March 28, 2024, 04:24:12 AM
Forum Rules: Read This Before Posting


Topic: Modelling the const P, Non-isothermal CSTR  (Read 2470 times)

0 Members and 1 Guest are viewing this topic.

Offline sid87pl

  • Very New Member
  • *
  • Posts: 1
  • Mole Snacks: +1/-0
Modelling the const P, Non-isothermal CSTR
« 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:
:rarrow: B + C
I have the following thermodata for the participating species: H, Cp

My inputs are:
mflow [kg/s]         only A is in the inlet stream
To [K]                 temperature of the inlet stream and inside the reactor at time t=0
Po=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 = Qinin - Q*ρ
2) d(V*Ca)/dt  = Qin*Cain - Q*Ca + r*V
3) ρ*Cpmix*V*dT/dt = Qinin*Cpin*(Tin-To) -Q*ρ*Cpmix*(T-To) + r*V*ΔHr

Qin      - [m3/s]   inlet volumetric flow rate
ρ        - [kg/m3]  density of the mixture inside the reactor and in the outlet stream
Cpmix  - [J/kg]     heat capacity of the mixture at a given temperature
Cpin    - [J/kg]     heat capacity of the inlet stream
ΔHr     - [J/mole]  heat of the reaction

My logic is to:
a) Use Po, To, initial concentration (xA=1, xB=xC=0) to work out the initial density of the mixture ρ
b) From the density, mflow 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), xi(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

Offline curiouscat

  • Chemist
  • Sr. Member
  • *
  • Posts: 3006
  • Mole Snacks: +121/-35
Re: Modelling the const P, Non-isothermal CSTR
« Reply #1 on: August 18, 2014, 01:12:29 PM »
You want to model steady state or the transient?

Offline curiouscat

  • Chemist
  • Sr. Member
  • *
  • Posts: 3006
  • Mole Snacks: +121/-35
Re: Modelling the const P, Non-isothermal CSTR
« Reply #2 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.
« Last Edit: August 18, 2014, 01:53:22 PM by curiouscat »

Sponsored Links