Mccabe thiele diagram ethanol water

Introduction:

During this experiment, a laboratory scale distillation column will be analyzed. The column is equipped for either batch or continuous distillation, but the separation performed in this experiment will be batch. The binary mixture to be separated contains ethanol and water. The first objective is to determine the effects of operating variables such as reflux ratio. An array of reflux ratios including total reflux, 3:1, 5:1, 7:1, 1:3, and 1:5 will be explored. The effect of each will be quantified by taking measurements of the composition of the condensate as well as that of the liquid in the reboiler. In addition, the boil-up rate will be calculated for a given power input under total reflux conditions. The second objective is to compare theoretical calculations to experimental results. The values to be compared include the number of theoretical plates for the separation of the ethanol-water mixture for the various reflux ratios, the minimum number of plates, the minimum reflux ratio, and the efficiency of the column. The Fenske Equation and the McCabe-Theile Method will be employed to calculate the values necessary for comparison.

Theory:

Distillation columns are used for separating different components of a liquid mixture. The separation is made possible by differences in the boiling points of the contents of a mixture. By operating the column at a temperature that is between the boiling points of two components in a binary mixture, the more volatile component can be separated from the less volatile component. Distillation can be done with or without reflux. In techniques that do not utilize reflux, the vapor of the more volatile liquid is condensed and not returned to the still. In the case of reflux, all or part of the condensate is returned to the still and this liquid comes into contact with the rising vapor. Distillation with reflux is more effective at separating components that have similar volatilities. In this lab, the separation will be carried out under various reflux ratios to determine which ratio provides the most successful separation for a given temperature and pressure. Whether the distillation involves reflux or not, the process can be continuous or batch. Continuous distillation is more widely used for large-scale production, but the distillation in this experiment will be carried out as a batch process.

The distillation column used is vertical, which allows for counter-current vapor and liquid flow under reflux conditions. The vapor moves up the column while liquid descends from the top of the column. For a batch process, there is not a continuous feed to the column. Rather, a set volume of feed mixture is loaded directly into the reboiler a single time. In this case, ten liters of twelve-weight percent ethanol-water mixture is loaded for distillation. Ethanol is the more volatile component, the MVC, and will vaporize through the column. The distillation column has a total of eight sieve plates. The plates are dispersed evenly between two glass sections. There are thermocouples that measure the temperature at each plate. There is also a thermocouple located in the reboiler and four other critical locations in the system. Each can be monitored from the counsel and used to ensure that the temperature of the column does not exceed the boiling point of the less volatile component. If the temperature of the reboiler exceeds the boiling point of water, the separation would no longer occur. Between the sections of plates, there is a feed section that can be utilized for continuous processes. A central rod supports the plates and each incorporates a weir and downcomer, which creates a liquid seal between the stages. This seal is created by a U-tube for the final plate in each section.

When the vapor reaches the top of the column, it exits and passes through a water-cooled condenser. From this point, the condensate can either be returned to the column or diverted to the top product receiver. The amount of product returned to the column is dependent on the reflux ratio, which can be set from the control counsel of the system. The reflux ratio is a ratio of the quantity of condensate returned to the column versus how much is collected as distillate. Total reflux is the condition where all condensed vapor is returned to the column. Equation 1 shows how reflux ratio is calculated.

The bottom product flows from the reboiler into a cooler and finally to a bottom product tank. However, in batch distillation, the reboiler is isolated so that there is no bottom product leaving the system. The level of the reboiler can be observed to monitor how much of the original charge has boiled into the column. An electrical heating element is responsible for heating of the reboiler. The power supplied to the heater can be adjusted, but this experiment calls for a power input of 0.75kW to achieve boiling. Samples will be taken from the reboiler and the condenser to monitor the composition at these two locations of the system.

To calculate the efficiency of the distillation column, it is necessary to compare the theoretical number of plates to the actual number of plates. The theoretical number of plates is found by constructing a McCabe-Thiele diagram. This diagram plots the mole fraction of a component in the liquid phase versus the mole fraction of that component in the vapor phase. In this lab, the mole fractions of ethanol will be plotted. In addition, a few lines are plotted in the graphing area. These are y=x, equilibrium line, and operating line. The equilibrium line for the mixture can be generated using vapor-liquid equilibrium data. The operating lines will look different depending on the reflux ratio.

For total reflux, there is no feed or removal of products. Due to these conditions, it can be assumed that the liquid flow in the column is equal to that of the vapor flow as shown in Equation 2.

From the relationships above, it can be deduced that the operating line for total reflux coincides with the y=x line. The reflux ratio approaches infinity under this set of conditions. After the lines are plotted on a McCabe-Thiele diagram, the “stepping down” method can be used to determine the number of theoretical plates needed to achieve each degree of separation. This method is shown in Figure 1. The step begins where the operating line intersects the mole fraction of the component in the overhead product,. From that point, stairs are drawn between the operating line and the equilibrium curve. The steps end where the operating line intersects the mole fraction of the component in the bottom, . It is important to note that the reboiler is an equilibrium stage so the number of steps corresponds to the number of trays in the column plus one.

For partial reflux, a material balance can be written for the top of the column and bottom of the column. Figure 2 shows the top section of the column for which a material balance can be written. Equation 6 is the discussed material balance. This is part of the Lewis-Sorel method and can be used to find the composition of and the number of plates.

Another simplification can be made based on the assumption that the liquid overflow in the column is constant. This means that Ln=Ln+1. The previous equation is rearranged to be in terms of and the assumption is applied to provide Equation 8.

Similarly, a material balance can be performed on the bottom of the distillation column. Figure 3 shows the portion of the column that is of interest for such a balance. Equation 9 provides the material balance. The material balance is then written with respect to the most volatile component, leading to Equation 10. As for the top plate, the liquid overflow for the bottom plate can be assumed to be constant. Equation 11 is the result after applying the assumption that Lm=Lm+1 and solving Equation 10 for .

Once the operating line has been determined for a given reflux ratio, the number of theoretical plates can be determined in the same way as described for the McCabe-Thiele diagram for total reflux conditions. The number of steps between the operating line and the equilibrium within the range of and will determine the theoretical number of stages. Figure 4 shows and example of a McCabe-Thiele diagram for partial reflux. For each given reflux ratio, the slope of the operating line will differ.

After determining the number of theoretical stages from the McCabe-Thiele diagram, Equation 13 can be used to calculate the efficiency of the column. There are eight actual stages in this experiment. Comparing to the Lewis-Sorel method to the McCabe-Thiele plot can further reinforce the total number of stages in the system.

Another theoretical value that will be used for comparison in this lab is the minimum number of theoretical plates. The equation that calculates this value is called the Fenske Equation, Equation 14. This equation is dependent on the ratio of average volatility of the more volatile component to the less volatile component. Equation 15 shows how the average relative volatility is calculated using values for relative volatility at the top and bottom of the column. The relative volatilities for the top and bottom of the column are calculated using Equation 16.