Separation Process Principles

J. D. Seader, Ernest J. Henley

Chapter 5 Cascades and Hybrid Systems - all with Video Answers

Educators

Chapter Questions

Problem 1

Devise an interlinked cascade of the type shown in Figure $5.2 \mathrm{e}$, but consisting of three columns for the separation of a four-component feed into four products.

Victor Salazar

Numerade Educator

01:04

Problem 2

A liquid-liquid extraction process is conducted batchwise as shown in Figure $5.23$. The process begins in vessel 1 (original),

Hast Aggarwal

Numerade Educator

04:43

Nitrogen is to be removed from a gas mixture with methane by gas permeation (see Table 1.2) using a glassy polymer membrane that is selective for nitrogen. However, the desired degree of separation cannot be achieved in one stage. Draw sketches of two different two-stage membrane cascades that might be considered to perform the desired separation.

Marissa Turner

Numerade Educator

04:03

Problem 4

In Example $4.9,83.25 \%$ of the oil in soybeans is leached by benzene using a single equilibrium stage. Calculate the percent extraction of oil if:
(a) Two countercurrent equilibrium stages are used to process $5,000 \mathrm{~kg} / \mathrm{h}$ of soybean meal with $5,000 \mathrm{~kg} / \mathrm{h}$ of benzene.
(b) Three countercurrent equilibrium stages are used to process the same flows as in part (a).
(c) Also, determine the number of countercurrent equilibrium stages required to extract $98.5$ of the oil if a solvent rate of twice the minimum value is used.

Susan Hallstrom

Numerade Educator

01:32

Problem 5

For Example 5.1, involving the separation of sodium carbonate from an insoluble oxide, compute the minimum solvent feed rate in pounds per hour. What is the ratio of actual solvent rate to the minimum solvent rate? Determine and plot the percent recovery of soluble solids with a cascade of five countercurrent equilibrium stages for solvent flow rates from $1.5$ to $7.5$ times the minimum value.

Penny Riley

Numerade Educator

12:21

Problem 6

Aluminum sulfate, commonly called alum, is produced as a concentrated aqueous solution from bauxite ore by reaction with aqueous sulfuric acid, followed by a three-stage, countercurrent washing operation to separate soluble aluminum sulfate from the insoluble content of the bauxite ore, followed by evaporation. In a typical process, $40,000 \mathrm{~kg} /$ day of solid bauxite ore containing 50 wr $\% \mathrm{Al}_{2} \mathrm{O}_{3}$ and $50 \%$ inert is crushed and fed together with the stoichiometric amount of $50 \mathrm{wt}$. aqueous sulfuric acid to a reactor, where the $\mathrm{Al}_{2} \mathrm{O}_{3}$ is reacted completely to alum by the reaction
$$
\mathrm{Al}_{2} \mathrm{O}_{3}+3 \mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}+3 \mathrm{H}_{2} \mathrm{O}
$$
The slurry effluent from the reactor (digester), consisting of solid inert material from the ore and an aqueous solution of aluminum sulfate is then fed to a three-stage, countercurrent washing unit to separate the aqueous aluminum sulfate from the inert material. If the solvent is $240,000 \mathrm{~kg} /$ day of water and the underflow from each washing stage is 50 wt\% water on a solute-free basis, compute the flow rates in kilograms per day of aluminum sulfate, water, and inert solid in each of the two product streams leaving the cascade. What is the percent recovery of the aluminum sulfate? Would the addition of one more stage be worthwhile?

Dr. Satish Ingale

Numerade Educator

01:27

Problem 7

(a) When rinsing clothes with a given amount of water, would one find it more efficient to divide the water and rinse several times; or should one use all the water in one rinse? Explain.
(b) Devise a clothes-washing machine that gives the most efficient rinse cycle for a fixed amount of water.

