Chapter 2 - Mass Balance in non-reactive systems - exercises PDF

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CAPÍTULO 2

Exercise 2-1

Desalination of sea water by freezing. One of the processes of obtaining fresh water from sea water is by partial freezing of it, with the formation of pure ice and a more concentrated salt solution. If sea water contains 3.5% w/w NaCl and if it is desired to concentrate the saline solution to 7% w/w, calculate the amount of sea water required for each kilogram of ice formed. Exercise 2-2 The residual acid from a nitration process contains 23% w/w HNO3, 57% w/w H2SO4 and 20% w/w H2O by weight. It is intended to concentrate this acid to contain 27% w/w HNO3 and 60% w/w H2SO4, adding concentrated sulfuric acid, containing 93% w/w H2SO4 and concentrated nitric acid containing 90% w/w of HNO3. Calculate the quantities of the residual acid and the concentrated acids to be employed to obtain 1000 lb of the desired blend. Exercise 2-3 A benzene-impregnated filter material containing 20% benzene and 80% of inerts is dried in a countercurrent flow dryer, using hot nitrogen. The nitrogen enters dry and leaves the dryer with 0.70 lb benzene per pound of N2. The solids contain after drying 4% benzene by weight. How many pounds of nitrogen pass through the dryer per pound of inert solids?

Exercise 2-4

Liquid-liquid extraction. A 20% w/w acrylamide solution in benzene is mixed with water in order to remove (extract) the acrylamide, since this is more soluble in water than in benzene. The mixture is then pumped to a tank where an organic phase containing 1% acrylamide and an aqueous phase containing 60% acrylamide are separated by densities. All percentages are by weight. Assuming that benzene and water are completely immiscible, calculate the water/benzene ratio that must be used to perform the extraction.

2

Exercise 2-5

a)

The feed to a refinery distillation column consists of a mixture of propane, butane and pentane, in the same proportion by weight, at a mass flow rate of 10,000 lb/h. The product at the top of the column contains 90% propane, 7% butane and 3% pentane and is produced at a flow rate of 2,800 lb/h. The side stream is produced at a flow rate of 3,500 lb/h and contains 20% propane, 70% butane and the balance in pentane. Calculate the flow rate of the waste and its composition.

b)

If the reserve tank is 3 ft in diameter and its level reaches 3 ft during an hour of operation, what is the flow of the side stream? (Assume 37.5 lb/ft3 as the current density)

Top stream product

Feed

Side stream

Bottom stream product

3 Exercise 2-6 D = 75

F

XDA = 0.9733 XDB = 0.02 XDC = ?

= 100

XFA = 0.74 XFB = 0.20 XFC = ?

XWA = ? XWB = ? XWC = ?

W = ?

Exercise 2-7 Refer to the exercise 2-6: F = 100 ; D = 75 ; W = 25 moles/h e XFA = 0.74 ; =0.04 .

XDA = 0.9733

XWA

Calculate: XFB, XDB, XDC, XWB, XWC.

Exercise 2-8 The figure below represents a fractionation column, operating continuously, under stationary steady conditions. The feed contains propane, butane and pentane, being 1 000 lb/h. The feed stream is continuously separated into propane-rich top stream and bottom product rich in butane and pentane.

Feed

G

Reflux D

Distiled

Recycle F

REBOILER

A

Column

CONDENS.

E

Residue

B

C

4 Part of the upper stream is recycled in form of reflux, the same happening to the lower stream. The upper stream contains 80% propane and 20% butane. The bottom stream contains 10% propane, 40% butane and 50% pentane. The flow rates are as follows: Total top current 600 lb/h, Recycle F, 300 lb/h, and the total bottom stream, 1000 lb/h. a)

Calculate the amount of reflux D returned per hour.

b)

What is the percentage of propane of the feed that is lost at the bottom stream?

Exercise 2-15

G

Benzeno

B

Acumulador

Feed

F

1

L

Xylene

2

X

Toluene

T

A mixture of toluene, benzene and xylene is separated by continuous fractionation in a series of two columns. A column 1 has xylene as the bottom product and a mixture of benzene and toluene as the top product. The top product is pumped into a storage tank, after which it feeds the column 2. In this column, benzene is the top product and toluene, the bottom product. The flow diagram is presented in the figure. The analysis of the process, after 24 hours, gave the following compositions: The accumulation tank has the capacity of 24 gallons/in. The liquid level at the beginning of the operation is 36 in and at the end, 62 in. a) What is the flow rate at the top of column 1? b) What is the composition and volume of the feed during 24 hour operation? c) What are the top and bottom flow rates of column 2, if the level of the accumulation tank remains constant during the 24 hours operation, if the same feed rate is used?

5

column 1

column 2

PRODUCT AT THE BOTTOM

PRODUCT AT THE TOP

PRODUCT AT THE BOTTOM

18.200

13.300

20.900

98.5 1.5 0.0

1.0 98.5 0.5

GALLONS A 60ºF

Composition: % v/v Benzene Toluene Xylene

0.0 0.7 99.3

Exercise 2-16 A wastewater treatment plant operates under stationary conditions, processing water containing 500 parts per million of toxic impurities. The impurities are removed with virtually no water loss. Local legislation imposes 100 ppm as the maximum limit of impurities for discharging the nearby river. The treatment plant reduces impurities up to 10 ppm. What is the fraction of untreated wastewater that can follow the by-pass?

