R8.4 Industrial Example of Nonadiabatic Reactor Operation: Oxidation of Sulfur Dioxide

R8.4.1 Manufacture of Sulfuric Acid

In the manufacture of sulfuric acid from sulfur, the first step is the burning ofsulfur in a furnace to form sulfur dioxide:

Following this step, the sulfur dioxide is converted to sulfur trioxide, using acatalyst:

A flowsheet of a typical sulfuric acid manufacturing plant is shown in FigureA8-1. It is the converter that we shall be treating in this section.

Although platinum catalysts once were used in the manufacture of sulfu-ric acid, the only catalysts presently in use employ supported vanadia.

12

Forour problem, we shall use a catalyst studied by Eklund, whose work was ech-oed extensively by Donovan

13

in his description of the kinetics of oxida-tion. The catalyst studied by Eklund was a Reymersholm catalystdeposited on a pumice carrier. The cylindrical pellets had a diameter of 8 mmand a length of 8 mm, with a bulk density of 33.8 lb/ . Between 818 and1029

�

F, the rate law for oxidation over this particular catalyst was

(R8.4-1)

in which was the partial pressure of species

i.

This equation can be usedwhen the conversion is greater than 5%. At all conversions below 5%, the rateis essentially that for 5% conversion.

Sulfuric acid manufacturing processes use different types of reactors.Perhaps the most common type has the reactor divided into adiabatic sectionswith cooling between the sections (recall Figure 8-8). One such layout isshown in Figure R8.4-2. In the process in Figure R8.4-2, gas is brought out ofthe converter to cool it between stages, using the hot converter reaction mix-ture to preheat boiler feedwater, produce steam, superheat steam, and reheatthe cold gas, all to increase the energy efficiency of the process. Another typehas cooling tubes embedded in the reacting mixture. The one illustrated in Fig-ure A8-3 uses incoming gas to cool the reacting mixture.

A typical sulfuric acid plant built in the 1970s produces 1000 to 2400 tonsof acid/day.

14

Using the numbers of Kastens and Hutchinson,

15

a 1000-ton/day

12

G. M. Cameron,

Chem. Eng. Prog., 78

(2), 71 (1982).

13

R. B. Eklund, Dissertation, Royal Institute of Technology, Stockholm, 1956, as quotedby J. R. Donovan, in

The Manufacture of Sulfuric Acid,

ACS Monograph Series 144,W. W. Duecker and J. R. West, eds. (New York: Reinhold, 1959), pp. 166–168.

14

L. F. Friedman,

Chem. Eng. Prog.,

78

(2), 51 (1982).

15

M. L. Kastens and J. C. Hutchinson,

Ind. Eng. Chem., 40,

1340 (1948).

S O2 SO2→�

SO212--- O2 ⎯⎯→ SO 3 �

V

2

O

5

SO2V2O5

ft3

SO2

r�SO2� k

PSO2

PSO3

---------- P O 2

P

SO

3

K

p

P

SO

2

----------------- ⎝ ⎠⎜ ⎟⎛ ⎞

2

��

Pi

An flow rateof 0.241 mol/s over

132.158 lb ofcatalyst can

produce 1000 tonsof acid per day.

SO2

126

Chap.

Fig

ure

R8.

4-1

Flow

shee

t of

a s

ulfu

ric

acid

man

ufac

turi

ng p

roce

ss.

[Rep

rint

ed

with

per

mis

sion

of

the

AIC

hE a

nd L

. J.

Fri

edm

an.

Cop

yrig

ht ©

198

2 A

IChE

. All

righ

ts r

eser

ved.

]

Sec. R8.4 Industrial Example of Nonadiabatic Reactor Operation: Oxidation of Sulfur Diox-

sulfuric acid plant might have a feed to the converter of 7900 lb mol/h,consisting of 11% , 10% , and 79% inerts (principally ). We shall usethese values.

For preliminary design purposes, we shall calculate the conversions fortwo situations and compare the results. Only one of the situations will be pre-sented in detail in this example.

1. The first situation concerns two stages of a typical commercial adia-batic reactor. The principles of calculating the conversion in an adia-batic reactor were covered earlier and illustrated in Section 8.3, sowill not be presented here but as a problem at the end of the chapter.

2. The second case concerns a reactor with the catalyst in tubes, with thewalls cooled by a constant-temperature boiling liquid. Calculationsfor this system are presented in detail next.

R8.4.2 Catalyst Quantities

Harrer

16

states that the volumetric flow rate in an adiabatic converter,measured at normal temperature and pressure, customarily is about 75 to 100

16

T. S. Harrer, in

Kirk-Othmer Encyclopedia of Chemical Technology,

2nd ed., Vol. 19(New York: Wiley-Interscience, 1969), p. 470.

