vaporization

II. Simple Distillation 1. Simple distillation apparatus and process Simple distillation, also known as differential distillation, is a batch, single-stage distillation process. The simple distillation apparatus and process are shown in Figures 1-8. The feed liquid is partially vaporized in the distillation vessel through indirect heating; the resulting steam enters a condenser where it is condensed, and the condensed liquid is discharged as a distillate product into a receiver. As the distillation process proceeds, the concentration of volatile components in the kettle liquid continues to decrease; accordingly, the composition of the vapor phase (i.e., the composition of the distillate) also drops, while the bubble point of the liquid in the kettle gradually rises. Distillation is stopped once the average composition of the distillate or the composition of the bottom liquid drops to a specified value. In a batch of operations, the distillate can be collected in stages to obtain distillates with different compositions. Simple distillation is commonly used for the preliminary separation of liquid mixtures. 【Images 1-8】Simple distillation apparatus and process. 2. Calculation of simple distillation: As mentioned earlier, in the process of simple distillation, the composition of volatile components in the distillate and the residue gradually decreases, while the temperature of the reactor gradually increases; therefore, simple distillation is a non-steady-state process. Therefore, the calculation for simple distillation should be carried out using differential balance. At a certain moment, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image042.gif, the amount of liquid in the reactor is Lkmol and its composition is given by http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image044.gif. After a differential time of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image046.gif, the amount of liquid in the reactor becomes http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image048.gif, and its composition is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image050.gif. The amount of vapor distilled off is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image052.gif, with a composition of y. By performing material balance at http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image053.gif, the overall material balance is obtained as http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image055.gif. The balance of volatile components is given by http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image057.gif. By combining these two equations and ignoring second-order infinitesimals, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image059.gif can be obtained. Integrating within the ranges of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image061.gif, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image063.gif, as well as http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image065.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image067.gif, yields http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image069.gif(1-24). If the vapor-liquid equilibrium relationships are known, then the relationships between F, W, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image071.gif, and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image073.gif can be determined using this equation. Assuming that the vapor-liquid equilibrium relationship can be expressed by Equation 1-13, integrating this equation yields http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image075.gif. The average composition of the distillate, given by Equation (1-25), can be determined through material balance calculations for a batch process, as shown in http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image077.gif; further details are provided in http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image079.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204025/image081.gif

Equilibrium distillation and simple distillation are single-stage separation processes, meaning that the liquid mixture is only partially vaporized and condensed once, so they can only achieve a preliminary separation of the liquid mixture. To achieve almost complete separation of a liquid mixture, multiple partial vaporizations and condensations are necessary; this process is known as distillation. I. Principles of the distillation process 1. Multiple partial vaporizations and condensations [Figure 1-9] Multiple partial vaporizations and condensations. The principle of the distillation process can be illustrated using a tx–y diagram. As shown in Figures 1-9, when a mixture with the composition indicated by http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image002.gif and a temperature of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image004.gif is heated above its boiling point, the mixture partially vaporizes, resulting in a two-phase system consisting of vapor and liquid, with compositions of y1 and x1 respectively; at this point, it is as shown in http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image006.gif. By separating the vapor and liquid phases and partially condensing the vapor mixture with composition y1, a vapor phase with composition y2 and a liquid phase with composition x2 can be obtained. By continuing to partially condense the vapor with composition y2, a vapor with composition y3 and a liquid phase with composition x3 are obtained; obviously, y3 > y2 > y1. By continuing in this manner, after all of the vapor phase has been condensed, a high-purity volatile component product can be obtained. Meanwhile, if the liquid phase with the composition