Migration of colloids in porous media has been mainly studied through laboratory column experiments and simulation of the resulting breakthrough curves. In recent years, visualization experiments using micromodels are used as a new approach for investigating mechanisms of colloidal retention in porous media at the pore-scale. However, parallel developments in conceptual models and related numerical methods are lacking. In this study, a particle-tracking framework was developed and solved numerically, which allows simulation of a 2-D flow field and colloidal retention and transport in a dense cubic packed medium. To conduct a simulation, the program is first run to establish steady-state flow that is driven by a pressure gradient before colloids are introduced. The model considers the Stokes drag force, Brownian force, colloid-grain and colloid-colloid interaction forces (including electrostatic double layer, van der Waals, and acid-base forces) on every colloid and predicts the moving trajectory and deposition in a defined domain. The differential equation of Newton's Second Law of Motion is solved numerically with the Adams-Bashforth-Moulton method. Effects of hydrodynamics, solution chemistry and surface properties of colloids are examined by changing flow velocity, solution pH and ionic strength, and surface hydrophobicity of colloids. Model analysis and simulation exercises indicate that this 2-D model is a very useful tool that can provide mechanistic insight for improved understanding of colloidal retention and transport processes and how these processes are affected by the relevant parameters. This model can also be used for guiding the design of and providing simulation to micromodel visualization experiments.