Zulfiqar Ali

Numerade Educator

05:09

Problem 8

An aqueous acetic-acid solution containing $6.0$ moles of acid per liter is to be extracted in the laboratory with chloroform at $25^{\circ} \mathrm{C}$ to recover the acid (B) from chloroform-insoluble impurities present in the water. The water (A) and chloroform (C) are essentially immiscible. If 10 liters of solution are to be extracted at $25^{\circ} \mathrm{C}, \mathrm{cal}-$ culate the percent extraction of acid obtained with 10 liters of chloroform under the following conditions:
(a) Using the entire quantity of solvent in a single batch extraction
(b) Using three batch extractions with one-third of the total solvent used in each batch
(c) Using three batch extractions with 5 liters of solvent in the first, 3 liters in the second, and 2 liters in the third batch

Assume that the volumetric amounts of the feed and solvent do not change during extraction. Also, assume the distribution coefficient for the acid, $K_{D_{B}}^{(\mu}=\left(c_{B}\right) c /\left(c_{B}\right)_{A}=2.8$, where $\left(c_{B}\right)_{C}=$ concentration of acid in chloroform and $\left(c_{B}\right)_{A}=$ concentration of acid in water, both in moles per liter.

Eileen Sullivan

Numerade Educator

01:28

Problem 9

A 20 wt $\%$ solution of uranyl nitrate (UN) in water is to be treated with tributyl phosphate (TBP) to remove $90 \%$ of the uranyl nitrate. All operations are to be batchwise equilibrium contacts. Assuming that water and TBP are mutually insoluble, how much TBP is required for $100 \mathrm{~g}$ of solution if at equilibrium (g UN/g TBP) $=$ $5.5\left(\mathrm{~g} \mathrm{UN} / \mathrm{g} \mathrm{H}_{2} \mathrm{O}\right)$ and:
(a) All the TBP is used at once in one stage?
(b) Half is used in each of two consecutive stages?

David Collins

Numerade Educator

01:28

Problem 10

The uranyl nitrate (UN) in $2 \mathrm{~kg}$ of a 20 wt $\%$ aqueous solution is to be extracted with $500 \mathrm{~g}$ of tributyl phosphate. Using the equilibrium data in Exercise 5.9, calculate and compare the percentage recoveries for the following alternative procedures:
(a) A single-stage batch extraction
(b) Three batch extractions with one-third of the total solvent used in each batch (the solvent is withdrawn after contacting the entire UN phase)
(c) A two-stage cocurrent extraction
(d) A three-stage countercurrent extraction
(e) An infinite-stage countercurrent extraction
(f) An infinite-stage crosscurrent extraction

David Collins

Numerade Educator

01:20

Problem 11

One thousand kilograms of a 30 wt\% dioxane in water solution is to be treated with benzene at $25^{\circ} \mathrm{C}$ to remove $95 \%$ of the dioxane. The benzene is dioxane-free, and the equilibrium data of Example $5.2$ can be used. Calculate the solvent requirements for:
(a) A single batch extraction
(b) Two crosscurrent stages using equal amounts of benzene
(c) Two countercurrent stages
(d) An infinite number of crosscurrent stages
(e) An infinite number of countercurrent stages

Hast Aggarwal

Numerade Educator

05:02

Problem 12

Chloroform is to be used to extract benzoic acid from wastewater effluent. The benzoic acid is present at a concentration of $0.05$ molliter in the effluent, which is discharged at a rate of 1,000 liter/h. The distribution coefficient for benzoic acid at process conditions is given by
$$
c^{\mathbb{I}}=K_{D}^{\mathbb{I}} c^{\mathbb{I}}
$$
where $K_{D}^{\mathrm{II}}=4.2, c^{1}=$ molar concentration of solute in solvent, and $c^{\mathrm{II}}=$ molar concentration of solute in water. Chloroform and water may be assumed immiscible. If 500 liters/h of chloroform is to be used, compare the fraction benzoic acid removed in
(a) A single equilibrium contact
(b) Three crosscurrent contacts with equal portions of chloroforn
(c) Three countercurrent contacts

Rashmi Sinha

Numerade Educator

06:30

Problem 13

Repeat Example $5.2$ with a solvent for which $E=0.90$. Display your results in a plot like Figure 5.7. Does countercurrent flow still have a marked advantage over crosscurrent flow? Is it desirable to choose the solvent and solvent rate so that $E>1 ?$ Explain.

