Joint estimation of transmissivity and storativity in a bedrock fracture

Abstract

The spatial variability of transmissivity (T) and storativity (S) in a sandstone bedding plane fracture was investigated through field and numerical hydraulic tomography experiments. Cross-hole pumping tests were conducted in a single subhorizontal bedrock fracture, thereby constraining the problem to two dimensions. A Bayesian method implementing pilot points was used to invert the drawdown, under the hypothesis that T and S are independent random space functions, where integral scale, mean, and variance of the random fields were parameters of inversion in addition to pilot point values. An ensemble of 20 Monte Carlo realizations was created for each model scenario. Inversion of the measured cross-hole drawdown resulted in spatially variable T and S fields. To determine the accuracy of the method, a suite of synthetic inversions modeled after the field site were also conducted. The synthetic experiments demonstrate that the assumed spatial structure of S influences the accuracy of both the T and S inversions. When the S field is spatially heterogeneous and is assumed to be heterogeneous in the inversion, a consistent representation of the T and S fields is obtained. When the S field is spatially heterogeneous but is assumed to be homogeneous in the inversion, a consistent representation of the T field is still obtained, but the S field is entirely misrepresented; if the S field is actually homogeneous but assumed to be heterogeneous, a poor representation of the T and S fields is obtained along with high uncertainty in the inversion statistics of confidence. Copyright 2011 by the American Geophysical Union.