Conditioning discrete fracture network models of groundwater flow
K. Cliffe 1, D. Holton 2, P. Houston 1, C. Jackson 2, S. Joyce 2, A. Milne 11 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
2 Serco, Harwell, UK.
Received by the editors February 7, 2011.
Many geological formations consist of crystalline rock that have very low matrix permeability but allow flow through an interconnected network of fractures. Understanding the flow of groundwater through such rocks is important in considering disposal of radioactive waste in underground repositories. A specific area of interest is the conditioning of fracture transmissivities on measured values of pressure in these formations. While there are existing methods to condition transmissivity fields on transmissivity, pressure and flow measurements for a continuous porous medium, considerably less work has been devoted to conditioning discrete fracture networks. This article presents two new methods for conditioning fracture transmissivities on measured pressures in a discrete fracture network. The first approach adopts a linear approximation when fracture transmissivities are mildly heterogeneous, while the minimisation of a suitable objective function is undertaken when fracture transmissivities are highly heterogeneous. The second conditioning algorithm is a Bayesian method that finds a maximum a posteriori (MAP) estimator which maximises the posterior distribution defined by Bayesˇ¦ theorem using information from the prior distribution of fracture transmissivities and observations in the form of measured pressures. The conditioning methods are tested on two separate, large scale test cases that model a potential site for radioactive waste disposal. Results from these test cases are shown and comparisons between the two conditioning methods are made.AMS subject classifications: 35L60, 35Q35, 76B15, 76B65
Key words: Conditioning, Groundwater Flow, Discrete Fracture Network, Finite Element Methods.