  We present results of our numerical simulation of three H2-bearing damped
Lyman alpha absorbers (DLAs) in the redshift interval ~ 2-3. The systems we
have modelled are the DLAs at zabs = 2.3377 towards the quasar LBQS 1232+0815,
at zabs = 2.41837 towards SDSS J143912.04+111740.5 and at zabs = 2.6265 towards
FBQS J081240.6+320808. We have used the spectral synthesis code CLOUDY to
simulate the physical environment of these DLAs, and constrain the density,
radiation field, geometry and dust-grain properties of the DLAs
self-consistently based on the observed column densities of various atomic and
molecular species such as H I, fine structure lines of C I and the rotational
level population of H2. In our models, we explore the effect of grain size
distribution on the predicted column densities of different species. Within the
allowed uncertainties in the inferred dust-to-gas ratio, both models with
standard ISM grains and smaller-sized grains reproduce the observations equally
well. Improved constraints on dust-to-gas ratio and line-of-sight extinction
are important for probing the grain size distribution in high-z DLAs. We find
the H2-bearing clouds to have line-of-sight thickness in the range 1-6 pc,
consistent with what has been found using partial coverage or 21-cm
observations in some high-z DLAs.
