  We present detailed modeling of the disk around the TW Hydrae Association
(TWA) brown dwarf 2MASSW J1207334-393254 (2M1207), using {\it Spitzer}
observations from 3.6 to 24 $\micron$. The spectral energy distribution (SED)
does not show a high amount of flaring. We have obtained a good fit using a
flat disk of mass between $10^{-4}$ and $10^{-6}$ $M_{\sun}$, $\dot{M}$
$\la10^{-11} M_{\sun}$/yr and a large inclination angle between 60$\degr$ and
70$\degr$. We have used three different grain models to fit the 10 $\micron$ Si
emission feature, and have found the results to be consistent with ISM-like
dust. In comparison with other TWA members, this suggests lesser dust
processing for 2M1207 which could be explained by mechanisms such as aggregate
fragmentation and/or turbulent mixing. We have found a good fit using an inner
disk radius equal to the dust sublimation radius, which indicates the absence
of an inner hole in the disk. This suggests the presence of a small
K-$L^{\prime}$ excess, similar to the observed K-[3.6] excess.
