  The Muskat problem, in its general setting, concerns the interface evolution
between two incompressible fluids of different densities and viscosities in
porous media. The interface motion is driven by gravity and capillarity forces,
where the latter is due to surface tension. To leading order, both the Muskat
problems with and without surface tension effect are scaling invariant in the
Sobolev space $H^{1+\frac{d}{2}}(\mathbb{R}^d)$, where $d$ is the dimension of
the interface. We prove that for any subcritical data satisfying the
Rayleigh-Taylor condition, solutions of the Muskat problem with surface tension
$\frak{s}$ converge to the unique solution of the Muskat problem without
surface tension locally in time with the rate $\sqrt{\frak{s}}$ when
$\frak{s}\to 0$. This allows for initial interfaces that have unbounded or even
not locally square integrable curvature. If in addition the initial curvature
is square integrable, we obtain the convergence with optimal rate $\frak{s}$.
