We simulate flows involving porous media and homogenous fluid using a single-domain finite-difference numerical method. We study numerically the settling of a porous sphere in a density-stratified ambient fluid. Simulations are validated against prior laboratory experiments and compared to two mathematical models. Two main effects cause the particle to slow down as it enters a density gradient: lighter fluid within the particle and entrainment of the density-stratified ambient fluid. The numerical simulations accurately capture the particle retention time. We quantify the delay in settling due to ambient fluid entrainment and lighter internal fluid becoming denser through diffusion as a function of the Reynolds, P