The second-order decomposition reaction A → B + 2C is carried out in a tubular reactor packed with catalyst pellets 0.4 cm in diameter. The reaction is internal-diffusion-limited. Pure A enters the reactor at a superficial velocity of 3 m/s, a temperature of 250°C, and a pressure of 500 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. Critique the numerical answer.
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Effective diffusivity: 2.66 x 108 m²/s Pellet density: 2 x 106 g/m³ Ineffective diffusivity: 0.00 m²/s Bed porosity: 0.4 Internal surface area: 400 m²/g