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Laminar dispersion of solutes in finite-length patterned microtubes is investigated at values of the Reynolds number below unity. Dispersion is strongly influenced by axial flow variations caused by patterns of periodic pillars and gaps in the flow direction. We focus on the Cassie-Baxter state, where the gaps are filled with air pockets, therefore enforcing free-slip boundary conditions at the flat liquid-air interface. The analysis of dispersion is approached by considering the temporal moments of solute concentration. Based on this approach, we investigate the dispersion properties in a wide range of values of the Peclet number, thus gaining insight into how the patterned structure of the microtube influences both the Taylor-Aris and the convection-dominated dispersion regimes. Numerical results for the velocity field and for the moment hierarchy are obtained by means of finite element method solution of the corresponding transport equations. We show that for different patterned geometries, in a range ...