Three Dimensional Stochastic Modeling of Conductivity Fields in a Fractured Rock Medium

1. Abstract Modeling flow and transport in a fractured rock formation requires in many instances an explicit representation of fractures. In such cases discrete fracture models do not always work properly because of the difficulty to be calibrated and the lack of flexibility to be adapted, in an automated calibration process, when the description of fracture locations is not accurate enough. In this case a pseudo porous media approach, in which fractures are represented by high hydraulic conductivity zones, is an alternative model that has already been successfully proven in real case studies. Fractures use to be the most relevant feature to describe when dealing with contaminants migration. In these 2D structures, hydraulic conductivity (K) is usually the most relevant parameter for mass transport modeling. K usually exhibits a high degree of spatial variability and direct measurements of it are very scarce, when available. Thus, in the same way found for a continuous medium, stochastic simulation techniques can be the most suitable tool to model K in fractures. Besides, the goal of obtaining more realistic predictions, while reducing uncertainty in model results, calls for conditioning K fields to the available pressure measurements. Based on a 3D real case study of flow and transport in a fractured crystalline rock, the paper addresses the way to model K in fractures, and the rock matrix, conditional to pressure data. It is assumed that K in fractures may not be multiGaussian. The simulation of these K fields is achieved by means of a method based on non-parametric statistics that yields K fields in which zones of extreme values of K may appear highly interconnected. The method can support the assumption of independent stochastic processes corresponding to different fracture families. This is achieved using a multi-parameterization approach implemented in the inversion technique known as Conditional Probabilities method. The paper shows how different can be mass transport predictions when Gaussian and nonGaussian models are assumed for K fields in fractures. The conclusion is that, in view of available data, models alternative to the common Gaussian assumption should always be considered.