| Safety assessment of deep geological repositories requires validated and calibrated flow and contaminant transport models. In this work, the model calibration of a discrete fracture network model for the radioactive tracer tests in fractured media is formulated as an inverse problem, and solved using the Bayesian paradigm.; A common inverse problem for contaminant transport in fractured rocks is the fracture aperture distribution reconstruction, characterized by significant non-uniqueness and prohibitive computational times. A Bayes-Markov inverse procedure for tracer tests evaluation is presented in this work. The prior information is assumed in the form of Markov random fields (MRF). In particular, the class of auto-models has been proven successful in reproducing the connectivity in extreme values of fracture apertures, and experimentally observed flow channeling. A continuous model, conditional autoregressive model, and a discrete, autobinomial 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 using an accelerated Fourier series. This methodology is free of numerical dispersion, but requires a large number of terms to reconstruct very steep contaminant fronts. Therefore, this approach is pretty slow on sequential computers, but it is very appropriate for concurrent computing.; A two-level estimation-reconstruction iterative procedure has been developed. On the first level, the fracture apertures are reconstructed using simulated annealing (SA), with the Metropolis-Hastings dynamics. Here the MRF parameters are assumed to be known. On the second level, after several sweeps of the entire field using SA, the MRF parameters are updated using the method of pseudolikelihood. The discrete model was reconstructed using a theoretically optimal logarithmic cooling. Although the number of allowed iterations is limited, the reconstruction reproduced the main spatial patterns. The convergence of the continuous prior model was too slow to reach a satisfactory solution. The decision between competing models is finally made based on an asymptotic form of the Bayes factor.; The presented methodology can calibrate simple synthetic models. Additional work is needed to assess its performance for more complex synthetic model structures, large scale discrete and continuous models, and field data. |
