Image-based relative permeability upscaling from the pore scale

•Microporosity has an impact on relative permeability functions.•The error of neglecting microporosity could be more than 90% even for Sw, micro > 0.9.•The macroscopic lattice Boltzmann methods was applied successfully for upscaling from pore scale.•Darcy’s equation is coupled with Stokes equations in upscaling process. High resolution images acquired from X-ray μ-CT are able to map the internal structure of porous media on which multiphase flow properties can be computed. While the resolution of a few micrometers may be sufficient for capturing the pore space of many sandstones, most carbonates exhibit a large amount of microporosity; pores which are below the image resolution and are not resolved at specific resolution. Neglecting the effect of micropores on fluid flow and transport properties of these rocks can cause erroneous results in particular at partial saturations. Current image-based pore scale models typically only consider macropores for simulating fluid flow. In this paper, we quantify the effect of microporosity on the effective permeability of the wetting phase for heterogeneous model structures with varying amount of micro-to-macro porosity. A multi-scale numerical approach is proposed to couple an average effect of micropores with an explicit representation of macropores. The Brinkman equation is solved using a lattice Boltzmann formulation to facilitate the coupling of Darcy and Stokes equations in micropores and macropores, respectively. The results show good agreement between the fine scale solution and the results of the upscaled models in which microporous regions are homogenised. The paper analyses in particular the choice of the momentum sink parameter at low wetting phase saturations. It is shown that this parameter can be found using either a flux-based calculation of permeability of microporous regions or chosen purely on the basis of the effective permeability of these regions.