Non-isothermal Reactor Design Questions and Answers

Answer: A

Correct answer: simultaneously with the energy balance

The two balances are coupled in both directions: the rate depends on temperature through the Arrhenius term, and the temperature depends on the rate through the heat released. Neither can be solved first, so they must be integrated together. That coupling is the whole of non-isothermal design, and it is what makes multiple steady states and runaway possible at all.

Answer: B

Both are true and the reason gives the coupling, which is why non-isothermal problems are almost always solved numerically rather than by hand. Each balance contains the other's variable. The coupling is what makes them hard.

Answer: C

It is the heat of reaction divided by the heat capacity of the mixture and is a single number characterising the hazard. A large value means the reaction cannot safely be run adiabatically. Dilution lowers the rise by raising heat capacity.

Answer: D

One hundred thousand joules divided by two hundred joules per kelvin gives five hundred kelvin. A rise of that size would be quite unmanageable without either dilution or heat removal. The number characterises the hazard in one figure.

Answer: A

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the magnitude of the danger. The adiabatic temperature rise is \[ \Delta T_{ad} = \frac{(-\Delta H_r)C_{A0}}{\rho c_p}, \] and for many industrial reactions it runs to hundreds of degrees - enough to decompose the product, boil the solvent or burst the vessel. Diluting the feed raises the denominator and cooling removes the heat, and the two are the standard responses.

Answer: B

The first two are correct and make adiabatic operation particularly easy to analyse. The third is quite wrong, since adiabatic operation offers no means of arresting a runaway once it has begun. The straight line makes the algebra simple.

Answer: C

The generation curve is an S shape while the removal line is straight, and they can intersect three times. The middle intersection is unstable and cannot be held without control. The curve is S-shaped and the line is straight.

Answer: D

Both are true and the reason gives the instability criterion: the system runs away to the upper state or falls back to the lower one, and only feedback control can hold it between. The outer two states are both stable.

Answer: A

Reading the diagram tells you at once how many steady states exist and which of them the reactor will settle into. Moving the removal line by changing the coolant is what shifts the picture. The number of intersections can be one or three.

Answer: B

Correct answer: a jump from a low to a high conversion state

As the feed temperature is raised the heat generation curve, which is sigmoidal in temperature, eventually loses its lower intersection with the straight heat removal line. The reactor then jumps to the only remaining steady state, at high temperature and high conversion, and the transition is abrupt rather than gradual. It is called ignition by analogy with combustion and has nothing to do with flame.