Concept Of Tortuosity Research Articles

Tortuous flow in porous media.

The concept of tortuosity of fluid flow in porous media is discussed. A lattice-gas cellular automaton method is applied to solve the flow of a Newtonian uncompressible fluid in a two-dimensional porous substance constructed by randomly placed rectangles of equal size and with unrestricted overlap. A clear correlation between the average tortuosity of the flow paths and the porosity of the substance has been found. \textcopyright{} 1996 The American Physical Society.

The tortuosity concept in fixed and fluidized bed

A new concept was suggested for the tortuosity of beds of particles based on the parallel-cappilary model. The resulting relation between the tortuosity and bed voidage is applicable over a wide range of conditions (from fixed to highly expanded bed). Even the simplified limiting form of eq. (6) seems to be fixed and fluidized bed.

Deterministic approaches to problems of diffusion, reaction and adsorption in a fractal porous catalyst

Modelling processes of diffusion and reaction or diffusion and adsorption requires the description of the pore-network geometry. Ordered structures in a constant-porosity material are commonly assumed, yielding a rough estimate for the tortousity factor and the effective diffusivity. Several preparation methods of catalyst or catalyst support are modelled by random-process simulations that produce selfsimilar structures of fractal nature. Specifically, the diffusion-limited-aggregation (DLA) process may account for precipation while cluster-cluster aggregation resembles gelation. Recent measurements confirm the fractal structure and give a dimension ( D) between 2 and 3. The concept of tortuosity and diffusion in a fractal porous structure are reviewed. The reaction rate or adsorption uptake are computed deterministically for two structures. In a DLA aggregate, the density declines in proportion to r D−3 and the solution is based on this property. The second structure is a self-similar branching pore-tree in which every pore bifurcates into several smaller ones, yielding a fractal pore size distribution. Numerical, approximate and asymptotic solutions are derived for a first-order reaction and irreversible or linear adsorption isotherms. The deviation between rates in the classical (nonfractal) and fractal structures is the largest when the process is confined to the surface; fast reaction and short adsorption times. In the DLA structure the characteristic curves of effectiveness factor and adsorption uptake are qualitatively similar to the classical solutions. These solutions provide a reasonable approximation when plotted vs the surface Thiele modulus or the surface time constant. The solution to the branching pore-tree acquires an intermediate asymptote in which the effectiveness factor is solely determined by the pore-network geometry and is independent of the kinetics and diffusivity.

Transport properties of rocks from statistics and percolation

Two simplified microstructural models that account for permeability and conductivity of low-porosity rocks are compared. Both models result from statistics and percolation theory. The first model assumes that transport results from the connection of 1D objects or “pipes”; the second model assumes that transport results from the connection of 2D objects or “cracks.” In both cases, statistical methods permit calculation of permeability k and conductivity σ, which are dependent on three independent microvariables: average pipe (crack) length, average pipe radius (crack aperture), and average pipe (crack) spacing. The degree of connection is one aspect of percolation theory. Results show that use of the mathematical concept of percolation and use of the rock physics concept of tortuosity are equivalent. Percolation is used to discuss k and σ near the threshold where these parameters vanish. Relations between bulk parameters (permeability, conductivity, porosity) are calculated and discussed in terms of microvariables.

Effective transport coefficients in heterogeneous media

The paper emphasizes the commonality of a number of trnasport phenomena in heterogeneous media. The computation of an effective transport coefficient is then illustrated by Monte Carlo simulation of the diffusion of a gas molecule in a porous solid. Both physical and stochastic descriptions of molecular motion in a porous solid are presented, the latter being more rigorous and presenting a different insight into the concept of tortuosity. The Monte Carlo simulations yielded results that are consistent with classical predictions for effective transport coefficients. The consistency was maintained even at low volume fractions of the conducting phase which are beyond the limit of validity of the assumptions made in classical predictions.

Tortuosity

Tortuosity is defined for a particular separator model and basic equations are derived. The deficiencies of an averaged tortuosity derived from steady state measurements are discussed, particularly as applied to non-steady-state situations. Two experimental procedures are outlined whereby more information can be obtained on the distribution of pore tortuosities in a given separator. The difficulties of applying the tortuosity concept to membranes with fixed charges are outlined.

Percolation theory and models of unsaturated porous media

Concepts from percolation theory (Broadbent and Hammersley, 1957) are applied to a model of unsaturated flow through porous media. This approach in principle allows one to build into the model aspects of the topological structure of pore space. At a very general level the input of results from percolation theory gives a relationship between minimum and maximum saturation values for a medium which should be experimentally checkable, though probably not without sophisticated techniques. Also, it gives some qualitative insight into known properties of unsaturated flow. Furthermore, there emerges a way of looking at the phenomenon of hysteresis that is quite different from the standard approach. This aspect is explored in some detail, and two possible new models are presented. A subsidiary result obtained from the detailed model used is that in a simple pore model the inclusion of a pore length parameter, statistically correlated with pore radius, is equivalent, at least in a restricted sense, to incorporating into the model the concept of tortuosity.