Abstract ：

Droplet snap off is one of the most usual phenomena in oil recovery during water injection in water-wet porous media. In this work, the droplet dynamic snap-off process in a short, abrupt constriction is investigated. Three different phenomena, i.e. total breakup, partial breakup and non-breakup, of the nonwetting phase droplets are observed, the flow characteristics of droplets in each phenomenon and relevant physical mechanisms are analyzed. We find that both the initial size and velocity of the droplet greatly influence the breakup process. The viscosity of droplet also affects the breakup state. The critical conditions of each phenomenon are obtained based on dimensionless droplet size and capillary number, which could be used to predict the droplet breakup state. Under a certain capillary number, daughter droplet distribution is influenced by initial droplet size. (c) 2021 Elsevier Ltd. All rights reserved.

Keyword ：

Abrupt constriction Breakup Droplets Microfluidics Snap off Two-phase flow

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Abstract ：

A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. Two kinds of moments (i.e., point values (PV moment) at cell interfaces and volume integrated average (VIA moment) value) are defined within a single cell. The PV moment is updated by a conventional semi-Lagrangian method, while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation. Different from the spatial approximation used in the CSL2 (conservative semi-Lagrangian scheme with second order polynomial function) scheme, a monotonic rational function which can effectively remove non-physical oscillations is reconstructed within a single cell by the PV moments and VIA moment. To achieve exactly positive-definite preserving, two kinds of corrections are made on the original conservative semi-Lagrangian with rational function (CSLR) scheme. The resulting scheme is inherently conservative, non-negative, and allows a Courant number larger than one. Moreover, the spatial reconstruction can be performed within a single cell, which is very efficient and economical for practical implementation. In addition, a dimension-splitting approach coupled with multi-moment finite volume scheme is adopted on cubed-sphere geometry, which benefitsthe implementation of the 1D CSLR solver with large Courant number. The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry. Numerical results show that the proposed transport model can effectively remove nonphysical oscillations and preserve the numerical non-negativity, and it has the potential to transport the tracers accurately in a real atmospheric model.

Keyword ：

conservative semi-Lagrangian method cubed-sphere grid global transport model multi-moment method single-cell-based scheme

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Abstract ：

A new multimoment global shallow-water model on the cubed sphere is proposed by adopting a two-stage fourth-order Runge-Kutta time integration. Through calculating the values of predicted variables at half time step t + t(n) + (1/2)Delta(t) by a second-order formulation, a fourth- order scheme can be derived using only two stages within one time step. This time integration method is implemented in our multimoment global shallow-water model to build and validate a new and more efficient numerical integration framework for dynamical cores. As the key task, the numerical formulation for evaluating the derivatives in time has been developed through the Cauchy- Kowalewski procedure and the spatial discretization of the multimoment finite- volume method, which ensures fourth-order accuracy in both time and space. Several major benchmark tests are used to verify the proposed numerical framework in comparison with the existing four-stage fourth-order Runge-Kutta method, which is based on the method of lines framework. The two-stage fourthorder scheme saves about 30% of the computational cost in comparison with the four-stage Runge-Kutta scheme for global advection and shallow- water models. The proposed two-stage fourth- order framework offers a new option to develop high-performance time marching strategy of practical significance in dynamical cores for atmospheric and oceanic models.

Keyword ：

Advection Coordinate systems Grid systems Nonlinear models Shallow-water equations

