  Context. Continuum time delays from accretion disks in active galactic nuclei
(AGN) has been proposed long time ago as a tool for measuring distances to the
monitored sources. However, the method faces serious problems as a number of
effects must be taken into account, including the contribution from the Broad
Line Region (BLR). Aims. In this paper, we model the expected time delays when
both the disk reprocessing of the incident X-ray flux and further reprocessing
by the BLR are included, with the aim to see if the two effects can be
disentangled. Methods. We use simple response function for the accretion disk,
without relativistic effects, and we use a parametric description to account
for the BLR contribution. We include only scattering of the disk emission by
the BLR inter-cloud medium. We also use artificial lightcurves with 1-day
sampling to check if the effects are likely to be seen in real data. Results.
We show that the effect of the BLR scattering on the predicted time delay is
very similar to the effect of rising height of the X-ray source, without any
BLR contribution. This brings additional degeneracy if we want in the future to
recover the parameters of the system from the observed time delays in a
specific object. Both effects, however, modify the slope of the delay versus
wavelength curve when plotted in log space which opens a way to obtaining bare
disk time delay needed for cosmology. In addition, when the disk irradiation is
strong, the modification of the predicted delay by the BLR scattering and by
X-ray source height become considerably different. However, the required data
quality must be high since our artificial curves with 1-day sampling give
rather noisy results.
