Tortuosity Assessment for Reliable Permeability Quantification Using Integration of Hydraulic and Electric Current Flow in Complex Carbonates

Permeability assessment in rocks with complex pore structure would require reliable quantification of pore- body- and pore-throat-size distribution as well as tortuosity. Among these properties, pore-body- and pore- throat-size can often be estimated reliably within each rock type using nuclear magnetic resonance (NMR) T2 and mercury injection capillary pressure (MICP) measurements. Tortuosity, however, is more challenging to quantify. Typical methods for tortuosity quantification include modeling of electrical current flow, fluid flow, heat transfer, and molecular diffusion. These methods, however, can provide nonunique estimates of tortuosity and consequently, significant uncertainties in permeability assessment. Moreover, in rocks with the presence of microporosity, additional challenges exist for tortuosity assessment. It is also challenging to upscale the aforementioned tortuosity estimates to the well-log domain for depth-by-depth assessment of tortuosity and permeability. The objectives of this paper are (a) to quantify hydraulic and electrical tortuosity in the pore-scale domain in the presence of microporosity, (b) to quantify the impacts of hydraulic and electrical tortuosity on permeability estimates in the pore-scale domain, (c) to upscale flow-based tortuosity estimates to the well-log domain, and (d) to quantify depth-by-depth permeability in the well-log domain honoring flow- based tortuosity. To achieve the abovementioned objectives, we developed a workflow that integrates NMR and MICP measurements, as well as pore-scale image analysis to estimate depth-by-depth permeability in the well-log domain. The introduced permeability model takes as inputs the pore-body-size distribution, constriction factor, and tortuosity of the rock. We use NMR data corrected for the impacts of reservoir fluids and mud for depth-by-depth assessment of the pore-body-size distribution. Next, we perform rock classification and select MICP measurements within each rock class to estimate pore-throat-size distribution in all the rock types. Then, we use the estimated pore-body- and pore- throat-size distribution to assess the constriction factor at each rock type. We conduct numerical simulations of electrical potential distribution and fluid flow to estimate the electrical and hydraulic tortuosity, respectively, in each rock class. Then, we use the estimated tortuosity at each rock class to obtain its representative elementary volume (REV). By performing simulations within a wide range of voxel numbers of microcomputed tomography (micro-CT) scan images (from 100x100x100 to 400x400x400 voxels). The definition of REV is critical for reliable upscaling of tortuosity values to the well-log domain. Finally, we use the aforementioned estimated properties for depth-by-depth assessment of permeability. We successfully applied the proposed workflow to a complex carbonate formation in the Brazilian pre-salt reservoirs. By the integration of fluid-based tortuosity quantification with NMR and MICP measurements in the well-log domain, permeability estimates indicated 89% improvement compared to those obtained from the integration of NMR, MICP, and electrical tortuosity. The results were in agreement with the experimental measurements. They also demonstrated the importance of hydraulic tortuosity assessment in reliable quantification of the pore structure, which is required for reliable permeability assessment in rocks with complex pore structure, such as those containing microporosity. The novelty of this workflow is the integration of multi- scale formation data (i.e., pore-scale image analysis and log-scale measurements) for enhanced interpretation of fluid flow in spatially heterogeneous carbonate formations. The introduced method also enables depth- by-depth assessment of tortuosity in the well-log domain.