A pilot plant consisting of a Continuously–Stirred Tank Reactor (CSTR) is used to investigate the production of different grades of a chemical species via a simple reaction A?B

having second–order kinetics given by the rate equation

r_A=-kC_A^2

A dynamic model of the process is required to be developed to assist in test scheduling.

The CSTR has a fixed volume Vm3 of and volumetric flow rate (both in and out) of F m3/min . The concentration of reactant A is monitored at the plant inlet and outlet, with concentrations denoted by CAO and CA respectively. The reaction rate constant is k m^3 ?mol?^(-1) ?min?^(-1)
The values of all system parameters are shown in Table 1 and are unique for each student.

. Continuously–Stirred Tank Reactor

Use mass balance techniques to develop a differential equation representation of the system. State any assumptions you have made in developing the model.

Determine initial and final steady state outlet concentrations CA for a step change in inlet concentration as defined by ?C_AO in the individual values in

Linearise the non–linearity in the equation developed in 1(a) and use it to propose a linear model of the process in differential equation form.

Develop a Transfer Function model of the process by applying deviation variables.

Solve the equation and plot the linearised time response of the system.

. Develop a Simulink Model of the original nonlinear model found in part 1(a) and simulate the response of the system to the same step change as described in part

. Compare the linear and non–linear model responses and comment.

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