of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image008.gif is partially vaporized, an vapor phase with the composition of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image010.gif and a liquid phase with the composition of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image012.gif are obtained. By further partially vaporizing the liquid phase with the composition of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image013.gif, a vapor phase with the composition of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image015.gif and a liquid phase with the composition of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image017.gif are obtained; obviously, it is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image019.gif. By continuing in this manner, the final liquid phase will be a high-purity product of the poorly volatile components. It can be seen that after multiple cycles of partial vaporization and condensation, a liquid mixture can be almost completely separated, which is the basic principle of the distillation process. 2. Distillation column model: The multiple partial vaporization and condensation processes mentioned above take place within a distillation column, and Figure 1-10 shows a model diagram of the distillation column. A distillation tower is usually equipped with either some trays or packing of a certain height; the former is known as a tray tower, while the latter is called a packed tower. Taking a plate tower as an example, the distillation process that takes place within the tower will now be explained. 、【Image 1-10】Distillation column model 【Play animation 1-2】Operational conditions on the tray 【Image 1-11】Operational conditions on the tray Image 1-11 shows the operational conditions on the n-th tray in the distillation column. On the tray, vapor rise channels (such as sieve holes, bubble caps, or floating valves) are provided, through which steam rising from the lower tray (tray n+1) passes via the rise channels of tray n ； The liquid on the upper tray (tray n-1) descends to tray n through the downcomer, flows laterally on that tray, and then enters the next layer of trays. Steam bubbles up through the liquid layer, exchanging heat and mass with the liquid phase. Let the vapor composition and temperature entering plate n be http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image021.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image023.gif, respectively; the liquid composition and temperature be http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image025.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image027.gif, respectively. Moreover, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image029.gif is greater than http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image031.gif, and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image033.gif is greater than the liquid composition in equilibrium with http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image035.gif, which is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image037.gif. Due to temperature and concentration differences, partial condensation occurs in the vapor phase; since the less volatile components are more prone to condensation, some of these less volatile components in the vapor phase condense and enter the liquid phase ； At the same time, the liquid phase undergoes partial vaporization; since the more volatile components are easier to vaporize, some of these volatile components in the liquid phase turn into vapor and enter the gas phase. As a result, the composition of volatile components in the vapor leaving plate n is higher than when it entered that plate, as shown in http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image039.gif, whereas the composition of volatile components in the liquid leaving that plate is lower than when it entered the plate, as shown in http://www.cngspw.com/Doc/data.WebNoteBooks/20060430204312/image041.gif. It can be seen that as the gas passes through one tray, it undergoes one process of partial vaporization and condensation. As they pass through multiple layers of trays, they undergo multiple processes of partial vaporization and condensation; ultimately, a relatively pure volatile component is obtained in the vapor phase at the top of the tower, while a relatively pure non-volatile component is obtained in the liquid phase at the bottom of the tower, thereby achieving the separation of the liquid mixture. It should be noted that the heat exchange and mass exchange that occur on each tray of the tower are closely related; the greater the temperature difference between the vapor and liquid phases, the more mass is exchanged. After the vapor and liquid phases come into contact on the tray, the temperature of the vapor phase decreases while the temperature of the liquid phase increases. The latent heat required for the liquid phase to vaporize is exactly equal to the latent heat released when the vapor phase condenses; therefore, there is no need to install heaters or condensers on each tray. It should also be noted that the tray is the location where heat and mass transfer occur between the vapor and liquid phases, and both vapor and liquid phases must flow across each tray. To achieve the above operations, it is necessary to introduce a downward liquid flow (i.e., reflux) from the top of the tower and generate an upward steam flow from the bottom of the tower, in order to establish a vapor-liquid two-phase system. Therefore, liquid reflux from the top of the tower and rising vapor flow from the bottom of the tower are necessary conditions for the continuous operation of the distillation process. Backflow is the essential difference between distillation and ordinary distillation.

