A reactor has a container through which a reactive medium is passed and a plurality of plates in the container defining a plurality of between-plate reaction spaces through which the reactive medium travels. The plates are self-supporting and fixed in the container. Respective self-contained packings each formed by a support independent of the container are each of a flat shape that completely or almost completely fills the between-plate space and are each fittable to a variable depth in and removable from a respective one of the spaces. The supports each hold a catalyst for the reactive medium and are also removable from and insertable with the respective catalyst into the respective spaces such that when the catalyst is exhausted the packings can be replaced with fresh packings.