with addition packing and the system had a reflux ratio of 0.5. The vapours were condensed and collected over time. The density of the residue and distillate were measured with a pycnometer. Rayleigh’s equation was proved to be applicable to the simple batch distillation unit, with only a 24.7% error. Even though the error for the batch rectification unit was lower, at 21%, Rayleigh’s equation was not applicable to this unit. The rectification unit was more efficient in producing a purer distillate than the simple batch but it had also lost more solution in the process. In conclusion, the experiment was successful at demonstrating Rayleigh’s equation and determining which process was efficient. Table of Contents 22 44 44 66 66 88 99 1010 1212 1313 1414 1515 15 List of Tables 66 66 1616 1919 19 List of Figures 1010 1111 1111 1515 1818 18 Objectives and Experimental Design The objective of this experiment is to verify the applicability of Rayleigh’s equation, to determine the efficiency of a simple batch and rectification distillation unit, and to determine the number of theoretical stages in the rectification unit. This was achieved by mixing a methanol and water solution together. In the batch distillation, the solution was heated in a heating kettle over time. The vapours were condensed and collected. The density of the residue and distillate were measured with a pycnometer. In the rectification distillation unit, the solution was heated in a flask vessel with addition packing and the system had a reflux ratio of 0.5. The vapours were condensed and collected over time. The density of the residue and distillate were measured with a pycnometer. Introduction and Theoretical Background Distillation derived from the Latin word “destillare,” meaning dripping or trickling down [5]. Binary distillation is the process of separating a feed mixture of two components into two phases, where one component is predominately in the vapour phase and the other in the liquid [6]. The liquid phase is at the bottom while the vapour phase moves to the top. In this experiment, methanol and water will be used. The composition of the vapour and the liquid depends on the relative volatility, ? [5]. For good separation between the two components, a high relative volatility is recommended, greater than 2 [5]. Relative volatility is expressed as ? = K1/ K2, where 1 is the most volatile component (methanol) and 2 is the less volatile component (water) [6]. In general, the most volatile component is the component with a lower boiling point. The two K-values are based on Raoult’s law, , where Psat is the pressure of a component at saturation and P is the total pressure of the system; therefore [6]. Since, the two components are always in contact with each other, they will always be in equilibrium, thus the relative volatility is constant [5]. From Raoult’s law y*iP = xiPsat, where x is the mole fraction in the liquid phase of species i and y* is the mole fraction in the vapour phase of species i. Also, y* is in equilibrium with x. The relative volatility can be expressed in mole fraction [6]: (1) rearranging, (2) In a simple differential batch process, a binary liquid mixture is heated in a heated kettle. The liquid slowly boils and vapors are passed through a condenser. The condensed vapours (distillate) are collected. The vapour phase will be rich in the most volatile compound (methanol). From, this Rayleigh’s equation can be derived as shown below: overall mole balance dV = -dL (3) mole balance for methanol: (y*)(dV)= -d(Lx) (4) (y*)(dV)= -L(dx) – x(dL) combining (3) (y* – x)dL = -L(dx) rearrange (5) integrating for start-up time and final time, yield’s Rayleigh’s equation [6]: (6) where V – total moles in the vapour phase L – total moles in the liquid phase L1 – total moles of solution at time zero in the liquid phase L2 – total moles of solution at the differential time, dt, in the liquid phase x1 – mole fraction of methanol at time zero in the liquid phase x2 – mole fraction of methanol at the differential time, dt, in the liquid phase y* - mole fraction of methanol in vapour phase with respect to x in equilibrium In a rectification, a reflux is added to a batch distillation process by attaching an additional column to the vessel containing the original mixture [5]. The attachment causes some of the vapours to condense, which acts as a reflux, where the liquid flows countercurrent to the vapour. The higher the reflux ratio, the more pure the distillate becomes. Experimental Set-up Figure 1: Simple Batch Distillation Figure 2: Batch Rectification Experimental Procedure A solution of methanol and distilled water was retrieved from the “waste methanol” drum. The density of this solution was determined by weighting an empty pycnometer, filling it with the solution and then