A general method for treating the transport of particles in dilute gas-particle flows is presented. This method formulates the particle transport equations as a dynamical system and utilizes the corresponding theory to analyze the resulting dynamics. As an illustration of this technique, the transport of contaminant particles in a barrel-type chemical vapor deposition reactor is analyzed. The background gas flow field is determined via a numerical simulation of the Navier-Stokes equations. The analysis reveals the presence of particle attractors in the flow which are particle size specific. The features of these attractors are discussed, as is their behavior with varying particle size.