Distillation Distillation may be defined as the separation of the components of a liquid mixture by a process involving partial vaporization. The vapor evolved is usually recovered by condensation. Volatility The volatility of any substance in a liquid solution may be defined as the equilibrium partial pressure of the substance in the vapor phase devided by the mole fraction of the substance in the liquid solution: va volatility of component a in a liquid solution = p xa The volatility of a material in the pure state is equal to the vapor pressure of the material in the pure state. Similarly, the volatility of a component in a liquid mixture which follows Raoult s law must be equal to the vapor pressure of that component in the pure state. a Relative volatility In order to determine the possible extent of separation between the components of a mixture by the use of distillation, it is neccessary to know the relative ease of vaporization of the individual components. Hence we introduce a Relative volatility (), which is defined as the volatility of one component of a liquid mixture divided by the volatility of another component of the liquid mixture. Usually Relative volatilities are expressed with the higher of the two volatilities in the numerator. va pa xb ab (1) vb xa pb If the vapors follow Dalton s law, pa yap & p b ybp where P is the total pressure of the vapors, then ya xb ab (2) yb xa This is often given as the definition of relative volatility, it can be calculated directly from vapor-liquid equilibrium data. For binary mixtures, y 1 y &x b 1 x xa ya 1 1x a b a a, hence (3) x a ya 1 y a (4) 49 50
Simple Batch (differential) Distillation 1. Liquid is charged to a heated kettle 2. The liquid charge is boiled slowly 3. The vapors are withdrawn as quickly as they form to a condenser 4. 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. i.e., the composition changes with time. The total mole amount in the liquid is L with the molol fraction of A being x. Assume a small amount of dl is vaporized so that the composition of the liquid changes from x to (x-dx) and the amount of liquid from L to (LdL). Let y be the composition of A in the vapor. The material balance of A gives xl = (x-dx)(l-dl) + ydl (5) Expanding the right side, we have xl = xl xdl Ldx +dxdl +ydl (6) 51 Ignoring the double derivative term dxdl and rearranging, 7 Integrating, ln 8 where L 1 is the original moles charged, L 2 the moles left in the still, x 1 the original composition, and x 2 the final composition of liquid. Equation (8) is known as the Rayleigh equation. The equilibrium curve gives the relationship between y and x. Then the integration of Rayleigh equation can be done numerically or graphically between x 1 and x 2. The average composition of total material distilled, y av, can be obtained using the material balance: L 1 x 1 = L 2 x 2 + V y av (9) V = L 1 L 2 = moles distilled (10) Example D1: A mixture of 100 mol containing 50 mol % n-pentane and 50 mol % n-heptane is distilled under differential conditions at 101.2 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: x 1 0.867 0.594 0.398 0.254 0.145 0.059 0 y 1 0.984 0.925 0.836 0.701 0.521 0.271 0 52
Solution: The given values for the Rayleigh equation are L 1 = 100 mol, x 1 = 0.50, L 2 = 60 mole, V = 40 mol. ln 100. 60 0.510 The unknown is x 2. To solve this by numerical integration, the equilibrium relationship is converted to the function of 1/(y-x) vs x as the following figure. x 1 0.867 0.594 0.398 0.254 0.145 0.059 0 y 1 0.984 0.925 0.836 0.701 0.521 0.271 0 1/(y-x) 8.547 3.021 2.283 2.237 2.660 4.717 Flash (single stage, continuous) Distillation Flash distillation vaporizes a definite fraction of the liquid, the evolved vapor is in equilibrium with the residual liquid, the vapor is separated from the liquid and condensed. Plant for flash distillation. The integration is done graphically from x 1 = 0.5 to x 2 such that the integral (shaded area) = 0.510. Hence x 2 = 0.277. Substituting into Eq. (5) to solve for the average composition of the 40 mol distilled, 100(0.50) = 60(0.277) + 40 y av y av = 0.835 Consider 1 mole of a binary mixture fed to the above equipment. By a material balance for the more volatile component, we have xf fyd ( 1 f) xb (11) where x F = concentration (mole fraction) of A in the feed y D and x B = concentrations of A in the vapor and liquid 53 54