weighing it again. The percent concentration of methanol was then determined from Figure 3. The concentration of methanol determined from the plot was decided to be sufficient for the experiment. The simple batch distillation equipment, as seen in Figure 1, was then prepared in the fume hood. The empty receiver flask and empty boiler flask were weighed and their weight recorded. The boiler flask was then filled approximately half full (125 mL) with the solution retrieved from the “waste” drum. The boiler flask was then re-weighed containing the solution and the value was recorded. Cold tap water was run on the shell side of the condenser, to cool the condenser tube, and discharged into the sink. A hot plate was used as the source of heat. During the experiment the boiler flask was boiled gently ensuring that the temperature did not greatly exceed that of the boiling point of methanol to avoid condensing water. Distillation was continued until approximately 1/3 of the original boiler charge was in the receiver. The residue and the distillate were then allowed to cool to approximately 20°C. At this point, the receiver flask containing the distillate and the boiler flask containing the residue were weighed and the weights recorded. The densities of the distillate and the residue were then determined by weighing two empty pycnometers, filling each with one of the solutions and then re-weighing the pycnometers full of solution. The equipment was dismantled and put away and the distillate and residue were placed into the “waste methanol” drum. As the simple batch distillation was being performed the batch rectification part of the experiment was started. It was ensured that the batch rectification equipment set-up resembled that of Figure 2 and the equipment was plugged in. The empty receiver flask and empty boiler flask were weighed and their weight recorded. The boiler flask was then filled approximately half full (500 mL) with the solution retrieved from the “waste” drum. The boiler flask was then re-weighed containing the solution and the value was recorded. An electric heating mantle was utilized as the source of heat in the batch rectification. The heat was turned on and the boiler flask was boiled gently ensuring that the temperature did not greatly exceed that of the boiling point of methanol to avoid condensing water. The packed column was kept at total reflux for approximately 5-10 minutes after it began refluxing. The time was then set on the reflux controller to 10 seconds reflux and 20 seconds collection. The distillation was continued until the receiver was approximately full or charge from the boiler. The residue and the distillate were then allowed to cool to approximately 20°C. At this point, the receiver flask containing the distillate and the boiler flask containing the residue were weighed and the weights recorded. The densities of the distillate and the residue were then determined by weighing two empty pycnometers, filling each with one of the solutions and then re-weighing the pycnometers full of solution. The equipment was dismantled and put away and the distillate and residue were placed into the “waste methanol” drum. Safety and Environmental Concerns during the Experiment: Avoid inhalation, eye contact and ingestion of the methanol and wear gloves when handling methanol to avoid absorption through skin in the laboratory as it is harmful and may be fatal or cause blindness and causes irritation of skin, eyes and respiratory tract. Methanol is flammable in both liquid and vapour phases and care should be taken around heat sources (water may not be an effective means of extinguishing flames and alcohol foam, dry chemical or carbon dioxide may need to be utilized). Further, care should be taken when working with methanol due to it affecting the central nervous system and liver [4]. If methanol vapours are inhaled the individual should be removed to an area containing fresh air and given medical attention if not breathing or having trouble breathing. If ingested, one should immediately induce vomiting and receive medical attention. If methanol comes into contact with skin or eyes flush the area immediately for at least 15 minutes and receive medical attention if appropriate [4]. Methanol when released into soil is expected to biodegrade, leach into groundwater, and evaporate quickly. When released into the air it is expected to exist in the aerosol phase, readily degrade (by reaction with hydroxyl radicals), and readily be removed by wet deposition. When released into the water methanol is expected to readily biodegrade, have a half-life of 1 to 10 days and be slightly toxic to aquatic life [4]. Whatever methanol cannot be recovered or recycled should be treated as hazardous waste and disposed of accordingly [4]. Care must be taken