The following differential equation has been derived to describe the temperature in a continuous reactor:

 

Where T₀ is the inlet temperature, q is the feed rate, C_A is the concentration of reactants and T_j is the temperature of fluid in the cooling jacket.  Typical operating conditions for the reactor are:

T₀ = 450 K; q = 1 m³/min; C_A = 2 mol/m³; T_j = 550 K; k = 0.2 K/(mol/m³)²

 

1. Determine the steady state operating temperature that is achieved using these typical conditions. (1 point)
2. Linearize the differential equation around the steady state. (2 points)
3. Determine the transfer function between the inlet temperature (T'₀) and the reactor temperature (T') (i.e., G₁(s) = T'(s) / T'₀(s)) (1 point)
4. Determine the transfer function between the cooling jacket temperature (T'_j) and the reactor temperature (T'), (i.e., G₂(s) = T'(s) / T'_j(s)) (1 point)
5. Is the outlet temperature more sensitive to changes in inlet temperature or jacket temperature or is the output equally sensitive to both inputs, why?
    

 

Transcribed Image Text:

dT dt = 4q (ToT) +kC2 + 2 (T; − T) dT dt = 4q (ToT) +kC2 + 2 (T; − T)

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