11.3. SIMPLE DISTILLATION METHODS
11.3A. Introduction
The separation process known as distillation is a method for separating the various components of a liquid solution which depends upon the distribution of these components between a vapor phase and a liquid phase. All components are present in both phases. The vapor phase is created from the liquid phase by vaporization at the boiling point.
The basic requirement for the separation of components by distillation is that the composition of the vapor be different from the composition of the liquid with which it is in equilibrium at the boiling point of the liquid. Distillation is concerned with solutions where all components are appreciably volatile, such as ammonia–water or ethanol–water solutions, where both components will be in the vapor phase. In evaporation, by contrast, of a solution of salt and water, for example the water is vaporized but the salt is not. The process of absorption differs from distillation in that one of the components in absorption is essentially insoluble in the liquid phase. An example is absorption of ammonia from air by water, where air is insoluble in the water–ammonia solution.
11.3B. Relative Volatility of Vapor–Liquid Systems
In Fig. 11.1-2, the equilibrium diagram for a binary mixture of A and B, the greater the distance between the equilibrium line and the 45° line, the greater the difference between the vapor composition yA and liquid composition xA. Hence, the separation is more easily made. A numerical measure of this separation is the relative volatility αAB. This is defined as the ratio of the concentration of A in the vapor to the concentration of A in the liquid divided by the ratio of the concentration of B in the vapor to the concentration of B in the liquid:
Equation 11.3-1
where αAB is the relative volatility of A with respect to B in the binary system.
If the system obeys Raoult's law, as does the benzene–toluene system,
Equation 11.3-2
Substituting Eq. (11.3-2) into (11.3-1) for an ideal system,
Equation 11.3-3
Equation (11.3-1) can be rearranged to give
Equation 11.3-4
where α = αAB. When the value of α is above 1.0, a separation is possible. The value of α may change as concentration changes. When binary systems follow Raoult's law, the relative volatility often varies only slightly over a large concentration range at constant total pressure.
EXAMPLE 11.3-1. Relative Volatility for Benzene–Toluene SystemUsing the data from Table 11.1-1, calculate the relative volatility for the benzene–toluene system at 85°C (358.2 K) and 105°C (378.2 K). Solution: At 85°C, substituting into Eq. (11.3-3) for a system following Raoult's law,
Similarly at 105°C,
The variation in α is about 7%. |
11.3C. Equilibrium or Flash Distillation
1. Introduction to distillation methods
Distillation can be carried out by either of two main methods in practice. The first method of distillation involves the production of a vapor by boiling the liquid mixture to be separated in a single stage and recovering and condensing the vapors. No liquid is allowed to return to the single-stage still to contact the rising vapors. The second method of distillation involves the returning of a portion of the condensate to the still. The vapors rise through a series of stages or trays, and part of the condensate flows downward through the series of stages or trays countercurrent to the vapors. This second method is called fractional distillation, distillation with reflux, or rectification.
There are three important types of distillation that occur in a single stage or still and that do not involve rectification. The first of these is equilibrium or flash distillation, the second is simple batch or differential distillation, and the third is simple steam distillation.
2. Equilibrium or flash distillation
In equilibrium or flash distillation, which occurs in a single stage, a liquid mixture is partially vaporized. The vapor is allowed to come to equilibrium with the liquid, and the vapor and liquid phases are then separated. This can be done batchwise or continuously.
In Fig. 11.3-1 a binary mixture of components A and B flowing at the rate of F mol/h into a heater is partially vaporized. Then the mixture reaches equilibrium and is separated. The composition of F is xF mole fraction of A. A total material balance on component A is as follows:
Equation 11.3-5
Figure 11.3-1. Equilibrium or flash distillation.
Since L = F − V, Eq. (11.3-5) becomes
Equation 11.3-6
Usually, the moles per hour of feed F, moles per hour of vapor V, and moles per hour of L are known or set. Hence, there are two unknowns x and y in Eq. (11.3-6). The other relationship needed in order to solve Eq. (11.3-6) is the equilibrium line. A convenient method to use is to plot Eq. (11.3-6) on the x-y equilibrium diagram. The intersection of the equation and the equilibrium line is the desired solution. This is similar to Example 11.2-1 and shown in Fig. 11.2-1.
11.3D. Simple Batch or Differential Distillation
In simple batch or differential distillation, liquid is first charged to a heated kettle. The liquid charge is boiled slowly and the vapors are withdrawn as rapidly as they form to a condenser, where the condensed vapor (distillate) is collected. The first portion of vapor condensed will be richest in the more volatile component A. As vaporization proceeds, the vaporized product becomes leaner in A.
