ON THE SPATIAL-TEMPORAL AVERAGING METHOD FOR MODELING TRANSPORT IN POROUS-MEDIA

The spatial-temporal averaging procedure is considered with a nonhomog eneous distribution of elementary domains in the spatial-temporal spac e and the probabilistic interpretation of the ST-averaging is also giv en. Several averaging theorems and corollaries about the averages of s patial and temporal derivatives are presented and rigorously proved wh ich allow elementary domain to vary in space and time. The macroscopic transport equation in the most general condition and the simplified m acroscopic equation under the special form of distributions are develo ped which may be reduced to the classical macroscopic transport equati on as the spatial-temporal average degenerates into the volume average .