THE SPATIAL AND TEMPORAL MOMENTS OF TRACER CONCENTRATION IN DISORDERED POROUS-MEDIA

This study develops a methodology for deriving the spatial and temporal moments of tracer concentration in disordered geological formations and suggests a geostatistical formalism for interpolation and prediction of concentration, conditional to concentration measurements. The required spatial and temporal moments of the concentration are obtained by a biparticle tracking scheme which yields the bivariate probability distribution function of particle displacements in terms of the input log conductivity random field and the prevailing flow conditions. The structure of the moments of the concentration is discussed, and we show that (1) the concentration correlation function is anisotropic, nonstationary and nonsymmetrical; (2) there is a larger correlation between concentrations along the mean flow direction than normal to it; (3) the correlation between the concentration at any two points with fixed coordinates on a moving (Lagrangian) coordinate system increases with travel time; (4) the correlation function necessarily assumes negative values beyond a certain threshold distance; and (5) the concentration variance is finite even when neglecting pore-scale dispersion. Application of the geostatistical prediction algorithm using the concentration spatial/temporal moments shows a good potential for reducing prediction uncertainty.