Real-time completion monitoring with acoustic waves has been proposed recently as a method to monitor permeability changes along completions. Typical deepwater completions contain additional layers of sand screen, gravel sand, and perforated casing, which make them quite different from a fluid-filled open borehole. Monitoring changes in flow properties across the completion is crucial because impairment of permeability in any of these layers could cause reduced well productivity. In contrast to an open-hole model, a sand-screened completion supports two tube waves related to an inner fluid column and a gravel suspension in the annulus. To study effects of screen and sand permeability on tube-wave signatures, we construct simple numerical models of various completion scenarios using poroelastic descriptions of screen and sand. Models generally predict that a fast tube wave does not attenuate at either low or high permeability, but experiences resonant attenuation at intermediate frequencies. In contrast, a slow tube wave attenuates completely above a certain permeability value. Models provide a qualitative and sometimes a semiquantitative description for signatures of the fast tube wave. However, they are unable to explain why the slow tube wave is observed in experiments with high permeabilities of sand and screen. We speculate that a better model of complex sand screens is required to match experimental data.