• Author / Uploaded
• Anel Viridiana Alfonso Bocarando

Citation preview

Chapter 8

329

Questions and Problems

PS-5 8

The production of maleic anhydride by the air oxidation of benzene was recently studied using a vanadium pentoxide catalyst [Chem. Eng. Sci ., 43 , I 051 (1988)] . The reactions that occur are: Reaction I: Reaction 2: Reaction 3: Because these reactions were carried out in excess air, volume change with reaction can be neglected, and the reactions can be written symbolically as a pseudo-first-order reaction sequence

where A = benzene, B = maleic anhydride, C = products (H 2 0 , C0 2 ), D = products (C0 2, H20). The corresponding pseudo specific reaction rates, k; are (in m3/kg catls): k 1 = 4280exp[-12, 660/T(K)]

k3

P8-6a 8

k2 =

70, IOOexp(-15, 000/T(K)]

= 26exp[-10, 800/T(K)]

At 848 K, k 1 = 1.4 x IQ- 3 , k2 = 1.46 x J0·3 , k3 = 7.65 x I0- 5 . These reactions are carried out isothermally in both a CSTR and a PBR. Benzene enters the reactor at a concentration of 0.01 mol/dm 3 . The total volumetric flow rate is 0.0025 m3/s. (a) Which reactions will dominate at low temperatures and which will dominate at high temperatures? For the sake of comparison, assume that 848 K is a moderate temperature. (b) For a catalytic weight of 50 kg, determine the exit concentration from a "fluidized" CSTR at 848 K. [Ans: C8 =0.3 moUdm 3] (c) What is the selectivity of B to C and of B to Din the CSTR? (d) Plot the concentrations of all species as a function of PBR catalyst weight (up to I 0 kg) assuming isothermal operation at 848 K. (e) What feed conditions and reactor or combinations of reactor shown in Figure 8-2 would you use to maximize the production of maleic anhydride? (0 How would your results in part (d) change if pressure drop were taken into account with a= 0.099 (kg car- 1) in the PBR? Make a plot similar to that in part (d) and describe any differences. The reaction

is carried out in a batch reactor in which there is pure A initially.

330

Multiple Reactions

Chapter 8

(a) Derive an equation for the concentration of A as a function of time. If k 1= 0.00 l s- 1, what is the ratio CA/CAo after 1.5 min? (b) Derive an equation that gives the concentration of 8 as a function of time. If k2 = 0.003 s- 1, k3 = 0.002 s- 1, and CAo = 0.2 g mol!dm3, what is the concentration of 8 after 2 mill? (c) What is the concentration of C after I min? 2 min? {d) Sketch the concentrations and as functions of time. At what time is the concentration of 8 at a maximum? (e) If the series reaction is carried out in a CSTR, determine the reactor volume that will maximize the production of 8 for a volumetric flow rate of 20 dm 3/min. P8-6bA Consider the following system of gas-phase reactions:

PS-7 8

1-lall of Fame

12

k, = 0.004(mol/dm3)

A----7 X

rx =k, C~

A ----7 B

r 8 =k 2 C A

k 2 = 0.3

A----7 y

2 ry=k3 CA

k 3 =0.25 dm 3/mol·min

112

.