II. Distillation Operation Process According to the principles of distillation, a distillation column alone is not sufficient to carry out distillation; it is also necessary to have a top condenser that provides the reflux liquid, a bottom reboiler that supplies the rising vapor stream, as well as other auxiliary equipment. By installing and combining these devices, a distillation process is established. Depending on the mode of operation, the distillation process is divided into two types: continuous distillation and batch distillation. 1. Continuous distillation operation process [Figure 1-12] Continuous distillation operation process. Figure 1-12 shows a typical continuous distillation operation process. During operation, the feed liquid is continuously added to the distillation tower. Part of the liquid is continuously removed from the reboiler as the bottom product (referred to as residue) ； Some of the liquid is vaporized, producing rising steam that passes through each layer of trays in sequence. The vapor at the top of the tower enters the condenser where it is completely condensed. Part of the condensed liquid is sent back to the top of the tower as reflux fluid using a pump (or by gravity), while the remaining part is collected as the product from the top of the tower (referred to as the distillate). Generally, the tray to which the feed liquid is added is called the feed tray. In the section of the tower above the feed plate, the less volatile components in the rising vapor phase are transferred to the liquid phase, while the concentration of the more volatile components gradually increases; as a result, the rising vapor phase is purified, which is why this section is called the distillation section. The section of the tower below the feed plate (including the feed plate) is responsible for removing the volatile components from the descending liquid, thereby increasing the yield of volatile components at the tower top. At the same time, a bottom product with a high content of non-volatile components is obtained; hence, this section is referred to as the stripping section. 2. Batch distillation operation process [Figure 1-13] Batch distillation operation process. Figure 1-13 shows the batch distillation operation process. Unlike continuous distillation, the feed liquid is added to the distillation vessel all at once; therefore, an intermittent distillation column has only a distillation section and no stripping section. During the distillation process, the composition of the liquid in the distillation vessel keeps changing; under the conditions of constant vapor flow from the bottom of the tower and constant reflux flow from the top of the tower, the composition of the distillate also gradually decreases. When the liquid level in the distillation vessel reaches the specified composition, the distillation process is stopped. It should be noted that sometimes coiled tubes are installed at the bottom of the tower as a substitute for a reboiler, and the reflux liquid at the top of the tower can also flow directly into the tower due to gravity, eliminating the need for a reflux pump.

I. Batch Distillation Batch distillation is also known as fractional distillation. In the batch distillation process, the material to be processed is added to the distillation vessel all at once, after which it is heated to vaporize. The steam generated at the top of the tower is condensed; part of this steam serves as the distilled product, while the other part is returned to the tower as reflux. Once the composition of the liquid in the vessel reaches the specified value, the distillation process is stopped, and the liquid in the vessel is discharged all at once, after which the next batch of distillation begins. Compared with continuous distillation, batch distillation has the following characteristics: (1) Batch distillation is a non-steady-state process. As the composition of the liquid phase in the kettle continuously decreases during the distillation process, the operating parameters inside the tower (such as temperature and composition) vary not only with position but also over time. (2) For a batch distillation column, the feed is always saturated vapor at the bottom, so such a column has only a distillation section. Intermittent distillation is mainly used in the following situations: when the feed liquid for distillation is obtained through batch production, the separation process also has to be carried out in batches ； In laboratory or research settings, distillation operations generally handle small volumes of material, and the type, composition, and degree of separation of the feedstocks often change; therefore, batch distillation is more flexible and convenient to use ； For the preliminary separation of multi-component mixtures, in order to obtain products with different fractions (composition ranges), batch distillation can also be employed. There are two basic operating modes for batch distillation: one is to maintain a constant composition of the distillate by continuously increasing the reflux ratio ； Secondly, with the reflux ratio kept constant, the composition of the distillate gradually decreases. In actual production, a combined operation method is often employed, that is, operation with a constant distillate composition is used in one stage (such as the early stage of operation), while operation with a constant reflux ratio is used in another stage (such as the later stage of operation). The method of collaboration can be determined based on the specific circumstances. (1) Batch distillation with a constant reflux ratio: In the batch distillation process with a constant reflux ratio, both the composition of the bottom liquid http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image002.gif and that of the distillate http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image004.gif decrease simultaneously. Therefore, at the beginning of the operation, the composition of the distillate must be higher than the average composition, in order to ensure that the average composition of the distillate meets the quality requirements. Usually, precise control is stopped once the composition of the kettle liquid reaches the specified value. The main calculations for batch distillation at a constant reflux ratio are as follows. 