Figure R8.4-2

Sulfur dioxide converter with internal cooling between catalyst layers. [Reprinted with permission of Barnes & Noble Books.]

SO2SO2 O2 N2

SO2

128

Chap.

/ of converter area. He also states that the catalyst beds in the con-verter may be from 20 to 50 in. deep.

It is desirable to have a low mass velocity through the bed to minimizeblower energy requirements, so the 75 / value will be used. Normalconversions in adiabatic converters are 70% in the first stage and an additional18% in the second.

17

Using Eklund’s Reymersholm catalyst, solution of the adi-abatic reactor problem at the end of the chapter shows that these conversionsrequire 1550 (23 in. deep) in the first stage and 2360 (35 in. deep) in thesecond. As a result, in our cooled tubular reactor, we shall use a total catalystvolume of 3910 .

R8.4.3 Reactor Configuration

The catalyst is packed in tubes, and the tubes are put in heat exchangers wherethey will be cooled by a boiling liquid. The outside diameter of the tubes willbe 3 in. Severe radial temperature gradients have been observed in oxida-tion systems,

18

although these systems had platinum catalysts and greatly dif-ferent operating conditions than those being considered here. The 3-in.diameter is chosen as a compromise between minimizing temperature gradi-

17

J. R. Donovan and J. M. Salamone, in

Kirk-Othmer Encyclopedia of Chemical Tech-nology,

3rd ed., Vol. 22 (New York: Wiley-Interscience, 1978), p. 190.

18

For example, R. W. Olson, R. W. Schuler, and J. M. Smith,

Chem Eng. Prog., 46

, 614(1950); and R. W. Schuler, V. P. Stallings, and J. M. Smith,

Chem. Eng. Prog. Symp.Ser. 48

(4), 19 (1952).

Figure R8.4-3 Sulfur dioxide converter with catalyst cooled by incoming reaction mixture. [Reprinted with permission of Barnes & Noble Books.]

ft3 min ft2�

ft3 min ft2�

ft3 ft3

ft3

Optimizing capitaland operating costs

SO2

Sec. R8.4 Industrial Example of Nonadiabatic Reactor Operation: Oxidation of Sulfur Diox-

ents and keeping the number of tubes low. For this service, 12-gauge thicknessis specified, which means a thickness of 0.109 in. and an inside diameter of2.782 in. A 20-ft length will be used, as a compromise between decreasingblower energy requirements (shorter tube length) and lowering capital costs(fewer tubes from a longer tube length). For 3910 of catalyst, the numberof tubes that will be required is

The total cross-sectional area of the tubes is

The overall heat-transfer coefficient between the reacting gaseous mixture andthe boiling coolant is assumed to be 10 Btu/ . This coefficient is towardthe upper end of the range of heat-transfer coefficients for such situations asreported by Colburn and Bergelin.

19

R8.4.4 Operating Conditions

Sulfur dioxide converters operate at pressures only slightly higher than atmo-spheric. An absolute pressure of 2 atm will be used in our designs. The inlettemperature to the reactor will be adjusted so as to give the maximum conver-sion. Two constraints are present here. The reaction rate over catalyst isnegligible below , and the reactor temperature should not exceed

at any point.

20

A series of inlet temperatures should be tested, and the

one above 760 giving the maximum conversion, yet having no reactor tem-perature exceeding 1120 , should be used.

The cooling substance should operate at a high temperature so as toimprove thermal efficiency by reuse of heat. The most suitable substanceappears to be Dowtherm A, with a normal operating limit of but whichon occasion has been used as the coolant in this preliminary design.

21

Example R8.4–1 Oxidation of

SO

2

The feed to an converter is 7900 lb mol/h and consists of 11% , 10% ,and 79% inerts (principally ). The converter consists of 4631 tubes packed withcatalyst, each 20 ft long. The tubes are 3 in. o.d. and 2.782 in. i.d. The tubes will be

19

Colburn and Bergelin, in

Chemical Engineers’ Handbook

; 3rd ed. (New York:McGraw-Hill, 1950).

20

J. R. Donovan and J. M. Salamone, in

Kirk-Othmer Encyclopedia of Chemical Tech-nology, 3rd ed. (New York: Wiley, 1984).

