We designed and implemented an experimental methodology to investigate gas hydrate formation and growth around a water guest meniscus in a thin glass capillary, thus mimicking pore-scale processes in sediments. The glass capillary acts as a high-pressure optical cell in a range of supercooling conditions from 0.1 degrees C, i.e., very close to hydrate dissociation conditions, to similar to 35 degrees C, very near the metastability limit. Liquid or gaseous CO2 is the guest phase in most of the experiments reported in this paper, and N-2 in a few of them. The setup affords detailed microscopic observation of the roles of the key parameters on hydrate growth and interaction with the substrate: supercooling and substrate wettability. At low supercooling (less than 0.5 degrees C), a novel hydrate growth process is discovered, which consists of a hollow crystal originating from the meniscus and advancing on the guest side along the glass, fed by a thick water layer sandwiched between the glass and this crystal.