process control

Problem 1. Derivate a model of a Continuous Stirred Tank Reactor (CSTR) with a jacket, in which a simple liquid phase irreversible chemical reaction takes place. The density and volume inside the reactor are constant. Reaction :AB r=kCA,r: rate of reaction k : reaction rate constant CA : molar concentration The heat transfer term is A and the coolant temperature is TC a) Obtain the total mass balance of the reactor for a constant volume. Use the component balance for concentrations CA and CB and obtain dtdCA and dtdCB. b) Use the energy balance to obtain dtdT of the system that has been cooling down by the jacket and include the effect of the reaction. If the reactor works under the following conditions and the reaction rate constant is represented by the Arrhenius equation: c) Use Laplace to find CA(s). d) Find the steady-state constant CA and Time constant . e) Write what is the maximum possible CA value, and how long it takes to reach 98% of this value. Problem 1. Derivate a model of a Continuous Stirred Tank Reactor (CSTR) with a jacket, in which a simple liquid phase irreversible chemical reaction takes place. The density and volume inside the reactor are constant. Reaction :AB r=kCA,r: rate of reaction k : reaction rate constant CA : molar concentration The heat transfer term is A and the coolant temperature is TC a) Obtain the total mass balance of the reactor for a constant volume. Use the component balance for concentrations CA and CB and obtain dtdCA and dtdCB. b) Use the energy balance to obtain dtdT of the system that has been cooling down by the jacket and include the effect of the reaction. If the reactor works under the following conditions and the reaction rate constant is represented by the Arrhenius equation: c) Use Laplace to find CA(s). d) Find the steady-state constant CA and Time constant . e) Write what is the maximum possible CA value, and how long it takes to reach 98% of this value