Coulson

Question 1

A finely ground mixture of galena and limestone in the proportion of 1 to 4 by mass is subjected to
elutriation by an upward-flowing stream of water flowing at a velocity of 5 mm/s. Assuming that
the size distribution for each material is the same, and is as shown in the following table, estimate
the percentage of galena in the material carried away and in the material left behind. The viscosity
of water is 1 mN s/m2 and Stokes’ equation (3.1) may be used

Answer 1

12. 7% in material removed

35. 4% in material remaining

Question 2

A slurry containing 5 kg of water/kg of solids is to be thickened to a sludge containing 1.5 kg of water/kg of solids in a continuous operation. Laboratory tests using five different concentrations of the slurry yielded the following results:
(table)
Calculate the minimum area of a thickener to effect the separation of 0.6 kg/s of solids

Answer 2

16.5 m2

Question 3

Glass spheres are fluidised by water at a velocity equal to one half of their terminal falling velocities. Calculate:
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(a) the density of the fluidised bed, (b) the pressure gradient in the bed attributable to the presence of the particles.
The particles are 2 mm in diameter and have a density of 2500 kg/m3. The density and viscosity of water are 1000 kg/m3 and 1 mNs/m2 respectively

Answer 3

e =0.755
density =1367 kg/m3
3605 (N/m2)/m

Question 4

A slurry, containing 0.2 kg of solid per kilogram of water, is fed to a rotary drum filter 0.6 m long
and 0.6 m diameter. The drum rotates at one revolution in 360 s and 20 per cent of the filtering
surface is in contact with the slurry at any instant. If filtrate is produced at the rate of 0.125 kg/s
and the cake has a voidage of 0.5, what thickness of cake is produced when filtering with a pressure
difference of 65 kN/m2? The density of the solids is 3000 kg/m3.
The rotary filter breaks down and the operation has to be carried out temporarily in a plate and
frame press with frames 0.3 m square. The press takes 120 s to dismantle and 120 s to reassemble
and, in addition, 120 s is required to remove the cake from each frame. If filtration is to be carried
out at the same overall rate as before, with an operating pressure difference of 175 kN/m2, what is
the minimum number of frames that needs to be used and what is the thickness of each? It may
be assumed that the cakes are incompressible and that the resistance of the filter medium may be
neglected.

Answer 4

Thickness of cake = 5.7 mm
Thickness of cake using filter press = 64 mm
N = 6 frames

Question 5

A slurry is filtered in a plate and frame press containing 12 frames, each 0.3 m square and 25 mm
thick. During the first 180 s the pressure difference for filtration is slowly raised to the final value
of 400 kN/m2 and, during this period, the rate of filtration is maintained constant. After the initial
period, filtration is carried out at constant pressure and the cakes are completely formed in a further
900 s. The cakes are then washed with a pressure difference of 275 kN/m2 for 600 s using thorough
washing (See the plate and frame press in Section 7.4.4). What is the volume of filtrate collected
per cycle and how much wash water is used?
A sample of the slurry had previously been tested with a leaf filter of 0 .05 m2 filtering surface
using a vacuum giving a pressure difference of 71 .3 kN/m2. The volume of filtrate collected in the
first 300 s, was 250 cm3 and, after a further 300 s, an additional 150 cm3 was collected. It may be
assumed that the cake is incompressible and that the cloth resistance is the same in the leaf as in
the filter p

Answer 5

Volume of filtrate= 0.062 m3

Amount of wash water = 0.004 m3

Question 6

A sludge is filtered in a plate and frame press fitted with 25 mm frames. For the first 600 s the
slurry pump runs at maximum capacity. During this period the pressure rises to 415 kN/m2 and
25 per cent of the total filtrate is obtained. The filtration takes a further 3600 s to complete at
constant pressure and 900 s is required for emptying and resetting the press.
It is found that if the cloths are precoated with filter aid to a depth of 1.6 mm, the cloth resistance
is reduced to 25 per cent of its former value. What will be the increase in the overall throughput
of the press if the precoat can be applied in 180 s?

