Hm nm+1

Hm nm+1

Equation 11.92 represents any operating line below the feed plate, and it shows that all such lines pass through a common pole M of coordinates xw and H'w. As with the rectifying section, a stream M may be defined by mass Lm+1 — Vm, composition xw and enthalpy H'w. Thus:

and:

It therefore follows that phases F, M, and N are on a straight line on the H — x chart, as shown in Figures 11.27 and 11.28.

11.5.2. Determination of the number of plates on the H — x diagram

The determination of the number of plates necessary for a desired separation is shown in Figure 11.28. The position of the feed (F, xf) is shown at F on the boiling line and the pole N is located as (xd, H'd), where:

Pole M is located as on the extension of NF cutting the ordinate at xw in M.

The condition of the vapour leaving the top plate is shown at V7 on the dew-point curve with abscissa xd. The condition of the liquid on the top plate is then found by drawing the tie line T7 from V7 to L7 on the boiling curve. The condition V6 of the vapour on the second plate is found, from equation 11.77, by drawing L7N to cut the dew-point curve on V6. L6 is then found on the tie line T6. The conditions of vapour and liquid V5, V4, V3 and L5, L4 are found in the same way. Tie line T3 gives L3, which has the same composition as the feed. V2 is then found using the line MFV2, as this represents the vapour on the top plate of the stripping section. L2, L1 and V1 are then found by a similar construction. L1 has the required composition of the bottoms, xw.

Alternatively, calculations may start with the feed condition and proceed up and down the column.

The pole N has coordinates H^ + Qc/D]. Qc/D is the heat removed in the condenser per unit mass of product, as liquid at its boiling point and is represented as shown in Figure 11.28. The number of plates in the rectifying section is determined, for a given feed xf and product xd, by the height of this pole N. As N is lowered to say N' the heat qc falls, although the number of plates required increases. When N lies at Nm on the isothermal through F, qc is a minimum although the number of plates required becomes infinite. Since the tie lines have different slopes, it follows that there is a minimum reflux for each plate, and the tie line cutting the vertical axis at the highest value of H will give the minimum practical reflux. This will frequently correspond to the tie line through F.

From equations 11.83 and 11.95 and writing QC/D = qc, then:

and: (qc)min = (HÏ - HfL+1) ( %d ~ Jf ) + Hj - Hjf (11.98)

The advantage of the H — x chart lies in the fact that the heat quantities required for the distillation are clearly indicated. Thus, the higher the reflux ratio the more heat must be removed per mole of product, and point N rises. This immediately shows that both qc and Qb are increased. The use of this method is illustrated by considering the separation of ammonia from an ammonia-water mixture, as occurs in the ammonia absorption unit for refrigeration.

It is required to separate 1 kg/s (3.6 tonnes/h) of a solution of ammonia in water, containing 30 per cent by mass of ammonia, to give a top product of 99.5 per cent purity and a weak solution containing 10 per cent by mass of ammonia.

Calculate the heat required in the boiler and the heat to be rejected in the condenser, assuming a reflux 8 per cent in excess of the minimum and a column pressure of 1000 kN/m2. The plates may be assumed to have an ideal efficiency of 60 per cent.

Solution

Taking a material balance for the whole throughput and for the ammonia gives:

D + W = 1.0 0.995D + 0.1 W = (1.0 x 0.3) Thus: D = 0.22 kg/s and: W = 0.78 kg/s

The enthalpy-composition chart for this system is shown in Figure 11.29. It is assumed that the feed F and the bottom product W are both liquids at their boiling points.

Location of the poles N and M

Nm for minimum reflux is found by drawing a tie-line through F, representing the feed, to cut the line x = 0.995 at Nm.

length NmA

The minimum reflux ratio, Rm =

length AL

Since the actual reflux is 8 per cent above the minimum, then:

Point N therefore has an ordinate of (437 + 1547) = 1984 and an abscissa of 0.995. Point M is found by drawing NF to cut the line x = 0.10, through W, at M. The number of theoretical plates is found, as on the diagram, to be 5+.

