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.
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