  We present theoretical predictions of the rotational line emission of
deuterated water in low-mass protostar collapsing envelopes. The model accounts
for the density and temperature structure of the envelope, according the
inside-out collapse framework. The deuterated water abundance profile is
approximated by a step function, with a low value in the cold outer envelope
and a higher value in the inner envelope where the grain mantles evaporate. The
two abundances are the two main parameters of the modeling, along with the
temperature at which the mantles evaporate. We report line flux predictions for
a 30 and 5 L$_\odot$ source luminosity respectively. We show that ground based
observations are capable to constrain the three parameters of the model in the
case of bright low-mass protostars (L$>$10 L$_{\odot}$), and that no space
based observations, like for example HSO observations, are required in this
case. On the contrary, we show that the study of low-luminosity sources (L$<$10
L$_{\odot}$), assuming the same HDO abundance profile, requires too much
integration time to be carried out either with available ground-based
telescopes or with the HIFI instrument on board HSO. For these sources, only
the large interferometer ALMA will allow to constrain the HDO abundance.
