At the 2006 European Short Course Swimming Championships in Helsinki, Finland, Geybel placed eleventh in the 50-metre breaststroke with a time of 27.65 seconds.

[4] In April 2008, at the 2008 World Short Course Championships in Manchester, England, Geybel started competition in the 100-metre breaststroke where he placed thirteenth in the semifinals with a time of 59.48 seconds, just two spots behind Ryan Lochte of the United States, and did not advance to the final of the event.

[11] At the 2009 Vladimir Salnikov Swimming Cup in Saint Petersburg, Russia, Geybel helped set new world, European, and Russian records in the 4×100-metre medley relay at 3:19.16, swimming the breaststroke leg of the relay with a split of 56.43 seconds while Stanislav Donets swam backstroke, Yevgeny Korotyshkin swam butterfly, and Danila Izotov swam freestyle, to help topple the former record set by the United States relay team of Nick Thoman, Mark Gangloff, Michael Phelps, and Nathan Adrian.

[12] At the 2010 European Short Course Swimming Championships in Eindhoven, Netherlands in November, Geybel tied for ninth place overall with a time of 59.24 seconds in the 100-metre breaststroke.

[23] In his individual event of the Championships, Geybel ranked eleventh overall and did not advance to the final of the 50-metre breaststroke with his time of 26.54 seconds.

[25] Following the 2022 Russian invasion of Ukraine in February 2022, Geybel was banned by LEN indefinitely from their competitions starting on 3 March and by FINA from their competitions effective at least from 21 April to 31 December 2022 as a means of keeping all Russians and Belarusians in-check by the international governing bodies (LEN - Europe; FINA - World).