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Abstract
High resolution images acquired from X-ray micro-tomography provide 3D pore geometry on which flow and transport properties can be computed. However, these images exhibit limited resolution in particular if field of view needs to be optimised at the same time. Constrained by the image resolution, the pore space is partitioned into macro-pores (resolvable porosity) and micro-pores, which are below the image resolution. The importance of micro-pores in fluid flow and solute transport has often been ignored. In this study, we quantify and couple the effect of sub-resolution pores into larger pores for different porous media with varying amount of micro- to macro-porosity. Both single phase and two-phase flow is considered.
Gaussian random fields (GRF) and particle based models are combined to generate heterogeneous model structures. The effect of micro-porosity on fluid flow is first examined through a critical length analysis and then confirmed using a flux analysis technique on the fully resolved pore space. Unified Brinkman equation is then solved to facilitate the coupling of Stokes and Darcy equations in the macro-phase and homogenised micro-phase.
For single phase flow in 3D model structures, the results highlight the significance of micro-pores on the fluid flow especially when macro-pores are just above the percolation threshold. The agreement between fine solution and upscaled solution, in which micro-porous region is homogenised and coupled with macro-pores, is excellent.
For two-phase flow simulations, a pore morphology based approach is implemented to simulate the drainage process and to obtain fluid distributions. While the effect of micro-porosity on the effective permeability of the wetting phase is more evident at lower saturations, the error associated with its exclusion is still significant at high wetting phase saturations. The results also prove that the proposed upscaling approach is superior compared to upscaling through the Laplace equation.
Apart from the application for carbonates, which are well-known for their micro-porosity signatures, the approach proposed here might be applicable for image-based computation of permeability in unconventional reservoir rocks where multiple length scales coexist.