Tortuosity: a guide through the maze

Abstract

Despite its widespread use in petrophysics, tortuosity remains a poorly understood concept. Tortuosity can have various meanings when used by physicists, engineers or geologists to describe different transport processes taking place in a porous material. Values for geometrical, electrical, diffusional and hydraulic tortuosity are in general different from one another. Electrical tortuosity is defined in terms of conductivity whereas hydraulic tortuosity is usually defined geometrically, and diffusional tortuosity is typically computed from temporal changes in concentration. A better approach may be to define tortuosity in terms of the underlying flux of material or electrical current with respect to the forces which drive this flow. Unsteady transport processes, including diffusion, can be described only by a population of tortuosities corresponding to the different flow paths taken by particles traversing the medium. In measurements of steady flow (e.g., those normally used to obtain resistivity or permeability), information about particle travel times is lost, and so the multiple values of tortuosity are homogenised. It can be shown that the maximum amount of information about pore structure is embedded in transport processes that combine advective and diffusive elements. Most existing formulations of tortuosity are model-dependent, and cannot be correlated with independently measurable pore-structure properties. Nevertheless, tortuosity underpins the rigorous relationships between transport processes in rocks, and ties them with the underlying geometry and topology of their pore spaces. Tortuosity can be redefined in terms of the energetic efficiency of a flow process. The efficiency is related to the rate of entropy dissipation (or isothermally, energy dissipation) with respect to a simple, non-tortuous model medium using the postulates of non-equilibrium thermodynamics. Through Onsager’s reciprocity relation for coupled flows it is possible to inter-relate efficiency for pairs of transport processes, and so go some way towards unifying tortuosity measures. In this way we can approach the goal of predicting the value of one transport parameter from measurements of another.

Parameter Determination Using 3D FIB-SEM Images for Development of Effective Model of Shale Gas Flow in Nanoscale Pore Clusters

“…Table 1 gives the determined tortuosities of all the pore clusters for Darcy flow. The values can be observed to range between 1.32 and 2.67, which is reasonable considering typical tortuosity values of 1.3 and 3 (Clennell 1997). The tortuosities in different directions of a given sample are also liable to differ significantly, due to the differing flow paths and flux distributions in the different directions.…”

Tortuosity in electrochemical devices: a review of calculation approaches

“…The random walk approach was first formulated in the 1990s 4,132,133 and found its way into electrochemistry via Kishimoto et al, 128 after having been used to extract the tortuosity of porous rocks. 134 However, the obtained tortuosity is affected by the number of walkers and by the number of time steps chosen for the calculation.…”

“…), each with associated definitions and areas of application. 4,5 The microstructure of porous electrode and support layers in electrochemical devices is the main contributor to performance losses, especially in mass transport limiting operating regimes. This is valid for batteries, fuel cells and oxygen transport membranes alike, where tortuosity is used to relate the effective transport properties of diffusion and electric or ionic flux, to its respective bulk property.…”

Microstructure-property relationships in a gas diffusion layer (GDL) for Polymer Electrolyte Fuel Cells, Part I: effect of compression and anisotropy of dry GDL

“…For example there exist various definitions for tortuosity (e.g. geometric, geodesic, hydraulic, electric or diffusional tortuosities), as discussed by Clennell [31]. Similarly, the constrictivity (b) strongly depends on the underlying geometrical concepts for the measurement of pore sizes (bulges) and bottleneck sizes [18][19][20].…”