to avoid any contact of water and the heating devices to avoid electrocution or any other adverse effects. In the case of an evacuation of the laboratory make certain that any heat sources are shut off before leaving and that an adequate ventilation source is operating. In summary, ensure that the following precautions are taken during the experiment due to the use of methanol use: avoid breathing vapour (use a fume hood), avoid contact with skin (wear gloves), eyes (wear goggles and avoid wearing contacts during the experiment) and clothes (wear a lab coat and closed shoes), wash hands after use, keep methanol container closed when not being used, use around adequate ventilation and take care around heat sources [4]. Further, care should be taken during the experiment to avoid water and electrical wire contact as well as slipping if water is sprayed onto the laboratory floor. Water may spray from the tube coming from the condenser and therefore the tube should be watched such that it is not able to spray on the electrical equipment and floor. Safety and Environmental Concerns in Industrial Applications: Distillation is utilized in the wastewater treatment, pharmaceutical, petroleum refining, food processing and alcohol brewing industries. Only a few will be discussed below. Distillation is utilized in the petroleum refining industry to separate different types of hydrocarbons using the fact that different hydrocarbons have varying boiling points. The lighter fractions travel to the top and the heavier ones stay at the bottom [2]. Care must be taken ensure workers wear proper safety equipment, i.e. hardhats, to prevent any accidents from occurring. In the pharmaceutical industry, batch rectification is used frequently. It can be used for a variety of products, such as for the concentration of vitamin A solution by removal of water. Safety concerns include controlling pressure build-up in the column. Many of the components in the pharmaceutical industry are also temperature sensitive and therefore care should be taken when working with them [3]. Results and Discussion In the simple differential distillation, the initial mole fraction of methanol was 0.2894. The final mole fraction of methanol was 0.1438 and 0.2169 in the residue and distillate respectively. In the rectification distillation, the initial mole fraction of methanol was 0.2894. The final mole fraction of methanol was 0.1942 and 1.000 in the residue and distillate respectively. It was shown in Table 1 that the distillate has more methanol than the residue because methanol would vaporize first, because it has a lower boiling point. The mole fraction of methanol in the distillate for the simple differential distillation was not expected to be less than the mole fraction of methanol initially. This may have occurred because the system was not fully closed and some methanol may have evaporated in the fume hood. In addition, it was evident that the rectification distillation unit had a purer product (distillate) than the simple differential distillation, as shown in Table 1 by the mole fraction of methanol. SIMPLE DISTILLATION BATCH RECTIFICATION Initial Residue Distillate Initial Residue Distillate Mole fraction of Methanol 0.289 0.144 0.217 0.289 0.194 1.000 Total Number of Moles 7.758 5.790 2.468 0.289 0.194 1.000 Table 1: Summary of Mole Fraction of Methanol and Total Number of Moles The total number of moles in each respective vessel was calculated as shown in Table 2 below. Since there was no reaction in this experiment and it only deals with separation, the total number of moles should remain constant from the beginning to the end. However, this was not the case for the simple distillation, as the final total amount of moles (residue + distillate) had more moles than the initial amount. Therefore, additional moles were accounted in the system. This may have been caused by possible contamination within the equipment. Also, this may have been due to the interpolation of the % weight of methanol at the specified density of the solution. In the rectification distillation, the total number of moles in the final product was less than the initial amount fed. This meant some of the components were “trapped” within the equipment. SIMPLE DISTILLATION BATCH RECTIFICATION Loss of Moles of Methanol 0.877 4.149 Loss of Total Moles of Solution -0.501 2.587 Efficiency (%) 76.2 78.6 Table 2: Losses during the experiment The efficiency of the batch rectification processes was proved to be higher than the efficiency of the simple distillation. This was expected as there was packing in the batch rectification apparatus which allowed for more surface area for the separation to occur. The reflux available for the batch rectification also increased the amount of methanol removed in relation to the amount of