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    1. Ch E 441 - Chemical Kinetics and Reaction Engineering Unsteady StateReactor Operation

    3. General Energy Balance Neglecting kinetic and potential energy changes, while substituting the internal energy in terms of enthalpy: Therefore,

    4. General Energy Balance Substitute this result back into the energy balance yields:

    5. General EB applied to CSTR The energy balance now takes the form:

    6. General EB applied to CSTR Which can be rearranged as:

    7. General EB applied to Batch Reactor For a batch reactor, set FAo to zero: In terms of conversion, which is coupled with mole balance:

    8. Adiabatic Batch Reactor

    9. Adiabatic Batch Reactor If the batch reactor operates adiabatically & work added by the stirrer is negligible,

    10. Adiabatic Batch Reactor If the batch reactor operates adiabatically & work added by the stirrer is negligible, Cancel dt, separate variables, integrate

    11. Transient Reactors with Non-Spatially Uniform Heat Exchange As first approximation, assume quasi-steady state for coolant flow, and neglect accumulation (dTa/dt = 0): Substitution into general energy balance:

    12. Transient Reactors with Non-Spatially Uniform Heat Exchange At steady state (dT/dt = 0),

    13. Example The Morning News, Wilmington, DE (08/03/77) Investigators sift through the debris from the blast in quest for the cause [that destroyed the new nitrous oxide plant]. A company spokesman said it appears more likely that the [fatal] blast was caused by another gas (ammonium nitrate) used to produce nitrous oxide. An 83% (wt) ammonium nitrate and 17% water solution is fed at 200F to a CSTR operated at a temperature of about 510?F. Molten ammonium nitrate decomposes directly to produce nitrous oxide and steam. It is believed that pressure fluctuations were observed in the system and as a result the molten ammonium nitrate feed to the reactor may have been shut off approximately 4 minutes prior to the explosion. Explain the explosion given the following: Feed rate = 310 lb/hr solution 500 lb ammonium nitrate in reactor at shutdown at 510?F.

    14. Example At shutdown, no flow in/out. Assume effluent value left open so reactor nearly at atmospheric. Energy balance reduces to: Assume first order kinetics

    15. Example Energy balance becomes: Where k(T) as:

    16. Another Example Start-up CSTR described in problem 8-5A elementary, irreversible, liquid phase reaction, carried out adiabatically must use full form of each: Species mole balance Rate law Energy balance stoichiometry

    17. Approach to Steady State It is important to know how temperature and concentration approach their steady state values to assure safe operation. Overshoot of temperature can lead to product degradation or runaway condtions. The practical stability limit of the reactor must be known. The unsteady-state mole balance is

    18. Approach to Steady State A typical plot of CA vs. T for steady-state operation (i.e., MB = 0) is shown below. i.e., if the reaction is irreversible and first-order, the "MB = 0 curve" would be

    19. Approach to Steady State This curve (i.e., MB = 0) divides the phase plane into two regions: MB > 0, where concentration increases with time, MB < 0, where concentration decreases with time.

    20. Approach to Steady State Consider relative magnitude of two terms, When (CAo CA) > -(rAt), dCA/dt is positive and concentration increases with time (MB > 0). When (CAo CA) < -(rAt), dCA/dt is negative and the concentration decreases with time (MB < 0)

    21. Approach to Steady State Consider CSTR Energy Balance (Ws = 0), a typical plot of CA vs.T for EB = 0.

    22. Approach to Steady State For an irreversible, 1st order reaction, the EB = 0 curve divides the phase plane into 2 regions: EB > 0, temperature increases with time EB < 0, temperature decreases with time

    23. Approach to Steady State Combining both figures, notice the region where the EB = 0 and MB = 0 curves cross. This point represents the steady-state value. However, the intersection also divides the phase plane into four quadrants.

    28. Approach to Steady State

    29. Approach to Steady State Temperature is increasing in Quadrants I and II and decreasing in III and IV Concentration is increasing in Quadrants I and IV and decreasing in II and III. With this information we may make qualitative sketches of the temperature-concentration pathways or trajectories

    30. Adding a Controller to a CSTR A generic diagram for the control of a chemical process is shown. The controller corrects or minimizes unexpected disturbances that may upset the process.

    31. Adding a Controller to a CSTR Control system measures output variable to be controlled (Y) and compares it to a desired (set point) value (YSP). Difference between actual and set point values is the error signal, e.

    32. Adding a Controller to a CSTR If the error signal is not zero, a controller will make appropriate changes in one of the system manipulated inputs, Z, to force the output variable, Y, to return to its setpoint, YSP.

    33. Adding a Controller to a CSTR Typical controller application on a CSTR Measured/controlled variable Y ? T Manipulated variable Z ? min of coolant

    34. Controller Actions Proportional action (P) adjustment of manipulated input variable (Z) is proportional to the error, e. Zo is called the bias, and is the value of the manipulated variable at the time the controller is turned on. kc is called the gain, with an optimum value that is dependent upon the process. Seldom actually used by itself.

    35. Controller Actions Integral action (I) Adjustment of input variable (Z) is proportional to the integral of the error, e. ?I is the integral time constant. For a reactor, it is the order of magnitude of the space-time. Over long term, measured value always returns to set point. Response can become oscillatory. Seldom actually used by itself.

    36. Controller Actions Derivative action (D) Rate of adjustment of the input variable is proportional to the time rate of change of error ?D is the derivative time can be very sensitive to noise; thus, error is normally filtered before entering controller. Seldom actually used by itself.

    37. Controller Actions Proportional-integral (PI) Adjustment of input variable accomplished by using both proportional and integral actions. Quick response to large errors without set-point offset. Measured variable can be returned to set point without excessive oscillation.

    38. Controller Actions Proportional-integral derivative (PID) Adjustment of input variable accomplished by using all three methods. Very rapid response. Must tune three parameters.

    39. Integral Control of a CSTR