a) Thermal theory of explosion: the batch reactor model

a) Thermal theory of explosion: the batch reactor model

The following diagram:

0 20 40 60 80 100

0 500 1000 1500 2000 2500

shows the time evolution of temperature in an adiabatic batch reactor described by the model

0

0

a

a

E RT

E

r RT

V

dC k e C

dt

dT H

k e C

dt c





  

  

 



with initial conditions

  0 0 ;   0 0

C  C T  T .

If we refer to the following quantities:

0

max ^r ; _a ^a

V

H C E

T T

c R

   

which one of these statements is true?

1. T a and T 0 are constant, ^{ T max 1} > ^{ T max 2} > ^{ T max 3} 2. T a and T 0 are constant,  T ^{max 1}

<  T ^{max 2}

<  T ^{max 3} 3.  T ^max and T 0 are constant, T a1 >T a2 >T a3

4.  T ^max and T 0 are constant, T a1 <T a2 <T a3

5. Nothing can be said Explain your answer.

T 1

T 2

T 3

t

b) Reactant and product mixtures

A combustor operates at an equivalence ratio of 0.25 with an air flowrate of 6.5 kg/s. The fuel is methane. Determine:

1. the fuel mass flowrate

2. the air-fuel ratio at which the engine operates 3. the mole fraction of oxygen in the product mixture

c) Adiabatic flame temperature

1. Estimate the constant-pressure adiabatic flame temperature for the combustion of a stoichiometric CH 4 –air mixture. The pressure is 1 bar and the initial reactant temperature is 298 K. Use the following assumptions:

 “Complete combustion”, i.e., the product mixture consists only of CO 2 , H 2 O, and N 2 .

 The enthalpy of the product mixture is estimated using constant specific heats

evaluated at 1200 K  (T i + T ad )/2, where T ad is guessed to be about 2100 K.