Single nanopore sensors enable capture and analysis of molecules that are driven to the pore entry from bulk solution. However, the distance between an analyte and the nanopore opening limits the detection efficiency. A theoretical basis for predicting particle capture rate is important for designing modified nanopore sensors, especially for those with covalently tethered reaction sites. Using the finite element method, we develop a soft-walled electrostatic block (SWEB) model for the alpha-hemolysin channel that produces a vector map of drift-producing forces on particles diffusing near the pore entrance. The maps are then coupled to a single-particle diffusion simulation to probe capture statistics and to track the trajectories of individual particles on the μs to ms time scales. The investigation enables evaluation of the interplay among the electrophoretic, electroosmotic, and thermal driving forces as a function of applied potential. The findings demonstrate how the complex drift-producing forces compete with diffusion over the nanoscale dimensions of the pore. The results also demonstrate the spatial and temporal limitations associated with nanopore detection and offer a basic theoretical framework to guide both the placement and kinetics of reaction sites located on, or near, the nanopore cap.