f = V/F = the molal fraction of the feed to be vaporized V = moles per hour of vapor F = moles per hour of feed L = F V = moles per hour of liquid Example D2: A mixture of 50 mole percent benzene and 50 mole percent toluene is subjest to flash distillation at a separator pressure of 1 atm. The vaporliquid equilibrium curve and boiling-point diagram are given below. Both y D and x B are unknown, but they are on the equilibrium curve. In general we have the following operating equation for flash distillation by rearranging eq. (11): f y 1 x x (12) f ff which passes the point (x F, x F ). Boiling-point diagram (system of benzene-toluene at 1 atm). Plot the following quantities, all as functions of f, the fractional vaporization: (a) the temperature in the separator (b) the composition of the liquid leaving the separator (c) the composition of the vapor leaving the separator 55 56
Solution: For each value of f, the corresponding quantity of [(f- 1)/f] is calculated, which is the slope of the operating line. By using this slope and the point (x F, x F ), one straight operating line can be drawn on the x-y diagram. different values of f, the solutions can be found. The results are given in the following figure and table. Equilibrium curve, system of benzene-toluene. The coordinate of the intersection of the equilibrium and operating lines gives the compositions of the leaving liquid and vapor as (x, y). From the value of x or y the temperature in the separator can be obtained from the boiling-point diagram. By doing this procedure for 57 58
Continuous Distillation with Reflux (Rectification) Flash distillation is not effective in separating components of comparable volatility, or in obtaining nearly pure components. Rectification on an ideal plate. Vapor leaving plate n = y n Liquid leaving plate n = x n Vapor enterrng plate n = y n+1 Liquid entering plate n = x n-1 y n+1 is in contact (same position) with x n For an ideal plate, y n is in equilibrium with x n Distillation Trays Allows efficient mixing of vapor and liquid enabling rapid equilibration Combination of rectification and stripping. If we want to obtain both near pure top and bottom products, the feed plate has to be in the central portion of the column. The bottom is called the reboiler. Rectification in the section below the feed plate is called stripping, the bottom product can be nearly pure B. 59 Rectifying (enriching) section: all plates above the feed. Stripping section: all plates below the feed, including the feed plate itself. Liquid flows down by gravity to reboiler. The bottom product is withdrawn from the pool of liquid on the downstream side of the weir and flows through the cooler G. 60
The vapors rising through the rectifying section are completely condensed in condenser C, and the condensate is collected in accumulator D. Distillation in the Enriching Section of Tower A portion of liquid from the accumulator is returned to the top plate, which is called reflux. It provides the downflowing liquid. Without the reflux, no rectification would happen in the rectifying section and the concentration of the overhead product would be the same as that of the vapor rising from the feed plate. Condensate not returned to the top plate is cooled in heat exchange E, called the product cooler, and withdrawn as the overhead product. Overal material balance for binary systems Total material balance: F = D + B (13) Component A balance: Fx F = Dx D + Bx B (14) Eliminating B gives Eliminating D gives Net flow rate in the rectifying section This is the overhead product, D = V a - L a = difference between the flow rates of vapor and liquid anywhere in the upper section above n+1. 61 Material balances Vn1 Ln D (15) Vn1yn1 Lnxn DxD (16) By rearranging Eq. (16) we obtain the operating line L Dx L Dx y n x D n x D n1 n n (17) V V L D L D n1 n1 n This is the operating line in the rectifying section. The reflux ratio, R = L n /D. If R is constant, the operating line will be straight on the y-x plot. R x y 1 x D n n (18) R 1 R 1 62 n
The slope is L n /V n+1 or R/(R+1). It intersects the y = x line (45 o diagonal line) at x = x D. The intercept of the operating line at x = 0 is y = x D /(R+1). Distillation in the Stripping Section of Tower The theoretical stages are determined by starting at the operating line at x D and moving horizontally to intersect the equilibrium line at x 1. Then y 2 is the composition of the vapor passing the liquid x 1. Similarly, other theoretical trays are stepped off down the tower in the enriching section to the feed tray. Material balances Lm Vm1 B (19) Lmxm Vm1y m1 BxB (20) so that the operating line is L Bx L Bx y m x B m x B m1 m m (21) Vm1 Vm1 Lm B Lm B This is the operating line in the stripping section. If equimolal flow is assumed, L m = L N = constant and V m+1 = V N = constant, Eq. (21) is a straight line when plotted as y vs x, with a slope of L m / V m+1. It intersects the y = x line at x = x B. The intercept at x =0 is y=-b x B / V m+1. 63 Again the theoretical stages for the stripping section are determined by starting at x B, going up to intersect the equilibrium line at y B, and then across to the operating line at x N, and so on. 64
