CHE 415 - Rectification Final Report 2007

(Data Reporter) (Leader) (Inspector) Experiment #1, Rectification Section #1, Group #5 (Data Reporter) (Leader) (Inspector) Experiment #1, Rectification Section #1, Group #5 (Data Reporter) (Leader) (Inspector) Experiment #1, Rectification Section #1, Group #5 Ryerson University Department of Chemical Engineering CHE 415 Unit Operations II Lab Report Experiment #1: Rectification Experiment Performed on November 6th, 2007 Report Submitted to Dr. Ginette Turcotte / Kiran Shah 1. /Leader By Group # 5 Section # 1 2. /Inspector 3. Data Reporter November 13, 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 The objectives of the experiment included determining the boil-up rate, investigating the entrainment of the column, and determining the overall separation efficiency and the thermal efficiency. Within the experiment, a methanol/water solution was distilled/separated utilizing a distillation unit equipped with six ceramic bubble-cap trays. The distillation column was heated with a reboiler and operated under total reflux. Once equilibrium and steady state (temperature no longer changed with time) were reached, a sample of the distillate as well as the residue was taken. The densities of the samples were then determined with the use of a pycnometer and the mole fraction of methanol present in each was calculated. The mole fractions were determined to be 0.98230 for the distillate and 0.08360 for the residue. The mole fraction of methanol in the residue was found to be slightly smaller than that present in the initial solution, 0.08379 (calculated based on the sample taken at the beginning of the experiment), due to an amount of methanol being separated and removed from the initial solution. The boil-up rate was then calculated to be 1.414 g/s and the flooding velocity and actual velocity were calculated to be 6.444 ft/s and 0.222 ft/s, respectively. Therefore, the column did not experience flooding during the experiment as the flooding velocity is much greater than the actual velocity. Further, the overall separation efficiency was found to be 100% as the number of theoretical stages and the number of actual plates were found to be equivalent. The thermal efficiency of the unit was calculated to be 64.5%. Overall, the experiment was successful as the objectives that were put in place were met and a sample of methanol was effectively separated from the initial solution utilizing the distillation unit. Table of Contents 22 44 44 88 88 99 1010 1010 1313 1414 1616 16 List of Figures 77 88 1111 2222 22 List of Tables 1111 1616 1616 1616 1717 1818 2020 20 Objectives and Experimental Design To determine the boil-up rate and the limits of capacity, due to entrainment, of a distillation unit. To determine the thermal efficiency and the overall separation efficiency of the process In order to achieve these objectives, methanol was separated from a binary solution of methanol and water using a distillation unit equipped with six ceramic bubble-cap trays. The distillation unit is heated with a reboiler and the system is operated under total reflux until a steady-state is achieved and a sample of the vapour at the condenser level is taken. Theoretical Background Rectification is essentially a multistage countercurrent distillation operation. The process is performed when it is necessary to separate a solution into its components, where the components are at different boiling points [1]. Therefore, purification can be achieved because in the vapour phase, there will be, predominantly, the most volatile component. This vapour may be condensed and collected. Alternatively, the vapour may be transported into a tray within the column where equilibrium can be established. At this equilibrium, there is further separation of the components, and there will be even more purification of the mixture. Therefore, a more purified product can be obtained by using more trays [2]. In this experiment, it is required to separate methanol from a binary mixture of methanol and water, using a distillation unit. The distillation unit is comprised of a reboiler at its base where the solution can be heated, and a condenser at the top, to condense the vapours. The distillation is performed under atmospheric pressure conditions. The condenser is configured to achieve total reflux until equilibrium is achieved, before collection of the distillate is performed. The distillation column contains a number of trays, each of which should, theoretically, act as an equilibrium stage where separation of the two components can occur. The boil-up rate, BP, can be