A Problem Reaktor2

Reactor for Manufacture of H2SO4 Process Basis and Data Available with Respect Thereto Composition of the gas on entering the reactor: SO2 0.06 O2 0.15 N2 0.790 SO3 0.000 Input Stream Temperature T0 = 693.0 ° K

The outlet is in agreement with chemical ba

where T2 is Output Stream Temperature. Degree of Conversion X = Output Stream Temperature T =

0.846 844.1 °K

Process Flow Sheet Flow Sheet

1

R1

2

List of Components, Streams and Blocks. List of Streams: 1 roasting gas

SO2,SO3,O2,N2

List of Components: 1 SO2

2 outlet from reactor

SO2,SO3,O2,N2

2 O2

32.00

3 N2

28.01

4 SO3

80.06

List of Blocks 1 reactor

molar mass 64.06

R1

Basis of Calculation and Conversion of Specified Flows and Compositions Molar Balance: Conversion: n1 x1;1

Reference Stream: n1· x1;1 = 1 For the reference stream defined in this manner is ζ = 16.667 0.060

x1;2 x1;3 x1;4

0.150 0.790 0.000

Chemical Reactions, Determination of Number of Independent Chemical Reactions Reactions: reactants 2.SO2 + O2

Stoichiometric Coefficients of Reactions:

products of reaction 2.SO 3

=

component SO2

reaction No. 1 -2

O2

-1

N2

0

SO3

2

Incidence Matrix stream reactor 1 1 -1 1

1 2 r1

Specification Table and Matrix of Coefficients Specification Table: stream node

1

2

reaction

component 16.667

n2

nr

1

SO2

0.060

x2;1

-2.000

1

2

O2

0.150

x2;2

-1.000

1

3

N2

0.790

x2;3

0.000

1

4

SO3

0.000

x2;4

2.000

1

number of real streams number of independent chemical reactions number of unknown compositions in stream 2 total sum of unknowns

2 1 4 7

sum of unknowns + 1 =

balance equations in node sum equations (stream 2) streams with fixed flows headings sum number of rows number of columns equations missing

Formulation of Additional Relations The last row in the matrix of coefficients corresponds to the additional relation nx2;4 = nx1;1*(Degree of Conversion) =

Matrix of Coefficients:

0.000

0.000

0.000

0.000

0.000

0

1

0 #VALUE!

0 #VALUE!

0 #VALUE!

0 #VALUE!

0 #VALUE!

0 #VALUE!

0 #VALUE!

Table of Solutions Containing Complete System Characteristic The values selected for ζ and T have n1

vector of solutions #VALUE!

16.667 n1

Table of Solutions: stream n1

flow of components SO2

nx1;1

1.000 n2

#VALUE!

nx1;2

2.500 nx2;1

#VALUE!

O2

2.500

nx1;3

13.167 nx2;2

#VALUE!

N2

13.167

nx1;4

0.000 nx2;3 nx2;4 nr

1.000

SO3 altogether

#VALUE! #VALUE! #VALUE!

0.000 16.667

temperature K pressure kPa

693.0 101

However, the values selected for ζ and T must satisfy two non-linear additional relations. The relation for equilibrium constant can be adjusted to have the following form

K (X ) =

X ⋅ n2

0,5

K (T ) = exp(

0,5 2;2

nx2;1 ⋅ nx

11524,4 −10,92) T

For the specified temperature T = 844.083 ° K is K = 15.38 For the specified value nx2;4 = 0.846 is K = #VALUE! difference of equilibrium constants #VALUE! =f(X , T) Enthalpy Balance CpA CpB CpC CpD Ho Hform SO2 23.85 0.07 0 0 9676.88 -297053.5 O2 28.11 0 0 0 8512.84 0 N2

31.15

-0.01

0

0

8898.03

0

SO3

25.13

0.11

-9.05E-05

2.61E-08

11852.07

-395527.1

stream SO2

specific enthalpy of component i in stream j 1 2 hr 18200.07

26059.98

594107

O2

12286.44

17357.82

0

N2

11730.52

16451.63

0

24626.96 693.000

35476.4 844.083

-791054.2 196947.2

SO3 T °K

Enthalpy Balance

n1·h1 n2·h2 nr·hr n1h1 - n2h2 + nrhr =

203368.0 kW #VALUE! #VALUE! #VALUE! = g(X , T)

Now it is necessary to find such values for X and T to make the values of functions g(X , T) and f(X , T) equal ze Set target cell > Equal to By changing cells

D11 D12

#VALUE! abs(f(X,T)) + abs(g(X,T)) 0 Degree of Conversion X Output Stream Temperature T

reement with chemical balance.

Stream Temperature.

kmol/s nx2;4

action No. 1

alance equations in node 1 m equations (stream 2) reams with fixed flows

umber of rows umber of columns quations missing

0.85

4 1 1 1 7 7 8 1

0.85

able of Solutions: kmol·s-1 n2 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

524,4 −10,92) T

844.1 101

X , T) and f(X , T) equal zero.