Knowledge of capillary migration of liquids in granular beds in microgravity is essential for the development of a substrate based nutrient delivery system for the growth of plants in space. This problem is also interesting from the theoretical as well as the practical point of view. The purpose of this study was to model capillary water propagation through a granular bed in microgravity. In our ground experiments, water propagation is driven primarily by capillary force. Data for spherical particle sizes in the range from 0.46 to 2 mm have been obtained. It was shown that the velocity of water propagation is very sensitive to particle size. Theoretical consideration is also provided. Actual space flight experiments are planned for the future to confirm our results.