Answer 6

Total cycle time = 5100 s

Increase = 9.1 per cent

Question 7

Filtration is carried out in a plate and frame filter press, with 20 frames 0.3 m square and 50 mm thick, and the rate of filtration is maintained constant for the first 300 s. During this period, the pressure is raised to 350 kN/m2, and one-quarter of the total filtrate per cycle is obtained. At the end of the constant rate period, filtration is continued at a constant pressure of 350 kN/m2 for a further 1800 s, after which the frames are full. The total volume of filtrate per cycle is 0.7 m3 and dismantling and refitting of the press takes 500 s. It is decided to use a rotary drum filter, 1.5 m long and 2.2 m in diameter, in place of the filter press. Assuming that the resistance of the cloth is the same in the two plants and that the filter cake is incompressible, calculate the speed of rotation of the drum which will result in the same overall rate of filtration as was obtained with the filter press. The filtration in the rotary filter is carried out at a constant pressure difference of 70 kN/m2, and the filter operates with 25 per cent of the drum submerged in the slurry at any instant.

Answer 7

The rate of filtration= 2.7×10^−4 m3/s
t =580 s
speed=0.002 Hz (0.12 rpm)

Question 8

A slurry containing 100 kg of whiting, of density 3000 kg/m3, per m3 of water, and, is filtered
in a plate and frame press, which takes 900 s to dismantle, clean, and re-assemble. If the cake is
incompressible and has a voidage of 0.4, what is the optimum thickness of cake for a filtration
pressure (−P) of 1000 kN/m2? The density of the whiting is 3000 kg/m3. If the cake is washed at
500 kN/m2 and the total volume of wash water employed is 25 per cent of that of the filtrate, how is
the optimum thickness of the cake affected? The resistance of the filter medium may be neglected
and the viscosity of water is 1 mNs/m2. In an experiment, a pressure difference of 165 kN/m2
produced a flow of water of 0.02 cm3/s through a centimetre cube of filter cake.

Answer 8

optimum frame thickness = 70 mm

Frame thickness = 59.2 ≈ 60 mm

Question 9

A centrifuge with a phosphor bronze basket, 380 mm in diameter, is to be run at 67 Hz with a 75 mm layer of liquid of density 1200 kg/m3 in the basket. What thickness of walls are required in the basket? The density of phosphor bronze is 8900 kg/m3 and the maximum safe stress for phosphor bronze is 87.6 MN/m2.

Answer 9

Pressure at walls = 2.43 x 10^6 N/m2
Safe stress = 87.6×10^6 N/m2
t= 15.1 mm

Question 10

0.4 kg/s of dry sea-shore sand, containing 1 per cent by mass of salt, is to be washed with 0.4 kg/s of fresh water running countercurrently to the sand through two classifiers in series. It may be assumed that perfect mixing of the sand and water occurs in each classifier and that the sand discharged from each classifier contains one part of water for every two of sand by mass. If the washed sand is dried in a kiln dryer, what percentage of salt will it retain? What wash rate would be required in a single classifier in order to wash the sand to the same extent?

Answer 10

X = 0.001 kg/s
Salt in dried sand = 0.249%
Y = 0.8 kg/s

Question 11

Soda ash is mixed with lime and the liquor from the second of three thickeners and passed to the first thickener where separation is effected. The quantity of this caustic solution leaving the first thickener is such as to yield 10 Mg of caustic soda per day of 24 hours. The solution contains 95 kg of caustic soda/1000 kg of water, whilst the sludge leaving each of the thickeners consists of one part of solids to one of liquid.

Answer 11

thickener = 14.34 per cent
thickener 2 = 0.47 per cent
thickener 3= 0.05 per cent

Question 12

Seeds, containing 20 per cent by mass of oil, are extracted in a countercurrent plant, and 90 per
cent of the oil is recovered in a solution containing 50 per cent by mass of oil. If the seeds are
extracted with fresh solvent and 1 kg of solution is removed in the underflow in association with
every 2 kg of insoluble matter, how many ideal stages are required?

