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By incorporating a distance function into the finite element simulation, we investigate the flow-driven competition between two soft capsules passing through a narrow pore, employing the arbitrary Lagrangian-Eulerian formulation to satisfy the boundary conditions for fluid flow and capsule deformation. In our simulations, the motion and deformation of the capsules can be described in an intuitive manner, and the order in which capsules of different sizes pass through a pore can be clearly determined. Meanwhile, when the capsules are near the narrow pore, the change of the flow field is also very interesting and can be expressed intuitively. It is shown that, driven by the Poiseuille flow, the larger capsule has a stronger tendency to pass through the pore than the small one, which can be attributed to the greater resistance and the volume advantage of the larger capsule. In addition, we demonstrate that this tendency can be reversed by changing the inlet velocity and setting the initial position of the smaller capsule closer to the axis of the pore. And as long as the large one passes through first, the small one will offset the axis to the same orientation as the initial, while the large one always moves along the axis.