Mathematical Modeling and Control of A Nonisothermal Continuous Stirred Tank Reactor, Cstr

Description

– Mathematical Modeling and Control of A Nonisothermal Continuous Stirred Tank Reactor, Cstr –

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Abstract

Mathematical Models describing the variations in the volume of the system, concentration of reactant (s) yet to react, temperature of the system, and the temperature of the cooling jacket over time in a non-isothermal CSTR that handles a simple, irreversible, first order or second order exothermic reaction in liquid phase were formulated.

This work is with a particular reference to the synthesis of propylene from cyclopropane and that of cumene (isopropyl benzene) from benzene and propylene. The models were solved simultaneously by analytical approach rather than the normal numerical approach employed for solving non-linear differential equations.

We noticed that the major determinants of  the  reactants  conversion level and the extent of reaction are the feed concentrations, feed temperature and the cooling jacket inlet temperature.

The system is found to have a single, locally stable, steady state with periodic (underdamped) behaviors due to the existence of both inherent negative and positive feedback in it.

Nonlinear feedforward control equations show that  feed  flowrate  does  not have to be changed when feed temperature T_i changes, rather its changes inversely with feed concentration C_Ai. Again, the cooling -jacket temperature T_c changes linearly with feed temperature T_i and nonlinearly (inversely) with feed concentration C_Ai.

Introduction

1.1 Background of the Study

This research work is based on the characterization of a processing system, non-isothermal continuous stirred tank reactor (CSTR) and its behavior using a  set  of  fundamental dependent quantities (mass, energy, and  momentum) whose values describe the  natural state of the system,

and the modeling of a set of equations in the dependent  variables which  describe how the natural state of the system changes with time.

The study is carried out by the use of mathematical models which are built based on the knowledge of the constitutive equations namely; transport rate equations, equations of state, chemical and phase equilibrium, kinetic rate equations, and dead-time.

These were used in characterizing the conservation balances on mass, energy, and momentum. This is done with particular interest on a non-isothermal CSTR reactor for simple irreversible, exothermic reactions in the same phase.

Every physical and chemical phenomenon applied, and the balance equations developed were all from the macroscopic viewpoint so as to moderate the size and complexity of the emerging models.

Since the fundamental variables cannot be measured conveniently and directly, other variables which can be measured conveniently, and when  grouped  appropriately determine  the values of the fundamental variables,  were selected.

Thus mass, energy, and  momentum  can be characterized by variables (state variables) such as density, concentration, temperature, pressure and flow rate which define the state of the system.

The equations that relate the state variables (dependent variables) to the various  independent  variables  are derived from application of the conservation principle on the fundamental quantities and are called state equations.

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