21The vapor pressure of Dowtherm A at is very high, and this pressure wouldhave to be maintained in the shell side of the reactor for boiling Dowtherm A to beused as a coolant at this temperature. This aspect will be included in the discussion ofthe problem results.

ft3

Ntvolume of catalystvolume per tube

-------------------------------------------- 391020( ) �( ) 2.782 12�( )2/4

----------------------------------------------------- 4631 tubes� � �

Ac3910 ft3

20 ft------------------- 195.5 ft2� �

h ft2 �F� �

V2O5~750�F

~1125�F�F

�F

~750�F

805�F

SO2 SO2 O2N2

130 Chap.

cooled by a boiling liquid at 805�F, so the coolant temperature is constant over thisvalue. The entering pressure is 2 atm.

For inlet temperatures of 740 and 940�F, plot the conversion, temperature, equi-librium conversion, and reaction rate profile down the reactor.

Additional information:

Using recent JANAF22 values of at 700 and 900 K, the equilibrium constant atany temperature T is

(ER8.4-1)

at 1600�R,

For rate constants, the data of Eklund23 can be correlated very well by the equation

(ER8.4-2)

where k is in lb mol /lb and T is in R.There are diffusional effects present in this catalyst at these temperatures, and

Equation (E8-10.2) should be regarded as an empirical equation that predicts theeffective reaction rate constant over the range of temperatures listed by Donovan (814to 1138�F). The JANAF tables were used to give the following:

where is in Btu/lb and T in �R.

22D. R. Stull and H. Prophet, Project Directors, JANAF Thermochemical Tables, 2nded., NSRDS-NBS 37 (Washington, D.C.: U.S. Government Printing Office, 1971).

23R. B. Eklund, as quoted by J. R. Donovan, in W. W. Duecker and J. R. West, TheManufacture of Sulfuric Acid (New York: Reinhold, 1959).

0.45 �

0 0.054 lb/ft3�

P0 2 atm�

Dp 0.015 ft �

� 0.090 lb/ft h at 1400 R ��

U 10 Btu/h ft2 R� ��

Ac 0.0422 ft2�

T

0

1400

�

R (also

T

0

1200 R) � �

g

c

4.17 108 lbm ft/ lbf h2����

b 33.8 lb/ft3 (bulk density)�

K p

K p42,311

RT---------------- 11.24�

⎝ ⎠⎜ ⎟⎛ ⎞

exp� K p in atm 1 2�� T in R ,( )

K p 7.8 atm 1 2���

k 176,008�T

------------------------ 110.1 Tln( )� 912.8�exp�

SO2 cat. s atm� �Kinetic and

thermodynamicproperties

HRx 800�F( ) 42,471 Btu/lb mol SO2��

CpSO27.208 5.633 10 3� T� 1.343 10 6� T 2����

CpO25.731 2.323 10 3� T� 4.886 10 7� T 2����

CpSO38.511 9.517 10 3� T� 2.325 10 6� T 2����

CpN26.248 8.778 10 4� T� 2.13 10 8� T 2����

Cp mol �R�

Sec. R8.4 Industrial Example of Nonadiabatic Reactor Operation: Oxidation of Sulfur Diox-

Solution

1. General procedure:a. Apply the plug-flow design equation relating catalyst weight to the rate of

reaction and conversion. Use stoichiometric relationships and feed specifi-cations to express the rate law as a function of conversion.

b. Apply the energy balance relating catalyst weight and temperature.c. Using the Ergun equation for pressure drop, determine the pressure as a

function of catalyst weight.d. State property values [e.g., k, , , ] and their respective

temperature dependences necessary to carry out the calculations.e. Numerically integrate the design equation, energy balance, and Ergun equa-

tion simultaneously to determine the exit conversion and the temperatureand concentration profiles.

2. Design equations. The general mole balance equations (design equations) basedon the weight of catalyst were given in their differential and integral forms by

3. Rate law:

4. Stoichiometric relationships and expressing as a function of X:

We let A represent and be the stoichiometric coefficient for species i:

(ER8.4-3)

Substituting for partial pressures in the rate law and combining yields

(ER8.4-4)

where , atm, , , , and

; lb mol/h, and lb mol/h.

