Liange Zheng

Inverse modeling of multicomponent reactive transport through single and dual porosity media

Compacted bentonite is foreseen as buffer material for high-level radioactive waste in deep geological repositories because it provides hydraulic isolation, chemical stability, and radionuclide sorption. A wide range of laboratory tests were performed within the framework of FEBEX (Full-scale Engineered Barrier EXperiment) project to characterize buffer properties and develop numerical models for FEBEX bentonite. Here we present inverse single and dual-continuum multicomponent reactive transport models of a long-term permeation test performed on a 2.5 cm long sample of FEBEX bentonite. Initial saline bentonite porewater was flushed with 5.5 pore volumes of fresh granitic water. Water flux and chemical composition of effluent waters were monitored during almost 4 years. The model accounts for solute advection and diffusion and geochemical reactions such as aqueous complexation, acid-base, cation exchange, protonation/deprotonation by surface complexation and dissolution/precipitation of calcite, chalcedony and gypsum. All of these processes are assumed at local equilibrium. Similar to previous studies of bentonite porewater chemistry on batch systems which attest the relevance of protonation/deprotonation on buffering pH, our results confirm that protonation/deprotonation is a key process in maintaining a stable pH under dynamic transport conditions. Breakthrough curves of reactive species are more sensitive to initial porewater concentration than to effective diffusion coefficient. Optimum estimates of initial porewater chemistry of saturated compacted FEBEX bentonite are obtained by solving the inverse problem of multicomponent reactive transport. While the single-continuum model reproduces the trends of measured data for most chemical species, it fails to match properly the long tails of most breakthrough curves. Such limitation is overcome by resorting to a dual-continuum reactive transport model.

A coupled THC model of the FEBEX in situ test with bentonite swelling and chemical and thermal osmosis

The performance assessment of a geological repository for radioactive waste requires quantifying the geochemical evolution of the bentonite engineered barrier. This barrier will be exposed to coupled thermal (T), hydrodynamic (H), mechanical (M) and chemical (C) processes. This paper presents a coupled THC model of the FEBEX (Full-scale Engineered Barrier EXperiment) in situ test which accounts for bentonite swelling and chemical and thermal osmosis. Model results attest the relevance of thermal osmosis and bentonite swelling for the geochemical evolution of the bentonite barrier while chemical osmosis is found to be almost irrelevant. The model has been tested with data collected after the dismantling of heater 1 of the in situ test. The model reproduces reasonably well the measured temperature, relative humidity, water content and inferred geochemical data. However, it fails to mimic the solute concentrations at the heater-bentonite and bentonite-granite interfaces because the model does not account for the volume change of bentonite, the CO(2)(g) degassing and the transport of vapor from the bentonite into the granite. The inferred HCO(3)(-) and pH data cannot be explained solely by solute transport, calcite dissolution and protonation/deprotonation by surface complexation, suggesting that such data may be affected also by other reactions.

Formulation of the inverse problem of non-isothermal multiphase flow and reactive transport in porous media

A methodology for solving the inverse problem of non-isothermal multiphase flow and multicomponent reactive solute transport is presented. Different types of data can be taken into account including heads or pressures, temperature, concentrations of dissolved components, total (dissolved plus sorbed) concentrations, water fluxes, water content, as well as parameter prior information. The inverse problem is solved by minimizing a generalized least-squares criterion with a Gauss-Newton-Levenberg-Marquardt method. Approximate confidence intervals are computed from the parameter covariance matrix. All these features are incorporated in INVERSE-FADES-CORE, a general code which solves both the forward and inverse problems. The code can estimate a wide range of different types of parameters including: intrinsic permeability, parameters of the relative permeability curve, parameters of retention curve, tortousity of vapor, thermal conductivity, dispersivity, distribution coefficient, molecular diffusion coefficient, initial and boundary concentrations, pH and pE, selectivity coefficients, cation exchange capacity, specific surface of minerals, and initial volume fraction of minerals. Synthetic data have been used to verify the formulation and study the convergence, uniqueness, and stability of the algorithm. The methodology has been applied to the estimation of transport and chemical parameters of a heating and hydration laboratory experiment performed on a sample of a compacted bentonite, which is planned to be used as buffer and sealing material for the disposal of high-level radioactive waste in several European countries.

Dual-continuum multicomponent reactive transport with nth-order solute transfer terms for structured porous media

The dual-continuum model (DCM) is a type of modeling approach often used to interpret anomalous and non-ergodic solute transport in which the breakthrough curve cannot be explained by the classical advection–dispersion equation. Experimental studies show that bentonites have a macro-porous domain containing free water and a micro-porous domain containing double-layer and interlayer water. Therefore, a DCM could be needed to describe water flow, solute transport, and chemical reactions through compacted bentonite. In most DCMs, the mass exchange between domains is based on a lumped first-order solute transfer term which is not always accurate. An nth-order solute transfer term for dual-continuum flow and reactive transport model for structured porous media is proposed here. The value of n is derived from the approximation of the analytical solution of diffusion through a thin slab. The parameters of DCMs are obtained by an inverse methodology. Solute transfer terms for compacted bentonite have been evaluated for 1-D and 2-D synthetic cases by solving the inverse problem for several values of n. The best results are obtained with an n of 0.72 and a scale term of 2.5. The reactive transport DCM has been tested with data from a permeability test conducted on a sample of full-scale engineered barrier experiment (FEBEX) bentonite. By accounting for the solute flux across the micro–macro interface, the DCM overcomes the limitations of the single-continuum model (SCM) which fails to reproduce the long tails of the breakthrough curves of most chemical species of this test. The exponent n and the scaling factor were estimated from Cl− data. They are similar to those obtained from the 2-D synthetic case, thus indicating that the exponent and the scaling factor derived for the FEBEX bentonite could be used for other compacted bentonites.

Forward and inverse modelling of multicomponent reactive transport in single and double porosity media

The term ‘double porosity’ is generally used to represent a conceptual model in which the medium is divided into two or more domains that are coupled by an interaction term for modeling flow and solute transport. While double porosity models are available for water flow and conservative transport, there is not much experience in the fourmulation of double porosity models for multicomponent reactive species. Here we analyze the double porosity behavior in a long-term permeation and tracer test performed on a sample of FEBEX compacted bentonite. FEBEX (Full-scale Engineered Barrier EXperiment) is a demonstration and research project dealing with the bentonite engineered barrier designed for sealing and containment of waste in a high level radioactive waste repository. Hydrogeochemical modelling of porewaters indicate that the main geochemical processes controlling the chemistry of the bentonite are acid-base reactions, aqueous complexation, cation exchange, dissolution/ex-solution of CO 2 , and dissolution and precipitation of highly soluble minerals such as calcite, dolomite, chalcedony, and gypsum/anhydrite. All these processes are assumed to take place under equilibrium conditions. Water flux and chemical data of effluent waters were measured during the experiment. Inverse modelling of this experiment has been carried out using single and double porosity models. The measured breakthrough curve of chloride is consistent with a double porosity model. The model reproduces the trends of measured data except for bicarbonate and pH which are affected by uncertainties in the evolution of CO 2 (g) pressures.