defined as the rate at which the vapours rise within the distillation column from the reboiler [1]. It can be calculated using equation (1) below. (1) Where, V = volumetric flow rate of vapour collected in the distillate (g/s) ? = density of the distillate (g/cm3) t = time taken to collect the distillate (s) The reflux ratio, R, is defined as the ratio between the flows of the distillate (D) and the reflux (L) streams [2]. In other words, it is a measure of the amount of vapours that is being returned to the column compared to the total amount that is leaving. It can be found using equation (2) [1]. (2) The maximum overall separation efficiency, ?s, can be considered to be equivalent to the performance of the trays where the separation occurs. It is desired to determine if the trays used in the distillation column have a positive effect on the separation of components of the mixture. In order to determine this, the number of theoretical stages, Nm, experienced has to first be determined. This can be accomplished using McCabe-Thiele graphical method applicable to tray towers, using the equilibrium curve shown below in Figure 1. When this is known, the ratio between the theoretical stages and the number of plates will represent the maximum overall efficiency, as shown in equation (3) below. If the number of theoretical stages is greater than or equal to the number of plates in the distillation column, the separation efficiency is acceptable. However, if the opposite is achieved, the trays will not have performed as desired and each did not assist in the separation as it should have. In this case, the separation efficiency is unacceptable. (3) The types of trays used in the distillation unit affects its overall separation efficiency. The trays used in this experiment are bubble-cap trays, which have openings under a cap connecting the upper level to the lower in terms to allow the vapour and liquid components to flow freely between the layers. It is designed in such a manner so that as the liquid is flowing downwards in the column, the vapour rising is forced through the opening under the bubble-cap and through the liquid, forming a bubble. It is on the surface of this bubble where the separation can occur. Other types of trays include sieve, floating valve or fixed valves, which differ from each other by the shape of the opening connecting the different sections of the distillation column [1]. Most of these trays are equipped with a weir, which acts as a guide to when the system has achieved a steady-state. Steady-state can be considered to be achieved when the level of liquid is at maximum height of the weir on all trays. It is important to consider the distance between the trays during the design of a distillation column. The aim is to design the column so that the patterns of the liquid flowing downwards on the surface of the column is such that there is scattering. When compared to other types of distillation units studied, the distillation column with trays may not be the best at separating the components of a solution [1]. It is more efficient than the simple distillation unit. However, the packed column may be better at separation because of the greater surface area on the packing for separation to occur. However, in the design of a distillation unit, it is important to consider the stresses that the material of which the column is constructed will be under. Packing for distillation columns are usually very heavy and therefore the material used for the construction must be capable of withstanding a great weight. Typically, cost of the units has to be considered. It may be more cost effective to build a taller distillation column with many trays rather than a shorter column with packing but made out of more durable and therefore more expensive materials. Entrainment occurs when the vapours are rising with such velocity as to force the liquid falling downwards to be pushed upwards. The liquid droplets are pushed into the condenser, and therefore, the separation occurring in the distillation column is negligible. This is an unwanted occurrence. The flooding velocity is the maximum velocity of the vapours before the distillation is rendered ineffective due to entrainment. This velocity can be found using equation (4) [4]. (4) Where, Uf = flooding velocity C = correction factor ?L = density of the liquid (g/cm3) ?V = density of the vapour (g/cm3) Figure 1: Equilibrium Curve of Methanol at 1 atm [3] Thermal efficiency of the distillation unit is a representation of the amount of energy required for the mixture to change from the liquid to the vapour states