min - I

min- 1

B is the desired product, and X and Y are foul pollutants that are expensive to get rid of. The specific reaction rates are at 27°C. The reaction system is to be operated at 27°C and 4 atm. Pure A enters the system at a volumetric flow rate of I 0 dm 3/min. (a) Sketch the instantaneous selectivities (S8 1X> SBIY• and S 8 rxv=ref(rx+ry)) as a function of the concentration of CA. (b) Consider a series of reactors. What should be the volume of the first reactor? (c) What are the effluent concentrations of A, B, X, andY from the first reactor? (d) What is the conversion of A in the first reactor? (e) If 99% conversion of A is desired, what reaction scheme and reactor sizes should you use to maximize S8 rxv? (0 Suppose that £ 1 = 20,000 cal/mol, £ 2 = 10,000 cal/mol, and £ 3 = 30,000 cal/mol. What temperature would you recommend for a single CSTR with a space time of 10 min and an entering concentration of A of 0.1 mol/dm 3? (g) If you cou ld vary the pressure between l and I 00 atm, what pressure would you choose? Pharmacokinetics concerns the ingestion, distribution, reaction, and elimination reaction of drugs in the body. Consider the application of pharmacokinetics to one of the major problems we have in the United States, drinking and driving. Here we shall model bow long one must wait to drive after having a tall martini. In most states, the legal intoxication limit is 0.8 g of ethanol per liter of body fluid. (In Sweden it is 0.5 g/L, and in Eastern Europe and Russia it is any value above 0.0 g/L.) The ingestion of ethanol into the bloodstream and subsequent elimination can be modeled as a series reaction. The rate of absorption from the gastrointestinal tract into the bloodstream and body is a first-order reaction with a specific reaction rate constant of I 0 h- 1 • The rate at which ethanol is broken down in the bioodstream is limited by regeneration of a coenzyme. Consequently, the process may be modeled as a zero-order reaction with a specific reaction rate of 0.192 g/h · L of body fluid. How long would a person have to wait (a) in the United States; (b) in Sweden; and (c) in Russia if they drank two tall martinis immediately after arriving at a party? How would your answer change if (d) the drinks were taken Y2 hour apart; (e) the two drinks were consumed at a uniform rate during the first hour?

Chapter 8

331

Questions and Problems

(f) Suppose that one went to a party, had one and a half tall martinis right away, and then received a phone call saying an emergency had come up and the person needed to drive home immediately. How many minutes would the individual have to reach home before he/she became legally intoxicated, assuming that the person had nothing further to drink? (g) How would your answers be different for a thin person? A heavy person ? [Hint: Base all ethanol concentrations on the volume of body fluid. Plot the concentration of ethanol in the blood as a function of time.] What generalizations can you make? What is the major unspoken point of this problem?

Additional information: Ethanol in a tall martini: 40 g Volume of body fluid : 40 L

(SADD-MADD problem)

[See Chapter 9 PRS R9-7 for a more in-depth look at alcohol metabolism .] PS-8 8

f-lail of Fame

(Pharmacokinetics) Tarzlon i a liquid antibiotic that is taken orally to treat infections of the spleen. It is effective only if it can maintain a concentration in the bloodstream (based on volume of body fluid) above 0.4 mg per dm 3 of body fluid. Ideally, a concentration of l.O mg/dm 3 in the blood should be realized. However, if the concentration in the blood exceeds 1.5 mg/dm 3, harmful side effects can occur. Once the Tarzlon reaches the stomach, it can proceed in two pathways, both of which are first order: (I) It can be absorbed into the bloodstream through the stomach walls; (2) it can pass out through the gastrointe tina] tract and not be absorbed into the blood. Both these processes are first order in Tarzlon concentration in the stomach. Once in the bloodstream, Tarzlon attacks bacterial cells and is subsequently degraded by a zero-order process. Tarzlon can also be removed from the blood and excreted in urine through a first-order process within the kidneys. In the stomach: Absorption into blood

k 1 = 0.15 h- 1

Elimination through gastrointestine

k2

= 0.6 h- 1

k4

= 0.2 h- 1

In the bloodstream:

Degradation of Tarzlon Elimination through urine

P8-9c

One dose of Tarzlon is 250 mg in liquid form: Volume of body fluid = 40 dm 3 . (a) Plot and analyze the concentration of Tarzlon in the blood as a function of time when 1 dose (i.e., one liquid capsule) of Tarzlon is taken. (b) How should the Tarzlon be administered (dosage and frequency) over a 48-h period to be most effective? (c) Comment on the dose concentrations and potential hazards . (d) How would your answers change if the drug were taken on a full or empty stomach? (Reactor selection and operating conditions) For each of the following sets of reactions, describe your reactor system and conditions to maximize the selectivity to D. Make sketches where necessary to support your choices. The rates are in (moUdm 3·s), and concentrations are in (moUdm 3). (a) (1) A+ B ~ D -riA= I exp(-8,000 KJncAcB (2)

