  We present new models of the deuterium chemistry in protoplanetary disks,
including, for the first time, multiply deuterated species. We use these models
to explore whether observations in combination with models can give us clues as
to which desorption processes occur in disks. We find, in common with other
authors, that photodesorption can allow strongly bound molecules such as HDO to
exist in the gas phase in a layer above the midplane. Models including this
process give the best agreement with the observations. In the midplane, cosmic
ray heating can desorb weakly bound molecules such as CO and N$_2$. We find the
observations suggest that N$_2$ is gaseous in this region, but that CO must be
retained on the grains to account for the observed DCO$^+$/HCO$^+$. This could
be achieved by CO having a higher binding energy than N$_2$ (as may be the case
when these molecules are accreted onto water ice) or by a smaller cosmic ray
desorption rate for CO than assumed here, as suggested by recent theoretical
work.
  For gaseous molecules the calculated deuteration can be greatly changed by
chemical processing in the disk from the input molecular cloud values. On the
grains singly deuterated species tend to retain the D/H ratio set in the
molecular cloud, whereas multiply deuterated species are more affected by the
disk chemistry. Consequently the D/H ratios observed in comets may be partly
set in the parent cloud and partly in the disk, depending on the molecule.
