Received 4 November 2005; revised 15 December 2005; accepted 20 December 2005; published 31 January 2006. [1] The relationship between permeability and porosity is reviewed and investigated. The classical Kozeny-Carman approach and a fractal pore-space geometry assumption are used to derive a new permeability-porosity equation. The equation contains only two fitting parameters: a Kozeny coefficient and a fractal exponent. The strongest features of the model are related to its simplicity and its capability to describe measured permeability values of different non-granular porous media better than other models. Citation: Costa, A. (2006), Permeability-porosity relationship: A reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption, Geophys. Res. Lett., 33, L02318, doi:10.1029/2005GL025134. [2] Estimation of permeability is of pivotal importance for the description of different physical processes, such as hydrocarbon recovery, fluid circulation in geothermal systems and degassing from vesiculating magmas. Mainly due to the intricate geometry of the connected pore space and to the complexity of porous media, it has been very difficult to formulate satisfactory theoretical models for permeability. One of the most largely used methods remains the KozenyCarman approach. [3] In this study we briefly review the Kozeny-Carman model. Then, using the hypothesis of a fractal pore-space geometry and the empirically based Archie law, we reformulate that model without introducing the concept of hydraulic radius and obtain a new simple permeabilityporosity equation. As an application, we used the obtained equation to predict permeability of fiber mat systems and of vesicular rocks.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2005GL025134

Permeability-porosity relationship: a reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption

Colloidal fouling in forward osmosis: Role of reverse salt diffusion

The reliable assessment of volcanic unrest must rest on an understanding of the rocks that form the edifice. It is their microstructure that dictates their physical properties and mechanical behavior and thus the response of the edifice to stress perturbations during unrest. We evaluate the interplay between microstructure and rock properties for a suite of edifice-forming rocks from Volcan de Colima (Mexico). Microstructural analyses expose (1) a pervasive, isotropic microcrack network, (2) a high, subspherical vesicle density, and (3) a wide vesicle size distribution. This complex microstructure severely impacts their physical and mechanical properties. In detail, porosities are high and range from 8 to 29%. As a consequence, elastic wave velocities, Youngs moduli, and uniaxial compressive strengths are low, and permeabilities are high. All of the rock properties demonstrate a wide range. For example, strength decreases by a factor of 8 and permeability increases by 4 orders of magnitude over the porosity range. Below a porosity of 11–14%, the permeability-porosity trend follows a power law with a much higher exponent. Microstructurally, this represents a critical vesicle content that efficiently connects the microcrack population and permits a much more direct path through the sample, rather than restricting flow to long and tortuous microcracks. Values of tortuosity inferred from the Kozeny-Carman permeability model support this hypothesis. However, we find that the complex microstructure precludes a complete description of their mechanical behavior through micromechanical modeling. We urge that the findings of this study be considered in volcanic hazard assessments at andesitic stratovolcanoes.

Microstructural controls on the physical and mechanical properties of edifice‐forming andesites at Volcán de Colima, Mexico

[1] The mesostructure (millimeter to micrometer scale) of clay-rich sedimentary rocks is generally characterized by a connected fine-grained clay matrix embedding coarser nonclay minerals. We use the Callovo-Oxfordian clay-rich rock formation (France) to illustrate how mesostructure influences solute transfer in clay-rich rocks at larger scales. Using micrometer resolution imaging techniques (SEM and micro-CT) major mineral phases (clay matrix, carbonates, tectosilicates, and heavy minerals) were mapped both in two dimensional (2-D) and three dimensional (3-D) at the mesoscale. Orientation and elongation distributions of carbonate and tectosilicate grains measured on mineral maps reveal an anisotropic mesostructure relative to the bedding plane, in agreement with the geological history of the sedimentary rock. Diffusion simulations were performed based on the 3-D mineral maps using a random walk method thus allowing direct computation of mesoscopic scale-related diffusion anisotropy and tortuosity. Considering an isotropic clay matrix, simulated diffusion anisotropy (1.11–1.26) was found lower than the one experimentally measured on macroscopic samples (1.5 to 2), due to the anisotropy feature of pores within the clay matrix. The effects of the mineral content variations on diffusion properties were then investigated by numerical modifications of a mineral map combined with diffusion simulations. Evolution of the tortuosity and diffusion anisotropy with the clay matrix content were successfully interpreted by the Koponen percolation/diffusion model, whereas the Archie approach fails to reproduce diffusion properties at low clay contents. A comparison of fitting parameters with those obtained experimentally indicates that diffusion coefficient variations observed at a large scale could be mainly controlled by the mesostructure.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2011WR011352

Effects of mineral distribution at mesoscopic scale on solute diffusion in a clay‐rich rock: Example of the Callovo‐Oxfordian mudstone (Bure, France)

[1] Rain splash transport of sediment on a sloping surface arises from a downslope drift of grains displaced ballistically by raindrop impacts. We use high-speed imaging of drop impacts on dry sand to describe the drop-to-grain momentum transfer as this varies with drop size and grain size and to clarify ingredients of downslope grain drift. The ‘‘splash’’ of many grains involves ejection of surface grains accelerated by grain-to-grain collisions ahead of the radially spreading front of a drop as it deforms into a saucer shape during impact. For a given sand size, splash distances are similar for different drop sizes, but the number of displaced grains increases with drop size in proportion to the momentum of the drop not infiltrated within the first millisecond of impact. We present a theoretical formulation for grain ejection which assumes that the proportion of ejected grains within any small azimuthal angular interval dq about the center of impact is proportional to the momentum density of the spreading drop within dq and that the momentum of ejected grains at angle q is, on average, proportional to the momentum of the spreading drop at q. This formulation, consistent with observed splash distances, suggests that downslope grain transport involves an asymmetry in both quantity and distance: more grains move downslope than upslope with increasing surface slope, and, on average, grains move farther downslope. This latter effect is primarily due to the radial variation in the surface-parallel momentum of the spreading drop. Surface-parallel transport increases approximately linearly with slope.