Exercise 2-17 Purification of milk in a by-passing operation. One process of removing radioactive strontium, Sr90, in milk is to contact the latter with a bed of HPO4-2. The process is so efficient that in fact, all the strontium can be removed from the milk; However, at the same time 97% of Ca+2 is absorbed. This raises the problem that health regulations impose a minimum limit of Ca+2 in milk of 0.05 mg/l. Thus, it is intended to process a milk containing 4.85 EXP (-14) g/l Sr90 and 1 mg/l Ca+2, so as to remove the maximum Sr90 compatible with the minimum Ca+2 content. Calculate the concentration of Strontium in the total effluent, for a plant operating at steady state.

6 Exercise 2-18 Recycling in drying. In order to achieve a slow drying rate and to prevent cracking of the material, the specifications for a particular product require the drying conditions to be at 23.8 C and 70% relative humidity. The air leaves at a relative humidity of 95%. Knowing that fresh air (ambient) has a dew point of 4.4ºC, calculate the fraction of air that passes through the dryer that has to be recycled, so that its mixture with fresh air results in the humidity required by the specifications for drying. Exercise 2-19 A wet material containing 1.50 lb of water/lb of the dried material is dried to a moisture content of 5.2% w/w. For this purpose the wet material is introduced into a continuous dryer, operating in countercurrent and with air recycling. For every 2.50lb of wet material entering, 50 lb of the dry air passes through the dryer, containing 0.06 lb of water/lb of dry air in the outlet. The unit operates at a constant temperature of 140 F. Fresh air is supplied with 0.005 lb of water/lb of dry air. a) Calculate the recycling rate. b) Calculate the amount of fresh, un-recycled moist air. c) Calculate the partial pressure of the water vapor at the outlet of the dryer. Exercise 2-20

A pigment containing 20% w/w water is dried to 5% w/w moisture, in an continuous dryer. The air entering the dryer consists a fresh air mixture containing 0.01 lb water/lb dry air and recycled air with 0.1 lb water/lb dry. The ratio of fresh and recycled air at the dryer inlet is 1: 3 on the dry basis. a) How many pounds of water are removed per 1000lbs of wet pigment? b) Calculate the amount of recycled air per 1000lbs of wet pigment?

Exercise 2-21 The diagram below represents two distillation columns, in which the feed is a solution of compounds A, B, and C.

Accumulator Of the top 2

Column 2

F

Accumulator Of the top 1

Column 1

Feed

Cond 2

Cond 1

7

K

M

Reb. 2

Reb. 1

Bottom accumulator 2

Bottom accumulator 1

N L These compounds are so similar that it may be considered to form an ideal solution. Column 1 yields the C-rich bottom product. The top stream of this column consists of A and B, which are separated in column 2, to yield the top and bottom fraction. The temperatures of the accumulators, the feed and all the streams are fixed.

In 24 hour operation the following products were discharged:

Column 2

Column 1 L Volume Composition (% vol.) A B C

During

this

same

M

N

5 220

7 690

6 600

0.1 2.7 97.2

98.0 1.9 0.1

0.8 99.0 0.2

period

the

level

of

the

liquid

in

the

8 accumulators changed, according to the table below:

Accumulator Accumulator Accumulator Accumulator

top bott top bott

Volume of liquid (gal/in level)

Initial level (in)

Final Level (in)

59 27 41 32

20 47 69 52

17 70 69 40

1 1 2 2

a) What is the volume and composition of the feed? b) What is the flow rate from the top accumulator 1? c) If the feed was the same as that calculated in (a) and there were no changes in the inventories of the reboiler, column and accumulators during operation, what would be the quantities K, L, M and N.

Exercise 2-22 In the operation represented by the flow chart below, the stationary conditions were reached. During the operation the quantities of the various streams are in pounds. What is the quantity of the feed F? (W) 2600 (M)

(Q)4500

(B)24400

1

(S)23800

(D)18700

3

2

(C)

(A)

(T) 3200

(G) 8000 (V) (F)

(P) 12000

(E) 25200

4

9

Exercise 2-23 The installation shown in the figure operates on a continuous basis. During 1 hour of operation the following data were collected: There is no accumulation or depletion in unit 1; 1000 lb load A, oxygen-free enter the unit; 2000 lb of solvent X enter with 35.0% oxygen. Stream W contains 33.3% oxygen. Feed F analyzes 82.5% carbon and 17.2% hydrogen.

Unit 3 Accumulator

X

D A

Unit 1 Extraction

F

T

UNIT 2 Distilation

W

L

P

B R

UNIT 4 Holding tank.

N There is no accumulation there is an accumulation draw-off N. An overhead contains 80.0% carbon and

or depletion in units 2 and 3. However, of 100 lb of B in tank 4, despite the product of 400 lb is drawn off P. Its 20.0% hydrogen.

The total feed T contains 83.3% carbon and 16.7% hydrogen. Using as a basis of calculation 1000 lb of the load A entering into the system, determine the R / F recycling rate....