Answer 12

mass fraction of insoluble material in the underflow = 0.667
xSn = 0.3166
xAn = 0.0167
N = 5 thickeners

Question 13

In the production of caustic soda by the action of calcium hydroxide on sodium carbonate, 1 kg/s of sodium carbonate is treated with the theoretical quantity of lime. The sodium carbonate is made up as a 20 per cent solution. The material from the extractors is fed to a countercurrent washing system where it is treated with 2 kg/s of clean water. The washing thickeners are so arranged that the ratio of the volume of liquid discharged in
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the liquid offtake to that discharged with the solid is the same in all the thickeners and is equal to 4.0. How many thickeners must be arranged in series so that not more than 1 per cent of the sodium hydroxide discharged with the solid from the first thickener is wasted?

Answer 13

Vol of soln in underflow=0.188 kg/s
NaOH in underflo =0.00188 kg/s
N = 5 washing thickeners

Question 14

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.

Answer 14

Rmin = 0.323
Heat input to boiler 617 kW
Condenser duty = 372 kW

Question 15

A mixture of water and ethyl alcohol containing 0.16 mole fraction alcohol is continuously distilled in a plate fractionating column to give a product containing 0.77 mole fraction alcohol and a waste of 0.02 mole fraction alcohol. It is proposed to withdraw 25 per cent of the alcohol in the entering stream as a side stream containing 0.50 mole fraction of alcohol. Determine the number of theoretical plates required and the plate from which the side stream should be withdrawn if the feed is liquor at its boiling point and a reflux ratio of 2 is used.

Answer 15

8 plates

fourth plate from the top.

Question 16

A continuous rectifying column handles a mixture consisting of 40 per cent of benzene by mass and 60 per cent of toluene at the rate of 4 kg/s, and separates it into a product containing 97 per cent of benzene and a liquid containing 98 per cent toluene. The feed is liquid at its boiling-point.

(a) Calculate the mass flows of distillate and waste liquor. (b) If a reflux ratio of 3.5 is employed, how many plates are required in the rectifying part of the column?
(b) What is the actual number of plates if the plate-efficiency is 60 per cent?
(c) Mole fraction of benzene in liquid 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Mole fraction of benzene in vapour 0.22 0.38 0.51 0.63 0.7 0.78 0.85 0.91 0.96

Answer 16

Bottoms = 2.4 kg/s
Distillate = 1.6 kg/s
N = 10
Nactual = 17

Question 17

A continuous fractionating column is to be designed to separate 2.5 kg/s of a mixture of 60 per cent toluene and 40 per cent benzene, so as to give an overhead of 97 per cent benzene and a bottom product containing 98 per cent toluene by mass. A reflux ratio of 3.5 kmol of reflux/kmol of product is to be used and the molar latent heat of benzene and toluene may be taken as 30 MJ/kmol. Calculate:
(a) The mass flow of top and bottom products. (b) The number of theoretical plates and position of the feed if the feed is liquid at 295 K, of specific heat capacity 1.84 kJ/kg K. (c) How much steam at 240 kN/m2 is required in the still. (d) What will be the required diameter of the column if it operates at atmospheric pressure and a vapour velocity of 1 m/s. (e) If the vapour velocity is to be 0.75 m/s, based on free area of column, determine the necessary diameter of the column. (f) The minimum possible reflux ratio, and the minimum number of plates for a feed entering at its boiling-point.

Answer 17

N = 10
Fifth from the top
Steam reqd = 0.95 kg/s
Column diameter = 1.67 m
Dt = 2.05 m

Question 18

In order to extract acetic acid from a dilute aqueous solution with isopropyl ether, the two immiscible phases are passed countercurrently through a packed column 3 m in length and 75 mm in diameter. It is found that if 0.5 kg/m2 of the pure ether is used to extract 0.25 kg/m2s of 4.0 per cent acid by mass, then the ether phase leaves the column with a concentration of 1.0 per cent acid by mass. Calculate:
(a) the number of overall transfer units, based on the raffinate phase, and (b) the overall extraction coefficient, based on the raffinate phase.

