A process and reaction unit for isothermal shift conversion of a carbon monoxide containing feed gas. The process comprises the steps of introducing the feed gas in a reaction unit into reactor tubes with a fixed bed of a shift conversion catalyst in a reaction zone, contacting the feed gas with the catalyst at conditions being effective in carbon monoxide shift conversion reaction with steam reactant to hydrogen and cooling the reaction by indirect heat exchange with a cooling agent by passing the cooling agent in a falling film along shell side of the reactor tubes and removing heated cooling agent from the falling film, passing hydrogen when it is formed by the shift conversion reaction through a hydrogen selective membrane to a permeate zone, and withdrawing hydrogen from the permeate zone and carbon monoxide depleted feed gas from the reaction zone.