(b) (l) (2)

A+B~U

A+B

~D

1/2

3/2

-r2A = 10 exp(-1,000 KJncA C8 -riA= 10 exp(-1,000 KJnCACB

332

Multiple Reactions

(c) (I)

A+B-tD

-r 1A = 10 exp(-1,000 K/T)CACB

(2)

B+D-tU

(d) (I)

A -------7 D

= 109 exp(-10,000 K/T)C 6 C0 -r 1A = 5000 exp(-12,000 KJT)CA -r20 = 10,100 exp(-15,000 K/T)C 0 -r3A = 26 exp(-18,800 K/T)CA 9 -r 1A = 10 exp(-10,000 K/T)CACB -r20 = 20 exp(-2,000 K/T)C 0 3 -r3A = 10 exp(-3,000 K/T)CACB

(2) (3)

o -------7 U 1 A -------7 u 2

(e) (l)

A+B-tD

(2)

D-tA+B

(3)

A+ B-tU

(t)

Chapter 8

-r26

Consider the following parallel reactions5 (I) A+B-tD -r 1A = 10 exp(-8,000 K/T)CACB

= 25 exp(-10,800

(2)

-r2 A

(3)

-r3u = 10,000 exp(- 15,000 KJT)Cu

KJT)CA

(g) For the following reactions (molldm 3/min) (I)

PS-10 8

PS-11 8

5

Green Engineering

A+ B -t D

-'iA

0.5 = 800exp( -8,000K) T CA C6

-300K) = lOexp( --TCA Cs

(2)

'2s

(3)

r30 = 10 exp (-8,000K) T C0 C6 6

The elementary liquid-phase-series reaction

is carried out in a 600-dm 3 batch reactor. The initial concentration of A is 2.0 mol/dm 3 . The desired product is B, and separation of the undesired product C is very difficult and costly. Because the reaction is carried out at a relatively high temperature, the reaction is easily quenched. (a) Plot and analyze the concentrations of A, B, and C as a function of time. Assume that each reaction i irreversible, with k 1 = 0.4 h- 1 and k2 = 0.0 I h- 1• (b) Plot and analyze the concentrations of A, B, and C as a function of time when the fir t reaction is reversible with k_1 = 0.25 h- 1• (c) Plot and analyze the concentrations of A, B, and C as a function of time for the case where both reactions are reversible with k_2 = 0.006 h- 1• (d) Compare (a), (b), and (c) and describe what you find. (e) Vary k 1 , k2 , L 1, and k_ 2 • Explain the consequence of k 1 > 100 and k2 < 0.1 with L 1 = L 2 = 0 and with L 2 = I, L 1 = 0, and L 2 = 0.25. (t) Apply one or more of the six ideas in Table P-3, page xviii to this problem. Solar energy capture has great potential to help meet the world ' growi ng energy demand, which is 12 terawatts in 20 I 0 and is expected to rise to 36 terawatts in 2050 (cf. P3-15 8 ). Professor AI Weiner and his students at the University of Colorado are engaged in developing methods of utilizing solarthermal energy. In solar-thermal reactors, mirrors are used to focu s and con-

Assume the reversible reactions are very fast. Techniques for minimizing the waste U are discussed in Green Engineering by D. Allen and D. Shonard (Upper Saddle River, N.J. : Prentice Hall , 2000).

Chapter 8

333

Questions and Problems

centrate the sun's energy on a flow-type cavity reactor where temperatures as high as 1200°C can be realized, as shown below.

'

Figure PS-11.1 Solar field design. Five 265 m tall towers with 275 acres of land in Daggett, CA. Net concentration 3,868 suns each solar reactor. (Melinda M. Channel, Jonathan Scheffe, Allan Weimer, November II , 2009). Also see (Chemical Engineering,

/

three heliostat fields/tower, and 295 MW delivered to Lewandowski, and Alan W. 116, p. 18, March 2009).

