The dispersion of massless tracer particles released from a point source in the wake of a two-dimensional elliptic cylinder is used to model worker exposure from a hand-held source. A discrete vortex flow model is combined with a particle tracking algorithm to calculate time-averaged concentrations in the plane of the source. By space-averaging these concentrations over a computational breathing zone, estimates of breathing zone concentrations are derived. The model predictions are found to be in good agreement with measured values from wind tunnel studies. Such computational models are powerful tools to study local exhaust ventilation.