On the use of block‐effective macrodispersion for numerical simulations of transport in heterogeneous formations

Abstract

The fundamental question we consider in this paper is how to allow flexibility in numerical grid design without discounting the dispersive action of the unmodeled variability. In doing that, we wish to preserve the interplay between all relevant length scales: those relevant to the spatial variability as well as those created by design. In this study we extend and test the concept of block‐scale macrodispersion introduced by Rubin et al. [1999] for modeling unresolved hydraulic property variations at scales smaller than the numerical grid blocks. We present closed‐form analytical results for the block‐scale macrodispersion and test them numerically. Closed‐form analytical results are presented for the large‐time aymptotic limits, and it is shown that these limits are attained very fast. The conditions of applicability are investigated, and we show that ergodicity with regard to block‐scale heterogeneity is attained surprisingly fast.