  We fit X-ray emission line profiles in high resolution XMM-Newton and Chandra
grating spectra of the early O supergiant Zeta Pup with models that include the
effects of porosity in the stellar wind. We explore the effects of porosity due
to both spherical and flattened clumps. We find that porosity models with
flattened clumps oriented parallel to the photosphere provide poor fits to
observed line shapes. However, porosity models with isotropic clumps can
provide acceptable fits to observed line shapes, but only if the porosity
effect is moderate. We quantify the degeneracy between porosity effects from
isotropic clumps and the mass-loss rate inferred from the X-ray line shapes,
and we show that only modest increases in the mass-loss rate (<~ 40%) are
allowed if moderate porosity effects (h_infinity <~ R_*) are assumed to be
important. Large porosity lengths, and thus strong porosity effects, are ruled
out regardless of assumptions about clump shape. Thus, X-ray mass-loss rate
estimates are relatively insensitive to both optically thin and optically thick
clumping. This supports the use of X-ray spectroscopy as a mass-loss rate
calibration for bright, nearby O stars.