compared to the amount of heat that is supplied to the reboiler. The amount of heat supplied to the reboiler is set. The amount of energy that is required for the phase change of the mixture can be found as shown in equation (5). (5) The thermal efficiency, ?, can therefore be calculated using equation (6). (6) Experimental Set-up Figure 2: Schematic Diagram of Experiment Equipment Experimental Procedure A solution mixture of methanol/water was present within the rectification unit. A sample was taken to determine the composition of the mixture. This was achieved by utilizing a pycnometer. All valves within the unit were closed prior to the experiment except for one, which allowed the non condensable gases to escape. The water supply for the condenser was turned on. The rheostat was turned on high giving heat to the boiling flask. Once the solution began to boil, the rheostat was turned on low to reduce the amount of heat to avoid entrainment and cracking of the vessel. The temperature of all four thermocouples was recorded over time. The amount of heat (via rheostat) was adjusted such that each tray was operating at steady state and at equilibrium. Equilibrium and steady state were determined visually and quantitatively (ie: temperature was stagnant). The distillate valve was opened, where a sample was taken over a 60 second interval. The mass of distillate collected was recorded and the composition was determined using a pycnometer. Also, a sample of the residue (reboiler) was taken. Both samples were cooled to 20ºC. The rheostat was turned off to allow the rectification unit to cool naturally. The condensing unit was left on until the rectification unit cooled to room temperature. Safety and Environmental Concerns during the Experiment: Methanol can cause blindness and irritation to the skin, eyes, and respiratory tract and therefore care must be taken when it is handled [8]. Also, it affects the central nervous system and liver [8]. Avoid inhalation, eye contact, and ingestion of methanol and make sure gloves are worn to avoid absorption through the skin. Since methanol is flammable in both phases, care is mandatory around heat sources as water is not an effective means of extinguishing the flames. Alcoholic foams, dry chemicals, or carbon dioxide should be used [8]. If methanol vapours are inhaled, individuals should be given medical attention and removed from the area. If ingested, one should immediately induced vomiting and receive medical attention. If in contact with skin or eyes, flush the area immediately for 15 minutes with cold water and receive medical attention [8]. Methanol should be stored as a hazardous waste and disposed of accordingly. The waste bin should not be stored near any heat source as explosion can occur. In case of an evacuation of the laboratory, all heat sources should be shut off and adequate ventilation turned on [8]. In summary, methanol is a dangerous chemical and a lot of care and prevention must be done. Use fume hoods to avoid breathing vapours, wear gloves and lab coats to avoid contact with skin, wear goggles to avoid contact with eyes, and continuously wash hands to avoid any methanol residue [8]. Safety and Environmental Concerns in Industrial Applications: Rectification, a distillation unit, is commonly used in the industry to separate multiple components. It is typically a continuous process, where the feed is constantly fed into the unit. Two major industrial applications are in the petroleum refining industry and brewing. In the petroleum refining sector, rectification is widely utilized to separate various hydrocarbon components. The lighter fractions travel to the top while the heavier ones sink to the bottom [9]. Care must be taken to ensure workers wear proper safety equipment, such as hardhats, to prevent accidents from occurring. Similar to petroleum refining, alcohol breweries or distilled beverages utilize distillation units. But, there is generally less components used [9]. In the endosperm of the corn contains starch, which can be broken down to glucose [10]. The glucose is fermented by yeast producing a dilute solution of ethanol. The dilute solution of ethanol is distilled to produce spirits of a specific taste such as whiskey and rum [10]. Results and Discussion Within the experiment, a large column was utilized in order to perform the distillation of the methanol/water solution present in the reboiler. Based on the temperature versus time plots found in Figure 3 for the four thermocouples located in the column, it is apparent that the column achieved steady state. As temperature was the only variable