Each Student must solve the following Problems and report it as a Final Examination Task. The final examination task document file (in .PDF file, where the filename should contain your full name) must be uploaded to the following URL (https://bit.ly/4f5LQHn ) before 18th December 2024:
- [Problem A, Score = 40] The irreversible gas-phase reaction: A ==> B (with presence of catalyst) is carried out adiabatically over a packed-bed of solid catalyst particles. The reaction is first order in the concentration of A on the catalyst surface: –r‘As = k‘ CAs. The feed consists of 70%mole A and 30 %mole inert, and enters the bed at a temperature of 600 K. The entering volumetric flow rate is 25 dm3/s (i.e. 25,000 cm3/s). The relationship between the Sherwood number and the Reynold number is: Sh = 100 Re1/2. As a first approximation, one may neglect pressure drop. The entering concentration of A is 2.3 M. Calculate the catalyst weight (W) necessary to achieve 85% conversion of A for: (a). isothermal operation; (b). adiabatic operation. Additional information: Kinematic viscosity (μ/ρ) = 0.03 cm2/s; Particle diameter (dp) = 0.23 cm; Superficial velocity (U) = 12 cm/s; Catalyst surface area/mass of catalyst bed (a) = 60 cm2/g-cat; Diffusivity of A (De) = 10-2 cm2/s; Heat of reaction (ΔHoRx = -10,000 cal/gmol A; Heat capacities (CpA = CpB) = 25 cal/gmol.K, CpS (solvent) = 75 cal/gmol.K; k‘ (400 K) = 0.01 cm3/s.g-cat with E = 4000 cal/mol).
- [Problem B, Score = 20] The reaction: A —> B is carried out in a differential packed-bed reactor at different temperatures, flow rates, and particle sizes. The results shown in Figure P15-3B below were obtained. (a). What regions (i.e. conditions dp, T, FT0) are external mass transfer-limited? ; (b). What regions are surface reaction rate-limited?; (c). What region is internal-diffusion-controlled?; (d). What is the internal effectiveness factor at T = 400 K and dp = 0.8 cm?
- [Problem C, Score = 40]: The second-order decomposition reaction: A —> B + 2C is carried out in a tubular reactor packed with catalyst pellets 0.5 cm in diameter. The reaction is internal-diffusion-limited. Pure reactant A enters the reactor at a superficial velocity of 8 m/s, a temperature of 350 oC, and a pressure of 600 kPa. Experiments carried out on smaller pellets where surface reaction is limiting yielded a specific reaction rate of 0.05 m6/mol.g-cat.s. Calculate the length of bed necessary to achieve 80% conversion.