A process for effecting chemical synthesis reactions from reaction gases in gaseous phase and under pressure in a reaction zone (8, see FIGS. 4 and 4A) defined as an enclosure of substantially cylindrical shape and of substantially circular transverse cross-section, the process being carried out in the presence of a solid catalyst, said process comprising circulating said reaction gases into the reaction zone (8) divided into a plurality of enclosures (9) containing the catalyst, said enclosures, being defined by adjacent walls (1, axial side walls such as 1a, 1b, 1c . . . ) parallel to one another and by side walls (2, axial end walls such as 2a, 2b, 2c . . . ) parallel to one another, said enclosures (9) being shaped as elongate parallelipipeds, substantially parallel to the axis of the reactor cylinder, and being adjacent to each other, the transverse cross-sections of the enclosures being substantially included in a circle coaxial to the circle defined by the circular section of the reaction zone, the adjacent walls (1) of these enclosures, or the common walls of the adjacent enclosures, being tight to the gases flowing through the reaction zone and forming a deflected path wherethrough the gas is compelled to flow, said side walls (2, axial end walls such as 2a, 2b, 3c . . . ) of said enclosures (9) being permeable to the gases, with these gases penetrating into each enclosure (9) through a permeable wall and issuing therefrom through a permeable wall opposite to the wall wherethrough the gases are admitted, flowing as a result progressively through each of the enclosures substantially perpendicular to the axis of the reaction zone, and said process comprising circulating a fluid heat carrier through said walls (1) which are hollow plates whose internal spaces communicate with each other, under a pressure substantially equal to the pressure to which are subjected the reaction gases.