Predictive scale-bridging simulations through active learning.

Throughout computational science, there is a growing need to utilize the continual improvements in raw computational horsepower to achieve greater physical fidelity through scale-bridging over brute-force increases in the number of mesh elements. For instance, quantitative predictions of transport in nanoporous media, critical to hydrocarbon extraction from tight shale formations, are impossible without accounting for molecular-level interactions. Similarly, inertial confinement fusion simulations rely on numerical diffusion to simulate molecular effects such as non-local transport and mixing without truly accounting for molecular interactions. With these two disparate applications in mind, we develop a novel capability which uses an active learning approach to optimize the use of local fine-scale simulations for informing coarse-scale hydrodynamics. Our approach addresses three challenges: forecasting continuum coarse-scale trajectory to speculatively execute new fine-scale molecular dynamics calculations, dynamically updating coarse-scale from fine-scale calculations, and quantifying uncertainty in neural network models.

A Dataset of 3D Structural and Simulated Transport Properties of Complex Porous Media.

Physical processes that occur within porous materials have wide-ranging applications including - but not limited to - carbon sequestration, battery technology, membranes, oil and gas, geothermal energy, nuclear waste disposal, water resource management. The equations that describe these physical processes have been studied extensively; however, approximating them numerically requires immense computational resources due to the complex behavior that arises from the geometrically-intricate solid boundary conditions in porous materials. Here, we introduce a new dataset of unprecedented scale and breadth, DRP-372: a catalog of 3D geometries, simulation results, and structural properties of samples hosted on the Digital Rocks Portal. The dataset includes 1736 flow and electrical simulation results on 217 samples, which required more than 500 core years of computation. This data can be used for many purposes, such as constructing empirical models, validating new simulation codes, and developing machine learning algorithms that closely match the extensive purely-physical simulation. This article offers a detailed description of the contents of the dataset including the data collection, simulation schemes, and data validation.

Lattice Boltzmann Modeling of Drying of Porous Media Considering Contact Angle Hysteresis.

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. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11242-021-01644-9.

Lattice Boltzmann modeling of heat conduction enhancement by colloidal nanoparticle deposition in microporous structures.

Drying of colloidal suspension towards the exploitation of the resultant nanoparticle deposition has been applied in different research and engineering fields. Recent experimental studies have shown that neck-based thermal structure (NTS) by colloidal nanoparticle deposition between microsize filler particle configuration (FPC) can significantly enhance vertical heat conduction in innovative three-dimensional chip stacks [Brunschwiler et al., J. Electron. Packag. 138, 041009 (2016)10.1115/1.4034927]. However, an in-depth understanding of the mechanisms of colloidal liquid drying, neck formation, and their influence on heat conduction is still lacking. In this paper, using the lattice Boltzmann method, we model neck formation in FPCs and evaluate the thermal performances of resultant NTSs. The colloidal liquid is found drying continuously from the periphery of the microstructure to its center with a decreasing drying rate. With drying, more necks of smaller size are formed between adjacent filler particles, while fewer necks of larger size are formed between filler particle and the top/bottom plate of the FPCs. The necks, forming critical throats between the filler particles, are found to improve the heat flux significantly, leading to an overall heat conduction enhancement of 2.4 times. In addition, the neck count, size, and distribution as well as the thermal performance of NTSs are found to be similar for three different FPCs at a constant filler particle volume fraction. Our simulation results on neck formation and thermal performances of NTSs are in good agreement with experimental results. This demonstrates that the current lattice Boltzmann models are accurate in modeling drying of colloidal suspension and heat conduction in microporous structures, and have high potentials to study other problems such as surface coating, salt transport, salt crystallization, and food preserving.

3D particle transport in multichannel microfluidic networks with rough surfaces.