that could be measured with respect to the change of time throughout the experiment, temperature was chosen as the variable by which steady state would be determined. Reaching steady state implies that the measured variable no longer changed with the passing of time and in the plot, the temperatures stop rising and become essentially constant and therefore steady state is achieved within the column. Figure 3: Steady State Determination The distillate sample collected within the experiment was collected when the vapour and liquid within the column appeared to be in equilibrium (there was liquid in each stage and there appeared to be a liquid “film” on the inside of the column in each stage) and the temperatures stopped rising (steady state was achieved). The mole fraction of methanol in the initial solution, the residue, and the collected distillate was calculated and can be found in Table 1. Mole Fraction of Methanol Initial Solution 0.08379 Residue 0.08360 Distillate 0.98230 Table 1: Methanol Mole Fractions The mole fraction of methanol in the residue was only slightly lower than that of the initial solution. The small difference in values can be explained by the fact that there was a significantly greater amount of initial solution compared to the amount of distillate collected and therefore there was only a small amount of methanol that was actually distilled and removed from the initial solution (most of the methanol was left in the residue and therefore the mole fraction does not notably change). The reflux ratio of the column was determined to be ?, infinity, as the column was operating under total reflux during the experiment and distillate was only collected for 60 seconds at the end of the experiment (once equilibrium and steady state were reached). Further, the boil-up rate of vapour through the column was calculated to be 1.414 g/s. The entrainment was investigated by calculating the flooding velocity of the column as well as the actual velocity. The flooding velocity and the actual velocity were calculated to be 6.444 ft/s and 0.222 ft/s, respectively. The fact that the actual velocity was calculated to be much smaller than the flooding velocity is an indication that the column did not experience flooding during the experiment. If the actual velocity was equivalent to or greater than the flooding velocity the column would experience flooding and therefore there would be an excessive amount of liquid carried up to the tray above. The overall separation efficiency was found to be 100%. It was defined as the number of theoretical stages over the number of actual plates. The theoretical stages were determined graphically using the McCabe-Thiele method as shown in the appendix section. The overall separation efficiency of 100% showed that the operation was effective at separating the methanol from the methanol-water mixture. The calculated overall separation efficiency is acceptable due to the number of theoretical stages being equal to the number of plates in the distillation column and therefore the trays performed as desired and each assisted in the separation as it should have. This is further evident as the methanol mole fraction in the distillate phase was 98.23%. Finally, the thermal efficiency was found to be 64.5%. Thermal efficiency was determined as the ratio of the amount of energy that is required for the phase change of the mixture to the heat supplied to the reboiler. The thermal efficiency could potentially be greater as the heat produced from the boiler may have been less. The heat gained by the methanol-water mixture could have been lost due to heat being lost around the sides of the column as the vapours travel up the unit. Also, the heat gained was determined by the boil up rate and the density of the distillate. The mole fraction of the distillate may have contained more methanol. Some of the methanol vapours may have been lost around the sides of the rectification unit and around the pipes in the distillation collection vessel. Also, over time, heaters undergo wear and tear, resulting in a decrease in the overall heat production, and the actual heat produced is less than the stated 2000W. Error Analysis Prior to activating the power to the reboiler, a sample of the initial solution was removed in order to determine its concentration. However, this solution was untouched for several days before this experiment was done. Some separation of the methanol and water may have occurred in the reboiler. The sample was taken from a valve located at the base of reboiler. If some separation had occurred, there would be a higher concentration