The behavior of gas-solid reactors known as compact-fixed and moving beds, is analyzed from a theoretical viewpoint. For a compact fixed-bed the solution of the energy balance equations is obtained for the cases of a uniform temperature inside the solid pellets (i.e., the Biot number is zero) and for the case in which there are temperature gradients within the pellets (Bi > 0). For short contact times, beds with Bi > 0 have gas- and solid- temperatures which are greater than the temperatures within beds with Bi = 0. For long times, the situation is reversed. For a compact-moving bed the solution of the mass balance equations is obtained for the cases of a feed-solid with constant concentration and a feed solid with an oscillating concentration. In both cases the steady states obtained are unique, and internal recycling is observed only for a feed-solid with an oscillating concentration. Recycling is that situation when the concentration of the solid falls below that of the gas for a bed in which the feed-solid is greater than the feed-gas. This occurred when the period of oscillation was smaller than the residence time of the solid provided that the residence time of the solid was not very short (i.e., provided that B(,s) > 0.1). For both types of beds there is an equivalence between mass transfer and energy transfer so that the solutions can be interchanged with suitable definitions of dimensionless variables.
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