Chemical Engineering

The University of Birmingham

School of Chemical Engineering

Process Systems (2PS)

Assessed Coursework – 2015/2016

(To be handed in by Thursday 21st January 2016, 15:00)

Concentration changes in a CSTR (continuous stirred tank reactor)

Please submit any files you produce as part of the assessed tutorial to the Canvas assignment.  The report should be uploaded as a word or pdf file and any supporting files (e.g. excel, matlab, simulink) be uploaded as a single zip.

Objectives of the Assessment

1. To develop a deviation variable model from a dynamic model of the concentration within a CSTR, in which the concentration is measured by a conductivity probe.
2. To solve the resulting differential equation analytically for two common types of input change
3. To use these analytic solutions to generate data showing measured concentration-vs-time response plots, and then to compare these plots with simulated response plots generated using Simulink™ (this is the system response without control – the open loop response).
4. To investigate the behaviour of a feedback loop simulating the controlled response of the concentration to both set point changes and disturbances.
5. Based on this behaviour, to comment on the suitability of different concentration controller designs for use in industrial CSTRs.

Within this coursework are a set of tasks that need to be completed. We recommend that you use the worksheet provided on Canvas.

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The system

The system to be investigated is a CSTR with two inlet streams and one outlet stream.  

[pic 1]

The reactor is well mixed and has a fluid volume of V (m3).

F1 is the volumetric flowrate of stream 1 (m3 s-1)

CA01 is the concentration of substance A in stream 1 (kmol m-3)

F2 is the volumetric flowrate of stream 2 (m3 s-1)

CA02 is the concentration of substance A in stream 2 (kmol m-3)

F is the volumetric flowrate of the outlet stream (m3 s-1)

CA is the concentration of A in the outlet stream (kmol m-3)

The CSTR is set up so that the concentration of A in stream 2 can be controlled, the concentration in stream 1 can be viewed as a disturbance (see Appendix A).

The reaction within the CSTR can be represented by the following 1st order reaction equation:

        [pic 2]                                                Eqn (2.1)

Task 2.1 (8% of the marks)

Using an unsteady state material balance show that the CSTR described above can be represented by Eqn(2.2) below.  What do τp, Kp1 and Kp2 represent and how are they related to the reactor parameters listed above?  Make a note of any assumptions used to derive the equation.

        [pic 3]                Eqn (2.2)

end of task 2.1

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To measure the concentration a conductivity probe is used.  The probe can be modelled using a first order differential equation of the form:

        [pic 4]                                Eqn (2.3)

Where τm (s) is the probe time constant, CAm (mA) is the probe signal (a representation of the concentration), Km (mA (kmol m-3)-1) is the probe gain and CA (kmol m-3) is the actual concentration.

The concentration CA needs to be controlled at the set point. In practice the control system would look to manipulate both τp and CA02 to achieve this.  Here however, τp is considered constant and control is achieved through manipulation of CA02 only.

Task 2.2 (2% of the marks)

Show that by combining Eqns (2.2) and (2.3) that the following 2nd order differential equation can be derived.

[pic 5]                Eqn (2.4)

Identify the parameters τ and ζ.

end of task 2.2

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System data and further information

Initially the system is at a steady-state with the following parameters.

• V = 10 m3
• F1 = 0.08 m3 s-1
• F2 = 0.02 m3 s-1
• F = 0.1 m3 s-1
• CA01 = 5 kmol m-3
• CA02 = 1 kmol m-3
• k = 0.01 s-1

• CAs = 2.1 kmol m-3
• τp = 50 s
• Kp1 = 0.4
• Kp2 = 0.1

The probe (sensor) has the following parameters

• Km = 4 mA (kmol m-3)-1
• τm = 15 s

As part of the CSTR / probe system there is a feedback control system which is able to adjust the value of CA02 by manipulating a valve, depending on what the value of the set point CA,set is (note: without changing the value of F2).  The feedback loop contains: