The Measurement of Tortuosity of Porous Media Using Imaging, Electrical Measurements, and Pulsed Field Gradient NMR

Abstract

Tortuosity, in general characterizes the geometric complexity of porous media. It is considered as one of the key factors in characterizing the heterogonous structure of porous media and has significant implications for macroscopic transport flow properties. There are four widely used definitions of tortuosity, that are relevant to different fields from hydrology to chemical and petroleum engineering, which are: geometric, hydraulic, electrical, and diffusional. Recent work showed that hydraulic, electrical and diffusional tortuosity values are roughly equal to each other in glass beads. Nevertheless, the relationship between the different definitions of Tortuosity in natural rocks is not well understood yet. Understanding the relationship between the different Tortuosity definitions in rocks can help to establish a workflow that allows us to estimate other types from the available technique. Therefore, the objective of this study is to investigate the relationship between the different tortuosity definitions in natural rocks. A major focus of this work is to utilize Nuclear Magnetic Resonance (NMR) technology to estimate Tortuosity. Such technique has been traditionally used to obtain diffusional tortuosity which can be defined as the ratio of the free fluid self-diffusion coefficient to the restricted fluid self-diffusion coefficient inside the porous media. In this study, the following techniques were used to quantify hydraulic, electrical, and diffusional tortuosity respectively on the same rock sample: (1) Microcomputed Tomography 3D imaging (2) Four-Electrodes resistivity measurements (3) Pulsed-Field Gradient Nuclear Magnetic Resonance (PFG NMR). PFG NMR is very powerful, non-invasive technique employed to measure the self-diffusion coefficient for free and confined fluids. The measurements were done based on two carbonate rock core plugs characterized by variable porosity, permeability and texture complexity. Results show that PFG NMR can be applied directionally to quantify the pore network anisotropy created by fractures. For both samples, hydraulic tortuosity was found to have the lowest magnitude compared to geometric, electrical and diffusional tortuosity. This could be explained by the more heterogeneous microstructure of carbonate rocks. NMR technique has however advantages over the other electrical and imaging techniques for tortuosity characterization: it is faster, non-destructive and can be applied in well bore environment (in situ). We therefore conclude that NMR can provide a tool for estimating not only diffusional tortuosity but also for indirectly obtaining hydraulic and electrical tortuosity.