water removed. The percent error was calculated as the difference between the left hand side and the right hand side of equation (6). These results are tabulated in table 3 below. The batch rectification yielded more comparable results than the simple distillation. SIMPLE DISTILLATION BATCH RECTIFICATION % Error 24.7 21.2 Table 3: % Error From these results, Rayleigh’s Equation can be applied to both the simple distillation and the batch rectification processes. However, it is known that Rayleigh’s Equation is not applicable to batch rectification processes. This is because, when performing a mole balance for distillation, equation (5) is achieved. If both sides of equation (5) were integrated, the result would be Rayleigh’s equation, equation (6). The x and y depend on the equilibrium relationship. However, it does not account for the reflux or the number of stages that are pertinent for the batch rectification process. There is no analytic solution to equation (7) that can be applied to batch rectification processes. Instead, the McCabe and Thiele stage-wise graphical approach can be used. Using the McCabe and Thiele graphical approach, the number of theoretical stages that the packed column can act as was 1 stage, as shown in the Appendix. The packed column should act as 3 theoretical stages. Error Analysis For the simple distillation experiment, the collector flask was open to the air. Methanol evaporates relatively easily and some of the methanol escaped from the system. The U-connector from the condenser to the collector flask also had a port where vacuum pressure can be applied. However, because no vacuum was used for the experiment, some methanol also escaped from this opening. To improve on this, the entire system should be closed. The port opening on the U-connector can be plugged with a rubber stopper. From the U-connector, the collector flask should fit snugly. There was also some vapour and condensed product remaining in the condenser after the process which could not be retrieved. This would have increased the distillate collected. For the rectification, the tube carry water away from the condenser erupted and water splashed onto to work-bench and floor surrounding the equipment. The water source was quickly shut-off. At the same time, the fuse controlling the heating element was “tripped” and heat was stopped being delivered to the flask. Even when the fuse was reset, when the heating element was reconnected, the fuse “tripped” again and again. While this was useful in that little vapour was lost because of the lack of condensing, the system required a long time to reheat to the desired temperature. The water source for the condenser was restarted, and the power source of the heating element was switched so that a grounded outlet on the wall was used. While measuring the masses of the pycnometer required to calculate the density of the solution, the temperature of the solution may not have been exactly 20ºC. The solutions were cooled using a cold tap water. For the simple batch distillation, boiling chips are usually added to the flask in order to provide sites for bubble nucleation. If there were no sites, the system would tend to exhibit large bubbles rising through the boiler flask and may overflow. For this experiment, however, no boiling chips were used. The boiler flask used in the experiment was used many times previous before, and some residue was still present that could not be removed. However, it was these residues that acted as sites for bubble nucleation, and there were numerous small streams for bubbles rising through the flask when the solution was at a boil. Conclusion and Recommendations In conclusion, the experiment was successful at verifying the applicability of Rayleigh’s equation for the simple batch distillation. However, even though the results obtained were satisfactory for applying Rayleigh’s equation to the batch rectification process, in literature, it has been proved that it is not applicable. Instead, the McCabe and Thiele graphical method is more appropriate to use. The initial solution used for the distillation should have a higher methanol concentration, which would allow a much larger difference between the initial and final mole fraction of methanol in the boiling flask to be observed. Also, a cold water batch or ice batch can be used to cool the solutions to 20ºC. During this experiment, all densities should have been taken at 20ºC. However, it was unsure whether this temperature was achieved. The water source for the condenser in the batch rectification process should be made independent of other equipment in the laboratory to avoid an increase of pressure in the tubes, which, during this experiment, caused a large eruption of water around the equipment, creating a safety hazard. The power source of the heating element should also be made independent from other equipment as well as to a grounded power source to avoid the “tripping” of the fuse in the laboratory. References: [1]. Turcotte, G. CHE415 - Unit Operations II Lab Manual – Exp 5 – Rayleigh’s Equation, Ryerson University, Fall 2007 [2] How Stuff Works. How Oil Refining Works. HowStuffWorks, Inc., 1998-2007. Oct 6, 2007 [3] Veksle, M.A., et. al. Automatic control of a batch rectifying column for the heteroazeotropic elimination of water. Pharm. Chan. J. Vol 6, #12, 1972. [4] Mallinckrodt Chemicals. Material Safety Data Sheet, Methyl Alcohol. Mallinckrodt Baker, Inc. Oct. 6, 2007. [5] Seader, J.D., Henley, E., Separation Process Principles. 