1. Determination of the number of theoretical plates: The principles for determining the number of theoretical plates in batch distillation are exactly the same as those in continuous distillation. In batch distillation with a constant reflux ratio, there is a corresponding relationship between the composition of the distillate and that of the bottom liquid. In the calculations, the initial operating conditions are used as a reference; at this point, the composition of the bottom liquid is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image006.gif, while the initial composition of the distillate is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image008.gif. Based on the definition of the minimum reflux ratio, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image010.gif, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image012.gif, and the vapor-liquid equilibrium relationship can be used to determine http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image014.gif; that is, the value in equation http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image016.gif – which represents the vapor phase composition in equilibrium with http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image019.gif, expressed as a molar fraction. The operating reflux ratio can be selected according to the relationship in http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image021.gif. In the image at http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image023.gif, the theoretical number of theoretical plates can be determined graphically using http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image024.gif, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image025.gif, and R, as shown in Figures 1–39. The figure indicates that 3 theoretical plates are required. 【Images 1-39】Determination of the number of theoretical plates in intermittent distillation with a constant reflux ratio. 2. Determine the operating parameters: (1) Determine the relationship between http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image027.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image029.gif at various moments during operation. Since the reflux ratio remains constant during batch distillation, the slope of the operating line at each moment http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image031.gif is the same, and thus the operating lines are parallel to one another. If several http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image033.gif values are arbitrarily selected within the range of the initial and final compositions of the distillate, a series of parallel lines with a slope of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image038.gif can be drawn through these points (http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image035.gif, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image037.gif); these lines correspond to the instantaneous operation lines for a certain http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image039.gif. Then, steps are drawn between each operating line and the balance line, such that their number equals the specified number of theoretical plates. The liquid phase composition reached by the last step corresponds to the value shown in http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image042.gif, which is equivalent to what is shown in http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image040.gif, as illustrated in Figures 1-40. 【Images 1-40】The relationship between http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image044.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image046.gif in intermittent distillation with a constant reflux ratio. (2) Determine the relationship between http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image048.gif (or http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image050.gif) and the amount of slurry in the reactor http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image052.gif, as well as the amount of distillate http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image054.gif, during the operation. In the case of batch distillation with a constant reflux ratio, the relationship between http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image056.gif (or http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image058.gif) and W and D should be determined through differential material balance calculations. This calculation result is similar to equation 1-24 derived for simple distillation; in that case, y and x in equation 1-24 must be replaced by the instantaneous values http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image060.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image062.gif, that is, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image064.gif. In equation (1-74), http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image066.gif represents the amount of slurry, in kmol, corresponding to the composition of the slurry http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image068.gif. In the integral term on the right-hand side of Equation 1-74, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image070.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image072.gif are both variables; the relationship between them can be determined using graphical methods. The value of the integral can be found either through graphical integration or numerical integration methods. Thus, it is possible to determine the amount of slurry corresponding to any http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image074.gif using this equation. (3) Calculation of the average composition of the distillate: http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image078.gif. This is done by performing material balance calculations for the batch distillation process; that is, the overall material balance http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image080.gif allows it to be possible to carry out component balance calculations http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image082.gif. By combining these two equations, the desired value can be obtained: http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image084.gif (1-75). (4) Time required per batch of distillation: Since the reflux ratio remains constant during batch distillation, the amount of vaporization V for one batch can be calculated using the following formula: http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image086.gif. The time required for each batch of distillation is then given by: http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image088.gif (1-76). In this formula, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image090.gif represents the vaporization rate, in kmol/h ； http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image092.gif ——Operation time required per batch of distillation, in hours. (II) Batch distillation with a constant distillate composition: During batch distillation, the composition of the liquid in the reactor continuously decreases; to maintain a constant distillate composition, the reflux ratio must be increased continuously. In this mode of operation, the amount of the feed liquid http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image094.gif and its composition http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image096.gif are usually known, as well as the composition of the distillate http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image098.gif and the final composition of the liquid remaining in the reactor http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image100.gif. The designer is required to determine factors such as the number of theoretical plates, the range of reflux ratio, and the amount of vaporization. 1. Determining the number of theoretical plates: For batch distillation with a constant composition in the distillate, since the composition of the liquid in the reactor is at its lowest at the end of the operation http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image102.gif, the required degree of separation is highest; therefore, the number of theoretical plates needed should be calculated based on the final stage of distillation. It is composed of the distillate http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image104.gif and the final residue in the reactor http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image106.gif. The minimum reflux ratio is determined using the following formula: http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image108.gif, where http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image110.gif represents the vapor phase composition in equilibrium with http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image112.gif, expressed as molar fractions. The operating reflux ratio in the final stage of distillation is determined based on http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image114.gif http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image116.gif . In the image at http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image118.gif, the theoretical number of plates can be determined graphically using http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image120.gif, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image122.gif, and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image124.gif. The graphical method is shown in Figures 1-41. The figure indicates that 4 theoretical plates are required. 【Images 1-41】Determination of the number of theoretical plates for intermittent distillation based on the composition of the constant distillate. 2. Determine the relevant operating parameters: (1) Determine the relationship between http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image125.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image127.gif. If the composition of the bottom liquid at a certain moment during the distillation process is known, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image129.gif, then the corresponding value for http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image131.gif can be determined using graphical iteration methods. That is, an initial value for http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image133.gif is assumed first, and then the number of theoretical plates is determined graphically using http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image135.gif. If the number of stages is equal to the given theoretical number of plates, then http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image137.gif is the desired value; otherwise, reset the value of http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image139.gif until the requirement is met. As shown in Figures 1-42. 【Images 1-42】The relationship between intermittent distillation under constant distillate composition and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image141.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image142.gif. (2) The time required for each batch of distillation is set at http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image144.gif; the amount of solution that vaporizes is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image146.gif kmol, the amount of distillate is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image148.gif kmol, and the instantaneous reflux ratio is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image150.gif. Based on material balance, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image152.gif(1-77) can be obtained. The amount of distillate at any given moment during a batch operation can be determined using material balance (ignoring the liquid holdup in the column), that is, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image156.gif(1-78). From differential equation 1-78, http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image158.gif is obtained. Substituting this expression into equation 1-77 yields http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image160.gif. Integrating this expression gives the total amount of vaporization when the composition of the bottom liquid is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image162.gif, which is http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211459/image164.gif(1-79). The time required for each batch of distillation can still be calculated using equation 1-76.

