Tortuosity

The aim of gravity thickening processes is to increase the solids concentration of particulate slurries. Gravity thickening depends on the difference in densities between the solid and liquid phases. The solids settle to a more concentrated slurry zone towards the underflow at the thickener base, while relatively solids free liquid rises to the overflow at the top. Predictive modelling of gravity thickener performance from experimentally determined material properties has been shown to under predict throughput by a factor of up to 100. One phenomenon proposed to account for some of this discrepancy is aggregate densification, whereby aggregates compact and become smaller when subjected to shear forces in the thickening process. As the aggregates decrease in size, through densification, the tortuosities around the aggregates will decrease, thus leading to a significant net decrease in the resistance to fluid flow. Dewatering theory has been applied to predict the impact of aggregate densification on the material properties that describe dewatering. The anticipated decrease in aggregate size and associated increase in the density of these aggregates is expected to increase the settling rate. It is further expected on this basis that the material will settle to higher solids concentrations. The impact of these changes on gravity thickening performance is modelled and predicted to be significant.

This study includes a detailed numerical investigation of the problem of gaseous diffusion in structures of randomly overlapping capillaries of various orientation distributions in the ordinary, transition, and Knudsen diffusion regimes. Effective diffusion coefficients are computed through a Monte Carlo simulation method based on the mean square displacement of random walkers traveling in the interior of the porous media. The simulation results reveal a strong dependence of the components of the effective diffusivity tensor of a capillary structure on its porosity, the Knudsen number, and the orientational distribution of the capillaries. The computed transition regime diffusivities are found to be in excellent agreement with those predicted by the reciprocal additivity or harmonic mean diffusivity expression (Bosanquet formula) using the computed diffusion coefficients in the ordinary and Knudsen diffusion regimes for all configurations of flow except for that parallel to unidirectional capillaries.

FOR CITATIONS:
SALEM, H.S., 1993. Derivation of the cementation factor (Archie's exponent) and the Kozeny-Carman constant from well log data, and their dependence on lithology and other physical parameters, SPE-26309: Society of Petroleum Engineers. (International E-Library Paper). http://www.onepetro.org/mslib/servlet/onepetropreview?id=00026309 

ABSTRACT:
The cementation factor or Archie's exponent (m) and the Kozeny-Carman constant (C) have specific effects
on electric and hydraulic conduction in porous media. In the present study, both parameters were derived from well
log data for fourteen Hibernia and Terra Nova wells in the Jeanne d'Arc Basin (JDB) offshore the eastern coast of
Newfoundland, Canada. The purpose of this study is to verify that both parameters (m and C) are applicable for
shaly-saline water formations under high overburden pressure at depths between 3 to 5 km, saturated with
multi-phase fluids. The results obtained show that the Kozeny-Carman constant (C), defined as the product of
tortuosity (T) times shape factor (S,), fits well with the product of tortuosity (T) times cementation factor (m). It is
suggested that it is more accurate to call (m) "shape factor" instead of "cementation factor" because it is a strong
indicator of shape of particles. It is also suggested that an average value for the Kozeny-Carman constant of 7.5 be
used in the Kozeny-Carman equation for consolidated sediments saturated with multi-phase fluids, and an average
value of 2.28 for the cementation factor be used in the Archie-Winsauer equation. Tortuosity, as a main parameter
controlling the variations in both m and C, indicates the complicated electric and hydraulic tortuous passages in the
JDB sediments.

The problem of bulk, transition and Knudsen regime diffusion in structures of freely overlapping fibers of various orientation distributions was numerically investigated, and the interrelation of the resulting effective diffusivities was examined. Fibers were randomly positioned and oriented in d = 1, 2, or 3 directions. A Monte Carlo simulation scheme was employed to determine the effective diffusivities from the mean-square displacement of random walkers traveling in the interior of the porous structure. The effective diffusivity was found to depend strongly on the orientational distribution of the fibers, porosity of the fibrous structures, and Knudsen number. The tortuosity factor decreased in general with increasing porosity, approaching at the limit of dilute beds the lower bound derived for each direction of diffusion from variational principles. The simulation results agreed well with experimental values of the bulk tortuosity of fibrous beds from the literature. It was also found that the reciprocal additivity or harmonic average effective diffusivity expression (Bosanquet formula), commonly used to estimate transition regime diffusivities from the values at the ordinary and Knudsen diffusion limits, provides an excellent approximation for the effective diffusivity of fibrous beds, except for that parallel to the fibers of a unidirectional structure.

