Inverse problem of multicomponent reactive chemical transport in porous media: Formulation and applications

Abstract

A general methodology for solving the inverse problem of multicomponent reactive solute transport in porous media is presented in this paper. In addition to prior information on model parameters the methodology relies on hydraulic heads, aqueous and total concentrations, water fluxes and water contents. The formulation is based on minimizing a generalized least squares criterion by means of a Gauss‐Newton‐Levenberg‐Marquardt method. The methodology copes with the simultaneous estimation of flow, transport, and geochemical parameters as well as initial and boundary pH, pE, and concentrations. It overcomes the limitations of the trial‐and‐error method and should enlarge the capabilities of hydrogeologists and hydrochemists to understand the complexities of reactive groundwater systems. This paper presents a mathematical and numerical formulation of the forward and inverse problems and illustrates its application to a synthetic experiment dealing with cation exchange and kinetically controlled calcite dissolution in a column. Parameter estimates are accurate when data are free of errors. Accurate solutions cannot be found, however, when synthetic data are corrupted with large lognormally distributed random noise unless prior information on model parameters is considered. Estimation improves significantly when prior information is taken into account, demonstrating its relevance for obtaining reliable parameter estimates. Solutions of the inverse problem for a real case study are presented, in which a stepwise inversion is proposed for identifying geochemical structures and estimating model parameters. This case deals with reactive solute transport in a column experiment performed by Appelo et al. [1990] in which the cation exchange complex of a clay sediment from the Ketelmeer aquifer was flushed with a SrCl2 solution. The inverse methodology has been found to be useful in investigating the relevance of calcite dissolution/precipitation under both local equilibrium and kinetic conditions.