Background

The presence of overlapping diffuse layers in clay media porosity is responsible for a remarkable array of coupled macro-scale processes.

1. The resulting partial or total repulsion of anions from the porosity explain the semi-permeable properties of clay materials: in the presence of a gradient of bulk electrolyte concentration, anions migration through the pores is hindered, as are cations because of electro-neutrality constraints, thus explaining salt-exclusionary properties of clays (Fritz, 1986).

2. The overlap of diffuse layers creates a difference in electrolyte concentrations between the clay pores and the water volumes not affected by the presence of clay surfaces, thus creating a difference in osmotic pressure between these two types of water domains (Wilson and Wilson, 2014). Together with clay mineral surface hydration forces, repulsive osmotic forces are responsible for swelling properties of clay materials (Liu, 2013). Osmotic pressure gradients may develop across the semi-permeable clay layers driving osmotic flow, and thus expulsion of water. Either osmotic flow, or flow driven by hydraulic gradients, may result in stripping of ions from the electrical double layer (EDL) and thus generate a streaming potential.

3. These swelling forces are responsible for a spatial rearrangements of clay mineral layers and particles during hydration of clay materials, or any other event that may change the chemical composition and/or the water activity in clay pores (Massat et al., 2016; Whittaker et al., 2019). These changes in microstructure may, in turn, change the transport diffusion and/or advection (flow) properties of clay materials (Melkior et al., 2009; Muurinen, 2009; Tournassat et al., 2016).

As a result of the anion exclusion (or more exactly, hindrance) in the clay media, diffusive transport cannot be treated with Fick’s Law alone. For diffusion processes, it is necessary to account for the electrophoretic processes corresponding to the coupling between the charge imbalance in the diffuse layer, the differences in concentration gradients for each species having different charges together with the diffusion coefficient of each individual species. This can be done by using the Nernst-Planck equations. Tournassat and Steefel (2015, 2019) reviewed the basics of the application of the Nernst-Planck equations applied to diffusive processes in the diffuse layer bordering charged surfaces in reactive transport codes. By combining with a Mean Electrostatic Approach model to account for the Poisson equation, we arrive at at an averaged treatment of the Poisson-Nernst-Planck (PNP) equations (see Kirby, 2010 for the fully resolved treatment in the presence of a simple electrolyte, Tournassat and Steefel, 2019 for an averaged, upscaled treatment in the presence of a complex electrolyte).

Proposed Work

Within the framework of the Berkeley Lab BES project, we will continue development of a fully coupled multicontinuum model to account for ion diffusive and advective transport, swelling, and osmotic flow (water diffusion). Currently CrunchClay can account for two continua or porosities, one corresponding to bulk water (electrically neutral), the other corresponding to the EDL, where the charge is balanced by the charge of the clays. We propose to add the capability for multi-continua, the most important of which is interlayer porosity in smectite. This nanometer scale porosity accounts for crystalline swelling (Holmboe et al. 2012; Subramanian et al. 2019).

In parallel, we will develop a swelling pressure model that eliminates the empirical parameters used presently in the literature. The swelling pressure that develops is a result of the overlap of electrical double layers and will be treated with a 1D Poisson-Boltzmann equation, or an approximate version of such. With the swelling model, we will be able to account for pressure driven grain mechanical reorganization and osmotic flow

Flow is currently allowed only in the bulk porosity (Fig. 1A) (Tournassat & Steefel, 2019). We will implement a more general form of the Nernst-Planck equation that includes flow (i.e. osmotic flow mentioned above) but also flow due to hydraulic gradients that may be present, and advective transport in the EDL porosity, where the possibility of generating a stream potential arises when ions are stripped from the diffuse layer (Fig. 1B). Indeed the new implementation will enable to deal with all of the off-diagonal coupling flux terms as shown in Table 1 with the exception of thermal gradient induced coupled fluxes. The terms that were not derived directly in the analysis made in Tournassat & Steefel (2019) will be deduced on the basis of Onsager’s reciprocal rules (Onsager 1931 a, b).

The inclusion of swelling pressure driven processes can drive grain reorganization (considered in Smectite Swelling), but also flow from one pore to another within a heterogeneous clay grain pack, and local changes of solid density. Consequently, we intend to couple the swelling clay models developed in task RRR with CrunchClay reactive transport framework in two steps. In the first step, the constant volume problem will be solved, for systems that are fully constrained in volume and for which pressure build-up can be monitored such as in oedometer cells. In a second step, the variable volume problem will be solved, for systems exhibiting fully or partly free swelling behaviors. The latest development will be based on the extension of a current ability of CrunchFlow to transport solid particles in erosion and sedimentation processes.

Another set of tasks involves the parallelization of CrunchClay using OpenMP and MPI. OpenMP is ideally suited for speeding up execution of single routines and loops, while MPI is designed for very large problems.

A summary of the current and planned status of CrunchClay is given below.

References