For the proposed Yucca Mountain site for a nuclear waste depository, the prediction of flow for the transport of contaminants is critical. Common standard methods of calculating vertical, unsaturated, single-phase flow between model grid cells can produce predicted flows in error up to six orders of magnitude, in the wrong direction, or with effectively misplaced hydrostatic conditions. This raises valid questions about assuring the eternal safety of any depository through such modeling.
Calculating Darcian mean flows between grid cells, derived directly from the modeling assumptions, depending on characteristics of both the medium and the model, addresses this issue. This provides a new mathematical and modeling framework with which to judge the appropriateness of such means and their approximations.
Using a presumed composite relative conductivity relation for Topopah Spring welded tuff, this work develops true Darcian means over many modeling regimes, and the viable approximations for general exponential and Brooks-Corey conductivity relations necessary for running models.
This demonstrates how very differently matrix and fracture flow must be treated in a model. It illustrates how a composite relation itself may be responsible for poor-posedness in the problem and suggests that separate, linked models for fracture and matrix flow may be in order.