We present a numerical framework to solve the dynamic model for electrokinetic flows in microchannels using coupled lattice Boltzmann methods. The governing equation for each transport process is ...solved by a lattice Boltzmann model and the entire process is simulated through an iteration procedure. After validation, the present method is used to study the applicability of the Poisson–Boltzmann model for electrokinetic flows in microchannels. Our results show that for homogeneously charged long channels, the Poisson–Boltzmann model is applicable for a wide range of electric double layer thickness. For the electric potential distribution, the Poisson–Boltzmann model can provide good predictions until the electric double layers fully overlap, meaning that the thickness of the double layer equals the channel width. For the electroosmotic velocity, the Poisson–Boltzmann model is valid even when the thickness of the double layer is 10 times of the channel width. For heterogeneously charged microchannels, a higher zeta potential and an enhanced velocity field may cause the Poisson–Boltzmann model to fail to provide accurate predictions. The ionic diffusion coefficients have little effect on the steady flows for either homogeneously or heterogeneously charged channels. However the ionic valence of solvent has remarkable influences on both the electric potential distribution and the flow velocity even in homogeneously charged microchannels. Both theoretical analyses and numerical results indicate that the valence and the concentration of the counter-ions dominate the Debye length, the electrical potential distribution, and the ions transport. The present results may improve the understanding of the electrokinetic transport characteristics in microchannels.
This article presents a critical review of the theory and applications of a multiphase model in the community of the lattice Boltzmann method (LBM), the pseudopotential model proposed by Shan and ...Chen (1993) 4, which has been successfully applied to a wide range of multiphase flow problems during the past two decades. The first part of the review begins with a description of the LBM and the original pseudopotential model. The distinct features and the limitations of the original model are described in detail. Then various enhancements necessary to improve the pseudopotential model in terms of decreasing the spurious currents, obtaining high density/viscosity ratio, reducing thermodynamic inconsistency, unraveling the coupling between surface tension and equations of state (EOS), and unraveling the coupling between viscosity and surface tension, are reviewed. Then the fluid–solid interactions are presented and schemes to obtain different contact angles are discussed. The final section of this part focuses on the multi-component multiphase pseudopotential model. The second part of this review describes fruitful applications of this model to various multiphase flows. Coupling of this model with other models for more complicated multiple physicochemical processes are also introduced in this part.
Drying of porous media is governed by a combination of evaporation and movement of the liquid phase within the porous structure. Contact angle hysteresis induced by surface roughness is shown to ...influence multi-phase flows, such as contact line motion of droplet, phase distribution during drainage and coffee ring formed after droplet drying in constant contact radius mode. However, the influence of contact angle hysteresis on liquid drying in porous media is still an unanswered question. Lattice Boltzmann model (LBM) is an advanced numerical approach increasingly used to study phase change problems including drying. In this paper, based on a geometric formulation scheme to prescribe contact angle, we implement a contact angle hysteresis model within the framework of a two-phase pseudopotential LBM. The capability and accuracy of prescribing and automatically measuring contact angles over a large range are tested and validated by simulating droplets sitting on flat and curved surfaces. Afterward, the proposed contact angle hysteresis model is validated by modeling droplet drying on flat and curved surfaces. Then, drying of two connected capillary tubes is studied, considering the influence of different contact angle hysteresis ranges on drying dynamics. Finally, the model is applied to study drying of a dual-porosity porous medium, where phase distribution and drying rate are compared with and without contact angle hysteresis. The proposed model is shown to be capable of dealing with different contact angle hysteresis ranges accurately and of capturing the physical mechanisms during drying in different porous media including flat and curved geometries.
•The advances and challenges of pore-scale modeling are summarized.•Porous structure imaging and computational reconstruction methods are reviewed.•Recent progresses in pore-scale numerical methods ...and schemes are introduced.•Pore-scale studies of transport processes in porous media are discussed.•Application of pore-scale modeling in geoscience and fuel cells are presented.