The transport of particles and fluids through multichannel microfluidic networks is influenced by details of the channels. Because channels have micro-scale textures and macro-scale geometries, this transport can differ from the case of ideally smooth channels. Surfaces of real channels have irregular boundary conditions to which streamlines adapt and with which particle interact. In low-Reynolds number flows, particles may experience inertial forces that result in trans-streamline movement and the reorganization of particle distributions. Such transport is intrinsically 3D and an accurate measurement must capture movement in all directions. To measure the effects of non-ideal surface textures on particle transport through complex networks, we developed an extended field-of-view 3D macroscope for high-resolution tracking across large volumes ([Formula: see text]) and investigated a model multichannel microfluidic network. A topographical profile of the microfluidic surfaces provided lattice Boltzmann simulations with a detailed feature map to precisely reconstruct the experimental environment. Particle distributions from simulations closely reproduced those observed experimentally and both measurements were sensitive to the effects of surface roughness. Under the conditions studied, inertial focusing organized large particles into an annular distribution that limited their transport throughout the network while small particles were transported uniformly to all regions.

Modeling and scale-bridging using machine learning: nanoconfinement effects in porous media.

Fine-scale models that represent first-principles physics are challenging to represent at larger scales of interest in many application areas. In nanoporous media such as tight-shale formations, where the typical pore size is less than 50 nm, confinement effects play a significant role in how fluids behave. At these scales, fluids are under confinement, affecting key properties such as density, viscosity, adsorption, etc. Pore-scale Lattice Boltzmann Methods (LBM) can simulate flow in complex pore structures relevant to predicting hydrocarbon production, but must be corrected to account for confinement effects. Molecular dynamics (MD) can model confinement effects but is computationally expensive in comparison. The hurdle to bridging MD with LBM is the computational expense of MD simulations needed to perform this correction. Here, we build a Machine Learning (ML) surrogate model that captures adsorption effects across a wide range of parameter space and bridges the MD and LBM scales using a relatively small number of MD calculations. The model computes upscaled adsorption parameters across varying density, temperature, and pore width. The ML model is 7 orders of magnitude faster than brute force MD. This workflow is agnostic to the physical system and could be generalized to further scale-bridging applications.

Tricoupled hybrid lattice Boltzmann model for nonisothermal drying of colloidal suspensions in micropore structures.

A tricoupled hybrid lattice Boltzmann model (LBM) is developed to simulate colloidal liquid evaporation and colloidal particle deposition during the nonisothermal drying of colloidal suspensions in micropore structures. An entropic multiple-relaxation-time multirange pseudopotential two-phase LBM for isothermal interfacial flow is first coupled to an extended temperature equation for simulating nonisothermal liquid drying. Then the coupled model is further coupled with a modified convection diffusion equation to consider the nonisothermal drying of colloidal suspensions. Two drying examples are considered. First, drying of colloidal suspensions in a two-pillar micropore structure is simulated in two dimensions (2D), and the final configuration of colloidal particles is compared with the experimental one. Good agreement is observed. Second, at the temperature of 343.15 K (70^{∘}C), drying of colloidal suspensions in a complex spiral-shaped micropore structure containing 220 pillars is simulated (also in 2D). The drying pattern follows the designed spiral shape due to capillary pumping, i.e., transport of the liquid from larger pores to smaller ones by capillary pressure difference. Since the colloidal particles are passively carried with liquid, they accumulate at the small menisci as drying proceeds. As liquid evaporates at the small menisci, colloidal particles are deposited, eventually forming solid structures between the pillars (primarily), and at the base of the pillars (secondarily). As a result, the particle deposition conforms to the spiral route. Qualitatively, the simulated liquid and particle configurations agree well with the experimental ones during the entire drying process. Quantitatively, the model demonstrates that the evaporation rate and the particle accumulation rate slowly decrease during drying, similar to what is seen in the experimental results, which is due to the reduction of the liquid-vapor interfacial area. In conclusion, the hybrid model shows the capability and accuracy for simulating nonisothermal drying of colloidal suspensions in a complex micropore structure both qualitatively and quantitatively, as it includes all the required physics and captures all the complex features observed experimentally. Such a tricoupled LBM has a high potential to become an efficient numerical tool for further investigation of real and complex engineering problems incorporating drying of colloidal suspensions in porous media.

Comprehensive comparison of pore-scale models for multiphase flow in porous media.

