Do not have anything on your George, but here are three Norvells who were in the 27th Texas Cavalry Regiment. Might be kin.

NORVELL, Lipscomb, 2nd Lt, Co. E, 27th TX CAV
NORVELL, Benjamin R., Pvt, Co. E, 27th TX CAV
NORVELL, William, Pvt, Co. E, 27th TX CAV