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 requires reliable quantification of pore-body/throat-size distribution as well as tortuosity. Pore body/throat size can often be estimated within each rock type using nuclear magnetic resonance (NMR) T2 and mercury injection capillary pressure (MICP) measurements. Tortuosity, however, is challenging to quantify. Tortuosity can be quantified in the pore-scale domain through modeling of electrical current flow, fluid flow, heat transfer, and molecular diffusion, which can be challenging in the presence of microporosity. These methods also provide nonunique estimates of tortuosity. It is also challenging to upscale these 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 assessment, (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 these objectives, we developed a workflow that integrates NMR and MICP measurements, as well as pore-scale images 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 use MICP measurements within each rock class to estimate pore-throat-size distribution. Then, the estimated pore-body and pore-throat-size distribution are adopted to assess the constriction factor in each rock class. We conduct numerical simulations of electrical potential distribution and fluid flow to estimate the electrical and hydraulic tortuosity, respectively, in each rock class, honoring a representative elementary volume (REV). We successfully applied the proposed workflow to a complex carbonate formation in the Brazilian presalt reservoirs. By the integration of fluid-based tortuosity with NMR and MICP measurements in the well-log domain, permeability estimates indicated 61.1% improvement compared to those obtained from the integration of NMR, MICP, and electrical tortuosity. Results demonstrated the importance of hydraulic tortuosity assessment for reliable permeability quantification in rocks with complex pore structure. The novelty of this workflow is the integration of multiscale formation data (i.e., pore-scale image analysis and well-log-scale measurements) for enhanced interpretation of fluid flow in spatially heterogeneous carbonate formations. The introduced method also enables depth-by-depth assessment of hydraulic tortuosity in the well-log domain.