The colloidal droplet spreading on and sorption into a porous medium is important to a variety of engineering applications including oil recovery, jet printing, polymer filling, and fuel cells. In this study, we conducted numerical simulation to investigate droplet spreading on and sorption into a powder bed and performed experiment to study the colloidal fluid distribution in the porous structure after sorption of single/multiple droplets in powder beds. The spreading of the droplet on the surface of the porous matrix is modeled based on the Navier-Stokes equation while the liquid sorption in the porous matrix is described using the Brinkman-Forchheimer-Darcy equation. Due to the presence of the free moving interface above and inside the porous medium, the smoothed particle hydrodynamic (SPH) particle method is used in the numerical simulation. A parametric study is conducted to investigate the effects of the droplet impact speed, the fluid viscosity, and the permeability of the porous matrix on the spreading diameter. We also use microCT imaging method to investigate the distribution of the colloidal fluid in the PMMA powder bed after absorption of ferrofluid droplets. The results show that a higher viscosity, a lower permeability of the porous matrix and a higher impact speed favors a larger spreading diameter of the droplet on the surface. The microCT images clearly reveal the boundary of the colloidal fluid in the powder bed. A high grayscale values are observed on the boundary of the colloidal fluid. This study is the first step towards a systematic study of colloidal particle distribution in a powder bed after the absorption of colloidal droplets.