Deepwater production often hinges on the ability to safely complete and effectively draw down a small number of very challenging wells. Chances of success are greatly increased if surveillance tools are available to quickly diagnose downhole conditions and detect potential issues early on. Real-time completion monitoring with acoustic waves (RTCM) has great potential for diagnosing problems in sand-screened deepwater completions. RTCM uses tube waves to detect permeability changes and passive noises to characterize perforation flow. Interaction of a single tube wave with permeable formations in open boreholes is well explained by Biot's theory of poroelasticity. However, experimental studies in laboratory models of sand-screened completions reveal that fast- and slow-tube waves behave differently. Further progress in acoustic surveillance requires better understanding on how signatures of fast- and slow-tube waves depend on completion properties. To this end, we simulate the dispersion and attenuation of the two tube waves by examining the solutions of Biot's equations of poroelasticity in cylindrical structures using a spectral method.