  We study the modeling of $t$-channel single top-quark production at Large
Hadron Collider (LHC) energies. We compare predictions at
next-to-next-to-leading order in a 5-flavor scheme to those of next-to-leading
order in a 4-flavor scheme, finding the two schemes agree within a few percent
in general for the shape of kinematic distributions of the top quark. The
predictions in the 5-flavor scheme show strong stability for both normalization
and distributions, and are superior to those of the 4-flavor scheme at
comparable orders. We present comparisons of the predictions with LHC data. Our
findings provide clear theoretical guidance for precision studies of single
top-quark physics at the LHC.