II. Special distillation: As mentioned earlier, the distillation process is based on the difference in relative volatility of various components within a liquid mixture; the greater the difference in volatility among these components, the easier it is to separate them. However, for certain liquid mixtures, the relative volatility between their components is close to 1 or azeotropes are formed, making it inappropriate or impossible to separate them using conventional distillation methods. Then special distillation methods need to be employed. Special distillation methods include azeotropic distillation, extractive distillation, salt-effect distillation, membrane distillation, catalytic distillation, adsorption distillation, etc. This section introduces the commonly used azeotropic distillation and extractive distillation; for other special distillation techniques, refer to relevant literature. 1. Azeotropic distillation: If a third component (referred to as an entrainer) is added to a two-component azeotic mixture, this component can form new azeotropes with one or both of the components in the feed mixture, thereby enabling the separation of the feed mixture using conventional distillation methods. This type of distillation operation is called azeotropic distillation. Azeotropic distillation can separate solutions with the lowest azeotopic point, solutions with the highest azeotropic point, as well as systems with similar volatilities. 【Images 1-43】Schematic diagram of the azeotropic distillation process. Figures 1-43 show schematic diagrams of the azeotropic distillation process for separating ethanol-water mixtures. An appropriate amount of the entrainer benzene was added to the feed solution; benzene formed a new ternary heterogeneous azeotrope with the feed solution (the corresponding azeotrope temperature was 64.85°C, and the azeotrope mole composition was 0.539 for benzene, 0.228 for ethanol, and 0.233 for water). As long as the amount of benzene added is appropriate, all the water in the feed solution can be transferred into the ternary azeotrope, thereby enabling the separation of the ethanol-water mixture. Since the azeotopic temperature of this three-component azeotrope at atmospheric pressure is 64.85°C, it evaporates from the top of the tower, while the product at the bottom of the tower is ethanol in a nearly pure state. After the vapor at the top of the tower enters condenser 4 and is condensed, part of the liquid phase returns to tower 1, while the remainder goes into separator 5, where it separates into light and heavy liquid layers. The light phase returns to Tower 1 as supplementary reflux. The heavy phase is sent back to the benzene recovery tower 2 to recover the benzene contained therein. The steam from Tower 2 is drawn from the top of the tower and also enters Condenser 4; the product at the bottom of Tower 2 is dilute ethanol, which is sent to Ethanol Recovery Tower 3. The top product of Tower 3 is an ethanol-water azeotrope, which is sent back to Tower 1 as a feedstock, while the bottom product is almost pure water. During operation, benzene is recycled, but due to losses, a certain amount of benzene needs to be replenished after some time. In azeotropic distillation, an appropriate entrainer must be selected. The requirements for the entrainer are as follows: ① The entrainer should be able to form a new azeotrope with the components to be separated; ideally, its azeotopic boiling point should be lower than that of the pure components, with a difference in boiling points of at least 10 between them℃ ； ②The lower the amount of entrainer contained in the new azeotrope, the better, in order to reduce the amount of entrainer required as well as the energy needed for vaporization and recovery ； ③The new azeotrope is preferably a heterogeneous mixture to facilitate separation by layering ； ④Non-toxic, non-corrosive, and good thermal stability ； ⑤It’s easy to obtain and inexpensive. 2. Extractive distillation: Similar to azeotropic distillation, extractive distillation is also a special type of distillation method in which a third component (referred to as an extractant or solvent) is added to the feed mixture in order to alter the relative volatility of the existing components and thus achieve the desired separation. The difference is that the boiling point of the extractant is much higher than that of the components in the feed solution, and it does not form an azeotrope with the components, making it easy to recover. Extractive distillation is often used to separate substances with boiling points of 80.1°C; the boiling point of cyclohexane is 80.73°C. When the extractant furfural is added to a benzene-cyclohexane solution, the relative volatility of the solution changes significantly, and this relative volatility increases as the amount of extractant used increases, as shown in Table 1-1. Table 1-1 Changes in the benzene-cyclohexane solution after adding furfural: http://www.cngspw.com/Doc/data.WebNoteBooks/20060430211801/image166.gif Moles fraction of furfural in the solution: 0.0, 0.2, 0.4, 0.5, 0.6, 0.7; Relative volatility: 0.98, 1.38, 1.86, 2.07, 2.36, 2.7. [Figure 1-44] Schematic diagram of the extraction distillation process for benzene and cyclohexane. Figures 1-44 show schematic diagrams of the extractive distillation process for separating benzene-cyclohexane solutions. The feed liquid enters extraction distillation column 1, and the extractant (furfural) is added from the top of column 1 so as to combine with benzene at each tray. The vapor evaporating from the top of the tower is cyclohexane vapor. To recover trace amounts of furfural vapor, a recovery section 2 is provided at the upper part of tower 1 (a recovery section may not be necessary if the boiling point of the extractant is very high). The liquid at the bottom of the tower is a mixture of benzene and furfural, which is then sent to benzene recovery tower 3. Since benzene has a boiling point of 80.1°C at atmospheric pressure, while furfural has a boiling point of 161.7°C, the two can be easily separated. The kettle liquid in Tower 3 is furfural, which can be recycled. During the distillation process, the extractant is essentially not vaporized, nor does it form an azeotrope with the feed liquid; these are features that differ from azeotropic distillation. When selecting an appropriate extractant, the following should be primarily considered: ① The extractant should cause a significant change in the relative volatility among the original components ； ②The extractant should have low volatility; that is, its boiling point should be higher than that of the pure components in the original mixture, and it should not form an azeotrope with those components ； ③ Non-toxic, non-corrosive, and good thermal stability ； ④ It’s readily available and inexpensive. In extractive distillation, a relatively large amount of extractant is used to ensure an adequate concentration of the additive in each tray of the column. Moreover, extractive distillation columns often use saturated steam as the feed source, so as to maintain a roughly equal concentration of the additive in the distillation section and the stripping section.

