The intermittent burst dynamics during the slow drainage of a porous medium is studied experimentally. We have shown that this system satisfies a set of conditions known to be true for critical systems, such as intermittent activity with bursts extending over several time and length scales, self-similar macroscopic fractal structure and $1/f^\alpha$ power spectrum. Additionally, we have verified a theoretically predicted scaling for the burst size distribution, previously assessed via numerical simulations. The observation of $1/f^\alpha$ power spectra is new for porous media flows and, for specific boundary conditions, we notice the occurrence of a transition from 1/f to 1/f 2 scaling. An analytically integrable mathematical framework was employed to explain this behavior.