Permeability is generally measured at the core scale and only at a few
sites. By using geostatistical techniques, one can generate alternati
ve high-resolution images of the reservoir at the measurement scale. T
hese images will honor both the data values at the data sites and some
prior structural information as modeled, for example, by a covariance
function. However, these images must be averaged to the scale of the
flow-simulation gridblocks. Two questions arise: (1) how should averag
ing be carried out? and (2) could the gridblock values be generated di
rectly from the core or log without the intermediary step of small-sca
le imaging? This paper proposes avenues to answer both questions. Firs
t, we propose an averaging technique from point to block permeabilitie
s, accounting for the tensorial character of permeability. Second, we
propose a method to infer the covariances and cross-covariances among
the different components of the block permeability tensor, and the cro
ss-covariances between these block values and the point measurements.
This set of covariances and cross-covariances is then used to generate
directly multiple, equally likely spatial realizations of gridblock p
ermeability tensors conditioned to the point measurements. The method
is not constrained by small variability of the underlying point permea
bility distribution, nor does it require a multi-Gaussian-related hypo
thesis.