From characterisation of pore-structures to simulations of pore-scale fluid flow and the upscaling of permeability using microtomography: A case study of heterogeneous carbonates

• A workflow of microtomographic analysis for permeability and upscaling
• Test the workflow using carbonate samples with strong heterogeneity
• Characterisation focuses on anisotropy and the critical pore diameter.
• Permeability compares with laboratory measurements and pore characterisation.
• Scaling parameters are extracted and different critical exponents are found.

We propose a workflow to provide detailed characterisation of microstructures, simulations of permeability at micro-scale, and to analyse the upscaling of permeability. The workflow is fully tested using two very different microtomographic datasets of carbonate samples with strong heterogeneity. The characterisation of microstructures includes not only routine parameters but also anisotropy of the pore-structure. The critical pore diameter is also obtained through morphological implementations. The method of stochastic analysis of extended local porosity theory is used to determine the sizes of representative volume elements (RVE). We demonstrate criteria for determining the size of the RVE and show a sample that satisfies the criterion. We also discuss a sample that does not suffice the RVE criterion, because of the strong anisotropy. Permeabilities are computed using Lattice-Boltzmann (LB) simulations on the RVE and compared with laboratory measurements. Techniques and procedures are used to extract scaling parameters for both of the samples including: 1) percolation threshold — by using a shrinking/expanding algorithm; 2) crossover length — by analysing the mass density; 3) the critical exponent of correlation length — by using the finite-size scaling scheme; and 4) the critical exponent of permeability — by running LB simulations on a series of derivative models close to the percolation threshold. Our results of critical exponents are different from the previous studies and the mass density distributions are irregular. This pilot study provides new information on the relationships between microstructures and permeability of natural rocks with complex microstructures. The study also reveals the scaling parameters. Our results clearly put into question whether natural rocks can be idealised by classical theoretical solutions. A robust workflow for embracing a computational approach of microstructures may provide a solution.