#cbe142 hw2

[neonberk]

cbe 142 hw 2

Problem 4 (5 points): Variable volumetric flowrate

A chemical reactor consists of a tube with gaseous inflow and outflow. Within the chem- ical reactor, a gas-phase chemical reaction occurs. Determine and state if the volumetric flowrate at the entrance is greater or less than the volumetric flowrate at the reactor exit for the following three situations. Please provide an explanation only in words. Assume that the gas phase is ideal.

(a) The reactor is at constant temperature and pressure. The gas phase reaction is A −−→ B+C.

(b)  The reaction is A −−→ B and at constant pressure. The temperature increases within the reactor.

(c)  The reaction is A −−→ B and at constant temperature. The pressure decreases within the reactor.

5/5 soln

[neonberk]

cbe 142 hw 2

Problem 3 (20 points): Graphical Reactor Sizing

In companies such as Shell, Dow, and BASF, polymers are a standard product. To cre- ate a polymer, we feed in monomers (A) to the system and we have an initiator acting as a catalyst to start the polymerization process. We can treat the system as a reactor in which the reaction occurs throughout the reaction volume. For a fixed initiator concentration, and a volumetric flow rate of 0.5 m3/min, the following results from an ideal isothermal liquid-phase CSTR were tabulated:

(a)  (8 points) Plot the Levenspiel graph (FA0/−rA vs. XA) for the reaction above.(At XA=0 (FA0/−rA =40)

(b)  (2 points) For 35% conversion, calculate the reactor volume if an ideal CSTR is used to conduct the reaction.

(c)  (4 points) For 35% conversion, calculate the reactor volume if an ideal PFR is used to conduct the reaction. Feel free to either use a numerical integrator or implement by hand a scheme like Simpson’s rule or the trapezoidal rule.

(d)  (2 points) Compare parts (b) and (c) and decide which reactor would occupy a lower volume in order to achieve 35% conversion.

(e)  (4 points) What is the optimal reactor configuration (single reactor, reactor in series) to reach 75% conversion? What are the suggested reactor volume(s) for the system?

[neonberk]

cbe 142 hw2

Problem 2 (10 points): Mole balance and stoichiometry

The reaction

2A + 3B → C (1)

takes place in an isothermal, unsteady CSTR. The feed consists of only A and B in stoichio- metric proportions. Which of the following set of equations gives the correct mole balances on A, B, and C? Species A and B are disappearing and Species C is being formed. Circle the correct answer where all mole balances are correct.

10/10 soln

[neonberk]

cbe 142 hw2

Problem 1 (15 points): Isothermal reactions, conversion

(a)  (7 points) Given a first-order isothermal reaction, A −−→ P, rA = −kcA , simplify the general mole balance equation to get the design equations for the following ideal liquid phase reactors operating under isothermal conditions : i) batch reactor, ii) CSTR and iii) PFR. Your final answer should be in terms of CA0,k,cA and the residence time τ. τ gives us the average time any volume element spends in the reactor for any flow reactor, given as V/q0. For a batch reactor it refers to how long the reaction has taken place in the reactor, which is the time t.

(b)  (8 points) Let the conversion of the reactant A be XA. Express the design equations from part a) in terms of XA, τ and k. Let k=1s−1. Plot XA versus τ for all the three reactor types. XA should vary from 0 to 0.9.Why does the plot for PFR and batch reactor look similar? Why is the conversion for the CSTR lower than the PFR?

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