Process for separating butenes from a C4-hydrocarbon stream which contains at least butenes and butanes by extractive distillation with a solvent, wherein the process comprises the steps of: a. at least partially evaporating the liquid C4-hydrocarbon stream in a feed evaporator, supplying the gaseous C4-hydrocarbon stream and supplying the liquid solvent above the C4-hydrocarbon stream to an absorber in which the C4-hydrocarbon stream and the solvent are contacted with one another to transfer predominantly butenes from the C4-hydrocarbon stream to the solvent, wherein the thus-laden solvent is collected in a liquid collector of the absorber, passed through an absorber evaporator and then passed into the bottom of the absorber below the liquid collector to outgas predominantly butanes from the laden solvent, wherein the laden solvent is subsequently passed to a desorber as bottoms stream and wherein a stream enriched in butanes relative to the employed C4-hydrocarbon stream and still containing at least 5% by weight of butenes, preferably at least 10% by weight of butenes, particularly preferably at least 15% by weight of butenes, is obtained at the top of the absorber; b. supplying the laden solvent to the desorber which is at an elevated temperature and preferably a lower pressure relative to the absorber and in which the butenes are separated from the solvent to obtain at the top of the desorber a stream enriched in butenes and in the bottom of the desorber the solvent at least partially freed of butenes, wherein the solvent, at least partially freed of butenes, is collected in a liquid collector of the desorber and passed through a desorber evaporator and then passed into the bottom of the desorber below the liquid collector to outgas any butenes remaining in the solvent and wherein the solvent is subsequently recycled to the absorber as bottoms stream; characterized in that the heat of the solvent withdrawn as a bottoms stream of the desorber is used for heat integration by employing the heat of the solvent in at least one respective heat exchanger for preheating the laden solvent passed to the desorber, for evaporation in the absorber evaporator and for evaporation of the liquid C4-hydrocarbon stream and in that the stream enriched in butanes is passed to an adiabatic oligomerization to oligomerize the butenes present in the stream. a. at least partially evaporating the liquid C4-hydrocarbon stream in a feed evaporator, supplying the gaseous C4-hydrocarbon stream and supplying the liquid solvent above the C4-hydrocarbon stream to an absorber in which the C4-hydrocarbon stream and the solvent are contacted with one another to transfer predominantly butenes from the C4-hydrocarbon stream to the solvent, wherein the thus-laden solvent is collected in a liquid collector of the absorber, passed through an absorber evaporator and then passed into the bottom of the absorber below the liquid collector to outgas predominantly butanes from the laden solvent, wherein the laden solvent is subsequently passed to a desorber as bottoms stream and wherein a stream enriched in butanes relative to the employed C4-hydrocarbon stream and still containing at least 5% by weight of butenes, preferably at least 10% by weight of butenes, particularly preferably at least 15% by weight of butenes, is obtained at the top of the absorber; b. supplying the laden solvent to the desorber which is at an elevated temperature and preferably a lower pressure relative to the absorber and in which the butenes are separated from the solvent to obtain at the top of the desorber a stream enriched in butenes and in the bottom of the desorber the solvent at least partially freed of butenes, wherein the solvent, at least partially freed of butenes, is collected in a liquid collector of the desorber and passed through a desorber evaporator and then passed into the bottom of the desorber below the liquid collector to outgas any butenes remaining in the solvent and wherein the solvent is subsequently recycled to the absorber as bottoms stream; characterized in that the heat of the solvent withdrawn as a bottoms stream of the desorber is used for heat integration by employing the heat of the solvent in at least one respective heat exchanger for preheating the laden solvent passed to the desorber, for evaporation in the absorber evaporator and for evaporation of the liquid C4-hydrocarbon stream and in that the stream enriched in butanes is passed to an adiabatic oligomerization to oligomerize the butenes present in the stream.