1. A process for oligomerizing ethene, comprising:(I) an oligomerization operation, in which a mixture comprising ethene and an inert medium contacts a solid catalyst, wherein the proportion by weight of the inert medium in the mixture is greater than the proportion by weight of ethene in the mixture, wherein the inert medium is a C3-C7 alkane or a C3-C7 cycloalkane, wherein the pressure and temperature of the mixture are chosen with respect to the proportion by weight of ethene in the mixture such that the ethene and the inert medium are in the supercritical state, and wherein the ethene and the inert medium each contact the solid catalyst in the supercritical state; and
(II) a regeneration operation, in which the solid catalyst in the absence of ethene, hydrogen, and oxygen is purged with a liquid purge medium, wherein:
a) operation is interchanged over time between the oligomerization operation and the regeneration operation, in such a way that a time-limited oligomerization operation is followed by a time-limited regeneration operation, and the latter in turn is followed by a time-limited oligomerization operation;
b) the solid catalyst is always at the same location during both the oligomerization operation and the regeneration operation;
c) the location of the solid catalyst is supplied with positive or negative thermal energy in order to impose a set temperature thereon during both the oligomerization operation and the regeneration operation;
d) the set temperature in the regeneration operation is lower than the set temperature in the oligomerization operation; and
e) the pressure at the location of the solid catalyst is lower in the regeneration operation than in the oligomerization operation.