4) It is desired to increase the productivity of a BF by 5%. To achieve this, th

4) It is desired to increase the productivity of a BF by 5%. To achieve this, the mass flow rate of gas in the reactor must be increased by about 5% (assuming that the furnace operates with a well-developed Chemical Reserve Zone).
Estimate the maximum pressure drop in the reactor with a length of approximately 15m, in order to avoid choking. For this purpose, assume a bed with hematite particles (w = 0.45), the gas is ideal, and the average gas pressure in the reactor (necessary to estimate its density) is equal to the top pressure (1 atm) plus half of the pressure drop.
The temperature in the reactor is around 1000°C. Based on the Ergun equation, considering a compressible fluid and only the turbulent contribution, develop an expression that characterizes the bed permeability. Explain, based on this expression, two ways to keep the pressure drop unchanged, even with increased productivity.