ON THE ESTIMATION OF GRID-BLOCK VALUES OF EFFECTIVE POROSITY IN HETEROGENEOUS MEDIA

A variety of numerical studies have investigated the scale-dependency of transport processes and their parameters in relation to providing block averaged values. Little attention, however, has been paid to upscaling effective porosity, a parameter significantly affects solute transport process. The objective of this study is to investigate how the value of effective porosity, which is estimated through theoretical tracer experiments, is affected by heterogeneous distribution of permeability at scales larger and smaller than the representative elemental volume (REV). Although effective porosity at a given scale is related to the pattern of heterogeneity, it has been assumed as a “constant” parameter in most of numerical modeling studies, which investigate solute transport in spatially-correlated random permeability fields. Our goal is to analyze for various permeability distributions the importance of the REV in hydraulic conductivity in providing constraints on the definition of block-scaled effective porosity values. A series of numerical experiments were conducted to achieve the objective. Numerical tracer simulations were performed in spatially-correlated random permeability fields. We varied the scale of regions of interest and their location within the larger simulation domain. We analyzed the experiment results and used an inverse method to obtain hydrological parameters including effective porosity. The preliminary results show that effective porosity is greatly affected by the combination of scale and the pattern of heterogeneity. For small regions of interest, effective porosity value is mainly controlled by the local distribution of high permeability layers, which enhance solute migration. Accordingly, for such sub-REV regions of interest, effective porosity values greatly fluctuate up to a certain scale and become constant at larger scales. This result indicates that numerical simulation of solute transport has greater uncertainties than generally thought, up to a certain scale caused by variation of effective porosity value.