Modeling of Coupled Non linear Reactor Separator Systems Prof S.Pushpavanam
Chemical Engineering Department
Indian Institute of Technology Madras
Chennai 600036 India
http://www.che.iitm.ac.in
Modeling of Coupled Non linear Reactor Separator Systems Prof S.Pushpavanam
Chemical Engineering Department
Indian Institute of Technology Madras
Chennai 600036 India
http://www.che.iitm.ac.in
Outline of the talk
Case study of a reactive flash
Singularity theory, principles
Coupled Reactor Separator systems
Motivation for the study
Issues involved
Different control strategies for reactor/separator
Mass coupling, energy coupling
Effect of delay or transportation lag
Effect of an azeotrope in VLE
Operating reactor under fixed pressure drop
Conclusions
Industrial Acetic acid Plant
Reactive flash
Reactive flash continued…
Model assumptions
nth order irreversible exothermic reaction
Reactor is modeled as a CSTR
CSTR is operated under boiling conditions
Dynamics of condenser neglected
Ideal VLE assumed
Model equations
Where xA is the mole fraction of component A α is ratio of activation energy of reaction to latent heat of vaporization And β is related to the difference in the boiling point Steady state is governed by xAf,Da, α, β and n.
Multiple steady states in two-phase reactors under boiling conditions may occur if the order of self-inhibition α is greater than the order n of the concentration dependency of the reaction rate.
Physical cause of multiplicity
Here a phase equilibrium driven self inhibition action causes steady state multiplicity in the system
When the reactant is more volatile then the product, then a decrease in reactant concentration causes an increase in temperature. This causes further increase in reaction rate and hence results in a decrease in reactant concentration.
This autocatalytic effect mentioned just above causes steady state multiplicity
Singularity theory
Most models are non linear. The processes occurring in them are non linear
Non linear equations which are well understood are polynomials
Hence we try to identify a polynomial which is identical to the nonlinear system which models our process
Singularity theory can be used for
To determine maximum number of solutions
and to determine the different kinds of bifurcation diagrams , dependency of x on Da
and identify parameter values α,β where the different bifurcation diagrams occur
It satisfies
Singularity theory draws analogies between polynomials and non linear functions
Consider a cubic polynomial
If the function satisfies Then f has a maximum of three solutions Consider a non linear function
Singularity theory continued…
x i.e. the state variable of the system is dependent on Da.
The behavior of x Vs Da depends on the values of α and β.
Critical surfaces are identified in
α-β plane across which the nature of bifurcation diagram changes.
Hysteresis variety
We solve for x, Da and α when other parameters are fixed
Isola variety
We solve for x, Da and α when other parameters are fixed
Bifurcation diagrams across hysteresis Variety
Low density Polyethylene Plant
HDA process
Coupled Reactor Separator
Motivation to study Coupled Reactor Separator systems
Individual reactors and separators have been analyzed
They exhibit steady-state multiplicity as well as sustained oscillations caused by a positive feedback or an autocatalytic effect
A typical plant consists of an upstream reactor coupled to a downstream separator
We want to understand how the behavior of the individual units gets modified by the coupling
Comments