The switch grass is fed to the 1200°C solar thermal reactor. At these temperatures, biomass can be converted to CO and H 2, i.e., syn gas, which then can be used for liquid fuels. Switch grass, which is approximately 7) cellulose (C 6 H 100 5) and }5 lignin (C 10H 120 3 ) will be fed with steam to produce CO, H 2 , and a small amount of ash, which we will neglect. In order to simplify this process into a tractable home problem, we assume the switch grass is volatilized immediately upon entering the plug-flow reactor and that the reactions and postulated rate laws are

(2) Lignin: [A!ChE J. 55, p. 286 (2009)]. Also see Science p. 326, 1472 (2009).

The rate laws and constants are hypothesized to be

P,

Total gas concentration in the feed and reactor with CTo

I atm

= R~o = (0.0 82 )(l 473 )

0.00828 mol/dm 3 with the entering molar flow rates of cellulose, lignin and water are Fco = 0.00411 molls and FLO = 0.0185 molls, Fwo = 0.02 molls, respectively. (a) Plot and analyze the molar flow rates as a function of PFR volume up to V = 0.417 dm3. (b) Plot and analyze Yc. Yw, YL and Sco;H2 down the reactor. (c) Repeat (a) for different molar flow rates of water.

334

Multiple Reactions

PS-12 8

Chapter 8

The solar-thermal biochar gasification has also been studied at the University of Colorado (See PS-17 8 ). Chemical Engineering and Processing: Process Intensification 48, p. 1279 (2009) and A!ChE 1. 55 p.286 (2009). While this process follows a shrinking core model (see DVD Chapter II), for the purposes of this example, we will use the following sequence. (I) Lignin:

C 10 H 120 3 (L) + 3H 20(W) ~ 3H 2 + 3CO +Char (e.g. , cresol)

(2) Char:

Char( Ch) + 4H 2 0 ~ I OH 2 + 7CO

The rate laws at 1200°C are hypothesized to be

-r2ch =

PS-13 8

~chCchC~ with ~ch = 1, 000( ~::

Jf

The entering molar flow rates are FLO= 0.0123 molls, Fwo = 0.111 molls, the total entering concentration is CTo = 0.2 molldm 3, and the reactor volume is 0.417 dm 3 (a) Plot and analyze Fch• FL, Fw, Fc0 , and FH down the length of a plug 2 flow reactor. (b) Repeat (a) for the concentrations Cc, Cch• etc. (c) Plot and analyze the selectivity Sco/H 2 and yields Yw and YL down the PFR. (d) At what point is the char molar flow rate a maximum? How does it change with changing feed conditions, such as the ratio of CFwof FLO) , CTO• etc? Terephthalic acid (TPA) finds extensive use in the manufacture of synthetic fibers (e.g., Dacron) and as an intermediate for polyester films (e.g., Mylar). The formation of potassium terephthalate from potassium benzoate was studied using a tubular reactor [Ind. Eng. Chem. Res., 26, 1691 ( 1987)]. It was found that the intermediates (primarily K-phthalates) formed from the dissociation of K-benzoate over a CdCI 2 catalyst reacted with K-terephthalate in an autocatalytic reaction step Series k

R+S~2S

Autocatalytic

where A = K-benzoate, R = lumped intermediates (K-phthalate , K-isophthalates, and K-benzenecarboxylates), and S = K-terephthalate. Pure A is charged to the reactor at a pressure of 110 kPa. The specific reaction rates at 4to•c are k 1 = 0.95 x IQ- 3 s- 1 with E 1 = 42.6 kcallmol , k2 = 1.25 x I0- 3 s- 1 with E2 = 48.6 kcallmol , k3 = I. 7 x I o-3 dm 3/mol · s with E3 = 32 kcallmol. (a) Plot and analyze the concentrations of A, R, and S as a function of time in a batch reactor at 41 o·c , noting when the maximum in R occurs. (b) Repeat (a) for temperatures of 43o·c and 39o·c . (c) What would be the exit concentrations from a CSTR operated at 41o·c and a space time of 1200 s?