of methanol at the top of the solution and a lower concentration where the sample was taken from, which would have affected the validity of the results for the initial concentration of the solution. Also, there may have been some solution of methanol and water remaining in the bulb of the collection valve. Therefore, the sample removed as the distillate may have been contaminated and the mole percent may have been different. Conclusion and Recommendations Overall, the experiment was successful in meeting the objectives put in place. The boil-up rate was calculated, entrainment in the column was investigated by calculating both the flooding velocity and actual velocity, and the overall separation efficiency and thermal efficiency were determined. The boil-up rate was calculated to be 1.414 g/s, and the flooding velocity and actual velocity were calculated to be 6.444 ft/s and 0.222 ft/s, respectively. Due to the flooding velocity being much greater than the actual velocity it was determined that the column did not experience flooding during the experiment. Further, the overall separation efficiency was found to be 100% for the set-up as the number of theoretical stages and the number of actual plates were found to be equivalent (6 without the reboiler). Also, the thermal efficiency of the column was calculated to be 64.5%. In recommendation, the column should be insulated to avoid heat loss from the equipment and therefore increase the thermal efficiency. Also, there should be some way to mixture the initial solution of methanol and water in the reboiler at the beginning of the experiment. Alternatively, a new solution of methanol and water can be used for the experiment. References: [1]. Benitez, J. Principles and Modern Applications of Mass Transfer Operations. New York: John Wiley and Sons, Inc., 2002. [2]. Treybal, R.E., Mass Transfer Operations, 3rd Ed., McGraw-Hill, New York, 1980. [3]. Perry, R.H., Green, D.W., Perry’s Chemical Engineers’ Handbook, 7th Edition, 1997, McGraw-Hill, Toronto [4]. Seader, J.D., Henley, E.J., Separation Process Principles, Toronto: John Wiley and Sons Inc., 1998. [5]. Turcotte, G., CHE425 Unit Operations II( Lab Manual) – Experiment 2 - Rectification, Ryerson University, Fall 2007. [6]. Winnick, J. Chemical Engineering Thermodynamics. John Wiley & Sins, Inc., 1997. [7]. Weast , R. C. and Astle M. J., Eds. CRC Handbook of Physics and Chemistry, 63 rd Edition. CRC Press, Boca Raton, Florida, 1982. [8] Bedasie R et al. Experiment 7 – Rayleigh’s Equation. October 16, 2007. [9] How Stuff Works. How Oil Refining Works. HowStuffWorks, Inc., 1998-2007. Oct 6, 2007, [10] Olar M. et al. Ethanol Industry in Canada. Centre for Research in the Economics of Agrifood. 2004. Appendix: Raw Data Temperature 1 (Condenser) 148.7 °F Temperature 2 149.1 °F Temperature 3 162.3 °F Temperature 4 (Reboiler) 196.9 °F Table 2: Temperature Raw Data Mass of empty 25 mL pyncometer 15.387 g Mass of pyncometer containing initial solution 39.772 g Mass of initial solution 24.385 g Density of initial solution 0.97540 g/mL Time required to collect distillate 1 min Volume of distillate collected 106.7386 mL Mass of empty 25 mL pyncometer 15.452 g Mass of pyncometer containing distillate 35.330 g Mass of distillate 19.878 g Density of distillate 0.79512 g/mL Mass of empty 25 mL pyncometer 15.402 g Mass of pyncometer containing residue 39.788 g Mass of the residue 24.386 g Density of the residue 0.97544 g/mL Table 3: Density Raw Data Time (min) T1 (°F) T2 (°F) T3 (°F) T4 (°F) 0 72.9 73.0 72.9 73.1 5 75.2 75.9 77.1 79.5 10 80.3 82.1 83.9 85.4 15 92.2 95.3 103.6 108.2 20 105.6 107.6 127.2 136.4 25 119.4 123.1 145.4 169.8 30 135.8 137.9 150.9 194.5 35 144.5 146.2 158.6 196.7 40 150.6 150.1 163.7 197.7 45 148.9 149.1 162.5 197.1 50 149.8 149.2 162.8 197.6 55 148.7 149.1 162.3 196.9 60 149.2 149.1 162.5 196.7 65 148.9 149.1 162.3 196.7 Table 4: Steady State Temperature Data Sample Calculations Temperature (ºC) ymethanol xmethanol 64.5 1.000 1.000 65.0 0.979 0.950 66.0 0.958 0.900 67.5 0.915 0.800 69.3 0.870 0.700 71.2 0.825 0.600 73.1 0.779 0.500 75.3 0.729 0.400 78.0 0.665 0.300 81.7 0.579 0.200 84.4 0.517 0.150 87.7 0.418 0.100 89.3 0.365 0.080 91.2 0.304 0.060 93.5 0.230 0.040 96.4 0.134 0.020 100.0 0.000 0.000 Table 5: Constant Pressure Equilibrium Data for Methanol and Water [3] Boil up rate Operating under total reflux: R = L/D = ? and L/V = 1 where: R = reflux ratio L = mass flow rate of liquid D = mass flow rate of distillate V = mass flow rate of vapour Boil up (BP) = (v*?)