2nd ed., John Wiley & Sons, Inc. 2006. [6] Treybal, R., Mass Transfer Operations. McGraw-Hill. 1980. Appendix: RAW DATA SIMPLE BATCH RECTIFICATION INITIAL FINAL DISTILLATE INITIAL FINAL DISTILLATE Empty Flask 129.548 119.889 255 37.395 Flask + Solution 300.618 245.425 171.813 730 620 80.159 Empty Pycnometer 15.365 15.365 15.306 15.365 15.371 15.315 Pyncometer + Solution 38.553 39.416 35.988 38.553 39.145 35.109 SAMPLE CALCULATIONS Density of solution (using pycnometer) (eg finding density of initial water-methanol solution) Volume of pycnometer = 25 mL (1) Mass of empty pycnometer =15.365g (measured) (2) Mass of pycnometer + solution = 38.553g (measured) (3) Mass of solution = (2) – (3) = 15.365-38.553 = 23.188g (4) Density of solution = (4) / (1) = 23.188/25 = 0.928g/mL From Perry’s Handbook, a relationship between the density and the weight percent is tabulate. Sample of data is shown below in table 1: % Density % Density 0 0.9982 55 0.9052 5 0.9896 60 0.8946 10 0.9815 65 0.8834 15 0.9740 70 0.8715 20 0.9666 75 0.8592 25 0.9592 80 0.8469 30 0.9515 85 0.8340 35 0.9433 90 0.8202 40 0.9345 95 0.8062 45 0.9252 100 0.7917 50 0.9156     Table 4: Tabulated data of the relationship between weight % and density of Methanol at 20ºC This data was graphed in figure 1 below: Figure 3: Graph of Weight % of methanol vs. Density of methanol/water mixture From this graph, any density calculated using the pycnometer as described above can be converted to the weight % of methanol in the solution. The maximum temperature that data is available is 20ºC. Because the distillation processes are done at much higher temperatures, the solution that the weights required to find the density must be measured at 20ºC. Using the graph above, for a density of 0.928g/mL, the weight % of methanol is found to be 42%. SIMPLE RECTIFICATION Weight of total initial amount (material in flask prior to distillation) = 171.070g (5) Density of initial amount = 0.928 g/mL Weight percent of methanol in initial amount = 42% (6) Weight of total residue (material left in flask after distillation) = 115.877g (7) Density of residue = 0.962g/mL Weight percent of methanol in residue = 23% (8) Moles of methanol in initial solution = [(5)*(6)]/[MWmethanol] (9) = [171.070*42%]/[32] = 2.25 mol Methanol NB: MWmethanol= 32g/mol Moles of water in initial solution = [(1-(6))*(5)]/[Mwater] (10) = [(1 - 42%)* 171.070]/[18] =5.51 mol Water NB: MWwater=18g/mol Total # Moles initial solution = (9) + (10) (11) = 2.25 + 5.51 = 7.75 mol Moles of methanol in Initial Solution = (9)/(11) = 2.25/7.75 = 0.289 Rayleighs Equation Rayleighs Equation is as follows: The integral on the left hand side of the equation would result in the area beneath the curve of [1/(y*-x)] vs x. This can be estimated using Simpson’s Rule: where f(x0) and f(x2) are the moles of methanol remaining in the solution before and after distillation respectively. f(x1) can be read off the graph at the mid-point between x0 and x1. L1 and L2 are the total number of moles before and after distillation, respectively. i 0 1 2 xi 0.2894 0.2166 0.1438 f(xi) 2.710 2.650 2.700 h = 0.0728 The equilibrium curve as well as the [1/(y*-x)] vs x are show below. They were developed from the data of methanol and water mole fractions at equilibrium from Perry’s Handbook, summarized in table 2 below. x y 1/(y*-x) 0.000 0.001 1000 0.020 0.134 8.77193 0.040 0.230 5.263158 0.060 0.304 4.098361 0.080 0.365 3.508772 0.100 0.418 3.144654 0.150 0.517 2.724796 0.200 0.579 2.638522 0.300 0.665 2.739726 0.400 0.729 3.039514 0.500 0.779 3.584229 0.600 0.825 4.444444 0.700 0.870 5.882353 0.800 0.915 8.695652 0.900 0.958 17.24138 0.950 0.979 34.48276 0.999 1.000 1000 Table 5: Equilibrium Data for Methanol and Water [1] Figure 4: Curve for Rayleigh’s Equation Relationship of (1/(y-x)) vs. x Efficiency Efficiency, ?, of either process, simple batch or batch rectification, can be calculated using the following equation: ? = (#Mole methanol before distillation in boiling flask) – (#Mole of methanol in Distillate) (#Mole methanol before distillation in boiling flask) - 1 - - 1 - - 1 -