Porous media play important roles in a wide range of scientific and engineering problems. Recently, with their increasing application in energy conversion and storage devices, such as fuel cells, batteries and supercapacitors, it has been realized that transport processes and reactions occurring in the pores and at the interfaces of different constituents significantly affect the performance of the porous media, yet these pore-scale transport phenomena are not well described or even neglected in the conventional numerical models based on the representative element volume (REV). Pore-scale modeling is an efficient tool for the simulation of pore-scale transport and reactions in porous media because of its ability to accurately characterize these processes and to provide the distribution details of important variables which are challenging for current experimental techniques to provide either due to lack of in-situ measurement capability or due to the limited spatial and temporal resolution. In the present review, the advances and challenges of the state-of-the-art pore-scale modeling are summarized. The practical applications of pore-scale modeling in the fields of geoscience, polymer exchange membrane fuel cells (PEMFC) and solid oxide fuel cells (SOFC) are discussed. Notable results from the pore-scale modeling are presented, and the challenges facing the pore-scale model development are discussed. This in-depth review is intended to give a well-rounded introduction of critical aspects on which the pore-scale modeling can shed light in the development of relevant scientific and engineering systems.
•Multiphase reactive transport during CO2 dissolution trapping is studied.•A pore-scale numerical model for above physicochemical processes is developed.•Pore-scale multiphase flow, mass transport ...and reactions are discussed in detail.•Evolutions of specific interfacial and efficient dissolution rate are analyzed.•Effects of wettability on the multiphase reactive transport processes are explored.
Solubility trapping is crucial for permanent CO2 sequestration in deep saline aquifers. For the first time, a pore-scale numerical method is developed to investigate coupled scCO2-water two-phase flow, multicomponent (CO2(aq), H+, HCO3−, CO32− and OH−) mass transport, heterogeneous interfacial dissolution reaction, and homogeneous dissociation reactions. Pore-scale details of evolutions of multiphase distributions and concentration fields are presented and discussed. Time evolutions of several variables including averaged CO2(aq) concentration, scCO2 saturation, and pH value are analyzed. Specific interfacial length, an important variable which cannot be determined but is required by continuum models, is investigated in detail. Mass transport coefficient or efficient dissolution rate is also evaluated. The pore-scale results show strong non-equilibrium characteristics during solubility trapping due to non-uniform distributions of multiphase as well as slow mass transport process. Complicated coupling mechanisms between multiphase flow, mass transport and chemical reactions are also revealed. Finally, effects of wettability are also studied. The pore-scale studies provide deep understanding of non-linear non-equilibrium multiple physicochemical processes during CO2 solubility trapping processes, and also allow to quantitatively predict some important empirical relationships, such as saturation-interfacial surface area, for continuum models.
•Lattice Boltzmann method for isothermal micro-gas flow is reviewed.•Different boundary conditions in capturing gas–solid interfacial slip phenomenon are summarized.•Current treatments in LBM for ...capturing the Knudsen layer effect are discussed.•Applications of the pore scale and REV scale LBM in shale gas flow simulation are evaluated.
The lattice Boltzmann method (LBM) has experienced tremendous advances and been well accepted as a popular method for simulating various fluid flow problems in porous media. With the introduction of an effective relaxation time and slip boundary conditions, the LBM has been successfully extended to solve micro-gaseous transport phenomena. As a result, the LBM has the potential to become an effective numerical method for gas flow in shale matrix in slip flow and transition flow regimes. Additionally, it is very difficult to experimentally determine the permeability of extremely low permeable media like shale. In this paper an extensive review on a number of slip boundary conditions and Knudsen layer treatments used in LB models for micro-gaseous flow is carried out. Furthermore, potential applications of the LBM in flow simulation in shale gas reservoirs on pore scale and representative elementary volume (REV) scale are evaluated and summarized. Our review indicates that the LBM is capable of capturing gas flow in continuum to slip flow regimes which cover significant proportion of the pores in shale gas reservoirs and identifies opportunities for future research.