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A new direct numerical simulation algorithm is developed for particle pore-scale transport through the porous media with arbitrarily polyhedral mesh. In the algorithm, the Navier-Stokes Equation is used to describe the continuous phase motion in the Eulerian framework: Newton's Second Law is used to describe the particle dynamics in the Lagrangian framework; Discrete element method is used to describe the particle-particle interactions and particle-wall interactions; RIGID is used to detect the contact state between particles with arbitrarily shaped pore walls. To suppress the spurious force oscillations (SFO) and improve the numerical accuracy of the evaluation of fluid-particle interaction, a novel consistent fictitious domain method (CFDM) in the arbitrarily collocated polyhedral mesh is developed. Numerical results of six test cases show that CFDM is accurate and second order in space, and no obvious SFO is found. Finally, the new direct numerical simulation algorithm is used to simulate the particle transport through three-dimensional porous media reconstructed from micro-CT scans from a real rock. The numerical results of a serial of tests with different particle sizes reveal several distinct microscopic flow mechanisms and the corresponding macroscopic characteristics. The change of channel resistance leads to the formation of particle motion paths in succession; Along a certain motion path, the particle moving velocity can be different at different sites: With the increase of particle size, the particle average retention time and particle average transit time increase: Particle velocity presents lognormal distribution, which becomes wider with the increase of partide size. The newly developed algorithm can be adopted as a direct numerical simulation tool to simulate particle motion in arbitrarily complex pore space. (C) 2020 Elsevier B.V. All rights reserved.

Keyword ：

Discrete element method Fictitious domain method OpenFOAM Polyhedral mesh Pore scale

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Abstract ：

An oscillation-less multimoment global transport model was proposed by Tang et al. in 2018 by introducing a slope limiter based on the weighted essentially non-oscillatory (WENO) concept. The spurious oscillations around the discontinuities and strong gradients can be effectively removed and the model preserves the fourth-order accuracy in spherical geometry for smooth solutions. However, the WENO limiter does not strictly guarantee the non-negativity of numerical solution and the resulting model will violate the physical principle due to the existence of the nonphysical negative undershoots. As the numerical fluxes, which determine the time tendency of the volume-integrated average, are evaluated by the point values (PVs) defined along the cell boundaries in the multimoment finite-volume schemes, the non-negativity preserving model can be accomplished by modifying those PVs to implement the corrections on the numerical fluxes proposed in the positive definite flux-corrected transport (FCT) method by Smolarkiewicz in 1989. In this study, a non-negativity correction algorithm is proposed for a global transport model using the MM-FVM_WENO scheme and verified by simulating the widely used benchmark tests.

Keyword ：

cubed sphere multimoment method non-negativity scheme transport model WENO method

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In this work, a direct numerical simulation method, for pore scale particle-water-oil transport in porous media is proposed in hybrid Eulerian-Lagrangian framework. In this method, Navier-Stokes equation in Eulerian framework is coupled with discrete element method (DEM) in Lagrangian framework through direct numerical evaluation of fluid-particle interaction using fictitious domain method (FDM). In Eulerian framework, volume of fluid (VOF) method is employed to capture immiscible two-phase interface; Ghost fluid method and balanced-force scheme are used to treat the surface tension to lower interface spurious currents. In Lagrangian framework, RIGID algorithm is employed to detect the contact states between spherical particles with arbitrarily topological pore walls, making the method adapt to arbitrary pore space; Injection of particles with arbitrary size distribution at a specific mass flow rate makes the method adapt to open system. After validating the new method using two benchmark test cases, a numerical simulation of particle flooding process in a real rock is performed. Numerical results show that in the particle flooding process, three different stages, i.e. drainage period, analogy water flooding period and effective period of particle flooding, are involved. Distinct macroscopic flow characteristics are observed in different periods. Particle size is an important factor influencing the pore scale behaviors (such as, particle space translation and diffusion, remaining oil distribution, degree of fluid diversion) and macroscopic flow phenomena (such as, average oil fraction, average water or oil migration velocity in mainstream direction and transverse direction, sweeping efficiency).

