  We report numerical studies of the cluster development of two-phase flow in a
steady-state environment of porous media. This is done by including biperiodic
boundary conditions in a two-dimensional flow simulator. Initial transients of
wetting and non-wetting phases that evolve before steady-state has occurred,
undergo a cross-over where every initial patterns are broken up. For flow
dominated by capillary effects with capillary numbers in order of $10^{-5}$, we
find that around a critical saturation of non-wetting fluid the non-wetting
clusters of size $s$ have a power-law distribution $n_s \sim s^{-\tau}$ with
the exponent $\tau = 1.92 \pm 0.04$ for large clusters. This is a lower value
than the result for ordinary percolation. We also present scaling relation and
time evolution of the structure and global pressure.
