We report here the quantitative comparisons between the measured NMR flow propagator of a carbonate rock and the flow propagator calculated with a porous network extracted from the micro-CT image of the twin plug. We developed a numerical model based on a particle tracking algorithm in pore space. The particle tracking in throats is described using the first arrival time distribution. As pores have an important volume fraction in the sample considered, we implemented a time-delay mechanism for particle transport in the pores. We consider that the nodes have volume and there is a transport of the tracking particles inside the nodes, which leads to an "apparent" time-delay. Simulations of flow propagator show good agreement with low field NMR experiments performed on the twin plug of the sample used for pore network extraction with a single adjustable parameter (that describes the dynamics in the pores). These results lead us to a better understanding of the connection between pore structure and the behavior of NMR flow propagator in fluid-saturated rocks and are essential in interpreting the experimental data and correlating NMR parameters to petrophysical properties.