A STREAM TUBE MODEL FOR MISCIBLE FLOW .2. MACRODISPERSION IN POROUS-MEDIA WITH LONG-RANGE CORRELATIONS

Large-scale dispersion in heterogeneous porous media is studied by usi ng a simple model based on stochastic calculation of convective flow i n a bundle of stream tubes. The advantage of this approach is that the re is a local relationship between velocity and permeability in the 1- dimensional space of the stream tubes. Dispersion is due to the variat ion in stream tube cross-section, related to the permeability field. F irst, the arrival times of the tracer in the stream tubes are related to the stochastic properties of the permeability field (variance and c ovariance). Then, transport equations are derived from the moments of the arrival times. The results agree with more complicated studies. Fo r a permeability field with long-range correlation, the transport equa tion is not unique. It depends on the assumptions involving moments hi gher than two. Assuming a Gaussian shape for the tracer flux leads to equations similar to the ones obtained in previous studies of time-dep endent dispersivity. Without this approximation, the equation is non-l ocal (integrodifferential) and leads to a memory effect. In the last p art of this paper, the general results are illustrated with several co rrelation functions for the permeability field: purely random, exponen tial and power law covariance, and perfectly layered media.