Condenser and top plate The material balance diagram for the top plate and condenser is shown in the figure. Bottom plate and reboiler The material balance diagram for the top plate and condenser is shown in the figure. At the top plate, the composition is (x C, y 1 ). The simplest case is a total condenser, which condense all the vapor so that the liquid has the same composition as the vapor. Hence, x C = x D = y 1. The enriching line starts with (x D, x D ), which is in the diagonal line. Triangle abc in the figure represents the top plate. 65 The lowest point on the operating line for the column is the bottom plate (x b, y r ), which are the liquid concentration leaving the bottom plate and the vapor concentration leaving the reboiler. However, as shown in the stripping section, the operating line can be extended to cross the diagonal at point (x B, x B ). In a common reboiler, the vapor leaving the reboiler is in equilibrium with the liquid leaving as bottom product.then x B and y r are in equilibrium curve, and the reboiler acts as an ideal plate. Triangles cde and abc are the reboiler and bottom plates. 66
Effect of feed conditions The condition of the feed stream F entering the tower determines the relation between the vapor V m in the stripping section and V n in the enriching section as well as between L m and L n. If the feed is part liquid and part vapor, the vapor will add to V m to give V n, and the liqud will add to L n to give L m. We define 1 1 (22) Where H V is the enthalpy of the feed at the dew point, H L the enthalpy of the feed at the boiling point (bubble point), and H F the enthalpy of the feed at its entrance conditions. Feed conditions: (a) cold liquid, q>1 (b) at bubble point (saturated liquid), q=1 (c) partial vapor, 0<q<1 (d) at dew point, q=0 (saturated vapor) (e) superheated vapor, q<0 67 q can also be considered as the number of moles of saturated liquid produced on the feed plate by each mole of feed added to the tower. L m = L n + qf (23) V n = V m + (1 - q)f (24) The point of intersection of the enriching and stripping operating line equations on the y-x plot can be derived as follows. Eqs. (16) and (20) can be rewritten as follows without the tray subscripts: Vn y Ln x DxD (25) Vm y Lm x BxB (26) Where the y and x values are the point of intersection of the two operating lines. (25) - (26) gives Vm Vn y Lm Ln x DxD BxB (27) Replacing by Eqs. (14), (23, (24), we have (q-1)fy = qfx Fx F (28) This is the q-line equation and it passes the intersection of the two operating lines. The q-line has a slope of q/(q-1) and passes through the 45 o line at y = x = x F. The right figure is an example of a feed of part liquid and part vapor (0<q<1). First draw the q-line, then the enriching line, the intercept of these two lines can be used to draw the stripping line. 68
Lacation of the feed tray in a tower and number of ideal plates; McCabe-Thiele method To determine the number of theoretical trays needed in a tower, the stripping and enriching lines are drawn to intersect on the q line as follows. In the above figure, the feed is part liquid and part vapor, since 0<q<1. Hence, in adding the feed to tray 2, the vapor portion of the feed is separated and added to below plate 2 and the liquid added to the liquid from above entering tray 2. If the feed is all liquid, it should be added to the liquid flowing to tray 2 from the tray above. If the feed is all vapor, it should be added below tray 2 and join in the vapor rising from the plate below. Since a reboiler is considered as a theoretical step, when the vapor yb is in equilibrium with xb, the number of theoretical trays in a tower is equal to the number of theoretical steps minus one. 1. Starting from the top at x D, the trays are stepped off along the enriching line. 2. It is important to switch to the stripping line when the triangle first passes the q line (intersection of the 2 operating lines), which is tray 2 in this case. 3. The trays are continued to step off along the stripping line. 4. The number of theoretical trays required is 3.7 with the feed on tray 2. 69 The value of q for cold liquid feed is 1 c T T The value of q for superheated vapor feed is 0 c T T where c pl = specific heat capacity of feed liquid c pv = specific heat capacity of feed vapor T F = temperature of feed T B = bubble point of feed T D = dew point of feed 70