The number of plates to be provided = (5/0.6) = 8.33, say 9.

The feed is introduced just below the third ideal plate from the top, or just below the fifth actual plate.

The heat input at the boiler per unit mass of bottom product is:

Condenser duty = length NL x D

11.5.4. Multiple feeds and sidestreams

The enthalpy-composition approach may also be used for multiple feeds and sidestreams for binary systems. For the condition of constant molar overflow, each additional sidestream or feed adds a further operating line and pole point to the system.

Taking the same system as used in Figure 11.22, with one sidestream only, the procedure is as shown in Figure 11.30.

Figure 11.30. Enthalpy-composition diagram for a system with one sidestream

Figure 11.30. Enthalpy-composition diagram for a system with one sidestream

The upper pole point N is located as before. The effect of removing a sidestream S' from the system is to produce an effective feed F', where F' = F — S' and where F'S'/F'F = F/S'. Thus, once S' and F have been located in the diagram, the position of F' may also be determined. The position of the lower pole point M, which must lie on the intersection of x = xw and the straight line drawn through NF', may then be found. N relates to the section of the column above the sidestream and M to that part below the feed plate. A third pole point must be defined to handle that part of the column between the feed and the sidestream.

The pole point for the intermediate section must be on the limiting operating line for the upper part of the column, that is NS'. This must also lie on the limiting operating line for the lower part of the column, that is MF or its extension. Thus the intersection of NS' and MF extended gives the position of the intermediate pole point O.

The number of stages required is determined in the same manner as before, using the upper pole point N for that part of the column between the sidestream and the top, the intermediate pole point O between the feed and the sidestream, and the lower pole point M between the feed and the bottom.

For the case of multiple feeds, the procedure is similar and may be followed by reference to Figure 11.31.

A mixture containing equal parts by mass of carbon tetrachloride and toluene is to be fractionated to give an overhead product containing 95 mass per cent carbon tetrachloride, a bottom product of 5 mass per cent carbon tetrachloride, and a sidestream containing 80 mass per cent carbon tetrachloride. Both the feed and sidestream may be regarded as liquids at their boiling points.

A mixture containing equal parts by mass of carbon tetrachloride and toluene is to be fractionated to give an overhead product containing 95 mass per cent carbon tetrachloride, a bottom product of 5 mass per cent carbon tetrachloride, and a sidestream containing 80 mass per cent carbon tetrachloride. Both the feed and sidestream may be regarded as liquids at their boiling points.

Figure 11.31. Enthalpy

-composition diagram for a system with two feeds

Figure 11.31. Enthalpy

-composition diagram for a system with two feeds

The rate of withdrawal of the sidestream is 10 per cent of the column feed rate and the external reflux ratio is 2.5. Using the enthalpy composition method, determine the number of theoretical stages required, and the amounts of bottom product and distillate as percentages of the feed rate.

It may be assumed that the enthalpies of liquid and vapour are linear functions of composition. Enthalpy and equilibrium data are provided.

Solution

Basis: 100 kg feed.

An overall material balance gives:

Fxf = Dxd + Wxw + S' xs' and: 50 = 0.95D + 0.05W + 8

Figure 11.32. Enthalpy-composition diagram for carbon tetrachloride-toluene separation with one side-

stream— Example 11.11

Figure 11.32. Enthalpy-composition diagram for carbon tetrachloride-toluene separation with one side-

stream— Example 11.11

From the enthalpy data and the reflux ratio, the upper pole point M may be located as shown in Figure 11.32. Points F and S' are located on the liquid line, and the position of the effective feed, such that F'S'/F'F = 10. NF' is joined and extended to cut x = xw at M, the lower pole point.

MF is Joined and extended to cut NS' at O, the immediate pole point. The number of stages required is then obtained from the figure and

13 theoretical stages are required.

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