Uncertainty quantification in Discrete Fracture Network models: Stochastic fracture transmissivity. (August 2015)

• Record Type: Journal Article
• Authors: Berrone, S.; Canuto, C.; Pieraccini, S.; Scialò, S.
• Is Part Of: Computers & mathematics with applications. Volume 70:issue 4(2015)
• Page Start: 603
• Page End: 623
• Publication Date: 2015-08
• Subjects: Fracture networks -- Darcy's law in fractured media -- Uncertainty quantification -- Stochastic collocation methods -- Sparse grids; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2015.05.013
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We consider flows in fractured media, described by Discrete Fracture Network (DFN) models. We perform an Uncertainty Quantification analysis, assuming the fractures' transmissivity coefficients to be random variables. Two probability distributions (log-uniform and log-normal) are used within different laws that express the coefficients in terms of a family of independent stochastic variables; truncated Karhunen–Loève expansions provide instances of such laws. The approximate computation of quantities of interest, such as mean value and variance for outgoing fluxes, is based on a stochastic collocation approach that uses suitable sparse grids in the range of the stochastic variables (whose number defines the stochastic dimension of the problem). This produces a non-intrusive computational method, in which the DFN flow solver is applied as a black-box. A very fast error decay, related to the analytical dependence of the observed quantities upon the stochastic variables, is obtained in the low dimensional cases using isotropic sparse grids; comparisons with Monte Carlo results show a clear gain in efficiency for the proposed method. For increasing dimensions attained via successive truncations of Karhunen–Loève expansions, results are still good although the rates of convergence are progressively reduced. Resorting to suitably tuned anisotropic grids is an effective way to contrast such curse of dimensionality: in the explored range of dimensions, the resulting convergence histories are nearly independent of the dimension.