Example D3. Rectification of a benzene-toluene mixture A liquid mixture of benzene-toluene is to be distilled in a fractionating tower at 101.3 kpa pressure. The feed of 100 kmol/h is liquid, containing 45 mol % benzene and 55 mol % toluene, and enters at 327.6 K. A distillate containing 95 mol % benzene and 5 mol % toluene and a bottoms containing 10 mol % benzene and 90 mol % toluene are to be obtained. The reflux ratio is 4:1. The average heat capacity of the feed is 159 kj/(kmol K) and the average latent heat is 32099 kj/kmol. Equilibrium data for this system are given in the table below. Calculate the distillate and bottoms in kmol/h, and the number of theoretical trays needed. Vapor-Pressure and Equilibrium-Mole-Fraction Data for Benzene-Toluene System Vapor pressure (kpa) Mole fraction of T (K) benzene at 101.325 kpa Benzene Toluene x A y A 353.3 101.32-1.000 1.000 358.2 116.9 46.0 0.780 0.900 363.2 135.5 54.0 0.581 0.777 368.2 155.7 63.3 0.411 0.632 373.2 179.2 74.3 0.258 0.456 378.2 204.2 86.0 0.130 0.261 383.8 240.0 101.32 0 0 F = 100 kmol/h, x F = 0.45, x D = 0.95, x B = 0.1, R = L n /D = 4. Overall material balance F = D + B 100 = D + B Benzene balance Fx F = Dx D + Bx B 100(0.45) = D(0.95) + (100-D)(0.10) D = 41.2 kmol/h B = 58.8 kmol/h The enriching operating line is R x 4 0.95 y 1 D n xn xn 0.80xn 0.19 R 1 R 1 4 1 4 1 The q line is 1 1 1 The value of H V H L = latent heat = 32099 kj/kmol. H L H F = c pl (T B T F ) where the heat capacity of the liquid feed c pl = 159 kj/(kmol K), T B = 366.7 K (boiling point of feed), and T F = 327.6 K (inlet feed temperature). 1 c T T 1 1.195 So the q line is 159366.7 327.6 32099 71 72
1.195 0.195 0.195 6.128 5.128 The enriching and q lines are plotted in the figure below. Their intersection identifys one point in the stripping line. Linking this point to the bottom point y = x = x B = 0.1, we obtain the stripping line. The number of theoretical steps is 7.6, or 7.6 steps minus a reboiler, which gives 6.6 theoretical trays. The feed is introduced on tray 5 from the top. Total reflux ratio In distillation of a binary mixture A and B, the feed conditions, distillate and bottoms compositions are usually specified and the number of theoretical trays are to be calculated. The number of theoretical trays depends on the operating lines. To fix the operating lines, the reflux ratio R = L n /D at the top must be set. One limiting case is total reflux, R =, or D = 0. The material balance becomes V n+1 = L n V n+1 y n+1 = L n x n Hence, the operating lines of both sections are on the 45 o line, y n+1 = x n. Total reflux is an extreme case, the number of theoretical trays required is at its minimum to obtain the given separation of x D and x B. However, in reality we have no product at all, and the twoer diameter is infinite. 73 74
Minimum reflux ratio Another limiting case is the minimum reflux ratio, R m, that will require infinite number of trays for the given separation of x D and x B. This corresponds to the minimum vapor flow in the tower, and hence the minimum reboiler and condenser sizes. In some cases, where the equilibrium line has an inflection in it as shown below, the operating line at minimum reflux will be tangent to the equilibrium line. If the reflux ratio R decreases, the slope of the enriching line R/(R+1) decreases, the intersection of this line and the stripping line with the q line moves farther from the 45 o line and closer to the equilibrium line. The number of steps required to give a fixed x D and x B increases. At the extreme case, the two operating lines touch the equilibrium line, a pinch point at y and x occurs, where the number of steps required is infinite. The slope of enriching line in this case is 1 75 The minimum reflux ratio refers to the situation that we can have the maximum products (D and B) but the number of trays required is infinite. Both total reflux and minimum reflux are impossible in actual operation. 76
Operating and optimum reflux ratio The actual operating reflux ratio lies between the two limits. To select the proper value of R requires a complete economic balance on the fixed costs of the tower and operating costs. By experience, the optimum reflux ratio has been shown to be between 1.2R m and 1.5R m. Solution: (a) First draw the equilibrium line and the q line as we did in Example D3. The operating line for minimum reflux ratio is plotted as a dashed line and intersects the equilibrium line at the same point the q line intersects. Reading the values of x = 0.49 and y = 0.702, we have 1 0.95 0.702 0.95 0.49 0.539 Hence, the minimum reflux ratio is R m = 1.17. Example D4: Minimum reflux ratio and total reflux ratio For the rectification in Exanple D3, where a benzenetoluene feed is being distilled to give a distillate composition of x D = 0.95 and a bottom product of x B = 0.10, calculate the following: (a) Minimum reflux ratio R m (b) Minimum number of theoretical plates at a total reflux 77 (b) The theoretical steps are drawn as shown between the equilibrium line and the 45 o line. The minimum number of theoretical steps is 5.8, which gives 4.8 theoretical trays plus a reboiler. 78