We report the application of machine learning methods for predicting the effective diffusivity (D
) of two-dimensional porous media from images of their structures. Pore structures are built using ...reconstruction methods and represented as images, and their effective diffusivity is computed by lattice Boltzmann (LBM) simulations. The datasets thus generated are used to train convolutional neural network (CNN) models and evaluate their performance. The trained model predicts the effective diffusivity of porous structures with computational cost orders of magnitude lower than LBM simulations. The optimized model performs well on porous media with realistic topology, large variation of porosity (0.28-0.98), and effective diffusivity spanning more than one order of magnitude (0.1 ≲ D
< 1), e.g., >95% of predicted D
have truncated relative error of <10% when the true D
is larger than 0.2. The CNN model provides better prediction than the empirical Bruggeman equation, especially for porous structure with small diffusivity. The relative error of CNN predictions, however, is rather high for structures with D
< 0.1. To address this issue, the porosity of porous structures is encoded directly into the neural network but the performance is enhanced marginally. Further improvement, i.e., 70% of the CNN predictions for structures with true D
< 0.1 have relative error <30%, is achieved by removing trapped regions and dead-end pathways using a simple algorithm. These results suggest that deep learning augmented by field knowledge can be a powerful technique for predicting the transport properties of porous media. Directions for future research of machine learning in porous media are discussed based on detailed analysis of the performance of CNN models in the present work.
•Hydraulic fracturing has increased shale gas production and lowered energy costs.•Water-based drawbacks: poor production, environmental impacts, water shortages.•Supercritical CO2 could enhance ...production while minimizing environmental concerns.•Through theory, modeling, & experiments, we explore CO2 opportunities & challenges.•CO2 has substantial potential to transform shale gas; further research is needed.
Hydraulic fracturing of shale formations in the United States has led to a domestic energy boom. Currently, water is the only fracturing fluid regularly used in commercial shale oil and gas production. Industry and researchers are interested in non-aqueous working fluids due to their potential to increase production, reduce water requirements, and to minimize environmental impacts. Using a combination of new experimental and modeling data at multiple scales, we analyze the benefits and drawbacks of using CO2 as a working fluid for shale gas production. We theorize and outline potential advantages of CO2 including enhanced fracturing and fracture propagation, reduction of flow-blocking mechanisms, increased desorption of methane adsorbed in organic-rich parts of the shale, and a reduction or elimination of the deep re-injection of flow-back water that has been linked to induced seismicity and other environmental concerns. We also examine likely disadvantages including costs and safety issues associated with handling large volumes of supercritical CO2. The advantages could have a significant impact over time leading to substantially increased gas production. In addition, if CO2 proves to be an effective fracturing fluid, then shale gas formations could become a major utilization option for carbon sequestration.
•Dissolution-induced changes in permeability/porosity studied at the pore scale.•Permeability porosity relationship explored for a wide range of Pe and Da.•A transition from transport-limited ...dissolution to wormholing is observed.
We apply a reactive transport lattice Boltzmann model developed in previous studies to study the dissolution-induced changes in permeability and porosity of two porous media at the pore scale. The permeability–porosity relationship is explored for a wide range of Peclet and Damkohler numbers. It is found that this relationship depends not only on different dissolution regimes characterized by Pe and Da, but also on the specific porous medium structure. The permeability–porosity relationship for the more geometrically complex porous medium shows much more complexity than that for the simple fractured medium. While a very small Da sets an upper bound for the permeability–porosity relationship for the simple medium, a combination of a high Da and Pe results in wormholing, and the fastest permeability increase for the complex medium. At a moderate Pe but large Da, a transition from transport-limited dissolution regime to wormholing is also observed for the complex medium.
Droplet wetting and distortion on flat surfaces with heterogeneous wettability are studied using the 3D Shan–Chen pseudopotential multiphase lattice Boltzmann model (LBM). The contact angles are ...compared with the Cassie mode, which predicts an apparent contact angle for flat surfaces with different wetting properties, where the droplet size is large compared to the size of the heterogeneity. In this study, the surface studied consists in a regular checkboard pattern with two different Young’s contact angles (hydrophilic and hydrophobic) and equal surface fraction. The droplet size and patch size of the checkboard are varied beyond the limit where Cassie’s equation is valid. A critical ratio of patch size to droplet radius is found below which the apparent contact angle follows the Cassie mode. Above the critical value, the droplet shape changes from a spherical cap to a more distorted form, and no single contact angle can be determined. The local contact angles are found to vary along the contact line between minimum and maximum values. The droplet is found to wet preferentially the hydrophilic region, and the wetted area fraction of the hydrophilic region increases quasi-linearly with the ratio between patch and droplet sizes. We propose a new equation beyond the critical ratio, defining an equivalent contact angle, where the wetted area fractions are used as weighting coefficients for the maximum and minimum local contact angles. This equivalent contact angle is found to equal Cassie’s contact angle.
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