(535c) Dissolution at the Pore Scale: Comparing Simulations and Experiments

Flow and transport in porous media is usually modeled at the Darcy scale, where the system is comprised of representative elementary volumes (REV's) described by average properties such as porosity, permeability, dispersion coefficients, and reactive surface area. Although this allows large volumes to be simulated efficiently, there are serious difficulties in developing suitable models for the properties of the REV's. When there is rapid dissolution, such as when brine pressurized with CO₂ encounters calcite, even the validity of the averaging process is called into doubt by the strong gradients in concentration within a single REV.

Pore-scale modeling overcomes many of the limitations of Darcy-scale models, albeit at much greater computational cost. Nevertheless, it is not yet clear that a single set of parameters – fluid viscosity, ion diffusion coefficients, and surface reaction rates – can consistently describe the dissolution of samples with different pore structures. Here we describe some preliminary results of comparisons of numerical simulations of the dissolution of a soluble cylinder with microfluidic experiments, and with approximate calculations from conformal mapping.

The numerical simulations used a finite-volume discretization, with an unstructured mesh that conforms to the shape of the dissolving object. By exploiting the intrinsic separation of time scales between transport and dissolution, precise simulations can be carried out with limited computational resources. We used the OpenFOAM toolkit with customized libraries to support mesh motion and relaxation around the dissolving object. Simulations take a few hours, in comparison with 1 month for the laboratory experiments.

Results will focus on the evolving shape of the dissolving cylinder. Because of the flow, the cylinder has a broken front-to-back symmetry, and develops a sharp cusp near the tail. The shapes predicted by numerical simulations can always be overlaid with the experimental measurements for the same total area.

The dissolution time scale in these experiments is primarily determined by the ion diffusion across the concentration boundary layer (transport-limited dissolution). Using the coefficients for dilute aqueous ions, we overpredict the dissolution rate by about 25%. However, including the Debye-Huckel correction for the ion activity gives a substantial reduction in diffusion across the high concentration region near the dissolving solid surface. Including Debye-Huckel corrections (from PHREEQC) brings the simulation time scale into quantitative agreement with experiment. The best fit is obtained with a reaction rate constant of about 0.01 mm/s, which is very close to independent measurements on similar samples of gypsum.

We will report on scaling laws for the size and shape of the dissolving disk that were discovered in both the experiments and the simulations, and compare these results with predictions from conformal mapping.

This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division under Award Numbers DE-FG02-98ER14853 and DE-SC0018676, and by the National Science Center (Poland) under research Grant No. 2012/07/E/ST3/01734