Stochastic inverse modelling of hydraulic conductivity fields taking into account independent stochastic structures: A 3D case study

Abstract

Major factors affecting groundwater flow through fractured rocks include the geometry of each fracture, its properties and the fracture-network connectivity together with the porosity and conductivity of the rock matrix. When modelling fractured rocks this is translated into attaining a characterization of the hydraulic conductivity (K) as adequately as possible, despite its high heterogeneity. This links with the main goal of this paper, which is to present an improvement of a stochastic inverse model, named as Gradual Conditioning (GC) method, to better characterise K in a fractured rock medium by considering different K stochastic structures, belonging to independent K statistical populations (SP) of fracture families and the rock matrix, each one with its own statistical properties. The new methodology is carried out by applying independent deformations to each SP during the conditioning process for constraining stochastic simulations to data. This allows that the statistical properties of each SPs tend to be preserved during the iterative optimization process. It is worthwhile mentioning that so far, no other stochastic inverse modelling technique, with the whole capabilities implemented in the GC method, is able to work with a domain covered by several different stochastic structures taking into account the independence of different populations. The GC method is based on a procedure that gradually changes an initial K field, which is conditioned only to K data, to approximate the reproduction of other types of information, i.e., piezometric head and solute concentration data. The approach is applied to the Aspo Hard Rock Laboratory (HRL) in Sweden, where, since the middle nineties, many experiments have been carried out to increase confidence in alternative radionuclide transport modelling approaches. Because the description of fracture locations and the distribution of hydrodynamic parameters within them are not accurate enough, we address the domain by using a pseudo porous media approach, in which fractures are represented by high K zones. This approach has already been proven to be successful in real case studies. Results of the K conditional fields have been compared to those obtained in a scenario where the independence of the different stochastic structures was not fully considered. After performing an uncertainty assessment, we have found that when using additional conditioning data (piezometric head data) and multiple SPs the reproduction of the hydraulic head field is significantly improved and uncertainty is reduced. However, honouring the independence of different SPs does not warrant a decrease of uncertainty but in fact due to a more realistic reproduction of the statistical features uncertainty can be increased.