Characterizing heterogeneous permeable media with spatial statistics and tracer data using sequential simulated annealing

Abstract

Characterizing heterogeneous permeable media using flow and transport data typically requires solution of an inverse problem. Such inverse problems are intensive computationally and may involve iterative procedures requiring many forward simulations of the flow and transport problem. Previous attempts have been limited mostly to flow data such as pressure transient (interference) tests using multiple observation wells. This paper discusses an approach to generating stochastic permeability fields conditioned to geologic data in the form of a vertical variogram derived from cores and logs as well as fluid flow and transport data, such as tracer concentration history, by sequential application of simulated annealing (SA). Thus, the method incorporates elements of geostatistics within the framework of inverse modeling. For tracer-transport calculations, we have used a semianalytic transit-time algorithm which is fast, accurate, and free of numerical dispersion. For steady velocity fields, we introduce a “transit-time function” which demonstrates the relative importance of data from different sources. The approach is illustrated by application to a set of spatial permeability measurements and tracer data from an experiment in the Antolini Sandstone, an eolian outcrop from northern Arizona. The results clearly reveal the importance of tracer data in reproducing the correlated features (channels) of the permeability field and the scale effects of heterogeneity.