Topics in flow in fractured media - Milne, Andrew (2011)
Many geological formations consist of crystalline rocks 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. This is the process where the values of fracture transmissivities in a model are adjusted to obtain a good fit of the calculated pressures to measured pressure values. While there are existing methods to condition transmissivity fields on transmissivity, pressure and flow measurements for a continuous porous medium there is little literature on conditioning fracture networks. Conditioning fracture transmissivities on pressure or flow values is a complex problem because the measured pressures are dependent on all the fracture transmissivities in the network. This thesis presents two new methods for conditioning fracture transmissivities in a discrete fracture network on measured pressure values. The first approach adopts a linear approximation when fracture transmissivities are mildly heterogeneous; this approach is then generalised to the minimisation of an objective function when fracture transmissivities are highly heterogeneous. This method is based on a generalisation of previous work on conditioning transmissivity values in a continuous porous medium. The second method developed is a Bayesian conditioning method. Bayes’ theorem is used to give an expression of proportionality for the posterior distribution of fracture log transmissivities in terms of the prior distribution and the data available through pressure measurements. The fracture transmissivities are assumed to be log normally distributed with a given mean and covariance, and the measured pressures are assumed to be normally distributed values each with a given error. From the expression of proportionality for the posterior distribution of fracture transmissivities the modes of the posterior distribution (the points of highest likelihood for the fracture transmissivities given the measured pressures) are numerically computed. Both algorithms are implemented in the existing finite element code NAPSAC developed and marketed by Serco Technical Services, which models groundwater flow in a fracture network.