The transient foam flow, i. e. the forward movement of foam front until breakthrough in a one-dimensional flow, in an oil-free porous medium was studied using the stochastic bubble population (SBP) model. The premise of this model is that foam flow in porous media is a complex fluid and bubble generation is a stochastic process. The SBP foam model describes the net bubble generation using three parameters: maximum bubble density and bubble generation and destruction coefficients. The corresponding governing equations, a system of nonlinear partial differential equations in the saturation, pressure and bubble density, were solved using the IMPES method. The sensitivity to the main physical parameters was also analyzed. It was found that the increase in the maximum bubble density leads to the generation of stronger foam, characterized by a slower foam propagation rate and a larger foam mobility reduction. The bubble generation coefficient mainly controlled the foam generation rate such that a higher led to a more rapidly increasing bubble density. A comparison between the numerically obtained saturation and pressure data with those obtained from the experiments at which foam was generated by co-injecting nitrogen and alpha olefin sulfonate surfactant in Bentheimer sandstone was provided. X-ray CT scans were also obtained to visualize the foam displacement process and to determine fluid saturations at different times. A good match was obtained between the numerical and the experimental data, which confirms that the SBP foam model is robust and reproduces the main features of the transient behavior of foam flow in a homogeneous porous media.