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Specialty Chemistry Forums => Chemical Engineering Forum => Topic started by: sid87pl on August 18, 2014, 10:52:28 AM

Title: Modelling the const P, Non-isothermal CSTR
Post by: sid87pl on August 18, 2014, 10:52:28 AM

Dear all,

For couple of days I have been trying to model non-isothermal CSTR behaviour at constant pressure.
The problem that I am considering is a simple irreversible gas-phase reaction of the form:
A  :rarrow: B + C
I have the following thermodata for the participating species: H, Cp

My inputs are:
m_flow [kg/s]         only A is in the inlet stream
T_o [K]                 temperature of the inlet stream and inside the reactor at time t=0
P_o=const [Pa]      pressure
τ=const  [sec]     residence time, defined as V/Q

Can anyone tell me if my model equations are correct and how can I actually solve it? I particulary mean, how to simplify the equation 1) to somehow separate ρ and V in order to track their change over time separately in my ODEs solver?

I also assume that this is non-constant density and non-constant volume problem.

Model equations:
1) d(ρ*V)/dt = Q_in*ρ_in - Q*ρ
2) d(V*Ca)/dt  = Q_in*Ca_in - Q*Ca + r*V
3) ρ*Cp_mix*V*dT/dt = Q_in*ρ_in*Cp_in*(T_in-T^o) -Q*ρ*Cp_mix*(T-T^o) + r*V*ΔH_r

Q_in      - [m3/s]   inlet volumetric flow rate
ρ        - [kg/m3]  density of the mixture inside the reactor and in the outlet stream
Cp_mix  - [J/kg]     heat capacity of the mixture at a given temperature
Cp_in    - [J/kg]     heat capacity of the inlet stream
ΔH_r     - [J/mole]  heat of the reaction

My logic is to:
a) Use P_o, T_o, initial concentration (x_A=1, x_B=x_C=0) to work out the initial density of the mixture ρ
b) From the density, m_flow and assumed residence time τ I can find the initial volume
c) From this point I think that it is possible to initialize the solver to find ρ(t), V(t), x_i(t), T(t)

The only thing that cause the problem is the non-constant density condition. I was able to solve it for ρ=const , however this is not what I am looking for in this case I guess.

I would be very grateful for any help,
Daniel

Title: Re: Modelling the const P, Non-isothermal CSTR
Post by: curiouscat on August 18, 2014, 01:12:29 PM

You want to model steady state or the transient?

Title: Re: Modelling the const P, Non-isothermal CSTR
Post by: curiouscat on August 18, 2014, 01:15:03 PM

Can't you add in the gas law as an additional equation?

density = PM / RT or something similar?

Also, be careful with this: τ=const  [sec]     residence time, defined as V/Q

You must specify whether Q is referred to at inlet or exit conditions.

PS. You'd also need an explicit stoichiometry constraint or one more species balance. As I see it, your Material Balance currently has four variables: Q, V, ρ, Ca but only 2 eqns.