Multiphase flows in porous media are important in many natural and industrial processes. Pore-scale models for multiphase flows have seen rapid development in recent years and are becoming increasingly useful as predictive tools in both academic and industrial applications. However, quantitative comparisons between different pore-scale models, and between these models and experimental data, are lacking. Here, we perform an objective comparison of a variety of state-of-the-art pore-scale models, including lattice Boltzmann, stochastic rotation dynamics, volume-of-fluid, level-set, phase-field, and pore-network models. As the basis for this comparison, we use a dataset from recent microfluidic experiments with precisely controlled pore geometry and wettability conditions, which offers an unprecedented benchmarking opportunity. We compare the results of the 14 participating teams both qualitatively and quantitatively using several standard metrics, such as fractal dimension, finger width, and displacement efficiency. We find that no single method excels across all conditions and that thin films and corner flow present substantial modeling and computational challenges.

Predicting Effective Diffusivity of Porous Media from Images by Deep Learning.

We report the application of machine learning methods for predicting the effective diffusivity (De) 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 ≲ De < 1), e.g., >95% of predicted De have truncated relative error of <10% when the true De 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 De < 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 De < 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.

Beyond-Cassie Mode of Wetting and Local Contact Angles of Droplets on Checkboard-Patterned Surfaces.

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.

Multiple-relaxation-time color-gradient lattice Boltzmann model for simulating two-phase flows with high density ratio.

In this paper we propose a color-gradient lattice Boltzmann (LB) model for simulating two-phase flows with high density ratio and high Reynolds number. The model applies a multirelaxation-time (MRT) collision operator to enhance the stability of the simulation. A source term, which is derived by the Chapman-Enskog analysis, is added into the MRT LB equation so that the Navier-Stokes equations can be exactly recovered. Also, a form of the equilibrium density distribution function is used to simplify the source term. To validate the proposed model, steady flows of a static droplet and the layered channel flow are first simulated with density ratios up to 1000. Small values of spurious velocities and interfacial tension errors are found in the static droplet test, and improved profiles of velocity are obtained by the present model in simulating channel flows. Then, two cases of unsteady flows, Rayleigh-Taylor instability and droplet splashing on a thin film, are simulated. In the former case, the density ratio of 3 and Reynolds numbers of 256 and 2048 are considered. The interface shapes and spike and bubble positions are in good agreement with the results of previous studies. In the latter case, the droplet spreading radius is found to obey the power law proposed in previous studies for the density ratio of 100 and Reynolds number up to 500.

Generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg's effect.

Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. [Phys. Rev. E 65, 046308 (2002)]. The second-order Beskok and Karniadakis-Civan's correlation [A. Beskok and G. Karniadakis, Microscale Thermophys. Eng. 3, 43 (1999) and F. Civan, Transp. Porous Med. 82, 375 (2010)] is adopted to calculate the apparent permeability based on intrinsic permeability and the Knudsen number. Fluid flow between two parallel plates filled with porous media is simulated to validate the model. Simulations performed in a heterogeneous porous medium with components of different porosity and permeability indicate that Klinkenberg's effect plays a significant role on fluid flow in low-permeability porous media, and it is more pronounced as the Knudsen number increases. Fluid flow in a shale matrix with and without fractures is also studied, and it is found that the fractures greatly enhance the fluid flow and Klinkenberg's effect leads to higher global permeability of the shale matrix.

Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity.

Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.

Pore-scale modeling of multiphase reactive transport with phase transitions and dissolution-precipitation processes in closed systems.

A pore-scale model based on the lattice Boltzmann (LB) method is developed for multiphase reactive transport with phase transitions and dissolution-precipitation processes. The model combines the single-component multiphase Shan-Chen LB model [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)], the mass transport LB model [S. P. Sullivan et al., Chem. Eng. Sci. 60, 3405 (2005)], and the dissolution-precipitation model [Q. Kang et al., J. Geophys. Res. 111, B05203 (2006)]. Care is taken to handle information on computational nodes undergoing solid-liquid or liquid-vapor phase changes to guarantee mass and momentum conservation. A general LB concentration boundary condition is proposed that can handle various concentration boundaries including reactive and moving boundaries with complex geometries. The pore-scale model can capture coupled nonlinear multiple physicochemical processes including multiphase flow with phase separations, mass transport, chemical reactions, dissolution-precipitation processes, and dynamic evolution of the pore geometries. The model is validated using several multiphase flow and reactive transport problems and then used to study the thermal migration of a brine inclusion in a salt crystal. Multiphase reactive transport phenomena with phase transitions between liquid-vapor phases and dissolution-precipitation processes of the salt in the closed inclusion are simulated and the effects of the initial inclusion size and temperature gradient on the thermal migration are investigated.

Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows.

A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions.

Mesoscopic study of the effects of gel concentration and materials on the formation of precipitation patterns.

A mesoscopic model based on the lattice Boltzmann method (LBM) is proposed to simulate the formation of Liesegang precipitation patterns and investigate the effects of gel on the morphology of the precipitates. In this model, nucleation is introduced on the basis of Ostwald's supersaturation theory, and subsequent crystal growth on the precipitate surface is simulated using a crystal growth model by taking into account the heterogeneous reaction on the surface of the precipitate. This model can capture the porous structures of the precipitates and can take into account the effects of the gel concentration and material by adjusting the gel porosity and nucleation threshold. The density of the precipitate nodes in the model is limited. A wide range of precipitation patterns is predicted under different gel concentrations, including regular bands, treelike patterns, and for the first time with numerical models, transition patterns between regular bands and treelike patterns. Both the spacing law and the width law are carefully investigated with different gel concentrations and gel materials, and the obtained α in the width law (w(n) ≈ x(n)(α), where x(n) and w(n) are the position and the width of the nth band, respectively) is in the range of 0.58-0.67, sandwiched by previously predicted ranges.

Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations.

We present an improved three-dimensional 19-velocity lattice Boltzmann model for immisicible binary fluids with variable viscosity and density ratios. This model uses a perturbation step to generate the interfacial tension and a recoloring step to promote phase segregation and maintain surfaces. A generalized perturbation operator is derived using the concept of a continuum surface force together with the constraints of mass and momentum conservation. A theoretical expression for the interfacial tension is determined directly without any additional analysis and assumptions. The recoloring algorithm proposed by Latva-Kokko and Rothman is applied for phase segregation, which minimizes the spurious velocities and removes lattice pinning. This model is first validated against the Laplace law for a stationary bubble. It is found that the interfacial tension is predicted well for density ratios up to 1000. The model is then used to simulate droplet deformation and breakup in simple shear flow. We compute droplet deformation at small capillary numbers in the Stokes regime and find excellent agreement with the theoretical Taylor relation for the segregation parameter ß=0.7. In the limit of creeping flow, droplet breakup occurs at a critical capillary number 0.35

Lattice Boltzmann method on quadtree grids.

A lattice Boltzmann method on nonuniform quadtree grids is proposed. Our method employs the interpolation-supplemented lattice Boltzmann model. The advantages of the quadtree grid are preserved by using linear interpolation instead of quadratic interpolation to complete the streaming step in the lattice Boltzmann method. The back-and-forth error compensation and correction (BFECC) method is used to improve the accuracy, so that the second-order accuracy of the conventional lattice Boltzmann method is maintained. Several numerical cases, including a BFECC streaming test, lid-driven cavity flow, and flow over an asymmetrically placed cylinder in a channel, are carried out to demonstrate the accuracy and efficiency of our method.

Modeling of electrokinetic transport in silica nanofluidic channels.

We present a theoretical and numerical modeling study of the multiphysicochemical process in electrokinetic transport in silica nanochannels. The electrochemical boundary condition is solved by considering both the chemical equilibrium on solid-liquid interfaces and the salt concentration enrichment caused by the double layer interaction. The transport behavior is modeled numerically by solving the governing equations using the lattice Poisson-Boltzmann method. The framework is validated by good agreements with the experimental data for all range of ionic concentrations. The modeling results suggest that when the double layers interact, the bulk salt concentration enrichment results in the saturation of conductances for low ionic concentrations. Both the streaming conductance and the electrical conductance are enhanced by the double layer interaction, and such enhancements diminish when the channel size is larger than 10 times of the Debye length. The streaming conductance increases with pH almost linearly when pH<8, while the electrical conductance increases with pH exponentially.