  Carbon isotope fractionation of CO has been reported in the disk around TW
Hya,where elemental carbon is more abundant than elemental oxygen ([C/O]$_{\rm
elem}$> 1). We investigated the effects of the [C/O]$_{\rm elem}$ ratio on
carbon fractionation using astrochemical models that incorporate
isotope-selective photodissociation and isotope-exchange reactions. The
$^{12}$CO/$^{13}$CO ratio could be lower than the elemental carbon isotope
ratio due to isotope exchange reactions when the [C/O]$_{\rm elem}$ ratio
exceeds unity. The observed $^{12}$CO/$^{13}$CO and H$^{12}$CN/H$^{13}$CN
ratios around TW Hya could be reproduced when the [C/O]$_{\rm elem}$ ratio is
2~5. In the vicinity of the lower boundary of the warm molecular layer, the
formation of ices leads to the gas phase [C/O]$_{\rm elem}$ ratio approaching
unity, irrespective of the total (gas + ice) [C/O]$_{\rm elem}$ ratio. This
phenomenon reduces the variation in the $^{12}$CO/$^{13}$CO ratio across
different [C/O]$_{\rm elem}$ ratios.
