Image-based flow simulation integrated with nuclear magnetic resonance for heterogeneous natural carbonate rocks

With the rapid development of X-ray CT scanning, image-based numerical simulation has been widely studied to understand the pore-scale physics in porous rocks. Sandstones are known for their homogenous pore structure, which can be captured with a single resolution by X-ray CT scanning. Flow simulations and consequent characterization of the transport properties of sandstones have been successful due to their homogeneous pore structures because the pore volumes are resolved enough to segment the critical flow paths in the sandstones properly. However, flow phenomena in natural carbonate rocks are rarely understood by the image-based flow simulation. Carbonate rocks include multiscale heterogeneity such that the pore size distribution ranges over 6 orders of magnitudes. Thus, it is impossible to resolve the entire pore volume in carbonate rocks by X-ray CT scanning at one resolution.

This study tackles the uncertainties related to the unresolved pores in highly heterogeneous natural carbonate rocks to conduct reliable image-based flow simulations regardless of the image resolutions. The X-ray CT images of carbonate rocks retrieved from Abu Dhabi are integrated with the pore size distribution measured by nuclear magnetic resonance test to classify the images into ternary phases. Unresolved gray-pore voxels are characterized by the pore size distribution, and a local permeability estimated from the pore size is assigned to the gray-pore voxels to be used for the Brinkman-force lattice Boltzmann model to simulate the Stokes-Brinkman flow. It is shown that the permeability estimated from the X-ray CT images with resolution of 6 μm ranges over 5 - 1000 mD in one specimen having a diameter of 1 cm. Also, the bulk permeability of each specimen is estimated to be under 100 mD from the X-ray CT images with a resolution of 30 μm. The results confirm that the permeability of carbonate rocks is governed by the matrix with low permeability, whereas the locality of permeability ranges over 3 orders of magnitudes due to the extreme heterogeneity. Finally, the results show that the proposed method reliably evaluates the transport properties of natural carbonate rocks from images with different resolutions, and approximate the experimental trends.