Reference no: EM132502424

Question 1. Consider the following reaction scheme:

X + Y = 2D (reaction 1, rate constant k₁, irreversible reaction) 2X = 2U (reaction 2, rate constant k₂, irreversible reaction)

D is the desired product, and U is the undesired side-product. The optimal chemical environment within the reactor would be low concentration of X and high concentration of Y (this can be shown through a trivial analysis of the expression for fractional yield). One reactor configuration that can be conceptualized to achieve this optimal environment is a tubular reactor with periodic side-stream feeds of X augmenting the main feed, where the side-stream feed addition distribution function is given by f(V) fini side-stream feed/ h.m³ reactor volume]. The concentration of X in the side-stream-feed-supply tube is Cxw. Assume the reactor is an isothermal plug flow reactor.

a. Derive the total mass balance [in terms of RV)] and the mass balances for X and Y

b. To approximate an optimal design, the side-stream feed inputs will be adjusted to maintain Cx constant throughout the reactor, in other words, Cx = Cx. = Cx„ where L is reactor length). Also, a high conversion of X is desired, and the side-stream feed concentration is assumed to be high to simplify calculations, in other words, C_xw >> C_x. Re-derive the mass balances of part (a) under these assumptions.

c. Under the assumptions of part (b), derive expressions for f(V) and for total reactor volume (VI)

d. If equal stoichiometric feeds of X and Y are to be used (considering the reactor as a whole) derive the relationship between the outlet concentrations C_XL, and C_yL.

e. If yield is defined by the ratio: [Total "D" formed / Total "X" fed], compare this yield to the conversion of X for: i) The reactor configuration discussed above; ii) A single CSTR, and lii) A PFR without the side-stream feed arrangement.

f. How would you achieve operation such as the one envisioned in this question in practice?

Question 2.

Styrene (ST)is produced industrially by catalytic dehydrogenation of cthylbenzene (EB) on an iron catalyst. The reaction is endothermic and reversible and takes place with an increase in the number of moles. The feed is diluted by means of an inert component, such as steam. The steam also serves as a heat carrier, reducing the temperature drop under adiabatic operation.

Part a. If the conversions are defined as:

Conversion of ethylbenzene (EB): X_EB = F⁰_EB - F_EB/F⁰_EB

Conversion of EB into product j: x_j = Fj - F⁰j/F⁰_EB

for j: ST, BZ, TO, H₂, H₂O, CH₄, and C₂H₄. (Steam is considered as an inert)

Simulate the profiles of EB conversion and conversion of EB into styrene (ST), benzene (BZ), and toluene(T0), and the temperature and pressure profiles in the reactor. Assume that because of their limited concentrations in the reactor, CH₄ and C₂H₄ can be neglected in the energy balance formulation.

Part b. Evaluate and comment on the error in the profiles if you were to neglect pellet diffusion (internal mass transport limitations).

Part c. The above assumed no internal heat transport limitations, and no external transport limitations (heat or mass). Are these assumptions valid? Why (or) why not?

Part d. Would you expect to see steady state multiplicity in this reactor? Explain why or why not. (Brief mathematical and/or graphical justification is adequate)

Attachment:- Assignment.rar