Degrees of Freedom in a Chemical Process

Hello everyone

I am currently doing an exercise of a process to make styrene from ethylbenzene and benzene. First task is to analyze the degrees of freedom to see if they are saturated. And then saturate the degrees of freedom for both distillate columns. The flowsheet is the following:

Two reactions take place in the reactor (second unit):

- C₈H₁₀ -> C₈H₈ + H₂

- C₆H₆ + 3 H₂ -> C₆H₁₂

They occur in gas-phase at 1.3 bar. Both reaction conversion (X_A and X_B) are known. The feed is only ethylbenzene and benzene (5:1 molar ratio).

We remove H₂ as soon as possible as it is dangerous. Both distillations columns contain a partial reboiler and total condenser. Styrene is removed by the first column at low pressure and low temperature. The second distillation column is working at atmospheric pressure.

What I've done for the degrees of freedom (in order of the flowsheet):

- Mixer : d = 4 . Saturate with both inlet streams (u₀ and u_5.2) as well as P_Mix and T_Mix.

- RXN : d = 3 . Saturate with inlet stream (u₁ ) as well as P_Rxn and T_Rxn.

- Flash : d = 3 . Saturate with inlet stream (u₂ ) as well as T_Flash and the recovery of one key component (eg: we suppose that this is Hydrogen and recovery of 1% (to be realistic) since we want to take it off).

- Dist 1 : d = (P+Q) +5 (from my notes...). Saturate with inlet stream (u_3.2 ) as well as P_dist1 , receovery of light key component and also the one of the heavy key component. The two remaining we can fix reflux ratio to infinite at the top and the bottom if we assume Fenske conditions. (Q denotes thermal behaviour that we fix at 0 except from reboiler and condenser because of adiabatic conditions).

- Dist 2 : Same as Dist 1 except inlet stream and pressure are different.

I was first wondering if all of this was correct. Moreover, I will need to guess some parameters before doing my shortcut model I suppose. How could I guess the temperature of the Flash if I don't know the temperature of the reaction? I suppose it will be around the cooling water temperature (so maybe 37°C ??). I guess the choice needs to be done according to hydrogen to avoid any explosion.