Per tube:

Weight of catalyst in one lb cat./tube

K p H �Rx TR( ) CPi

FA0 dXdW -------- r � A ��

r�SO2� k

PSO2

PSO3

---------- P O2

P

SO3 K

p

P

SO2

----------------- ⎝ ⎠⎜ ⎟⎛ ⎞

2

��

r�SO2�

SO212--- O2 ⎯⎯→←⎯⎯ SO 3 �

A

12

---

B ⎯⎯→←⎯⎯ C �

SO2 vi

Pi Ci RT( ) CA0 �

i

v

i X

� ( )

RT ( )

P

1

�

X

�

( ) T T

0

�

( )

P

0

-------------------------------------------- P A0 �

i v

i X

� ( )

P

1 � X

�

( )

P

0

------------------------------ � � �

dXdW--------

r�A�

FA0

---------- kFA0

-------- 1 X ��

SO3

X

�

---------------------- PP

0 ----- P A0

�

O2

12

---

X

�

1

�

X

�

---------------------- �

SO3

X

�

1

X

� ----------------------

⎝ ⎠⎜ ⎟⎛ ⎞

2

1 K

p

2 ------ �� �

� 0.055�� PA0 0.22� �SO21.0� �O2

0.91� �SO30.0�

�N27.17� FT0 7900� FA0 869�

tube W b�D2 4� L 28.54� � �

FA08694631------------ 0.188 lb mol/h tube�� �

132 Chap.

Substituting these values gives us

(ER8.4-5)

that is,

(ER8.4-6)

The limits of integration are from zero to the weight of catalyst in one tube,28.54 lb.

5. Energy balance. For steady-state operation and no shaft work, Equation (8-56)can be rewritten in terms of catalyst weight as the spatial variable, that is,

(ER8.4-7)

6. Evaluating the energy balance parameters:

Heat of reaction:

(ER8.4-8)

For the oxidation, ,

Similarly,

Substituting into Equation (ER8.4-8) with TR � 1260�R, we have

Heat-transfer coefficient term:

(ER8.4-9)

The combined molebalance, rate law,and stoichiometry

dXdW--------

r�A�

FA0

---------- 5.32k 1 X � X

------------- 0.2 0.11 X � 1 0.055

X � ----------------------------

⎝ ⎠⎜ ⎟⎛ ⎞

PP

0

----- X 1

X

�

( )

K

p

------------------------

2

� ⎩ ⎭⎨ ⎬⎧ ⎫

� �

dXdW-------- f 1 X T P, ,( )�

dTdW--------

4U/bD( ) Ta T�( ) r�A�( ) HRx T( )�[ ]�

FA0 � �i CPiX CP�( )

--------------------------------------------------------------------------------------------------�

HRx T( ) H �Rx TR( ) � T TR�( ) �2

------- T 2 TR2

�( ) �3

------- T 3 TR3

�( )� � ��

SO2 SO212--- O2 SO3→�

� �SO3

12--- �O2

� �SO2� 8.511 0.5( ) 5.731( )� 7.208� 1.563�� � �

� 0.00262� and � 0.738 10 6����

HRx T( ) 42,471� 1.563( ) T 1260�( )� 1.36 10 3��( ) T 2 12602�( )2.459 10 7��( ) T 3 12603�( )�

��

� �i CPi57.23 0.014T 1.94 10 6� T 2����

U�Db Ac

------------- 4Ub D---------- 4 10 Btu/h ft2 �R� �( )

33.8 lb/ft3( ) 2.78/12( ) ft[ ]--------------------------------------------------------------� �

5.11 Btu/h lb cat R� ��

Energy balancedTdW--------

5.11 Ta T�( ) r�A�( ) HRx T( )�[ ]�

0.188 � �i CPiX CP�( )

------------------------------------------------------------------------------------�

Sec. R8.4 Industrial Example of Nonadiabatic Reactor Operation: Oxidation of Sulfur Diox-

that is,

(ER8.4-10)

7. Pressure drop: After rearranging Equation (4-23), the pressure drop is given by

where

Recalling that , we obtain

(ER8.4-11)

8. Evaluating the pressure-drop parameters:

Substituting in Equation (ER8.4-11), we get

(ER8.4-12)

We wish to obtain an order-of-magnitude estimate of the pressure drop. Toobtain this estimate, we consider the reaction to be carried out isothermallywith ,

Integrating with limits atm at and at lb of cat-alyst yields

Because the gas-phase viscosity is a weakly varying function of temperature(i.e., ), we shall consider viscosity to be independent of temperature:

dTdW-------- f 2 T P X, ,( )�

Momentum balancedPdz------ 1 �( )G 1 �X�( )

0 P P0�( ) T0 T�( ) gc Dp3------------------------------------------------------------ 150

� 1

� ( )

