The cyclic steady state (CSS) of the industrial-scale, seven-zone, simulated moving-bed (SMB) unit for p-xylene (p-x) purification (Parex unit) with three types of dead volumes-bed lines, push-around and pump-around circulation lines, and bed heads-is analyzed. In particular, the effects of the size and level of hydrodynamic dispersion of each dead volume on process performance and on its CSS are studied in detail. The circulation lines change the CSS behavior from t*-periodic to Nt*-periodic, where t* is the switching interval and N = 12 is the number of columns in each adsorbent chamber. A high level of axial dispersion in the bed lines, characterized by Peclet numbers smaller than 100, affects the p-x purity. Moreover, the bed lines lower the average p-x concentration in the extract, which reduces the p-x recovery. If the small time lags introduced by the circulation lines are neglected, it is possible to develop a detailed process model that considers the operation of the Parex unit over a single switching interval as opposed to a full cycle, and whose CSS solution can be efficiently computed using a full-discretization approach. Finally, it is shown that the volume of the bed heads influences significantly the performance of the Parex unit, and that its impact on the location of the operating point with respect to the boundaries of the separation region can be approximately taken into account using the standard true moving-bed-SMB equivalence rules if they are corrected for the presence of extra interparticle fluid. (C) 2015 American Institute of Chemical Engineers