ChE 349-HW #6-Due Monday, 3/5/18 The gas phase, endothermic isomerization A B is

Question

ChE 349-HW #6-Due Monday, 3/5/18 The gas phase, endothermic isomerization A B is to be run in a steady-state PBR with a preheated pure feed of A. The reaction rate follows unusual zero order kinetics: The reactor is filled with catalyst pellets, but treat the reactor as a PFR of bed volume V The flow rate is sufficiently low, and the pellets large enough, that the pressure drop across the reactor is minimal (P Po). The reactor has a heating jacket to control the reacting gas temperature. The jacket flui temperature Ta is a function of reactor volume V. Post-reactor processing issues require that the reactor temperature drop in a slow. linear ramp, ie. dT/dV =-oc (value below). catalyst in reactor not shown) . Derive an integrated relationship for reactor temperature T as a function of reactor volume V. HINT: You do not need the energy balance here! Derive a relationship for T, as a function of T that meets the required reactor T ramp. HINTS: Now use the energy balance. For the Ej Fjepj, look at the data provided below and in the problem statement to help you decide how to write this term. * .Change this result so that T, is a function of V Derive an integrated relationship for Xa as a function ofV .Using the data beow, make a plot of T and T, vs. V (left vertical axis) and X vs. V (right vertical axis, on the same graph) FAo-10 mole's 500 K pA 50 J/mole-K (independent of T) k, = 0.0008 mole!iter-s-K AH.-25000. Innole A (~ indep. of T) Useful data: =2K/liter Ua = 150 J/s-K-liter

Explanation / Answer

At first, a material balance needs to be considered on the reactor.

Thereafter, as stated in the question, the energy balance needs to be taken into account.

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