I. Overview of the Distillation Process 1. Application of the Distillation Process in the Chemical Industry In chemical production, it is often necessary to separate raw materials, intermediate products, or crude products in order to obtain chemical products or intermediates that meet the requirements of the manufacturing process. Common separation processes in the chemical industry include distillation, absorption, extraction, drying, and crystallization. Among these, distillation is a typical unit operation for separating liquid mixtures and is the most widely used. For example, distilling crude oil can yield gasoline, kerosene, diesel, and heavy oil, among others ； Distilling mixed aromatics can yield benzene, toluene, xylene, and others ； Liquid air distillation can yield pure liquid oxygen, liquid nitrogen, and the like. Distillation is a method for separating homogeneous liquid mixtures. Distillation separation is based on the difference in volatility (or boiling point) of the various components in a solution, which allows those components to be separated from one another. Among them, those that are more volatile are called volatile components (or light components) ； Those that are more difficult to evaporate are called poorly volatile components (or heavy components). For example, a solution of benzene and toluene in a container is heated to cause partial vaporization, resulting in a two-phase system of vapor and liquid. When the vapor-liquid phase reaches equilibrium, since benzene has a stronger volatility than toluene (i.e., its boiling point is lower than that of toluene), the concentration of benzene in the vapor phase is necessarily higher than that in the original solution. By extracting the vapor and condensing it, a liquid with a higher benzene content can be obtained. The liquid remaining in the container has a lower benzene content than that of the original solution; in other words, the toluene content is higher than in the original solution. In this way, the solution is initially separated. By repeating the above separation process multiple times, relatively pure benzene and toluene can be obtained. 2. Characteristics of distillation separation: Distillation is the most widely used method for separating liquid mixtures, and it has the following characteristics: (1) The desired product can be obtained directly through distillation separation, whereas separation methods such as absorption and extraction require the use of an external solvent; thus, the extracted components need to be separated from this external component further. As a result, the distillation process is usually relatively simple. (2) Distillation separation has a wide range of applications; it can not only separate liquid mixtures but also be used for the separation of gaseous or solid mixtures. For example, air can be pressurized to liquefy, and then products such as oxygen and nitrogen can be obtained through distillation ； For another example, a mixture of fatty acids can be melted by heating, and a vapor-liquid two-phase system can be established under reduced pressure, allowing for separation via distillation. (3) The distillation process is suitable for the separation of mixtures of various concentrations, whereas operations such as absorption and extraction are more economical only when the concentration of the component to be extracted is low. (4) The distillation process creates a vapor-liquid two-phase system by heating the mixture, and the resulting vapor must be condensed back into a liquid state. Therefore, the distillation process consumes a lot of energy. Energy saving during the distillation process is an issue that deserves attention. 3. Classification of distillation processes Industrially, distillation operations can be classified in the following ways: (1) Distillation methods can be divided into simple distillation, equilibrium distillation (flash distillation), rectification, and special rectifications. Simple distillation and equilibrium distillation are single-stage distillation processes, commonly used in situations where the volatility of the various components in a mixture differs significantly and the separation requirements are not high ； Distillation is a multi-stage distillation process, suitable for systems that are difficult to separate or in situations where high separation standards are required ； Special distillation is suitable for certain systems that are difficult or impossible to separate using conventional distillation. Distillation is the most widely used in industrial production. (2) The distillation process can be divided into batch distillation and continuous distillation. Intermittent distillation offers advantages such as flexible operation and strong adaptability, and is mainly used in small-scale operations, for multiple product types, or in situations with special requirements ； Continuous distillation has advantages such as high production capacity, stable product quality, and easy operation, and is mainly used in applications requiring large production scales and high standards for product quality. Intermittent distillation is a non-steady-state operation, while continuous distillation is a steady-state operation. (3) The number of components in a system can be classified into two-component distillation and multi-component distillation. In industrial production, multi-component distillation is the predominant form, but the principles and calculation methods of two-component distillation also apply to multi-component distillation; it is merely more complex when dealing with multi-component distillation processes, which is why two-component distillation is often used as a basis. (4) Operating pressure can be divided into pressurized, atmospheric, and vacuum distillation. Mixtures that are gaseous at atmospheric pressure (such as air and propane) or whose bubble point at atmospheric pressure is at room temperature are typically subjected to distillation under pressure ； At atmospheric pressure, mixtures with a bubble point ranging from room temperature to around 150°C are generally distilled under normal pressure ； For mixtures with a high bubble point at atmospheric pressure or those that are heat-sensitive (prone to decomposition, polymerization, and other degradation reactions at high temperatures), vacuum distillation is advisable to reduce the operating temperature. This chapter focuses on the principles and calculation methods of continuous distillation for two-component systems.

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