Answer 18

N = 5.53
Ka = 0.461 kg/m^3 s (kg/kg)
Conc of acid in extract = 1%
Conc of acid in raffinate = 2%

Question 19

A forward-feed double-effect evaporator, having 10 m2 of heating surface in each effect, is used to concentrate 0.4 kg/s of caustic soda solution from 10 to 50 per cent by mass. During a particular run, when the feed is at 328 K, the pressures in the two calandrias are 375 and 180 kN/m2 respectively, and the condenser operates at 15 kN/m2. For these conditions, calculate: (a) the load on the condenser; (b) the steam economy and (c) the overall heat transfer coefficient in each effect. Would there be any advantages in using backward feed in this case? Heat losses to the surroundings are negligible.

Answer 19

Load on condenser = 0.15 kg/s
U1 = 2.53 kW/m^2K
U2 = 1.84 kW/m^2K

Question 20

A forward-feed double-effect standard vertical evaporator with equal heating areas in each effect is fed with 5 kg/s of a liquor of specific heat capacity of 4.18 kJ/kgK, and with no boiling-point rise, so that 50 per cent of the feed liquor is evaporated. The overall heat transfer coefficient in the second effect is 75 per cent of that in the first effect. Steam is fed at 395 K and the boiling-point in the second effect is 373 K. The feed is heated to its boiling point by an external heater in the first effect. It is decided to bleed off 0.25 kg/s of vapour from the vapour line to the second effect for use in another process. If the feed is still heated to the boiling-point of the first effect by external means, what will be the change in the steam consumption of the evaporator unit? For the purposes of calculation, the latent heat of the vapours and of the live steam may be taken as 2230 kJ/k

Answer 20

Do = 1.21 kg/s
Do = 1.33 kg/s
Change in steam consumption = 0.12 kg/s

Question 21

1.25 kg/s of a solution is concentrated from 10 to 50 per cent solids in a triple-effect evaporator using steam at 393 K, and a vacuum such that the boiling point in the last effect is 325 K. If the feed is initially at 297 K and backward feed is used, what is the steam consumption, the temperature distribution in the system and the heat transfer area in each effect, each effect being identical? For the purpose of calculation, it may be assumed that the specific heat capacity is 4.18 kJ/kgK, that there is no boiling point rise, and that the latent heat of vaporisation is constant at 2330 kJ/kg over the temperature range in the system. The overall heat transfer coefficients may be taken as 2.5, 2.0 and 1.6 kW/m2 K in the first, second and third effects, respectively.

Answer 21

Area = 18 m^2
Steam consumption = 0.432 kg/s
Temp in each effect = 374 K, 350K, 325 K

Question 22

A triple-effect backward-feed evaporator concentrates 5 kg/s of liquor from 10 per cent to 50 per cent solids. Steam is available at 375 kN/m2 and the condenser operates at 13.5 kN/m2. What is the area required in each effect, assumed identical, and the economy of the unit? The specific heat capacity is 4.18 kJ/kgK at all concentrations and that there is no boiling-point rise. The overall heat transfer coefficients are 2.3, 2.0 and 1.7 kW/m2 K respectively in the three effects, and the feed enters the third effect at 300 K.

Answer 22

Steam economy = 2.52

Area for each effect = 57 m^2

Question 23

A triple-effect evaporator is fed with 5 kg/s of a liquor containing 15 per cent solids. The concentration in the last effect, which operates at 13.5 kN/m2, is 60 per cent solids. If the overall heat transfer coefficients in the three effects are 2.5, 2.0, and 1.1 kW/m2 K, respectively, and the steam is fed at 388 K to the first effect, determine the temperature distribution and the area of heating surface required in each effect? The calandrias are identical. What is the economy and what is the heat load on the condenser? The feed temperature is 294 K and the specific heat capacity of all liquors is 4.18 kJ/kgK.

Answer 23

T = 368, 354, 325 K
A = 89 m^2
Economy = 2.0
Heat load on condenser = 31.8 kW

Question 24

A single-effect evaporator with a heating surface area of 10 m2 is used to concentrate a NaOH solution flowing at 0.38 kg/s from 10 per cent to 33.3 per cent. The feed enters at 338 K and its specific heat capacity is 3.2 kJ/kgK. The pressure in the vapour space is 13.5 kN/m2 and 0.3 kg/s of steam is used from a supply at 375 K. Calculate:
(a) The apparent overall heat transfer coefficient. (b) The coefficient corrected for boiling point rise of dissolved solids. (c) The corrected coefficient if the depth of liquid is 1.5 m.