Chapter 8

335

Questions and Problems

P8-14A The following liquid-phase reactions were carried out in a CSTR at 325 K.

Sketch the trends or results you expect before working out the details of the problem.

3A~B+C

k 1A = 6.0 min-I

2C+A~3D

k2D

4D+3C~3E

k3E = 5.0

S

dm6

= 4.0 - - - -

mof2·min

dm3 . mol · mtn

The concentrations measured inside the reactor were CA = 0.10, C 8 = 0.93, Cc = 0.51, and C 0 = 0.049 all in moUdrn 3. (a) What are r 1A, r 2A, and r3 A? (r 1A = -0.7 moUdm 3 ·min) (b) What are r 18 , r 28 , and r 38 ? (c) What are r 1c, r 2c, and r3c? Cr 1c = 0.23 moUdm 3 ·min) (d) What are r 10 , r 20 , and r 30 ? (e) What are r 1E, r 2 E, and r 3E? (0 What are the net rates of formation of A, B, C, D, and E? (g) The entering volumetric flow rate is 100 dm3/min and the entering concentration of A is 3M. What is the CSTR reactor volume? (Ans.: 400 dm 3.) (h) What are the exit molar flow rates from 400 drn3 CSTRs? (i) PFR. Now assume the reactions take place in the gas phase. Use the preceding data to plot the molar flow rate's selectivity andy as a function of PFR volume up to 400 dm 3. The pressure drop parameter is 0.001 dm-3, the total concentratjon enteri!)g the reactor is 0.2 moUdm 3, and v0 = 100 drn 3/min. What are SolE and SC/D ? G) Membrane Reactor. Repeat (i) when species C diffuses out of a membrane reactor and the transport coefficient, kc, is 10 min- 1• Compare your results with part (i). PS-15 8 In this problem, the complex reactions described below will first be carried out in the liquid phase (Parts (a) through (d)) and then in the gas phase. (Parts (e) through (g)). One need not solve the liquid phase to solve the gas phase problems. The following reactions are carried out isothermally. 2

A+2B~C+D

rlD=klDCACB

2D+3A~C+E

r2E=k2ECACD

B+2C~D+E

r3E = k3ECsCc

2

Additional information:

kiD

=

0.3 drn 6/moJ2 · min

10 dm 3fmin

k2E = 0.2 dm 3/mol · min k3E = 6.0 dm 6/moJ2 · min

1.5 moUdm 3

C80

=

2.0 moUdm 3

(a) Consider the reactions to be liquid phase and plot the species concentrations and the conversion of A as a function of the distance (i.e., volume) down a 50-drn 3 PFR. Note any maxima. (b) Consider the reactions to be liquid phase and determine the effluent concentrations and conversion from a 50-dm3 CSTR.

336

Multiple Reactions

PS-16 8

Chapter 8

(c) Plot and analyze the species concentrations and the conversion of A as a function of time when the reaction is carried out in a semibatch reactor initially containing 40 dm 3 of liquid. Consider two case : ( I ) A is fed to 8 , and (2) 8 is fed to A. What differences do you observe for these two cases? (d) Vary the ratio of 8 to A ( I < 0 8 < I 0) in the feed to the PFR and describe what you find. What generalizations can you make from this problem? (e) Rework (a) for the case when the reaction is a gas-phase reaction . We will keep the constants the same so you won't have to make too many changes in your Polymath program, but we will make v0 = I 00 dm 3/min, CTo = 0.4 molldm 3, V = 500 dm 3, and an equal molar feed of A and B. Plot the molar flow rates and SCJD and SFJF down a PFR. (f) Repeat (e) when D diffuses out through the sides of a membrane reactor where the mass transfer coefficient, kc 0 , can be varied between 0.1 min- 1 and I 0 min- 1• What trends do you find ? (g) Repeat (e) when 8 is fed through the sides of a membrane reactor. The complex reactions involved in the oxidation of formaldehyde to formic acid over a Vanadium titanium oxide catalyst [Ind. Eng. Clzem. Res. 28, p. 387 (1989)] are shown below. Each reaction follows an elementary rate law.