In Fig. 11.3-2 a simple still is shown. Originally, a charge of L1 moles of components A and B with a composition of x1 mole fraction of A is placed in the still. At any given time, there are L moles of liquid left in the still with composition x, and the composition of the vapor leaving in equilibrium is y. A differential amount dL is vaporized.
Figure 11.3-2. Simple batch or differential distillation.
The composition in the still pot changes with time. In deriving the equation for this process, we assume that a small amount of dL is vaporized. The composition of the liquid changes from x to x − dx and the amount of liquid from L to L − dL. A material balance on A can be made, where the original amount = the amount left in the liquid + the amount of vapor:
Equation 11.3-7
Multiplying out the right side,
Equation 11.3-8
Neglecting the term dx dL and rearranging,
Equation 11.3-9
Integrating,
Equation 11.3-10
where L1 is the original moles charged, L2 the moles left in the still, x1 the original composition, and x2 the final composition of liquid.
The equilibrium curve gives the relationship between y and x. The integration of Eq. (11.3-10) can be done by calculating values of f(x) = 1/(y − x) and numerically or graphically integrating Eq. (11.3-10) between x1 and x2. Equation (11.3-10) is known as the Rayleigh equation. The average composition of total material distilled, yav, can be obtained by material balance:
Equation 11.3-11
EXAMPLE 11.3-2. Simple Differential DistillationA mixture of 100 mol containing 50 mol % n-pentane and 50 mol % n-heptane is distilled under differential conditions at 101.3 kPa until 40 mol is distilled. What is the average composition of the total vapor distilled and the composition of the liquid left? The equilibrium data are as follows, where x and y are mole fractions of n-pentane:
Solution: The given values to be used in Eq. (11.3-10) are L1 = 100 mol, x1 = 0.50, L2 = 60 mol, and V (moles distilled) = 40 mol. Substituting into Eq. (11.3-10), Equation 11.3-12
The unknown is x2, the composition of the liquid L2 at the end of the differential distillation. To solve this by numerical integration, equilibrium values of y versus x are plotted so values of y can be obtained from this curve at small intervals of x. Alternatively, instead of plotting, the equilibrium data can be fitted to a polynomial function. For x = 0.594, the equilibrium value of y = 0.925. Then f(x) = 1/(y − x) = 1/(0.925 − 0.594) = 3.02. Other values of f(y) are similarly calculated. The numerical integration of Eq. (11.3-10) is performed from x1 = 0.5 to x2 such that the integral = 0.510 by Eq. (11.3-12) in Fig. 11.3-3. Hence, x2 = 0.277. Substituting into Eq. (11.3-11) and solving for the average composition of the 40 mol distilled,
Figure 11.3-3. Numerical integration for Example 11.3-2.
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11.3E. Simple Steam Distillation
At atmospheric pressure high-boiling liquids cannot be purified by distillation, since the components of the liquid may decompose at the high temperatures required. Often the high-boiling substances are essentially insoluble in water, so a separation at lower temperatures can be obtained by simple steam distillation. This method is often used to separate a high-boiling component from small amounts of nonvolatile impurities.
If a layer of liquid water (A) and an immiscible high-boiling component (B) such as a hydrocarbon are boiled at 101.3 kPa abs pressure, then, by the phase rule, Eq. (10.2-1), for three phases and two components,
Hence, if the total pressure is fixed, the system is fixed. Since there are two liquid phases, each will exert its own vapor pressure at the prevailing temperature and cannot be influenced by the presence of the other. When the sum of the separate vapor pressures equals the total pressure, the mixture boils and
Equation 11.3-13
where PA is vapor pressure of pure water A and PB is vapor pressure of pure B. Then the vapor composition is
Equation 11.3-14
As long as the two liquid phases are present, the mixture will boil at the same temperature, giving a vapor of constant composition yA. The temperature is found by using the vapor-pressure curves for pure A and pure B.
Note that by steam distillation, as long as liquid water is present, the high-boiling component B vaporizes at a temperature well below its normal boiling point without using a vacuum. The vapors of water (A) and high-boiling component (B) are usually condensed in a condenser and the resulting two immiscible liquid phases separated. This method has the disadvantage that large amounts of heat must be used to evaporate the water simultaneously with the high-boiling compound.
The ratio moles of B distilled to moles of A distilled is
Equation 11.3-15
Steam distillation is sometimes used in the food industry for the removal of volatile taints and flavors from edible fats and oils. In many cases vacuum distillation is used instead of steam distillation to purify high-boiling materials. The total pressure is quite low so that the vapor pressure of the system reaches the total pressure at relatively low temperatures.
Van Winkle (V1) derives equations for steam distillation where an appreciable amount of a nonvolatile component is present with the high-boiling component. This involves a three-component system. He also considers other cases for binary batch, continuous, and multicomponent batch steam distillation.