Problem statement Steam reforming of methane is a key hydrogen production technology which services many industrial catalytic processes such as hydrotreating and ammonia synthesis. In a typical reactor unit, banks of fixed bed reactor tubes are arranged in parallel inside the radiant section of a direct fired heater. The latter is used to attain the relatively high reforming temperatures (700 - 1000 C). Under cold conditions (prior to start-up), the reactor tube has a diameter D. and is packed with a nickel-based catalyst up to about 90% capacity. The process engineers have used these dimensions as the design basis. Pressure drop, at these dimensions, is estimated to be about 8% of the total head pressure. The reactor is subjected to thermal cycling. When the reactor is initial heated-up the diameter of the tube expands by 50% and is operated at these conditions for a period of time. When the unit is shut down for maintenance the diameter of the tube returns to the original size, and under extreme tube forces the catalyst is crushed. When the reactor is started up again, the tube expands by 50% once more. These changes under thermal cycling were not considered during the design phase. Your Task The operators have noticed that the performance of the reactor is somewhat different to the design specifications and suspect that the thermal cycling may be responsible. The senior process engineer would like you to analyse two periods: - The period when the reactor is initially heated up and held at the operating temperature. - The period after the reactor is taken offline for maintenance and then heated up again. You should consider the effect of the tube expansion on the operating variables and the overall effect on pressure drop and conversion. Compare these responses to the estimated performance according to the design basis. You may include any equations or diagrams that you consider necessary to support your discussion. A numerical solution is not required. Hints: A general consideration of the design method for fixed bed reactors may reveal relationships between operating and performance variables