A method for desublimation of carbon dioxide from at least one carrier gas to form a solid, comprising: providing a bed of particles located in a first chamber; providing a plurality of conduits positioned inside the first chamber for holding cooling substances; providing a separator for separating particles; providing a top aperture coupling the first chamber with the separator or a side port coupling the first chamber with the separator; providing a conduit oriented to transport substances from the first chamber to the separator, providing an out-bed heat exchanger coupled to the separator and to the first chamber; passing a process stream that includes the carbon dioxide and the at least one carrier gas through the bed of particles located in the first chamber, the bed of particles comprising a portion of solid particles and the plurality of conduits for holding cooling substances; fluidizing a portion of the solid particles of the bed, wherein some of the portion of the solid particles exits the first chamber via the top aperture coupled to a separator or via the side port coupled to the separator; cooling the at least one carrier gas, wherein the at least one carrier gas exits the first chamber via a conduit oriented to transport substances to the separator; receiving in the separator the portion of the solid particles and the at least one carrier gas; separating, via the separator, the portion of the solid particles from the at least one carrier gas; sending the portion of the solid particles to the out-bed heat exchanger located outside of the first chamber; subcooling the portion of the solid particles in the out-bed heat exchanger to a temperature that lowers solid carbon dioxide to a lower temperature; and, reinjecting substantially all of the portion of the solid particles in the out-bed heat exchanger into the bed of particles of the first chamber so as to desublimate a second portion of carbon dioxide located in the first chamber. providing a bed of particles located in a first chamber; providing a plurality of conduits positioned inside the first chamber for holding cooling substances; providing a separator for separating particles; providing a top aperture coupling the first chamber with the separator or a side port coupling the first chamber with the separator; providing a conduit oriented to transport substances from the first chamber to the separator, providing an out-bed heat exchanger coupled to the separator and to the first chamber; passing a process stream that includes the carbon dioxide and the at least one carrier gas through the bed of particles located in the first chamber, the bed of particles comprising a portion of solid particles and the plurality of conduits for holding cooling substances; fluidizing a portion of the solid particles of the bed, wherein some of the portion of the solid particles exits the first chamber via the top aperture coupled to a separator or via the side port coupled to the separator; cooling the at least one carrier gas, wherein the at least one carrier gas exits the first chamber via a conduit oriented to transport substances to the separator; receiving in the separator the portion of the solid particles and the at least one carrier gas; separating, via the separator, the portion of the solid particles from the at least one carrier gas; sending the portion of the solid particles to the out-bed heat exchanger located outside of the first chamber; subcooling the portion of the solid particles in the out-bed heat exchanger to a temperature that lowers solid carbon dioxide to a lower temperature; and, reinjecting substantially all of the portion of the solid particles in the out-bed heat exchanger into the bed of particles of the first chamber so as to desublimate a second portion of carbon dioxide located in the first chamber.