The paper under review deals with the capture dynamics of a particle undergoing a random walk in a half-space bounded by a planar surface with a periodic array of absorbing pores and reflecting otherwise. The authors develop a Kinetic Monte Carlo method for the solution of the boundary value problem of the mathematical model. Then they apply homogenization theory to the problem and derive high-order asymptotic estimates for the leakage parameter in the dilute fraction regime, i.e., when the surface is mostly reflecting. Finally, a variety of numerical results complete the paper.