Susan Hallstrom

Numerade Educator

01:27

Problem 14

Repeat Example $5.3$ for $N=1,3,10$, and 30 stages. Plot the percent absorption of each of the five hydrocarbons and the total feed gas, as well as the percent stripping of the oil versus the number of stages, $N$. What can you conclude about the effect of the number of stages on each component?

Ahmed Ali

Numerade Educator

00:37

Problem 15

Solve Example $5.3$ for an absorbent flow rate of $330 \mathrm{lbmol/h}$ and three theoretical stages. Compare your results to the results of Example $5.3$ and discuss the effect of trading stages for absorbent flow.

Amy Jiang

Numerade Educator

06:12

Problem 16

Estimate the minimum absorbent flow rate required for the separation calculated in Example $5.3$ assuming that the key component is propane, whose flow rate in the exit vapor is to be $155.4 \mathrm{lbmol} / \mathrm{h}$.

Chareen Guzman

Numerade Educator

08:40

Problem 17

Solve Example $5.3$ with the addition of a heat exchanger at each stage so as to maintain isothermal operation of the absorber at
(a) $125^{\circ} \mathrm{F}$
(b) $150^{\circ} \mathrm{F}$
What is the effect of temperature on absorption in the range of 100 to $150^{\circ} \mathrm{F}$ ?

Averell Hause

Carnegie Mellon University

07:51

Problem 18

One million pound-moles per day of a gas of the following composition is to be absorbed by $n$-heptane at $-30^{\circ} \mathrm{F}$ and 550 psia in an absorber having 10 theoretical stages so as to absorb $50 \%$ of the ethane. Calculate the required flow rate of absorbent and the distribution, in $\mathrm{Ibmol} / \mathrm{h}$, of all the components between the exiting gas and liquid streams.
$\begin{array}{ccc} & & K \text {-value @ } \\ \text { Component } & \begin{array}{c}\text { Mole Percent } \\ \text { in Feed Gas }\end{array} & \begin{array}{c}-30^{\circ} \mathrm{F} \text { and } \\ 550 \mathrm{psia}\end{array} \\ \mathrm{C}_{1} & 94.9 & 2.85 \\ \mathrm{C}_{2} & 4.2 & 0.36 \\ \mathrm{C}_{3} & 0.7 & 0.066 \\ n \mathrm{C}_{4} & 0.1 & 0.017 \\ n \mathrm{C}_{5} & 0.1 & 0.004\end{array}$

Niamat Khuda

Numerade Educator

06:24

Problem 19

A stripper operating at 50 psia with three equilibrium stages is used to strip $1,000 \mathrm{kmol} / \mathrm{h}$ of liquid at $300^{\circ} \mathrm{F}$ having the following molar composition: $0.03 \% \mathrm{C}_{1}, 0.22 \% \mathrm{C}_{2}, 1.82 \% \mathrm{C}_{3}, 4.47 \%$ $n \mathrm{C}_{4}, 8.59 \% n \mathrm{C}_{5}, 84.87 \% n \mathrm{C}_{10}$. The stripping agent is $1,000 \mathrm{kmol} / \mathrm{h}$ of superheated steam at $300^{\circ} \mathrm{F}$ and 50 psia. Use the Kremser equaltion to estimate the compositions and flow rates of the stripped liquid and exiting rich gas.

Assume a $K$-value for $\mathrm{C}_{10}$ of $0.20$ and assume that no steam is absorbed. However, calculate the dew-point temperature of the exiting rich gas at $50 \mathrm{psia}$. If that temperature is above $300^{\circ} \mathrm{F}$, what would you suggest be done?

James Kiss

Numerade Educator

04:34

Problem 20

In Figure $5.12$, is anything gained by totally condensing the vapor leaving each stage? Alter the processes in Figure 5.12a and $5.12 b$ so as to eliminate the addition of heat to stages 2 and 3 and still achieve the same separations.

