  Understanding the transport properties of a porous medium from a knowledge of
its microstructure is a problem of great interest in the physical, chemical and
biological sciences. Using a first-passage time method, we compute the mean
survival time $\tau$ of a Brownian particle among perfectly absorbing traps for
a wide class of triply-periodic porous media, including minimal surfaces. We
find that the porous medium with an interface that is the Schwartz P minimal
surface maximizes the mean survival time among this class. This adds to the
growing evidence of the multifunctional optimality of this bicontinuous porous
medium. We conjecture that the mean survival time (like the fluid permeability)
is maximized for triply periodic porous media with a simply connected pore
space at porosity $\phi=1/2$ by the structure that globally optimizes the
specific surface. We also compute pore-size statistics of the model
microstructures in order to ascertain the validity of a "universal curve" for
the mean survival time for these porous media. This represents the first
nontrivial statistical characterization of triply periodic minimal surfaces.