D

p ------------------------------- 1.75 G ���

G� Fi0 Mi

Ac

------------------- Mi molecular weight of i�( )�

1307.6 lb/ft2 h��

Ac cross-sectional area �D2 4��

W b Ac z�

dPdW--------

GTP0 1 �( ) 1 �X�( )b Ac 0 T0 PDP gc

3------------------------------------------------------ 150 1 � ( ) �

D

P

------------------------------- 1.75 G ���

f 3 X T P, ,( )GTP0 1 �( ) 1 �X�( )b Ac 0 T0 3DP gc P

------------------------------------------------------ 150 1 � ( ) � D

P

------------------------------- 1.75 G ���

dPdW-------- 1.12 10 8�� 1 0.55X�( )T�

P-------------------------------------------------------------------- 5500 � 2288 � ( ) �

� 0�

dPdW-------- 0.0432�

P---------------------�

Back-of-the-envelope

calculation for P

P0 2� W 0� P P� W 28.54�

P2 4�2

--------------- 0.0432 0 28.54�( )��

P 1.239 atm�

P 2 1.24� 0.76 atm� �

� T�

134

Chap.

(ER8.4-13)

9.

Solution procedure

. There are three coupled differential equations that mustbe solved simultaneously:

Mole balance: (ER8.4-14)

Energy balance: (ER8.4-15)

Momentum balance: (ER8.4-16)

10.

Numerical procedure

. The rate equation is independent of conversionbetween

X

�

0.0 and

X

�

0.05, and the rate of disappearance of over thisrange is equal to the rate of reaction at

X

�

0.05:

(ER8.4-17)

a. Set , , and .b. Calculate

k

from Equation (ER8.4-2).c. Calculate from Equation (ER8.4-1).d. If , calculate from Equation (ER8.4-17). If , use

Equation (ER8.4-5).e. Calculate

X

,

T

, and

P from a numerical solution to Equations (ER8.4-5),(ER8.4-9) and (ER8.4-12).

The Polymath program is given in Table ER8.4-1.

11. Discussion of results. Figures ER8.4-1.1(a) and (b) show the profiles for inlettemperatures of 1200�R and 1400�R, respectively. Only 68.5% conversion isachieved for � 1200�R, even though � 0.99. For an entering tempera-ture of 1400�R, the major portion of the reaction takes place in the first 6 ft ofthe reactor. At this point, the conversion is 0.81, with only another 0.06 of theconversion occurring in the remaining 14 ft, as shown in Figure ER8.4-1.1(b).The cause of this low amount of conversion in the final 14 ft is the steadilydropping temperature in the reactor. Beyond the 6-ft point, the temperature istoo low for much reaction to take place, which means that the reactor iscooled too much.

This detrimental situation indicates that the coolant temperature is too lowfor obtaining maximum conversion. Thus even boiling Dowtherm A at itshighest possible operating temperature is not a suitable coolant. Perhaps a gaswould give a better performance as a coolant in this reaction system. Twoproblems at the end of the chapter pursue this aspect. One of them seeks theoptimum coolant temperature for a constant-coolant-temperature system, andthe other uses inlet gas as a coolant.

dPdW-------- f 3 T P X, ,( )�

dXdW-------- f 1 T P X, ,( )�

The coupleddifferential

equations to besolved with an ODE

solver

dTdW-------- f 2 T P X, ,( )�

dPdW-------- f 3 T P X, ,( )�

SO2

r�SO2� k 0.848 0.012

K p2

-------------�⎝ ⎠⎜ ⎟⎛ ⎞

�

X 0.00� T T0� P P0�

K p

X 0.05� r�SO2� X 0.05�

T0 Xe

Sec. R8.4 Industrial Example of Nonadiabatic Reactor Operation: Oxidation of Sulfur Diox-

TABLE ER84-1 SO3 OXIDATION POLYMATH PROGRAM

Equations:

Figure ER8.4-1.1(a) Conversion, temperature, and equilibrium conversion profiles within the reactor: (a) inlet temperature at 1200�R; (b) inlet temperature at 1400�R.

Figure ER8.4-1.1(b) Conversion, temperature, and equilibrium conversion profiles within the reactor: (a) inlet temperature at 1200�R; (b) inlet temperature at 1400�R.

136 Chap.

Another possible way to operate such a reactor is to use multiple-stage operationwith progressively higher coolant temperatures. Because pressure drop over thereactor is small (�0.7 atm), neglecting the pressure drop does not affect the exitconversion significantly (Figures ER8.4-1.1 or ER8.4-1.2)). The effect is more sig-nificant at lower reactor inlet temperatures because the rate of reaction is apprecia-ble over a longer portion of the reactor bed. At higher inlet temperatures, theconversion is limited by the approach to equilibrium, and hence the pressure drophas a negligible effect.

Figure ER84-1.2 Profile of molar flow rates FA, FB, and FC.

Analyzing theeffects of pressure

drop

Sec. R8.4 Industrial Example of Nonadiabatic Reactor Operation: Oxidation of Sulfur Diox-