Susan Hallstrom

Numerade Educator

04:46

Problem 21

Repeat Example $5.4$ for external reflux flow rates $L_{0}$ of
(a) $1,500 \mathrm{lbmol} / \mathrm{h}$
(b) $2,000 \mathrm{lbmol} / \mathrm{h}$
(c) $2,500 \mathrm{lbmol} / \mathrm{h}$
Plot $d_{\mathrm{C}_{9}} / b_{\mathrm{C}_{2}}$ as a function of $L_{0}$ from 1,000 to $2,500 \mathrm{lbmol} / \mathrm{h}$. In making the calculations, assume that stage temperatures do not change from the results of Example 5.4. Discuss the effect of reflux ratio on the separation.

Hariprasad Annamalai

Numerade Educator

01:54

Problem 22

Repeat Example $5.4$ for the following numbers of equilibrium stages (see Figure 5.15):
(a) $M=10, N=10$
(b) $M=15, N=15$
Plot $d c_{3} / b c_{3}$ as a function of $M+N$ from 10 to 30 stages. In making the calculations, assume that state temperatures and total flow rates do not change from the results of Example 5.4. Discuss the effect of the number of stages on the separation.

Kyle Gassaway

Numerade Educator

02:56

Problem 23

Use the Edmister group method to determine the compositions of the distillate and bottoms for the distillation operation shown in Figure 5.24. At column conditions, the feed is approximately $23 \mathrm{~mol} \%$ vapor.

Eileen Sullivan

Numerade Educator

01:30

Problem 24

A bubble-point liquid feed is to be distilled as shown in Figure 5.25. Use the Edmister group method to estimate the molefraction compositions of the distillate and bottoms. Assume initial overhead and bottoms temperatures are 150 and $250^{\circ} \mathrm{F}$, respectively.

Kratika Bhadauria

Numerade Educator

04:00

Problem 25

Verify the values given in Table $5.3$ for $N_{V}, N_{E}$, and $N_{D}$ for a partial reboiler and a total condenser.

Thomas Emment

Numerade Educator

01:27

Problem 26

Verify the values given in Table $5.3$ for $N_{V}, N_{E r}$ and $N_{D}$ for a stream mixer and a stream divider.

Manik Pulyani

Numerade Educator

06:18

Problem 27

A mixture of maleic anhydride and benzoic acid containing $10 \mathrm{~mol} \%$ acid is a product of the manufacture of phthalic anhydride. The mixture is to be distilled continuously in a column with a total condenser and a partial reboiler at a pressure of $13.2 \mathrm{kPa}$ (100 torr) with a reflux ratio of $1.2$ times the minimum value to give a product of $99.5 \mathrm{~mol} \%$ maleic anhydride and a bottoms of $0.5 \mathrm{~mol} \%$ anhydride. Is this problem completely specified?

Pam Owens

Numerade Educator

03:49

Problem 28

Verify $N_{D}$ for the following unit operations in Table $5.4:(b)$, (c), and (g). How would $N_{D}$ change if two feeds were used instead of one?

P Krishnamurthy

Numerade Educator

01:37

Problem 29

Verify $N_{D}$ for unit operations $(e)$ and $(f)$ in Table $5.4$. How would $N_{D}$ change if a vapor side stream was pulled off some stage located between the feed stage and the bottom stage?

Narayan Hari

Numerade Educator

02:09

Problem 30

Verify $N_{D}$ for unit operation $(h)$ in Table $5.4$. How would $N_{D}$ change if a liquid side stream was added to a stage that was located between the feed stage and stage 2 ?

Arwa Ali

Numerade Educator

02:00

Problem 31

The following are not listed as design variables for the distillation unit operations in Table 5.4:
(a) Condenser heat duty
(b) Stage temperature
(c) Intermediate-stage vapor rate
(d) Reboiler heat load
Under what conditions might these become design variables? If so, which variables listed in Table $5.4$ would you eliminate?