Keyword ：

Discrete element method Fictitious domain method OpenFOAM Pore scale RIGID

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Abstract ：

A computational platform for direct numerical simulation of fluid-particle two-phase flow in porous media is presented in this study. In the proposed platform, the Navier-Stokes equations are used to describe the motion of the continuous phase, while the discrete element method (DEM) is employed to evaluate particle-particle and particle-wall interactions, with a fictitious domain method being adopted to evaluate particle-fluid interactions. Particle-wall contact states are detected by the ERIGID scheme. Moreover, a new scheme, namely, base point-increment method is developed to improve the accuracy of particle tracking in porous media. In order to improve computationally efficiency, a time splitting strategy is applied to couple the fluid and DEM solvers, allowing different time steps to be used which are adaptively determined according to the stability conditions of each solver. The proposed platform is applied to particle transport in a porous medium with its pore structure being reconstructed from micro-CT scans from a real rock. By incorporating the effect of pore structure which has a comparable size to the particles, numerical results reveal a number of distinct microscopic flow mechanisms and the corresponding macroscopic characteristics. The time evolution of the inlet to outlet pressure-difference consists of large-scale spikes and small-scale fluctuations. Apart from the influence through direct contacts between particles, the motion of a particle can also be affected by particles without contact through blocking a nearby passage for fluid flow. Particle size has a profound influence on the macroscopic motion behavior of particles. Small particles are easier to move along the main stream and less dispersive in the direction perpendicular to the flow than large particles. (C) 2019 Elsevier Ltd. All rights reserved.

Keyword ：

Discrete element method Fictitious domain method Fluid-particle flow Pore scale

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In this paper, we present a new numerical scheme to describe the dynamic evolution of multiphase polydisperse systems in terms of time, space, and properties by coupling the Eulerian-Lagrangian method for air-particle two-phase flow and population balance equations to describe particle property evolution due to microbehaviors (eg, aggregation, breakage, and growth). This coupling scheme was used to comprehensively simulate the two-phase flow structure, particle size spectrum, particle number, and volume concentrations. These were characterized by a high-resolution particle tracking using the Lagrangian approach and the high precision of moments of the particle size spectrum by solving the population balance equation with the quadrature method of moments. The algorithm of the coupling scheme was incorporated into the open source computational fluid dynamics software OpenFOAM to simulate the dynamic evolution of vehicle exhaust plume. The impacts of vehicle velocity, exhaust temperature, and aggregation efficiency on the distribution of auto exhaust particles in space and changes in their properties were analyzed. The results indicate that the particle number concentration, volume concentration, and average diameter of particles in the vehicle exhaust plume could be strongly affected by the plume structure and flow properties.

Keyword ：

Eulerian-Lagrangian method multiphase polydisperse systems particle size spectrum population balance equations quadrature method of moments vehicle exhaust plume

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Abstract ：

At the high water cut stage, the residual oil in a reservoir becomes complex and dispersed. Moreover, it is challenging to achieve good predictions of the movement of oil and water in a reservoir according to the macroscopic models based on the statistic parameters of this scenario. However, pore-scale simulation technology based on directly tracking the interaction among different phases can make an accurate prediction of the fluid distribution in the pore space, which is highly important in the improvement of the recovery rate. In this work, pore-scale simulation methods, including the pore network model, lattice Boltzmann method, Navier-Stokes equation-based interface tracking methods, and smoothed particle hydrodynamics, and relevant technologies are summarized. The principles, advantages, and disadvantages, as well as the degree of difficulty in the implementation are analyzed and compared. Problems in the current simulation technologies, micro sub-models, and applications in physicochemical percolation are also discussed. Finally, potential developments and prospects in this field are summarized.

Keyword ：

lattice Boltzmann method pore network model pore-scale simulation smoothed particle hydrodynamics volume of fluid

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Abstract ：

A local fixed pivot quadrature method of moments (LFPQMOM) is proposed for the solution of the population balance equation (PBE) for the aggregation and breakage process. First, the sectional representation for aggregation and breakage is presented. The continuous summation of the Dirac Delta function is adopted as the discrete form of the continuous particle size distribution in the local section as performed in short time Fourier transformation (STFT) and the moments in local sections are tracked successfully. Numerical simulation of benchmark test cases including aggregation, breakage, and aggregation breakage combined processes demonstrate that the new method could make good predictions for the moments along with particle size distribution without further assumption. The accuracy in the numerical results of the moments is comparable to or higher than the quadrature method of moment (QMOM) in most of the test cases. In theory, any number of moments can be tracked with the new method, but the computational expense can be relatively large due to many scalar equations that may be included.

Keyword ：

aggregation breakage local fixed pivot quadrature method of moment population balance equation

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