tutorialsheet02

5/20/2018 tutorialsheet02

1/6

1|P a g e

CHL 723: Chemical Reaction and Reactor Engineering

Tutorial Sheet 2

(26.08.2014)

Derive the following relationships for reaction time in a batch reactor as a function of

concentration of unreacted reactant A (problems 1-5).

1. Second order reaction (single reactant): Aproducts

tkCX

C

C

A

A

A

A

00 1

11

+==

2. First order reversible reaction: ArR

+

+=

+

+

=AAe

AeAe

AeA

AeAA

Ae

XX

X

rM

rXM

CC

CC

rM

C

CrM

kt lnln

100

3. Second order reaction (two reactants):

BAA CkCrproductsbBA =+

A

BAo

bMC

CMktbC ln)1( =

)1(ln

A

A

XM

XM

=

For ...1=M A

A

A

AoBo

X

X

C

CktC

==

11

or BoAo

A

ktCCC

+=

11

What happens when ?)1( >>>> MbCC AoBo How to interpret it physically?

1=Ao

Bo

bC

CM


2/6

2|P a g e

4. Third Order Reaction:

CBAA CCkCrproductsCBA =++

(a)

ForCoBoAo CCC

( )( ) ( )( )

( )( )

+

+

=

C

Co

BoCoAoCo

B

Bo

CoBoAoBoA

Ao

CoAoBoAo

C

C

CCCC

C

C

CCCCC

C

CCCCkt

ln1

ln1

ln1

(b) ForBoCoAo

CCC =

( )AoBokt CC 22

( )( )

AoB

ABo

AAo

AAoAoBo

CC

CC

CC

CCCCln

2+

=

(c)

ForCoBoAo CCC ==

22

112AoA

CCkt =

221

1

AoAo

A

ktCC

C

+==

5. Reactions of shifting order:

A

AA

CM

kCr

productsA

+=

(1storder at low AC

0 order at high AC )

AAo

A

Ao CCC

CMkt += ln

AAoAAo

AAo

CC

tkM

CC

CC

/ln/ln+=


3/6

3|P a g e

6. Levenspiel problem 3.9


8.

Levenspiel problem 3.14

9.






Problem 14:

Consider a long PFR of length L in which a fluid with reactants is flowing with linear

velocity u. Thus the space time is vessel is =L/u. Consider a first order reaction (with

rate constant k) taking place in the PFR.

a.

Write the governing design equation (differential equation) for steady state operation.

b. Now lets say you wish to discretize this equation into Nsegments, so that you have a

equivalent finite difference equation. The segments are all equal and of length z, andthe end nodes are labelledj =0, 1, 2, N. Thus, N.z = L. Let the space time in each

segment, bea

=z/u.c.

Write an explicit finite difference scheme for the concentration of the reactant species

at the end of the (j+1)stnode in terms of concentration at the jthnode (i.e, over the jth

segment).

d.

Let the conversion in thejth segment bexj. Simplify the expression in c. to getxj,a, k

and cj.

e. From d., what do you conclude about the behavior of sub-segments that make up a

PFR.

Problem 15:

Now consider a CSTR with space time is vessel is a. Consider a first order reaction (with

rate constant k) taking place in the CSTR.

f. Write the governing design equation (now a difference equation) for steady state

operation. Let the incoming concentration be c0 and the outgoing concentration be c1.

g. Now lets say you add a second identical CSTR in series to the first one. Now the

incoming concentration in this is c1 and the outgoing concentration is c2. Write now

first the design equation for the second CSTR, and then express the concentration at the

end of the second CSTR in terms of the incoming concentration c0.

h.

Repeat this exercise forNsuch identical CSTRs all connected in series, i.e., express the

concentration at the end of theNthCSTR in terms of the incoming concentration c0.

i. Simplify the expression obtained in part c. when N. Use mathematical limits as

appropriate.


4/6

4|P a g e

j. The expression obtained in part d. is a solution to which first order ODE with what

initial/boundary conditions? What physical system does such a ODE represent? What

do you conclude (mathematically, and physically)?

16. Refer to Table 5.1 of Levenspiel's book.

Derive the following expressions from first principles:

(a) PFR and CSTR (MFR) expressions for Damkohler number as a function of conversion for

n-order irreversible reaction (row 4 in the Table)

(a) PFR and CSTR (MFR) expressions for Damkohler number as a function of conversion for

first order reversible reaction (row 5 in the Table).

17.


18.


19.





23. Refer to Page 127-128 of Levenspiel's book.

(a) Derive equations (6a) and (6b)

(b) Derive equation (8a).

