Modelling and Upscaling of Transport in Carbonates During Dissolution: Validation and Calibration with NMR Experiments

We present an experimental and numerical study of transport in carbonates during dissolution and its upscaling from the pore (∼ μm) to core (∼ cm) scale. For the experimental part, we use nuclear magnetic resonance (NMR) to probe molecular displacements (propagators) of an aqueous hydrochloric acid (HCl) solution through a Ketton limestone core. A series of propagator profiles are obtained at a large number of spatial points along the core at multiple time-steps during dissolution. For the numerical part, first, the transport model—a particle-tracking method based on Continuous Time Random Walks (CTRW) by Rhodes et al. (2008)—is validated at the pore scale by matching to the NMR-measured propagators in a beadpack, Bentheimer sandstone, and Portland carbonate Scheven et al. (2005). It was found that the emerging distribution of particle transit times in these samples can be approximated satisfactorily using the power law function ψ(t) ∼ t ^−1 −β, where 0 < β < 2. Next, the evolution of the propagators during reaction is modelled: at the pore scale, the experimental data is used to calibrate the CTRW parameters; then the shape of the propagators is predicted at later observation times. Finally, a numerical upscaling technique is employed to obtain CTRW parameters for the core. From the NMR-measured propagators, an increasing frequency of displacements in stagnant regions was apparent as the reaction progressed. The present model predicts that non-Fickian behaviour exhibited at the pore scale persists on the centimetre scale.