A Novel Method for Streamline-Based Tortuosity Calculation and Investigation of Obstacles Shape Effect on Tortuosity in Porous Media with Random Elliptical Obstacles Using Lattice Boltzmann Method

Evaluation of geometric tortuosity for 3D digitally generated porous media considering the pore size distribution and the A-star algorithm

Porous materials are of great interest in multiple applications due to their usefulness in energy conversion devices and their ability to modify structural and diffusive properties. Geometric tortuosity plays an important role in characterizing the complexity of a porous medium. The literature on several occasions has related it as a parameter dependent on porosity only. However, due to its direct relationship with the morphology of the medium, a deeper analysis is necessary. For this reason, in the present study, the analysis of the geometric tortuosity is proposed considering the porosity and the pore size distribution. Geometric tortuosity in artificially generated digital porous media is estimated using the A-star algorithm and the Pore Centroid method. By performing changes in the size of the medium and the distribution of the pore size, results are obtained that indicate that the geometric tortuosity does not only depend on the porosity. By maintaining the same porosity, the geometric tortuosity increases if the pore size is reduced. Similarly, these pore size effects are greater if the size of the medium is reduced. The A-star algorithm was found to be more suitable to characterize the majority of paths within the half-pore. On the other hand, to increase the size, the Pore Centroid method is the most appropriate. Finally, three types of correlations were generated relating tortuosity with porosity and pore size. All the correlations were determined with 95% of interval confidence.

An Alternative Methodology to Compute the Geometric Tortuosity in 2D Porous Media Using the A-Star Pathfinding Algorithm

Geometric tortuosity is an essential characteristic to consider when studying a porous medium’s morphology. Knowing the material’s tortuosity allows us to understand and estimate the different diffusion transport properties of the analyzed material. Geometric tortuosity is useful to compute parameters, such as the effective diffusion coefficient, inertial factor, and diffusibility, which are commonly found in porous media materials. This study proposes an alternative method to estimate the geometric tortuosity of digitally created two-dimensional porous media. The porous microstructure is generated by using the PoreSpy library of Python and converted to a binary matrix for the computation of the parameters involved in this work. As a first step, porous media are digitally generated with porosity values from 0.5 to 0.9; then, the geometric tortuosity is determined using the A-star algorithm. This approach, commonly used in pathfinding problems, improves the use of computational resources and complies with the theory found in the literature. Based on the obtained results, the best geometric tortuosity–porosity correlations are proposed. The selection of the best correlation considers the coefficient of determination value (99.7%) with a confidence interval of 95%.

Characteristics Description of Shale Fracture Surface Morphology: A Case Study of Shale Samples from Barnett Shale

Shale reservoirs are the hot issue in unconventional resources. The key to the development of shale reservoirs lies in the complex fractures, which are the only path for fluid to migrate from the matrix to the wellbore in shale reservoirs. Therefore, the characteristics of shale fracture surface morphology directly affect fluid migration in shale reservoirs. However, there are few reports about the characteristics of shale fracture surface morphology as the parallel plate model was commonly used to characterize the fracture, neglecting its surface morphology characteristics and leading to great deviation. Thus, description methods were introduced to characterize shale fracture surface morphology with the aim to provide a foundation for the development of shale resources. Three shale samples were fractured by the Brazilian test, and the height distribution of the fracture surface was captured by a three-dimensional profilometer. Then, three-dimensional fracture surface morphology was regarded as a set of two-dimensional profiles, which converted three-dimensional information into two-dimensional data. Roughness, joint roughness coefficient, fractal dimension, tortuosity, and dip angle were employed to characterize shale fracture surface morphology, and their calculation methods were also, respectively, proposed. It was found that roughness, joint roughness coefficient, fractal dimension, tortuosity, and dip angle were all directional, and they varied greatly along with different directions. Roughness, joint roughness coefficient, fractal dimension, tortuosity, absolute dip angle, and overall trend dip angle were among 0.0834–0.2427 mm, 2.5715–10.9368, 2.1000–2.1364, 1.0732–1.1879, 17.7498°–24.5941°, and −3.7223°–13.3042°, respectively. Joint roughness coefficient, fractal dimension, tortuosity, and dip angle were all positively correlated with roughness.

The Mass Transfer Index (MTI): A semi-empirical approach for quantifying transport of solutes in variably saturated porous media

The processes impacting solute transport through unsaturated porous media have been receiving renewed attention due to their relevance to the transport of emerging contaminants. A set of well-monitored and highly controlled experiments in sand columns were conducted to determine the effect of partial saturation on conservative solute breakthrough in porous media. The results suggest traditional transport parameter estimation methods inadequately account for the pore-scale processes of mass transfer to the immobile zones and the effects of partial saturation on advective transport, even for conservative tracers. Accurate estimation of these basic transport parameters is critical to evaluate the multi-phase partitioning of nonconservative solutes, as any errors in these parameters would bias the estimates of multi-phase partitioning parameters. Herein, we introduced the Mass Transfer Index (MTI), a semi-empirical approach for quantifying the impact of non-Fickian elements of pore-scale unsaturated solute transport (i.e. immobile water, tortuous flow paths, and non-uniform solute distribution), which become increasingly important as the wetting fluid saturation decreases. Importantly, this MTI was determined independently of chemically driven phase partitioning and is supported by experimental data. Based on this conceptualization, the 1-D equilibrium advection dispersion equation was modified to incorporate the MTI as a lumped parameter which quantifies resistance to (MTI > 1) or promotion of (MTI < 1) of advective solute flux. Analytical solutions to the modified advection-dispersion-reaction equation for pulse and step inputs were developed. Conservative tracer experiments were conducted in variably saturated sand columns to validate both the MTI conceptualization and the inversion method used to estimate the MTI. These experiments involved the use of X-ray absorption spectroscopy integrated with sensor-based measurements of soil moisture, temperature, and electrical conductivity for tracer breakthrough. The mathematical model developed herein adapts traditional macroscopic models of solute transport to account for the non-Fickian pore-scale transport behaviors observed in unsaturated porous media with significant advective flux.