24. Refer to Section 6.3 of Levenspiel's book, on Recycle Reactors.

(a) Derive equations (18) and (19).

(b) Derive equation (22) and refer the integrals to Figure 6.14 (convince yourself about the

relevant areas).

(c) Carefully study and interpret Figures 6.16.

25. Refer to Section 6.4 of Levenspiel's book, on Autocatalytic Reactions

(a) Derive equation (28).

(b) Derive equation (22) and refer the integrals to Figure 6.14 (convince yourself about the

relevant areas).(c) Carefully study and interpret Figures 6.16.





30.



5/6

5|P a g e







37.


38.

Show that on adding any degree of recycle to a CSTR in which a liquid phase reaction

is being conducted, the exit conversion remains the same (as the CSTR withoutrecycle). (Hint: Start in the same way as the plug flow with recycle is derived, except

that the performance equation for the reactor to be used in the CSTR equation instead

of the plug flow equation.)

39. A quantity of ethyl ethanoate (A) is reacted in a batch with an excess of sodium

hydroxide (B) at 25 C. 100 cc of the reaction mixture required 68.2 cc of 0.05 mol/l

HCl for neutralization at the beginning of the reaction. After 30 minutes, 100 cc of the

mixture similarly required 49.7 cc of the acid, and when the reaction was complete, 100

cc of the mixture required 15.6 cc of the acid. The reaction is not reversible. Find the

rate constant, assuming the reaction to be elementary.

40. The reaction A + B products is conducted in a three-stage CSTR battery of equal-

sized vessels. Specific rate constant is k = 25 l/mol-hr. Inlet concentrations are CA0=

0.15 mol/l, CB0= 0.20 mol/l. Net conversion of A of 90% is required, i.e., C A3= 0.015

mol/l. Find the residence time in each vessel.

41.

Consider the elementary series reaction scheme A R S in a plug flow reactor, in

which the reactant A reacts to form R by a zero order reaction (rate constant k1), while

R forms S by a first order reaction (rate constant k2). Only A is present in thefeedstream at the inlet of the plug flow reactor, with initial concentration CA0 (rest of

the feed being inerts).

42. Develop expressions for the concentrations of A, R and S as a function of length of the

reactor,z, assuming that the average velocity of flow is a constant value of u (and that

there is no change in density of the flowing phase). Sketch the trends of the

concentration plots on a single plane (i.e., concentration of each component withz).

At what length of the reactor (residence time), does the maximum in concentration of R

occur? What is the expression for the maximum concentration of R?


6/6

6|P a g e

43. It is sometimes stated as a rule of thumb that the rate of a chemical reaction doubles for

a 10 K increase in T. Is this in accordance with the Arrhenius equation? Determine the

value of the energy of activation, EA if this rule is applied for an increase from (a) 300

to 310 K, and (b) 800 to 810 K.What do you conclude from the relative values of

energy of activation?

44. A reaction with rate equation 2kCr= is carried out in a four stage reactor with

Damkhler number of 1.2 (for each stage). Find the fractional conversion at the end of

each stage.

45. A homogeneous liquid phase reaction has the rate equation:

==

edt

dC

K

C

Ckr

22

1

)2.2(

Initial concentration is C0 = 1.5, initial rate is r0= 1.076, and equilibrium concentration

is Ce =0.6798. Find the constants.

46.

A first order liquid phase reaction is taking place in a mixed reactor with 92%

conversion. It has been suggested that a fraction of the product stream is to be recycled,

with a recycle ratio of 0.75. If the fresh feed rate remains unchanged, what will be the

effect on conversion?

Derive your result.

47. A liquid phase reaction with rate equation 2kAr= takes place with 50% conversion in aCSTR.

(a) What will be the conversion if the reactor is replaced with one that is six times as

large?

(b) What will be the conversion if the original reactor is replaced by a PFR of the

same size?

48. A recent report of the Reserve Bank of India states that.. it costs Rs. 15 to print a

Rs. 100 note, and that approximately 2 billion of them are currently in circulation, of

which 1 billion need to be replaced annually.

Assume that the Rs. 100 notes are put in circulation at a constant rate and continuously,

and that they are withdrawn from circulation at the same constant rate without regard to

their age and condition, in a random manner. The whole exercise is designed by

Reserve Bank so that a constant number of bills (2 billion) are in circulation at any

time.

Suppose a new series of Rs. 100 notes are put in circulation today onwards replacing

the older bills that have been in circulation.

(a) How many new Rs. 100 notes will be in circulation at any time in the future?

(b)

After 15 years, how many old Rs. 100 notes are still expected to be in circulation?

Documents

tutorialsheet02