The motion of a less viscous, non-wetting gas into a liquid-saturated porous medium is known as drainage. Drainage is an important process in environmental applications, such as enhanced oil recovery and geologic CO2 sequestration. Understanding what conditions will increase the volume of gas that can saturate an initially water-saturated porous medium is of importance for predictions of the total CO2 volume that can be sequestered in known geologic formations. To further the understanding of how drainage flow properties are related to different injection flow-rates, a porous medium consisting of interconnected channels and pores was manufactured to perform bench-top experiments of drainage. Additionally, a finite-volume model of this interconnected channel matrix was constructed. Numerical simulations of constant-rate injection into the model porous medium are first shown to compare favorably to the bench-top experiments. The fluid and injection properties of the drainage process were then varied to evaluate the flow conditions which would maximize the volume of gas trapped within the porous medium. In particular, CO2 displacing brine within the porous medium was modeled, with representative subsurface temperatures and fluid properties. It was shown with these fluid conditions a higher final saturation of the invading less-viscous CO2 was obtained, as compared to air into water experiments at similar injection rates.