/t where: ? = density of distillate t = time v = volume of distillate collected Entrainment where and FF = foaming factor (1.0 for nonfoaming systems), FHA = 1.0 for Ah/Aa ? 0.10 and 5(Ah/Aa)+0.5 for 0.06? Ah/Aa?0.1, and CF is found from Figure 6.24 in Seader and Henley (page 308) [4]. To find CF from Figure 6.24 FLV needs to be calculated and the plate spacing must be know. where: MW,L = molecular weight of the residue; MW,V = molecular weight of the vapour ?V = density of the vapour; ?L = density of the residue % Density % Density % Density % Density 0 0.9982 26 0.9576 52 0.9114 78 0.8518 1 0.9965 27 0.9562 53 0.9094 79 0.8494 2 0.9948 28 0.9546 54 0.9073 80 0.8469 3 0.9931 29 0.9531 55 0.9052 81 0.8446 4 0.9914 30 0.9515 56 0.9032 82 0.842 5 0.9896 31 0.9499 57 0.901 83 0.8394 6 0.988 32 0.9483 58 0.8988 84 0.8366 7 0.9863 33 0.9466 59 0.8924 85 0.834 8 0.9847 34 0.945 60 0.8946 86 0.8314 9 0.9831 35 0.9433 61 0.8924 87 0.8286 10 0.9815 36 0.9416 62 0.8902 88 0.8258 11 0.9799 37 0.9398 63 0.8879 89 0.823 12 0.9784 38 0.9381 64 0.8856 90 0.8202 13 0.9768 39 0.9363 65 0.8834 91 0.8174 14 0.9754 40 0.9345 66 0.8811 92 0.8146 15 0.974 41 0.9327 67 0.8787 93 0.8118 16 0.9725 42 0.9309 68 0.8763 94 0.809 17 0.971 43 0.929 69 0.8738 95 0.8062 18 0.9696 44 0.9272 70 0.8715 96 0.8034 19 0.9681 45 0.9252 71 0.869 97 0.8005 20 0.9666 46 0.9234 72 0.8665 98 0.7976 21 0.9651 47 0.9214 73 0.8641 99 0.7948 22 0.9636 48 0.9196 74 0.8616 100 0.7917 23 0.9622 49 0.9176 75 0.8592     24 0.9607 50 0.9156 76 0.8567     25 0.9592 51 0.9135 77 0.8542     Table 6: Weight Percentage of Methanol The mole fraction of methanol in the residue and distillate are: ?L = 0.97544 g/mL; from Table 6 weight % of methanol: ; % Therefore, that of water (1-0.1397) = 0.8603 ; ; and (methanol) ?distillate = 0.79512 g/mL; from Table 6 weight % of methanol ~ 0.99% Therefore, that of water (1-0.99) = 0.01 ; ; and (methanol) MW,L = molecular weight of residue = xMethanol × MW, methanol + (1- xMethanol) × MW, water = (0.0836 × 32.04) + (0.9164 × 18) = 19.174 g/gmol MW,V = molecular weight of vapor = yMethanol × MW, methanol + (1- yMethanol) × MW, water = (0.9823 × 32.04) + (0.0177 × 18) = 31.791 g/gmol The density of the vapor is (with the use of the ideal gas law): and that of the residue is 0.97544 g/mL. From Figure 6.24 at a plate spacing of 9 in and an FLV value of 0.02067, CF ~ 0.18 ft/s. Next, the surface tension, ?, in [dynes/cm] is calculated as follows: For methanol: Tc = 512.6 K; Pc = 80.9 bar; Tb = 337.8 K Therefore, at a reboiler temperature of 91.6°C, 364.75 K: To find ? of the mixture, the mole fraction of methanol in the residue is 0.0836 and the surface tension of water is approximately 60.45 dynes/cm from Table 7 at 91.6°C. Temperature [ºC] Density [gm/cm3] Surface Tension [dyne/cm] 0 0.99987 75.6 5 0.99999 74.9 10 0.99973 74.22 15 0.99913 73.49 18 0.99862 73.05 20 0.99823 72.75 25 0.99707 71.97 30 0.99567 71.18 40 0.99224 69.56 50 0.98807 67.91 60 0.98324 66.18 70 0.97781 64.4 80 0.97183 62.6 100 0.95838 58.9 Table 7: Surface Tension and Density of Water against Air [7] Finally, assuming FF and FHA are 1.0: ; and therefore, Actual Gas Velocity N = Bp/Mw,v = (1.414 g/s)/(31.791g/gmol) = 0.04448 gmol/s The volumetric flowrate can be calculated utilizing the ideal gas law as follows: ? = NRT/P = (0.04448 × 82.057 × 337.95)/1 = 1233.482 cm3/s The column diameter is approximately 6 in. A = ?D2/4 = ?(6 in)2/4 = 28.27 in2 = 182.4 cm2 Actual Velocity = VA = ?/A = 1233.482/182.4 = 6.76 cm/s = 0.222 ft/s Maximum Overall Separation Efficiency From observation of the equipment the number of actual plates is 6 (without the reboiler). In order to determine the number of theoretical stages the McCabe-Thiele graphical method is utilized. To utilize the approach, the slope of the operating line is and therefore the operating line is the 45° line. The mole fraction of methanol in the distillate, 0.9832, and the initial mole fraction of methanol in the solution were plotted in Figure 4 (drawn utilizing Table 5) and the stages drawn in between them. ?initial = 0.97540 g/mL; from Table 6 weight % of methanol ~ 0.14% Therefore, that of water (1-0.14) = 0.86 ; ; and (methanol) From Figure 4, the number theoretical stages is determined to be ~ 6.5 (including the reboiler). This is rounded-up to 7 stages (cannot have half a stage) and therefore 6 without the reboiler. Therefore, % Thermal Efficiency QReboiler of the equipment is 2000 + 0.3(2000) = 2600 J/s The latent heat of vaporization of methanol is 1.167 KJ/g and that of water is 2.257 KJ/g [7]. The mole fraction of methanol in the distillate is 0.9832 at 64.8°C. Therefore, % Figure 4: Theoretical Number of Stages - 1 - - 1 - - 1 -