Numerical Study on the Tortuosity of Porous Media via Lattice Boltzmann Method
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Abstract. In this paper, we simulate the pressure driven fluid flow at the pore scalelevel through 2-D porous media,which is composed of different curved channels viathelatticeBoltzmannmethod. With thisdirectsimulation,therelationbetweenthetor-tuosityandthepermeabilityisexamined. Thenumericalresultsareingoodagreementwith the existing theory. AMS subject classifications : 76S05,80M25 Key words : Tortuosity, lattice Boltzmann, porous media, pore scale. 1 Introduction Fluid flow through porous media is a common phenomenon in science and engineering.Thus,thepredictionof thepermeability, as the main transportpropertyin porousmedia,isalong-standingproblemofgreatpractical importance. Existingexperimentresultsandtheoretical works [1–5] show that the permeability of various porous materials is deter-mined by theirstructureparameterssuch as porosity,specific surface area, tortuosityetc.Amongtheexistingtheories,theKozeny-Carman equation may be the mostfamous one,which can be expressedas: k = ǫ 3 k 0 TKeywords:
Tortuosity
Lattice Boltzmann methods
In this chapter, we describe the effects of defects in a homogeneous saturated porous medium. Defects are modelized by inclusions which disturb the motion of the viscous fluid flowing in the pore space of the medium. The seepage rate of the fluid in the host medium and in the inclusion is given by the Darcy's law. Disturbances thus produced modify the shape of the stream lines from which we establish the tortuosity induced by the defects and its implications on the acoustic waves propagation in saturated porous media.
Tortuosity
Confined space
Viscous fingering
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The pore tortuosity of flow paths in porous media plays a crucial role in the simulation of various petrophysical properties (e.g., absolute permeability). A geometric model composed of tortuous stream tubes in the three-dimensional porous media with cubic particles (grains) representing solid grains to calculate tortuosity is proposed under the assumption that the particles are allowed to overlap unrestrictedly and fluids are incompressible. The model is formulated as a function of porosity and contains no empirical constants, which helps to reveal the physical mechanism of tortuous pore paths for fluids to flow within porous media. The result performs better in approximating the results on three-dimensional porous rocks.
Tortuosity
Petrophysics
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Tortuosity is a measure of the geometric complexity of the porous media. Knowing the tortuosity value of the porous media is helpful to get detailed information about the fluid behavior at microscale. In order to calculate the tortuosity, the velocity field of the fluid troughthe porous media is determined using the lattice Boltzmann method (LBM). The particle size of the obstacles is varied, keeping the porosity of the material as a constant. As a result, a relationship to determine the particle diameter as a function of the number of particles for a specific porosity value is given, and the dependence of the tortuosity with respect to the main flow direction is demonstrated.
Tortuosity
Lattice Boltzmann methods
Microscale chemistry
Boltzmann constant
Particle (ecology)
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An understanding of fluid flow and transport in porous media is crucial in the development of better oil and gas recovery processes. With the emergence of parallel computing, today this is achieved more efficiently through direct numerical simulations of microscopic flow and transport. In order for this to be done, porous media models have to be created and multi-phase flow must be simulated. The Lattice Boltzmann Method (LBM) is a flexible computational tool that allows one to simulate fluid flow in complex heterogeneous media. It treats flow as the collective dynamics of pseudo particles and obtains a macroscopic equivalent to the Navier Stokes equations by approximating collision and propagation. For this research, the Rothman and Keller Lattice Boltzmann Method (LBM) was used to simulate two-phase fluid flow in two-dimensional porous media structures. This color gradient method can simulate different wettability and large viscosity ratios with ease and accuracy using a vectorized 2-Dimensional LBM code. Nine different artificial two-dimensional porous media across three porosity values (60%, 65%, and 70%) were created. This was done to understand the influence of pore structure and arrangement on fluid flow for porous medias with the same porosity value. A total of 81 simulations were conducted in which a “red” fluid was injected in a porous medium that was initially saturated with a “blue” fluid of a different viscosity. Different wetting angles and viscosity ratios were used for the simulation to understand their influence on the flow morphology. The result showed that the viscous fingers for the wetting fluid (𝜃 = 0◦) were somewhat broader and more rounded relative to the fingers of the non-wetting fluid (𝜃 = 180◦). It also showed that the recovery factor benefits from higher porosity values. Observing the flow patterns from the simulations showed that the flow morphology of porous medias with the same porosity are similar irrespective of the pore arrangement and structure. The results from this experiment show that with increased viscosity ratio, the recovery ratio is higher, which means more production.
Lattice Boltzmann methods
Multiphase flow
Viscous fingering
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We investigate the problem of transport of a single fluid droplet through a non-wettable superhydrophobic porous medium. A mechanical soft body model is developed and used to simulate the process of pushing fluid droplets through pore space of a random porous medium. Path lines of the center of mass of each droplet are used to calculate tortuosity of the media. Our results show that droplet based tortuosity increases with decreasing porosity of the porous samples. Although qualitatively this agrees with the behaviour observed for tortuosity derived from the fluid flow, the form of this relation is different.
Tortuosity
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Diffusive tortuosity factor is one of the key parameters in modeling solute diffusion in liquid-saturated porous media. However, the determination of diffusive tortuosity factor has to involve a diffusion process in liquid-saturated porous media, which was usually found complicated in laboratories. The incorrect use of diffusive tortuosity factor may cause significant errors in certain circumstances. This paper presents a method to evaluate the diffusive tortuosity factors for liquid-saturated consolidated porous media, i.e., sandstones, which are the typical porous media commonly encountered in contaminant transport in underground water and gas migration in liquid-saturated reservoirs. The proposed method applies two specific experiments to determine the diffusion coefficient in bulk liquid phase and the effective diffusion coefficient in liquid-saturated porous media, respectively. Diffusive tortuosity factor of the porous media is obtained by comparing the effective diffusion coefficient in porous media to the diffusion coefficient in bulk liquid. This study provides a procedure to evaluate the diffusive tortuosity factor for consolidated porous media and also the measured values of diffusive tortuosity factors for selected sandstone samples which can be used as input data for further studies. Another application of the proposed method is to determine the diffusion coefficient in bulk liquid phase for CO2 from the measured effective diffusion coefficients in porous media.
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The influence of porosity of 18 kinds of Cu - based catalysts of methanol synthesis on the effective diffusion coefficients is studied. The catalysts have the different parameters of pore structure. The catalyst pore is divided into micro- pores of larger than10nm and less than 10nm. The study indicates that,the tortuosity factors increases while the porosity of micro pore increases which means the increase of the diffusion resistance. An empirical equation expressing the relationship between porosity and tortuosity is then obtained which can be used to estimate tortuosity in commercial practice.
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