Gradual conditioning of non-Gaussian transmissivity fields to flow and mass transport data: 1. Theory

Abstract

The paper presents a new stochastic inverse method for the simulation of transmissivity ( T ) fields conditional to T measurements, secondary information obtained from expert judgement and geophysical surveys, transient piezometric and solute concentration measurements, and travel time data. The formulation of the method is simple and derived from the gradual deformation method. It basically consists of an iterative optimization procedure in which successive combinations of T fields, that honour T measurements and soft data (secondary data obtained from expert judgement and/or geophysical surveys), gradually lead to a simulated T field conditional to flow and mass transport data. Every combination of fields requires minimizing a penalty function that penalizes the difference between computed and measured conditioning data. This penalty function depends on only one parameter. Travel time conditioning data are considered by means of a backward-in-time probabilistic model, which extends the potential applications of the method to the characterization of groundwater contamination sources. In order to solve the mass transport equation, the method implements a Lagrangian approach that allows avoiding numerical problems usually found in Eulerian methods. Besides, to deal with highly heterogeneous and non-Gaussian media, being able to reproduce anomalous breakthrough curves, a dual-domain approach is implemented with a first-order mass transfer approach. To determine the particle distribution between the mobile domain and the immobile domain the method uses a Bernoulli trial on the appropriate phase transition probabilities, derived using the normalized zeroth spatial moments of the multirate transport equations. The presented method does not require assuming the classical multiGaussian hypothesis thus easing the reproduction of T spatial patterns where extreme values of T show high connectivity. This feature allows the reproduction of a property found in real formations, which is often crucial to obtain safe estimations of mass transport predictions. Furthermore, very few existing methods can afford with this stochastic property. In fact, this new approach gathers a set of capabilities so far not included in any existing method.