Joseph Fritchman

Numerade Educator

05:23

Problem 32

Show for distillation that, if a total condenser is replaced by a partial condenser, the number of degrees of freedom is reduced by 3 , provided that the distillate is removed solely as a vapor.

Eric Mockensturm

Numerade Educator

01:12

Problem 33

Unit operation (b) in Table $5.4$ is to be heated by injecting live steam directly into the bottom plate of the column instead of by using a reboiler, for a separation involving ethanol and water. Assuming a fixed feed, an adiabatic operation, atmospheric pressure throughout, and a top alcohol concentration specification:
(a) What is the total number of design variables for the general configuration?
(b) How many design variables are needed to complete the design? Which variables do you recommend?

Manik Pulyani

Numerade Educator

16:21

Problem 34

(a) For the distillation column shown in Figure $5.26$, determine the number of independent design variables.
(b) It is suggested that a fced consisting of $30 \% \mathrm{~A}, 20 \% \mathrm{~B}$, and $50 \% \mathrm{C}$, all in moles, at $37.8^{\circ} \mathrm{C}$ and $689 \mathrm{kPa}$, be processed in the unit of Figure $5.26$, consisting of a 15 -plate, 3 -m-diameter column that is designed to operate at vapor velocities of $0.3 \mathrm{~m} / \mathrm{s}$ and an $L / V$ of 1.2. The pressure drop per plate is $373 \mathrm{~Pa}$ at these conditions, and the condenser is cooled by plant water at $15.6^{\circ} \mathrm{C}$.

The product specifications in terms of the concentration of $\mathrm{A}$ in the distillate and $\mathrm{C}$ in the bottoms have been set by the process department, and the plant manager has asked you to specify a feed rate for the column. Write a memorandum to the plant manager pointing out why you can't do this, and suggest some alternatives.

Chareen Guzman

Numerade Educator

03:36

Problem 35

Calculate the number of degrees of freedom for the mixedfeed, triple-effect evaporator system shown in Figure 5.27. Assume that the steam and all drain streams are at saturated conditions and the foed is an aquecous solution of a dissolved organic solid. Also,

Mohammad Mehran

Numerade Educator

01:30

Problem 36

A reboiled stripper as shown in Figure $5.28$ is to be designed for the task shown. Determine
(a) The number of variables.
(b) The number of equations relating the variables.
(c) The number of degrees of freedom and indicate.
(d) Which additional variables, if any, need to be specified.

Timothy Telesca

Numerade Educator

01:01

Problem 37

The thermally coupled distillation system shown in Figure $5.29$ is to be used to separate a mixture of three components into three products. Determine for the system
(a) The number of variables.
(b) The number of equations relating the variables.
(c) The number of degrees of freedom and propose.
(d) A reasonable set of design variables.

Narayan Hari

Numerade Educator

00:00

Problem 38

When the feed to a distillation column contains a small amount of impurities that are much more volatile than the desired distillate, it is possible to separate the volatile impurities from the distillate by removing the distillate as a liquid sidestream from a stage located several stages below the top stage. As shown in Figure $5.30$, this additional top section of stages is referred to as a pasteurizing section.
(a) Determine the number of degrees of freedom for the unit
(b) Determine a reasonable set of design variables

Jennifer Stoner

Numerade Educator

02:27

Problem 39

A system for separating a mixture into three products is shown in Figure 5.31. For it, determine
(a) The number of variables.
(b) The number of equations relating the variables.
(c) The number of degrees of freedom and propose.
(d) A reasonable set of design variables.

Ankit Gupta

Numerade Educator

04:40

Problem 40

A system for separating a binary mixture by extractive distillation, followed by ordinary distillation for recovery and recycle of the solvent, is shown in Figure 5.32. Are the design variables shown sufficient to specify the problem completely? If not, what additional design variables(s) would you select?

Ronald Prasad

Numerade Educator

00:54

Problem 41

A single distillation column for separating a threecomponent mixture into three products is shown in Figure $5.33$. Are the design variables shown sufficient to specify the problem completely? If not, what additional design variable(s) would you select?

Aadit Sharma

Numerade Educator