HCH0+_!_0 2 ~HCOOH~CO+ H2 0 2

2HCHO~ HCOOCH 3 HCOOCH 3 ~CH 3 0H + HCOOH Let A = HCHO, 8 = 0 2 , C = HCOOH, D = HCOOCH 3 , E = CO, W = H20 , and G = CH 30H . The entering flow rates are FAo = 10 molls and F 80 = 5 molls and v 0 = 100 dm 3/s. At a total entering concentration CTo = 0.147 mol/dm 3. The suggested reactor volume is 1,000 dm 3 . Additional information: At 300 K

kl

= 0.014( ~::

k3 = 0.014/s. k4

rf. ~ 2

= 0.007 ~:~s

dm 3 mol· s

= 0.45--

(a) Plot and analyze Yc , SAlE , Sc,o, So a and the molar flow rates along the length of the reactor. Note any maximums and the volume at which they occur. (b) Plot and analyze the overall HCOOH yield and overall selectivity of HCOH to CO, of HCOOCH 3 to CH 30H, and of HCOOH to HCOOCH 3 as a function of the 0 0 . Suggest some conditions to best produce formic acid. Write a paragrap~ describing what you find. (c) Compare your plot in part (a) with a similar plot when pressure drop is taken into account with a = 0.002 dm - 3 . (d) Suppose that £ 1 = 10,000 cal/mol, £ 2 = 30,000 cal/mol , £ 3 = 20,000 cal/mol , and £ 4 = 10,000 cal/mol , what temperature would you recommend for a IOOO-dm 3 PFR?

Chapter 8

337

Questions and Problems

P8-17c The ethylene epoxydation is to be carried out using a cesium-doped silver catalyst in a packed bed reactor.

Along with the desired reaction, the complete combustion of ethylene also occurs (2)

C 2 H 4 +30 2 ~2C0 2 +2H 2 0

-r 2E =

k2EpEpg

3

,

(I +K2EP E)"

[M . Al-Juaied, D. Lafarga, and A. Varma, Chem. Eng. Sci. 56, 395 (200 I)] . It is proposed to replace the conventional PBR with a membrane reactor in order to improve the selectivity. As a rule of thumb, a 1% increase in the selectivity to ethylene oxide translates to an increase in profit of about $2 million/yr. The feed consists of 12% (mole) oxygen, 6% ethylene, and the remainder nitrogen at a temperature of 250"C and a pressure of 2 atm. The total molar flow rate is 0.0093 moUs to a reactor containing 2 kg of catalyst.

Additional information: k 1E=0.15

mol kg ·s atm u 8

k2 E= 0.0888

at523K with £ 1 =60.7kJ/ mol

mol at 523 K with £ 2 = 73 .2 kJ/mol 1.3 k g·s atm -1

K 1E = 6.50 atm ,K2 E = 4.33 atm

PS-18 8

-1

(a) What conversion and selectivity, S, are expected in a conventional PBR? (b) What would be the conversion and electivity if the total molar flow rate were divided and the 12% oxygen stream (no ethylene) were uniformly fed through the sides of the membrane reactor, and 6% ethylene (no oxygen) were fed at the entrance? (c) Repeat (b) for a case when ethylene is fed uniformly through the sides and oxygen is fed at the entrance. Compare with parts (a} and (b) . The gas-phase reactions take place isothermally in a membrane reactor packed with catalyst. Pure A enters the reactor at 24.6 atm and 500 K and a flow rate of A of I 0 moUmin

A

B+C

A~D

2C+D~2E

Only species B diffuses out of the reactor through the membrane. Additional Information: Overall mass transfer coefficient kc = 1.0 dm3 I kg cat · min k 1c= 2 dm 3 I kg cat · min K 1c = 0.2 mol I dm 3 k20 = 0.4 dm 3 I kg cat · min k3E = 5.0 dm 3 I moF · kg cat · min Wr = 100 kg a= 0.008 kg- 1

