Multi-scale Digital Rock: Application of a multi-scale multi-phase workflow to a Carbonate reservoir rock

In some of the challenging digital rock applications the trade-off between model resolution and representative elemental volume is not captured in a single resolution model satisfying the minimum requirements for both aspects. In the wide range of lithofacies found in carbonate reservoir rocks, some facies fall in this category, where large pores, ooids or vugs, are connected by small scale porous structures that could have orders of magnitude smaller pores. In these cases a multi-scale digital rock approach is needed. We recently developed an extension to a digital rock workflow that includes a way to handle sub-resolution pore structures in single phase and multi-phase flow scenarios in addition to regular resolvable pore structures. Here we present an application of this methodology to a multi-scale limestone carbonate rock. A microCT image captures the large pores for this sample, but does not resolve all the pores smaller than the pixel size. A three phase image segmentation that considers pore, solid and under-resolved pores or porous media (PM) is generated. A high resolution confocal image model is obtained for a representative region of the smaller pores or PM region. A set of constitutive relationships (namely permeability vs. porosity, capillary pressure vs saturation and relative permeability vs saturation) are obtained by simulation from the high resolution confocal model. The low resolution segmented image, a porosity distribution image, and the constitutive relationships for the PM are input in an extended LBM multi-scale multi-phase solver. First we present results for absolute permeability and show a parametric study on PM permeability. The model recovers the expected behaviour when the PM regions are considered pore or solid. A consistent value of permeability with experiments is obtained when we use the PM permeability from the high resolution model. To demonstrate the multi-phase behaviour, we present results for capillary pressure imbibition multi-scale simulations. Here a small model for a dual porosity system is created in order to compare single scale results with the multi-scale solver. Finally, capillary imbibition results for the whole domain are shown and different wettability scenario results are discussed. This application illustrates a novel multi-scale simulation approach that can address a long standing problem in digital rock