Process for producing premium gasoline by polymerizing C.sub.4 cuts

A process for producing premium gasoline from olefinic C.sub.4 cuts containing 1- and 2-butenes and isobutene and made free of at least a major part of the butadiene initially contained therein, the process consisting of converting at least 97% of the total isobutene content of the charge and at least the major portion of the 1- and 2-butenes thereof to C.sub.4 hydrocarbons dimers and trimers without producing substantial amounts of kerosene, said process comprising, in a first step, treating the olefinic C.sub.4 cut in a first so-called polmerization catalytic zone, at input and output temperatures ranging from 40.degree. to 250.degree. C., under a pressure from 0.1 to 10 MPa, with a flow rate of liquid hydrocarbons (space velocity) from about 0.05 to 5 volumes per volume of catalyst and per hour, in the presence of a catalyst selected from the group consisting of silica-aluminas, boron-containing aluminas and transition aluminas treated with at least one fluorine acid derivative, so as to convert at least 80% of the isobutene to isobutene dimers and trimers and to convert at most 45% of the mixture of 1- and 2-butenes to dimers and trimers thereof, in that, subsequently, fractionating the effluent from said first catalytic polymerization zone so as to recover, on the one hand, from the column bottom, essentially the C.sub.4 olefinic hydrocarbons dimers and trimers and, on the other hand, from the top of the column, a mixture containing the major part of the isobutene and 1- and 2-butenes not converted in said first catalytic polymerization zone, feeding said mixture, during a second step, at least partly to a second catalytic polymerization zone operating at input and output temperatures from 40.degree. to 250.degree. C., under a pressure from 0.1 to 10 MPa and with a flow rate of liquid hydrocarbons (space velocity) from about 0.05 to 5 volumes per volume of catalyst and per hour, the input and output temperatures of the second polymerization zone being each from 20.degree. to 60.degree. C. higher than the input and output temperatures of the first polymerization zone, the pressure in the second polymerization zone being from 0.4 to 3 MPa higher than the pressure in the first polymerization zone, in the presence of a catalyst selected from the group consisting of silica-aluminas, boron-containing aluminas and transition aluminas treated with at least one fluorine acid derivative, so as to convert (a) substantially the total amount of isobutene to isobutene dimers and trimers in said second zone and (b) at least 50% of the 1- and 2-butenes, supplied to said second zone, to n-butenes dimers and trimers.