Chemical reaction process performed in a reaction chamber containing a catalyst bed, the reaction chamber comprising a first end and a second end opposite the first end , the process alternately comprising: - a reaction phase, comprising the passage of a reaction stream in the reaction chamber from its first end to its second end ; and - a catalyst regeneration phase, comprising the passage of a regeneration stream in the reaction chamber from its second end to its first end , characterized in that the reaction chamber consists of a plurality of separate reaction compartments containing a catalyst bed and comprising a system for heat exchange therebetween, and said process being: - a process for the dehydration of glycerol to give acrolein; or - a process for the dehydration of lactic acid or ammonium lactate to give acrylic acid; or - a process for the dehydration of 3-hydroxypropionic acid or the ammonium salt thereof to give acrylic acid; or - a process for the dehydration of 2-hydroxyisobutyric acid or 3-hydroxyisobutyric acid or the corresponding ammonium salts thereof to give methacrylic acid; or - a process for the conversion of a chlorinated compound into a fluorinated compound, preferably a process for the preparation of a hydrofluoroolefin or of a hydrofluorocarbon, in particular a process for the preparation of a fluoropropene and very particularly preferably a process for the preparation of 2,3,3,3-tetrafluoropropene; or - a selective oxidation process such as the oxidation of methanol to give formaldehyde or dimethoxymethane; the oxidation of ethanol to give acetaldehyde or diethoxyethane; the oxidation of ortho-xylene or naphthalene to give phthalic anhydride; the oxidation of benzene, butene, butanol or butane to give maleic anhydride; the oxidation of propylene to give acrolein; or the oxidation of isobutene or tert-butanol to give methacrolein. - a reaction phase, comprising the passage of a reaction stream in the reaction chamber from its first end to its second end ; and - a catalyst regeneration phase, comprising the passage of a regeneration stream in the reaction chamber from its second end to its first end , - a process for the dehydration of glycerol to give acrolein; or - a process for the dehydration of lactic acid or ammonium lactate to give acrylic acid; or - a process for the dehydration of 3-hydroxypropionic acid or the ammonium salt thereof to give acrylic acid; or - a process for the dehydration of 2-hydroxyisobutyric acid or 3-hydroxyisobutyric acid or the corresponding ammonium salts thereof to give methacrylic acid; or - a process for the conversion of a chlorinated compound into a fluorinated compound, preferably a process for the preparation of a hydrofluoroolefin or of a hydrofluorocarbon, in particular a process for the preparation of a fluoropropene and very particularly preferably a process for the preparation of 2,3,3,3-tetrafluoropropene; or - a selective oxidation process such as the oxidation of methanol to give formaldehyde or dimethoxymethane; the oxidation of ethanol to give acetaldehyde or diethoxyethane; the oxidation of ortho-xylene or naphthalene to give phthalic anhydride; the oxidation of benzene, butene, butanol or butane to give maleic anhydride; the oxidation of propylene to give acrolein; or the oxidation of isobutene or tert-butanol to give methacrolein. <EOS>