Isothermal reactors unsteady-state operation

Gas-solid reactions are carried out on a commercial basis using fixed-bed, moving-bed, and fluidized-bed reactors. The fixed-bed reactor is an unsteady-state system as reactive gas is fed on a continuous basis through the reactor that is packed with a finite quantity of solid reactant. The solid is depleted and breakthrough of the gas reactant occurs after a certain reaction time. In the moving-bed reactor, both solid and gas are fed on a continuous basis and overall operation is steady state. The fluidized-bed reactor, where small solid particles are fluidized by upward flow of gas, also operates in a steady-state manner. Diffusional reaction resistances are reduced because of the small solid particles while solid backmixing reduces solid concentration gradients and promotes isothermal operation. 

Since the reactor does not operate isothermally, these five coupled mass balances must be solved in conjunction with the unsteady-state thermal energy balance for an adiabatic reactor, where (d Q/dt)jnpyit = 0. If pressure effects are negligible,... 

Batch operation is essentially unsteady-state, so the energy balance is drawn up with respect to conditions obtaining at some instant t. If the reactor is run isothermally the cooling requirements at t will be given by ... 

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