Gradual conditioning of non-Gaussian transmissivity fields to flow and mass transport data: 2. Demonstration on a synthetic aquifer

SummaryIn the first paper of this series a methodology for the generation of non-Gaussian transmissivity fields conditional to flow, mass transport and secondary data was presented. This methodology, referred to as the gradual conditioning (GC) method, constitutes a new and advanced powerful approach in the field of stochastic inverse modelling. It is based on gradually changing an initial transmissivity (T) field, conditioned only to T and secondary data, to honour flow and transport measured data. The process is based on combining the initial T field with other seed T fields in successive iterations maintaining the stochastic structure of T, previously inferred from data. The iterative procedure involves the minimization of a penalty function which depends on one parameter, and is made up by the weighted summation of the square deviations among flow and/or transport variables, and the corresponding known measurements. The GC method leads gradually to a final simulated field, uniformly converging to a better reproduction of conditioning data as more iterations are performed. The methodology is now demonstrated on a synthetic aquifer in a non-multi-Gaussian stochastic framework. First, an initial T field is simulated, and retained as reference T field. With prescribed head boundary conditions, transient flow created by an abstraction well and a mass solute plume migrating through the formation, a long-term and large scale hypothetical tracer experiment is run in this reference synthetic aquifer. Then T, piezometric head (h), solute concentration (c) and travel time (τ) are sampled at a limited number of points, and for different time steps where applicable. Using this limited amount of information the GC method is applied, conditioning to different sets of these sampled data and model results are compared to those from the reference synthetic aquifer. Results demonstrate the ability and robustness of the GC method to include different types of data without adopting any Gaussian assumptions, and its high potential to be used together with the Monte Carlo method for uncertainty analysis of flow and mass transport model results. Moreover, the simplicity of the formulation of the method, based on forward flow and mass transport solvers, the flexibility of the stochastic random definition required, and the simple form of the minimization problems solved during the iterative procedure, make this a very valuable tool and robust alternative to other methods for real applications.