In abdominal aortic aneurysm disease, the aortic wall is exposed to intense biological activity involving inflammation and matrix metalloproteinase-mediated degradation of the extracellular matrix. These processes are orchestrated by monocytes and rather than affecting the aorta uniformly, damage and weaken focal areas of the wall leaving it vulnerable to rupture. This study attempts to model numerically the deposition of monocytes using large eddy simulation, discrete phase modelling and near-wall particle residence time. The model was first applied to idealised aneurysms and then to three patient-specific lumen geometries using three-component inlet velocities derived from phase-contrast magnetic resonance imaging. The use of a novel, variable wall shear stress-limiter based on previous experimental data significantly improved the results. Simulations identified a critical diameter (1.8 times the inlet diameter) beyond which significant monocyte deposition is expected to occur. Monocyte adhesion occurred proximally in smaller abdominal aortic aneurysms and distally as the sac expands. The near-wall particle residence time observed in each of the patient-specific models was markedly different. Discrete hotspots of monocyte residence time were detected, suggesting that the monocyte infiltration responsible for the breakdown of the abdominal aortic aneurysm wall occurs heterogeneously. Peak monocyte residence time was found to increase with aneurysm sac size. Further work addressing certain limitations is needed in a larger cohort to determine clinical significance.