Answer 24

U1 = 1.28 kW/m^2 K
U1 = 2.21 kW/m^2 K
U1 = 1.89 kW/m^2 K
U1 = 1.43 kW/m^2 K

Question 25

10 Mg of a solution containing 0.3 kg Na2CO3/kg solution is cooled slowly to 293 K to form crystals of Na2CO3.10H2O. What is the yield of crystals if the solubility of Na2CO3 at 293 K is 21.5 kg/100 kg water and during cooling 3 per cent of the original solution is lost by evaporation?

Answer 25

6536 g

Question 26

Glauber’s salt, Na2SO4.10H2O, is to be produced in a Swenson–Walker crystalliser by cooling to 290 K a solution of anhydrous Na2SO4 which saturates between 300 K and 290 K. If cooling water enters and leaves the unit at 280 K and 290 K respectively and evaporation is negligible, how many sections of crystalliser, each 3 m long, will be required to process 0.25 kg/s of the product? The solubilities of anhydrous Na2SO4 in water are 40 and 14 kg/100 kg water at 300 K and 290 K respectively, the mean heat capacity of the liquor is 3.8 kJ/kgK and the heat of crystallisation is 230 kJ/kg. For the crystalliser, the available heat transfer area is 3 m2/m length, the overall coefficientof heat transfer is 0.15 kW/m2 K and the molecular masses are Na2SO4.10H2O=322 kg/kmol and Na2SO4 =142 kg/kmol.

Answer 26

Feed rate = 0.487 kg/s
A = 50.67 m^2
N = 6 sections

Question 27

A double-effect forward-feed evaporator is required to give a product consisting of 30 per cent crystals and a mother liquor containing 40 per cent by mass of dissolved solids. Heat transfer coefficients are 2.8 and 1.7 kW/m2 K in the first and second effects respectively. Dry saturated steam is supplied at 375 kN/m2 and the condenser operates at 13.5 kN/m2.
(a) What area of heating surface is required in each effect, assuming they are both identical, if the feed rate is 0.6 kg/s of liquor, containing 20 per cent by mass of dissolved solids, and the feed temperature is 313 K? (b) What is the pressure above the boiling liquid in the first effect?
The specific heat capacity may be taken as constant at 4.18 kJ/kgK, and the effects of boiling point rise and of hydrostatic head may be neglected.

Answer 27

A = 5.06 m^2
P = atmospheric

Question 28

Strips of a material 10 mm thick are dried under constant drying conditions from 28 per cent to 13 per cent moisture in 25 ks. If the equilibrium moisture content is 7 per cent, what is the time taken to dry 60 mm planks from 22 to 10 per cent moisture under the same conditions, assuming no loss from the edges? All moisture contents are expressed on the wet basis. The relation between E, the ratio of the average free moisture content at time t to the initial free moisture content, and the parameter f is given by: E 1 0.64 0.49 0.38 0.295 0.22 0.14 f 0 0.1 0.2 0.3 0.5 0.6 0.7 where f = kt/l2, k is a constant, t is the time in ks and 2l is the thickness of the sheet of material in mm.

Answer 28

T = 1090 ks or 12.6 days

Question 29

A granular material containing 40 per cent moisture is fed to a countercurrent rotary dryer at a
temperature of 295 K and is withdrawn at 305 K, containing 5 per cent moisture. The air supplied,
which contains 0.006 kg water vapour/kg dry air, enters at 385 K and leaves at 310 K. The dryer
handles 0.125 kg/s wet stock.
Assuming that radiation losses amount to 20 kJ/kg dry air used, determine the mass flowrate of
dry air supplied to the dryer and the humidity of the exit air

Answer 29

G = 2.07 kg/s
Heat content of dried solid = 2.59 kW
Humidity = 0.0284 kg/kg d.a.