Rain splash of dry sand revealed by high-speed imaging and sticky paper splash targets

Numerical study of flow through random packing of non-overlapping spheres in a cylindrical geometry is investigated. Dimensionless pressure drop has been studied for a fluid through the porous media at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), and numerical solution of Navier-Stokes equations in three dimensional porous packed bed illustrated in excellent agreement with those reported by Macdonald [1979] in the range of Reynolds number studied. The results compare to the previous work (Soleymani et al., 2002) show more accurate conclusion because the problem of channeling in a duct geometry. By injection of solute into the system, the dispersivity over a wide range of flow rate has been investigated. It is shown that the lateral fluid dispersion coefficients can be calculated by comparing the concentration profiles of solute obtained by numerical simulations and those derived analytically by solving the macroscopic dispersion equation for the present geometry.Copyright © 2006 by ASME

Simulation of Fluid Flow Through a Granular Bed

A mathematically rigorous, multiscale modeling methodology capable of coupling behaviors from the Kolmogorov turbulence scale through the full scale system in which a fiber suspension is flowing is presented. Here the key aspect is adaptive hierarchical modeling. Numerical results are presented focus of which are on fiber floc formation and destruction by hydrodynamic forces in turbulent flows. Specific consideration was given to molecular-dynamics simulations of viscoelastic fibers in which the fluid flow is predicted by a method which is a hybrid between direct numerical simulations and large eddy simulation techniques, and fluid fibrous structure interactions were taken into account. The present results may elucidate the physics behind the breakup of a fiber floc, opening the possibility for developing a meaningful numerical model of the fiber flow at the continuum level where an Eulerian multiphase flow model can be developed for industrial use.

Multiscale modeling of fluid turbulence and flocculation in fiber suspensions

Traditionally, solid-liquid mixing has always been regarded as an empirical technology with many aspects of mixing, dispersing, and contacting related to power draw. One important application of solid-liquid mixing is the preparation of brine from sodium formate. This material has been widely used as a drilling and completion fluid in challenging environments such as in the Barents Sea. In this paper large-eddy simulations, of a turbulent flow in a solid-liquid, baffled, cylindrical mixing vessel with a large number of solid particles, are performed to obtain insight into the fundamental aspects of a mixing tank. The impeller-induced flow at the blade tip radius is modeled by using the sliding mesh. The simulations are four-way coupled, which implies that both solid-liquid and solid-solid interactions are taken into account. By employing a soft particle approach the normal and tangential forces are calculated acting on a particle due to viscoelastic contacts with other neighboring particles. The results show that the granulated form of sodium formate may provide a mixture that allows faster and easier preparation of formate brine in a mixing tank. In addition it is found that exceeding a critical size for grains phenomena, such as caking, can be prevented. The obtained numerical results suggest that by choosing appropriate parameters a mixture can be produced that remains free-flowing no matter how long it is stored before use.

Large Eddy Simulations of a Brine-Mixing Tank

Computer simulation of flocs interactions: Application in fiber suspension

Traditionally, solid-liquid mixing has always been regarded as an empirical technology with many aspects of mixing, dispersing and contacting where related to power draw. One important application of solid-liquid mixing is the preparation of brine from sodium formate. This material has been widely used as a drilling and completion fluid in challenging environments such as in the Barents Sea. In this paper large-eddy simulations, of a turbulent flow in a solid-liquid, baffled, cylindrical mixing vessel with a large number of solid particles, are performed to obtain insight into the fundamental aspects of a mixing tank. The impeller-induced flow at the blade tip radius is modeled by using the dynamic-mesh Lagrangian method. The simulations are four-way coupled, which implies that both solid-liquid and solid-solid interactions are taken into account. By employing a soft particle approach the normal and tangential forces are calculated acting on a particle due to viscoelastic contacts with other neighboring particles. The results show that the granulated form of sodium formate may provide a mixture that allows faster and easier preparation of formate brine in a mixing tank. In addition it is found that exceeding a critical size for grains phenomena, such as caking, can be prevented. The obtained numerical results suggest that by choosing appropriate parameters a mixture can be produced that remains free-flowing no matter how long it is stored before use.Copyright © 2006 by ASME

S. Mohammad Mousavi

Papers

Simulation of Fluid Flow Through a Granular Bed

Multiscale modeling of fluid turbulence and flocculation in fiber suspensions

Large Eddy Simulations of a Brine-Mixing Tank

Computer simulation of flocs interactions: Application in fiber suspension

Large Eddy Simulations of a Brine-Mixing Tank