A Markov chain Monte Carlo inverse procedure for radioactive contaminant transport in fractured rock: 1. Forward model

Safety assessment of high-level radioactive waste repositories requires confidence in models for radioactive contaminant transport in fractured media. An approach for contaminant transport-model testing is calibration based on large-scale laboratory experiments. This paper is the first of two papers in which the calibration of a two-dimensional variable fracture network model for radioactive tracers is formulated as an inverse problem using a Bayes-Markov approach. This paper gives the framework for the inverse problem and decribes a novel contaminant transport model appropriate for this problem. The subsequent paper presents the details of the algorithm for the inverse problem solution. The prior information for fracture-aperture distribution is assumed in the form of Markov random fields (MRF). In particular, the class of auto-models has been successful in reproducing the connectivity in extreme values of fracture apertures, and experimentally observed flow channelling. A continuous model, conditional auto-regressive model, and a discrete, auto-binomial model have been applied. The mathematical model for the contaminant transport in the discrete fracture network is based on the numerical inversion of the Laplace transform. This methodology is free of numerical dispersion, but requires a large number of terms to reconstruct very steep contaminant fronts.