A reactor includes a vessel, a gas inlet, a solid outlet, a catalyst support configured to at least partially retain a catalyst material and allow a tail gas to pass therethrough, and a tail gas outlet. The gas inlet is in fluid communication with the solid outlet. A system for producing a solid product includes a reactor, a compressor, a heater, a make-up reactive gas inlet, and a solids discharge means for removing the solid product from the solid outlet of the reactor. Methods of forming solid products include providing a catalyst material in a vessel having a porous catalyst support, delivering a reactive gas to the vessel, reacting the reactive gas to form a solid product and a tail gas in the vessel, passing the tail gas through a portion of the catalyst material to separate the solid product from the tail gas, and removing the solid product.