338

Multiple Reactions

Chapter 8

(a) Plot and analyze the concentrations down the length of the reactor. (b) Explain why your curves look the way they do. (c) Describe the major differences you observe when C diffuses out instead

of B, with the same mass transfer coefficient. (d) Vary some of the parameters (e.g., k 8 , k 1c, K 1c) and write a paragraph describing what you find. P8-19A Go to Professor Herz's Reactor Lab on the DVD-ROM or on the Web at www.SimzLab.com. (a) Load Division 5, Lab 2 of the Reactor Lab from the DVD-ROM for the selective oxidation of ethylene to ethylene oxide. Click the [i] info button to get information about the system. Perform experiments and develop rate equations for the reactions. Write a technical memo that reports your results and includes plots and statistical measurements of how well your kinetic model fits experimental data. (b) Load Divi sion 5, Labs 3 and 4 of the Reactor Lab for batch reactors in which parallel and series reactions, respectively, can be carried out. Investigate how dilution with solvent affects the selectivity for different reaction orders, and write a memo describing your findings .

PS-20 8

What five things are wrong with this solution? The van de Vusse reactions

take place in the gas phase and all follow elementary rate laws. Pure A enters a 100 dm 3 PFR at a volumetric flow rate of 10 dm3/min at a concentration of 3 mollm 3 . k 1 = 0.05 min k3 = 0.015 (dm 3/mol)/min Kc = 0.5 drn 3/mol Plot CA, C 8 , Cc, and C 0 as a function of V.

Solution Taking A as the basis of calculation for both reactions

A~D/2 A

B+C

The equations for the Polymath solutions are shown below. Calculoted values of DE Yllrlllb&es Van.ble Initial velue Mlnlrn.l value Mui!Mlvolue Final value 1Ca

3.

0.45-41998

4.381897

0.45-41998

2Cb

0

0

2.809564

1.340173

3Cc

0

0

2.809564

1.340173

4Cd

0

0

3.885973

3.885973

sv

0

0

100.

100.

Differential equations 1 d(Cc)/d(V) = .OS*(Ca-cb*Cc/2) 2 d(Cb)/d(V) = O.OS*(Ca.Cb*Cc/2) 3 d(Ca)/d(V) = O.OS*(Ca-cb*Cc/2) -.OlS*Ca

4 d(Cd)/d(V) = O.OlS*Ca

Chapter 8

339

Supplementary Reading

l ) Line_ reads ________ , should read _ _ _ _ _ __

2) Line _ reads

, should read _ _ _ _ __

3) Line _ reads

, should read _ _ _ _ _ __

etc.

• Additional Homework Problems A number of homework problems that can be used for exams or supplementary problems or examples are found on the DVD-ROM and on the CRE Web site, http://www.engin.umich.edu/-cre.

New Problems on the Web CDP8-New From time to time new problems relating Chapter 8 material to everyday interests or emerging technologies will be placed on the Web. Solutions to these problems can be obtained by e-mailing the author. Also, one can go to the Web site, www.rowan.edu/greenengineering, and work the home problem on green engineering specific to this chapter.

Green Engineering

SUPPLEMENTARY

READING

I. Selectivity, reactor chemes, and staging for multiple reactions, together with evaluation of the corresponding design equations, are presented in BURGESS, THORNTON W., The Adventures of Chatterer the Red Squirrel, New York: Dover Publications, Inc., 1915. BuTT, JOHN B, Reaction Kinetics and Reactor Design, Second Edition, Revised and Expanded, New York: Marcel Dekker, Inc., 1999. DENBIGH , K. G., and J. C. R. TURNER, Chemical Reactor Theory, 2nd ed. Cambridge: Cambridge University Press, 1971 , Chap. 6. 2. Many analytical solutions for parallel , series, and combination reactions are presented in

S. M., Chemical Reaction Engineering Handbook of Solved Problems. Newark, N.J.: Gordon and Breach, 1995.

WALAS,