Nonadiabatic Tubular Reactor with Recycle

Lewis number

2.03

Consider a nonadiabatic tubular reactor with negligible mass and heat dispersions and recycle where a first-order exothermic reaction takes place [1]. This system is governed by the following two dimensionless partial differential equations and boundary conditions BC1 and BC2:

∂x

∂t

=-

R+1

Da

∂x

∂z

+(1-x)exp

θ

1+θ/γ

,

Lw

∂θ

∂t

=-

R+1

Da

∂θ

∂z

+B(1-x)exp

θ

1+θ/γ

-α(θ-

θ

c

)

,

BC1:

x(0,t)=

R

R+1

x(1,t)

,

BC2:

θ(0,t)=

R

R+1

θ(1,t)

.

Here

x

is concentration and

θ

is temperature,

γ=25

is the activation energy,

B=8.3

is the heat evolution parameter,

θ

c

=0.05

is the dimensionless cooling temperature,

α=2.0

is the dimensionless cooling parameter,

R=10

is the recycle ratio,

Da

is the Damköhler number, and

Lw

is the Lewis number.

As can be seen from snapshot 1, periodic solutions are obtained for

Lw=2.05

and

Da=0.53

. In the figure,

x

1

(t)=x(z=1,t)

and

θ

1

(t)=θ(z=1,t)

are plotted versus

t

in blue and green, respectively. Also, you can see from snapshot 1 that a limit cycle is obtained for the above values of the parameters.