Special case for rectification 1. Stripping-column distillation. In some cases the feed is added at the top of the stripping column because we would like to have bottoms product only. The feed is usually a saturated liquid at the boiling point, and the overhead product V D is the vapor rising from the top plate, which goes to a condenser with no relux returned to the tower. This stripping line is the same as that for a complete tower. It intersects the y = x line at x = x W, and the slope is constant at L m /V m+1. If the feed is saturated liquid, then L m = F. This is shown in the figure. Starting at x F, the steps are drawn down the tower. If the feed is cold liquid below the boiling point, the q line should should be used and q > 1: L m = qf. Example D5: Number of trays in stripping tower A liquid feed at the boiling point of 400 kmol/h containing 70 mol % benzene (A) and 30 mol % toluene (B) is fed to a stripping tower at 101.2 kpa pressure. The bottoms product flow is 60 kmol/h containing only 10 mol % A and the rest B. Calculate the kmol/h overhead vapor, its composition, and the number of theoretical steps required. The bottoms product W usually has a high concentration of the less volatile component B. Hence, the column operates as a stripping tower, with the vapor removing the more volatile A from the liquid as it flows downward. Assuming constant molar flow rates, a material balance of the more volatile component A around the dashed line gives, L 1 m Wx y W m xm V V m1 m1 Solution F = 400 kmol/h x F = 0.70 W = 60 kmol/h x W = 0.10 Plot the equilibrium and diagonal lines. Overall material balance gives F = W + V D 79 80
400 = 60 + V D V D = 340 kmol/h Component A balance gives Fx F = Wx W + V D y D 400(0.70) = 60(0.10) + 340y D y D = 0.806 For a saturated liquid, q=1, the q line is vertical. The operating line is plotted through the point y = y W = 0.10 and the intersection of y D = 0.806 with the q line. Alternatively, the slope of L m /V m+1 = 400/340 = 1.176 can be used. Stepping off the trays from the top, 5.3 theoretical steps or 4.3 theoretical trays plus a reboiler are needed. 2. Enriching-column distillation Enriching towers are also used at times, where the feed enters the bottom of the tower as a vapor. The overhead distillate is produced in the same way as in a complete fractionating tower and is usually quite rich in the more volatile component A. The liquid bottoms is usually comparable to the feed in composition, slightly leaner in A. If the feed is saturated vapor, the vapor in the tower V n = F. Plate Efficiency To translate ideal plates into actual plates Applicable to both distillation & absorption 1 Types of plate efficiency 1.1 overall efficiency 0 number of ideal plates number of actual plates for the entire column simple but the least fundamental 1.2 Murphree efficiency yn yn1 M * yn yn1 where y n = actural concentration of vapor leaving plate n y n+1 = actural concentration of vapor entering plate n * y n = concentration of vapor in equilibrium with liquid concentration x n leaving downpipe from plate n for a single plate in reality samples are taken of the liquid on the plates, and the vapor compositions are determined from a McCabe-Thiele diagram. 81 82
1.3 Local or point efficiency y' ny' n1 ' y' en y' n1 where y' n = concentration of vapor leaving a specific point in plate n y' n+1 = concentration of vapor entering plate n at the same location y' en = concentration of vapor in equilibrium with liquid at the same point (x' n ) for a specific location in a plate In large columns, incomplete mixing of the liquid occurs in the tray. M is the integration of ' over the entire tray. 2.2 Murphree & overall efficiencies ln 1 M ( mv / L 1) 0 ln mv / L where m is the slope of equilibrium line. When mv/l=1.0 or M 1.0, M = 0. This relationship depends on the relative slopes of equilibrium and operating lines. M < 0 (stripping section) M > 0 (enriching section) M 0 for the whole column if the feed plate is near the middle 3. Use of Murphree efficiency Draw an effective equilibrium line. Use McCable and Thiele method between the effective equilibrium line and the operating line. 2. Relationship between efficiencies 2.1 Murphree & local efficiencies In small columns, good mixing can be achieved so that the concentration is uniform in the tray. y' n = y n, y' n+1 =y n+1, and y' en = y * n. Therefore, ' M. 83 4. Factors influencing plate efficiency Adequate and intimate contact between liquid and vapor can enhance the efficiency; any excessive foaming or entrainment, poor distribution, or shortcircuiting, weeping, or dumping of liquid, lowers the plate efficiency. Rate of mass transfer between liquid and vapor. 84