Confidence in solutions of flow through stochastically generated hard rock formations

Confidence in solutions of flow through stochastically generated hard rock formations was studied with the aid of a simplified synthetic model. The formation is conceptualized as a fracture network intersecting an impervious rock mass. The geometrical properties of the fracture network were assumed to be known while fracture transmissivities were considered a stochastic process. First, network fracture transmissivities were generated using a given probability distribution function. This a priori model was considered the true formation. In a second step, only a limited amount of information, similar to that obtained in reality from boreholes, was used to construct a conditioned-by-measurement model. Identical flow tests were performed on a formation constructed with limited data and on the true formation. The ratio of the rates of flow resulting from these tests was considered a measure of confidence in the stochastically generated formation. The results, with this model and a particular data set, show uncertainty values between 47% to 63%, corresponding to fracture sample sizes of 11% and 2% respectively, from the total number in the network