Random walk simulation of miscible flow through heterogeneous 2D porous media considering dispersion tensor

Fayazi, Amir; Ghazanfari, Mohammad Hossein

doi:10.1016/j.ces.2015.03.071

Cited by 9 publications

(7 citation statements)

References 35 publications

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“…The first term describes the mechanical dispersion, which is caused by velocity variations in pore-level and macroscale. In this term, the (longitudinal) dispersivity tensor, α L , depends on heterogeneity, scale, and saturation; and n is an empirical constant close to unity. , The second term accounts for the molecular diffusion process, which occurs due to the existence of a concentration gradient and is present regardless of whether there is flow or not . Molecular diffusion is a very slow process and depends on the physical properties of the system .…”

Section: Methodsmentioning

confidence: 99%

“…60,62 The second term accounts for the molecular diffusion process, which occurs due to the existence of a concentration gradient and is present regardless of whether there is flow or not. 63 Molecular diffusion is a very slow process and depends on the physical properties of the system. 64 Depending on the Pećlet number, which is defined as Pe = u ̅ l c /D m in which u ̅ and l c are the average fluid velocity and the characteristic length, respectively, the molecular diffusion (Pe < 0.1) or the mechanical dispersion (Pe > 1000) can be the prevailing mechanism of dispersion.…”

Section: Initial and Boundary Conditionsmentioning

confidence: 99%

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A Pore-Scale Model for Dispersion and Mass Transfer during Acoustically Assisted Miscible Displacements in Porous Media

Khasi

Fayazi

Kantzas

2021

Ind. Eng. Chem. Res.

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Enhancing flow and transport in porous media by acoustic stimulation has been investigated for the past several decades. Most studies focused on the effect of sound propagation in immiscible displacements. Much less emphasis has been given to understand the beneficial mechanisms during miscible displacements. In this work, a pore-scale model is developed to study the influence of acoustic excitation on dispersion and mass transfer in porous media. The modeling involves first solving for the single-phase fluid flow without the acoustic field, then calculating an external acoustic pressure field across a stationary saturated medium, and finally evaluating the interaction between the acoustic field and the flowing fluid. Simulations are run at different injection velocities, wave frequencies, and acceleration amplitudes. Concentration profiles of the pore-scale model show that the mass transfer between the mobile and immobile regions is accelerated under the sonication. In addition, the dispersion coefficient is increased due to the enhanced effective diffusivity and the additional acoustically induced velocity. To quantify the enhancement in transport, dispersion and mass transfer coefficients are calculated by matching the analytical solutions of the continuum transport model with effluent concentration profiles obtained by pore-scale simulations. At lower injection rates, dispersion coefficient is more affected by acoustic excitation compared to mass transfer coefficient. Lower frequencies and higher acceleration amplitudes of the propagated waves increase the enhancements in dispersion and mass transfer coefficients. The results at higher viscosity ratios indicate that low-frequency excitation could be a promising technique for improving miscible displacements. The effects of controlling parameters are summarized in a proposed dimensionless group of AD for designing effective acoustically assisted experiments in the laboratory.

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Section: Methodsmentioning

confidence: 99%

Section: Initial and Boundary Conditionsmentioning

confidence: 99%

A Pore-Scale Model for Dispersion and Mass Transfer during Acoustically Assisted Miscible Displacements in Porous Media

Khasi

Fayazi

Kantzas

2021

Ind. Eng. Chem. Res.

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“…Using the velocity field, each particle moves through the porous media by advection and hydrodynamic dispersion process. The particle's position in an unsteady nonuniform flow can be expressed by the Ito‐Taylor integration scheme (Fayazi & Ghazanfari, ; Hassan & Mohamed, ; Park et al, ; Sun et al, ):

x_{t + normalΔ t} = x_{t} + ([],, u_{x} + \frac{\partial D_{xx}}{\partial x} + \frac{\partial D_{xy}}{\partial y}) normalΔ t + r_{1} \times \sqrt{2 D_{xx} normalΔ t} + r_{2} \times \sqrt{2 D_{xy} normalΔ t},

y_{t + normalΔ t} = y_{t} + ([],, u_{y} + \frac{\partial D_{yx}}{\partial x} + \frac{\partial D_{yy}}{\partial y}) normalΔ t + r_{3} \times \sqrt{2 D_{yx} normalΔ t} + r_{4} \times \sqrt{2 D_{yy} normalΔ t},

where ( x t + Δ t , y t + Δ t ) is the position of a particle at the time ' t + Δ t ' (L); ( x t , y t ) is the position of a particle at time ' t ' (L); r i ( i = 1, 2, 3, 4) is the Gaussian distribution of random variables with zero mean and unit variance.…”

Section: Methodsmentioning

confidence: 99%

“…Using the velocity field, each particle moves through the porous media by advection and hydrodynamic dispersion process. The particle's position in an unsteady nonuniform flow can be expressed by the Ito-Taylor integration scheme (Fayazi & Ghazanfari, 2015;Hassan & Mohamed, 2003;Park et al, 2008;Sun et al, 2015):…”

Section: Random Walk Particle Trackingmentioning

confidence: 99%

“…Thereafter, each particle moves through the porous media by advection and hydrodynamic dispersion. RWPT is completely free from the numerical dispersion, as it skips solving the transport equation directly (Fayazi & Ghazanfari, 2015;Salamon et al, 2006). In RWPT, no particles are lost or destroyed during the simulation process; hence, mass conservation property is satisfied automatically (Bechtold et al, 2011;Sun, 2013).…”

Section: Introductionmentioning

confidence: 99%

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Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking

Majumder

Eldho

2017

Hydrological Processes

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Groundwater contaminant transport processes are usually simulated by the finite difference (FDM) or finite element methods (FEM). However, they are susceptible to numerical dispersion for advection‐dominated transport. In this study, a numerical dispersion‐free coupled flow and transport model is developed by combining the analytic element method (AEM) with random walk particle tracking (RWPT). As AEM produces continuous velocity distribution over the entire aquifer domain, it is more suitable for RWPT than FDM/finite element methods. Using the AEM solutions, RWPT tracks all the particles in a vectorized manner, thereby improving the computational efficiency. The present model performs a convolution integral of the response of an impulse contaminant injection to generate concentration distributions due to a permanent contaminant source. The RWPT model is validated with an available analytical solution and compared to an FDM solution, the RWPT model more accurately replicates the analytical solution. Further, the coupled AEM‐RWPT model has been applied to simulate the flow and transport in hypothetical and field aquifer problems. The results are compared with the FDM solutions and found to be satisfactory. The results demonstrate the efficacy of the proposed method.

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Stochastic axial dispersion model for tubular equipment

Nakama

Siqueira

Vianna

2017

Chemical Engineering Science

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Random walk simulation of miscible flow through heterogeneous 2D porous media considering dispersion tensor

Cited by 9 publications

References 35 publications

A Pore-Scale Model for Dispersion and Mass Transfer during Acoustically Assisted Miscible Displacements in Porous Media

A Pore-Scale Model for Dispersion and Mass Transfer during Acoustically Assisted Miscible Displacements in Porous Media

Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking

Stochastic axial dispersion model for tubular equipment

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