Dispersion on kriged hydraulic conductivity fields

Abstract

Geostatistical interpolation of log conductivity measurements leads to velocity fields lacking small‐scale variability whereas large‐scale features are covered well. The unresolved, small‐scale velocity fluctuations cause underestimation of macrodispersion, dilution, and mixing in subsequent transport calculations. The same holds when the best linear unbiased estimate of geostatistical inverse methods is used in flow and transport simulations. Considering a regular grid of measurement points, we approximate the lack of dispersion, to which we refer as correction dispersion, by applying first‐order theory to the conditional covariance of the kriged log conductivity field. The nonstationarity of the conditional covariance is removed by averaging it over space. We distinguish between macrodispersion, describing the rate of change in the second spatial moments of a large plume, and effective dispersion of a plume introduced as a point source, parameterizing dilution and mixing. Depending on the objective, we either add a correction macrodispersion tensor or a correction effective dispersion tensor to the true local dispersion tensor in transport calculations on the smoothed log conductivity field. The numerical application to a two‐dimensional periodic domain shows excellent agreement in the one‐ and two‐particle moments between simulations on the highly resolved field and those on the interpolated one using corrected values for the local dispersion coefficients.