The method consists in the polymerization of olefins with a prevailing content of 1-butene and cis- and trans-2-butenes in the mixture of hydrocarbons known as rafinate II, which is derived from the C₄-fractions after separation of 1,3-butadiene and isobutylene, under initiation with boron trifluoride (BF₃) or alkylaluminium chlorides with the general formulae R₂AlCl and RAlCl₂ (in which each R represents a C₁ to C₆-alkyl group) in the presence of hydrogen chloride (HCl), hydrogen fluoride (HF), or organic compounds with a reactive chlorine or fluorine bonded to a tertiary-, benzyl- or allyl-carbon atom, as coinitiators.
The method according to the solution may be carried out in such a way, that rafinate II derived from the production of methyl tert-butyl ether or from the selective polymerization of isobutylene, in which 1-butene present in a concentration at least 20% is polymerized together with cis- and trans-2-butenes present in a concentration of at least 15%, at a temperature of +100°C to -70°C, to form to oily products with molar mass M n = 300 to 1200. Preferably the mixture derived as rafinate II from the production of methyl tert-butyl ether is first freed of methanol to the content lower than 300p ppm.