An apparatus for carrying out a gas-phase olefin polymerization comprising - a first polymerization zone adapted and arranged for growing polymer particles to flow upward under fast fluidization or transport conditions comprising a cylindrical segment having a diameter D01; - a second polymerization zone adapted and arranged for the growing polymer particles to flow downward comprising a cylindrical upper part having a diameter D05 and a cylindrical lower part having a diameter D06; - a gas/solid separation zone of a cylindrical shape having a diameter D04 adapted and arranged for separating growing polymer particles from a gas flow which is arranged on top of the upper part of the second polymerization zone and is directly connected to the upper part of the second polymerization zone; - a tubular first connecting element having a diameter D03 adapted and arranged for connecting the cylindrical segment of the first polymerization zone to the gas/solid separation zone; - a tubular gas recycle line having a diameter D08 adapted and arranged for connecting the gas/solid separation zone to the first polymerization zone; - a tubular transition segment having a diameter D02 arranged between the gas recycle line and the cylindrical segment of the first polymerization zone; and - a tubular second connecting element having a diameter D09 adapted and arranged for connecting the lower part of the second polymerization zone to the transition segment; wherein the gas recycle line is equipped with a compressor adapted and arranged for circulating gas in the gas recycle line and a heat exchanger adapted and arranged for removing heat from the gas flowing in the gas recycle line; wherein the ratio of D04 to D05 is from 1.0 to 1.5 and the ratio of D05 to D06 is from 1.2 to 2; wherein the first connecting element is a bend having a radius R03 or is a tubular element comprising one or more bend parts having one or more radiuses R03 and one or more linear parts and the ratio of R03 to D03 is from 1 to 6 and the ratio of D03 to D01 is from 0.3 to 0.85; wherein the first connecting element comprises a connecting piece, the first connecting element and the gas/solid separation zone are connected by the connecting piece, and the connection of the connecting piece to the gas/solid separation zone is tangential and has an inclination so that the central axis of the connecting piece and the horizontal form an angle A16 and the angle A16 is in the range from 0° to 40°; wherein the transition segment is a bend or is a tubular element comprising one or more bend parts and one or more linear parts and the ratio of D08 to D02 is 1.0 to 2.2; and wherein the second connecting element is a bend or is a tubular element comprising one or more bend parts and one or more linear parts. - a first polymerization zone adapted and arranged for growing polymer particles to flow upward under fast fluidization or transport conditions comprising a cylindrical segment having a diameter D01; - a second polymerization zone adapted and arranged for the growing polymer particles to flow downward comprising a cylindrical upper part having a diameter D05 and a cylindrical lower part having a diameter D06; - a gas/solid separation zone of a cylindrical shape having a diameter D04 adapted and arranged for separating growing polymer particles from a gas flow which is arranged on top of the upper part of the second polymerization zone and is directly connected to the upper part of the second polymerization zone; - a tubular first connecting element having a diameter D03 adapted and arranged for connecting the cylindrical segment of the first polymerization zone to the gas/solid separation zone; - a tubular gas recycle line having a diameter D08 adapted and arranged for connecting the gas/solid separation zone to the first polymerization zone; - a tubular transition segment having a diameter D02 arranged between the gas recycle line and the cylindrical segment of the first polymerization zone; and - a tubular second connecting element having a diameter D09 adapted and arranged for connecting the lower part of the second polymerization zone to the transition segment; wherein the gas recycle line is equipped with a compressor adapted and arranged for circulating gas in the gas recycle line and a heat exchanger adapted and arranged for removing heat from the gas flowing in the gas recycle line; wherein the ratio of D04 to D05 is from 1.0 to 1.5 and the ratio of D05 to D06 is from 1.2 to 2; wherein the first connecting element is a bend having a radius R03 or is a tubular element comprising one or more bend parts having one or more radiuses R03 and one or more linear parts and the ratio of R03 to D03 is from 1 to 6 and the ratio of D03 to D01 is from 0.3 to 0.85; wherein the first connecting element comprises a connecting piece, the first connecting element and the gas/solid separation zone are connected by the connecting piece, and the connection of the connecting piece to the gas/solid separation zone is tangential and has an inclination so that the central axis of the connecting piece and the horizontal form an angle A16 and the angle A16 is in the range from 0° to 40°; wherein the transition segment is a bend or is a tubular element comprising one or more bend parts and one or more linear parts and the ratio of D08 to D02 is 1.0 to 2.2; and wherein the second connecting element is a bend or is a tubular element comprising one or more bend parts and one or more linear parts.