One of the parameters commonly used for the characterization of porous road pavements is the sound absorption coefficient. This parameter can be experimentally measured (ISO 13472-1, ISO 13472-2, ISO 10354-2), or theoretically estimated. A comprehensive literature review shows that the transfer-function method (ISO 10354-2) is a quite precise experimental method. On the other hand, one of the most accurate models for the theoretical estimation of the acoustic performance of a pavement has been proposed by Stinson and Champoux (1992). This model considers the sound absorption coefficient as a function of various physical factors of pavement, i.e. thickness, porosity, resistivity, tortuosity, thermal and viscous factors. The aim of the study described in this paper is to analyse how tortuosity and resistivity can be derived based on the remaining factors and/or based on mixture-related properties. In order to pursue this scope, the first step was the determination of the values of the two parameters in terms of an inverse problem, i.e., in terms of derivation of two model parameters (tortuosity and resistivity) based on data (starting from the absorption spectrum). The Stinson and Champoux model was used. In more detail, the input of the inverse problem were the acoustic absorption coefficient values measured, the real porosity, and the thickness (experimentally obtained). The second step was the estimation of the two parameters under investigation through models, based on mixture-related properties (e.g., real porosity and thickness). The third step was the comparison between the results of the first and the second step. The results show that several literature models can provide a good estimate of resistivity, while tortuosity prediction can be an issue. Further studies will be carried out using values of resistivi-ty measured in the laboratory, in order to theoretically estimate the acoustic absorption coefficient of a pavement with just one (main) unknown, i.e. the tortuosity.

This article is concerned with tortuosity effects in coupled transport and mechanical properties of fractured geomaterials. Experimental results on confined fractured argillite samples are presented in terms of (1) progressive fracture reclosure and (2) fracture in plane permeability evolution, both depending upon confinement intensity. The observed non-linear mechanical response (fracture reclosure law) is physically interpreted as the progressive reclosure of local pores. The weak correlation between mechanical and hydraulic measurements is attributed to tortuosity effects which enhance the initial decrease of the permeability. The classical Self-Consistent scheme is herewith developed to qualitatively and quantitatively give theoretical basis likely to account for these tortuosity effects on permeability evolution.

FOR CITATIONS:
SALEM, H.S., 2000. Fluid-flow characterization of porous media (for the example of the Jeanne d'Arc Basin consolidated reservoirs). Energy Sources. 22(6), July: 557-572.

ABSTRACT:
Flow of fluids in porous media is a complicated process governed by several physical parameters and properties of the solid particles and fluid molecules, as well as the interactions between them. The Kozeny-Carman equation is one of the powerful equations that provides a better understanding of fluid flow. The equation can be
successfully applied to viscous flow and laminar flow through unconsolidated and consolidated porous media if some of its elements are known. One of these elements is the Kozeny-Carman coefficient (Kcc ), which has a specific influence on the
mechanism of fluid flow in porous media. In this study, Kcc , along with other cc parameters, was obtained numerically from well-log measurements for several wells penetrating the Canadian offshore Jeanne d’Arc Basin reservoirs, which consist of consolidated and heterogeneous rocks characterized by a complex network of pores and pore channels. It is shown that Kcc is not a constant but a variable depending on several physical parameters and lithological attributes and strongly related to fluid flow as well as to electric-current conduction in porous media. The Kozeny-Carman
coefficient, obtained as tortuosity (t ) times shape factor (Shf ) agrees well with that obtained as (t) times Archie cementation factor (m). This observation suggests that Shf and m are analogous to each other. An average value of 7.5 was obtained for Kcc , which can be used for similar media instead of the value of 5.0 that is inaccurately used for consolidated porous media. Also, an average value of 3.3 was obtained for (t) and an average value of 2.28 was obtained for Shf (analogous to m). Empirical equations linking Kcc and a variety of petrophysical parameters were also
obtained."

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