He participated in at least one international game for the Danish selection, against a German team in Hamburg. The match was won 5–0 by the Danish team and had 5,000 spectators. Although it was a de facto international organized by the Danish Football Association (DBU), the game is not an official Danish national team match, as DBU did not register games as official until the 1908 Summer Olympics.
Byrval coached both B 93 and Frem, before he was appointed Danish national team coach in May 1913. He managed the Danish team to victory in his first eight games until October 1915, including 8–0 and 10–0 defeats of Sweden. The Danish team played four games without an official coach appointed in 1916, before Byrval once again coached the team from June 1917 to October 1918, including a 12–0 defeat of Norway. In all, he coached 16 national team games, winning 14, drawing one and losing one.
In his civil life, Byrval was a physical education schoolmaster with the municipal schools of Copenhagen, a voluntary Intendant with Korps Westenholz and a non-commissioned officer with the Royal Life Guards.