Carbonates are typically heterogeneous over multiple length scales. Due to varying connectivity of pore space features at different scales for carbonates, exhibiting bi-modal or multi-modal pore size distributions, the reliability of petrophysical cross-correlations for predicting the transport properties is reduced. The recent emergence of high resolution micro-CT technology in conjunction with robust numerical methods helps to address this problem. Due to the finite resolution of X-ray images current pore scale flow models only consider macro-pores; the pores which are resolved at the image resolution. The importance of micro-pores in fluid flow and solute transport has been proved, although qualitatively, in many applications including hydrocarbon production from carbonate rocks, CO2 storage and subsurface groundwater remediation. In this study we quantify the effect of microporosity on effective permeability for different porous media with exhibiting a varying amount of micro- and macro-porosity. We combine Gaussian random fields (GRF) and particle based models to construct model structures with dual-scale pore types. The Brinkman equation is solved directly on the images to calculate the effective permeability via the lattice Boltzmann method while quantifying the flux through the micro-porous regions. Connectivity analysis conducted on the samples revealed the connectedness of macro-pores through micro-pores. Micro-porosity incorporation increased the connectivity of the macro-pores and consequently the effective permeability of the whole system. This paper introduces a methodology to quantify the effect of microporosity on the fluid flow and incorporate it into the macropores. The approach was first tested on three homogeneous model structures and images of two sandstone rocks, before being implemented on more heterogeneous model structures with bi-modal pore size distribution. The work presented here enables us to couple the effect of sub-resolution pores and macropores in a physically meaningful way. This approach might have important applications to the calculation of permeability for unconventional reservoir rocks.


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