Problem

# (a) Example 12–1. Effective Diffusivity. Make a sketch of a diffusion path for which the t...

(a) Example 12–1. Effective Diffusivity. Make a sketch of a diffusion path for which the tortuosity is 5. How would your effective gas-phase diffusivity change if the absolute pressure were tripled and the temperature were increased by 50%?

(b) Example 12–2. Tissue Engineering. How would your answers change if the reaction kinetics were (1) first order in O2 concentration with k1 = 10-2 h−1? (2) For zero-order kinetics carry out a quasi steady state analysis using Equation (E12-2.19) along with the overall balance

to predict the O2 flux and collagen build-up as a function of time. Sketch Ψ versus λ at different times. Sketch λc as a function of time. Hint: See P12-10B. Note: V = ACL. Assume α= 10 and the sloichiometric coefficient for oxygen to collagen, vc, is 0.05 mass fraction of cell/mol O2. Ac = 2 cm2

(c) Example 12–3. (1) What is the percent of the total resistance for internal diffusion and for reaction rate for each of the three particles studied? (2) Apply the Weisz-Prater criteria to a particle 0.005 m in diameter.

(d) Example 12–4. Overall Effectiveness Factor. (1) Calculate the percent of the total resistance for external diffusion, internal diffusion, and surface reaction. Qualitatively how would each of your percentages change (2) if the temperature were increased significantly? (3) if the gas velocity were tripled? (4) if the particle size were decreased by a factor of 2? How would the reactor length change in each case? (5) What length would be required to achieve 99.99% conversion of the pollutant NO? What if…

(e) you applied the Mears and Weisz-Prater criteria to Examples 11-4 and 12-4? What would you find? What would you learn if ΔHRX = −25 kcal/mol, h = 100 Btu/h ft2-°F and E = 20 kcal/mol?

(f) we let γ = 30, β = 0.4, and φ = 0.4 in Figure 12-7? What would cause you to go from the upper steady state to the lower steady state and vice versa?

(g) your internal surface area decreased with time because of sintering. How would your effectiveness factor change and the rate of reaction change with time if kd = 0.01h-1 and η  = 0.01 at t = 0? Explain.

(h) someone had used the false kinetics (i.e., wrong E, wrong n)? Would their catalyst weight be overdesigned or underdesigned? What are other positive or negative effects that occur?

(i) you were to assume the resistance to gas absorption in CDROM Example R12.1 were the same as in Example R12.3 and that the liquid phase reactor volume in Example R12.3 was 50% of the total, could you estimate the controlling resistance? If so, what is it? What other things could you calculate in Example R12.1 (e.g., selectivity, conversion, molar flow rates in and out)? Hint: Some of the other reactions that occur include

(j) the temperature in CDROM Example R12.2 were increased? How would the relative resistances in the slurry reactor change?

(k) you were asked for all the things that could go wrong in the operation of a slurry reactor, what would you say?

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