Batch Systems with Heat Effects Example | top |
Balance on a system volume that is well-mixed:
Adiabatic batch reactor with no work:
The following reaction occurs in a batch reactor:
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7) |
Parameter Values |
Adiabatic Reaction
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or use one of the integration formulas, e.g.: , to find the reaction time, t. Even better, use Polymath. |
Cooling:
Control of Chemical Reactors | top |
Unsteady State CSTR: |
For a batch reactor, FAO = 0 |
For the reaction in a CSTR: |
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Linearized Stability Theory | top |
Energy Balance (Applied to a CSTR) | |
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CSTR Mole Balance |
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Manipulating the Energy and Mole Balances |
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Let andsignify steady state values. Then at steady state: |
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Adding equations (6) and (7): |
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Linearizingby expanding it in a Taylor Series: |
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To obtain: |
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Let |
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Using these substitutions, we can arrive at the following equations that describe the behavior of temperature and concentration, when the steady state conditions are perturbed in a CSTR: |
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22. |
Predicting the Behavior of a CSTR using LST | top |
At time t = 0, y1 = y10, where:
Making use of Equation 20
we notice that for the case of b2 = 4c:
if b < 0 , then the amplitude (i.e., T - TS) will increase
if b > 0 , then the amplitude (i.e., T - TS) will decrease
and that:
if b2 > 4c , thenis real (i.e., non-oscillatory behavior)
if b2 < 4c , thenis imaginary (i.e., oscillatory behavior)
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Reference: |
* All chapter references are for the 4th Edition of the text Elements of Chemical Reaction Engineering .