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

Impact of Wettability on CO2 Dynamic Dissolution in Three-Dimensional Porous Media: Pore-Scale Simulation Using the Lattice Boltzmann Method

Understanding the dissolution behavior of supercritical CO2 (scCO2) in porous media is crucial for efficient CO2 storage. However, the precise modeling of dynamic dissolution behavior at this pore scale remains a huge challenge, and the impact of wettability on this process still needs to be clarified. In this study, the influence of rock wettability on CO2 dynamic dissolution in the three-dimensional porous media is investigated using the lattice Boltzmann method (LBM). The LBM is coupled with scCO2-water two-phase flow, solute transport, and heterogeneous and homogeneous reactions. The size, number, and dissolution pattern of scCO2 bubbles during the dissolution process are observed under strongly water-wet, weakly water-wet, intermediate-wet, and mixed-wet conditions. The CO2(aq) concentration and pH are investigated, followed by a quantitative investigation of the impact of wettability on the specific interface area and the mass transfer coefficient. An empirical relationship between the specific interface area and scCO2 saturation is established. The findings reveal that under weakly water-wet and intermediate-wet conditions, the sizes of scCO2 clusters and monomers are small and mostly distributed at the dead end of the pores. In contrast, under strongly water-wet and mixed-wet conditions, the clusters are larger and interconnected, and distributed in the center of the pore. This results in a greater scCO2-water interface area, consequently enhancing the dissolution rate. Furthermore, a strong linear correlation is observed between scCO2 saturation and specific interface area. It is noted that as the hydrophilicity of the rock increases, the mass transfer coefficient initially rises and then declines.

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge.

Study on the Ways to Improve the CO2-H2O Displacement Efficiency in Heterogeneous Porous Media by Lattice Boltzmann Simulation

To improve the efficiency of CO₂ geological sequestration, it is of great significance to in-depth study the physical mechanism of the immiscible CO₂-water displacement process, where the influential factors can be divided into fluid-fluid and fluid-solid interactions and porous media characteristics. Based on the previous studies of the interfacial tension (capillary number) and viscosity ratio factors, we conduct a thorough study about the effects of fluid-solid interaction (i.e., wettability) and porous media characteristics (i.e., porosity and non-uniformity of granule size) on the two-phase displacement process by constructing porous media with various structural parameters and using a multiphase lattice Boltzmann method. The displacement efficiency of CO₂ is evaluated by the breakthrough time characterizing the displacement speed and the quasi-steady state saturation representing the displacement amount. It is shown that the breakthrough time of CO₂ becomes longer, but the quasi-steady state saturation increases markedly with the increase in CO₂ wettability with the surface, demonstrating an overall improvement of the displacement efficiency. Furthermore, the breakthrough time of CO₂ shortens and the saturation increases significantly with increasing porosity, granule size, and non-uniformity, showing the improvement of the displacement efficiency. Therefore, enhancing the wettability of CO₂ with the surface and selecting reservoirs with greater porosity, larger granule size, and non-uniformity can all contribute to the efficiency improvement of CO₂ geological sequestration.

Comparative investigation of a lattice Boltzmann boundary treatment of multiphase mass transport with heterogeneous chemical reactions

Multiphase reactive transport in porous media is an important component of many natural and engineering processes. In the present study, boundary schemes for the continuum species transport-lattice Boltzmann (CST-LB) mass transport model and the multicomponent pseudopotential model are proposed to simulate heterogeneous chemical reactions in a multiphase system. For the CST-LB model, a lattice-interface-tracking scheme for the heterogeneous chemical reaction boundary is provided. Meanwhile, a local-average virtual density boundary scheme for the multicomponent pseudopotential model is formulated based on the work of Li et al. [Li, Yu, and Luo, Phys. Rev. E 100, 053313 (2019)10.1103/PhysRevE.100.053313]. With these boundary treatments, a numerical implementation is put forward that couples the multiphase fluid flow, interfacial species transport, heterogeneous chemical reactions, and porous matrix structural evolution. A series of comparison benchmark cases are investigated to evaluate the numerical performance for different pseudopotential wetting boundary treatments, and an application case of multiphase dissolution in porous media is conducted to validate the present models' ability to solve complex problems. By applying the present LB models with reasonable boundary treatments, multiphase reactive transport in various natural or engineering scenarios can be simulated accurately.

Numerical Modelling of Reactive Flows through Porous Media

We consider a lattice Boltzmann (LB) model to solve the coupled Navier–Stokes and advection–diffusion equation with reactive boundary conditions at the interface between fluid and solid domains. The reactive boundary condition results in the position of the boundary changing continuously, and so boundary nodes may be partially filled with fluid at any instant. We develop the LB boundary conditions for both the velocity and concentration fields in the presence of partially filled boundary nodes and then validate this algorithm on some test cases—the Stefan problem for diffusion-dominated dissolution and kinetic-dominated dissolution. It is shown that the developed model agrees well with analytic results, so that they can be used for more general boundaries of arbitrary shape. Numerical simulations in three dimensions are then carried out on demonstration problems at various Peclet numbers to elucidate the transport mechanisms and their influence on solid grain dissolution.

Numerical Studies on Cellulose Hydrolysis in Organic-Liquid-Solid Phase Systems with a Liquid Membrane Catalysis Model

The catalytic hydrolysis of cellulose to produce 5-hydroxymethylfurfural (HMF) is a powerful means of biomass resources. The current efficient hydrolysis of cellulose to obtain HMF is dominated by multiphase reaction systems. However, there is still a lack of studies on the synergistic mechanisms and component transport between the various processes of cellulose hydrolysis in a complex multiphase system. In this paper, a liquid membrane catalytic model was developed to simulate the hydrolysis of cellulose and its further reactions, including the adsorption of the liquid membrane on cellulose particles, the consumption of cellulose solid particles, the complex chemical reactions in the liquid membrane, and the transfer of HMF at the phase interface. The simulations show the synergistic effect between cellulose hydrolysis and multiphase mass transfer. We defined an indicator () to characterize the sensitivity of HMF yield to the initial liquid membrane thickness at different reaction stages. decreased gradually when the glucose conversion increased from 0 to 80%, and increased with the thickening of the initial liquid membrane thickness. It was shown that the thickening of the initial liquid membrane thickness promoted the HMF yield under the same glucose conversion. In summary, our results reveal the mechanism of the interaction between multiple physicochemical processes of the cellulose liquid membrane reaction system.

Lattice Boltzmann modeling of interfacial mass transfer in a multiphase system

In the present study, a numerical model based on the lattice Boltzmann method (LBM) is proposed to simulate multiphase mass transfer, referred to as the CST-LB model. This model introduced continuum species transfer (CST) formulation by an additional collision term to model the mass transfer across the multiphase interface. The boundary condition treatment of this model is also discussed. In order to verify the applicability, the CST-LB model is combined with the pseudopotential multiphase model to simulate a series of benchmark cases, including concentration jump near the interface, gas dissolution in a closed system, species transport during drainage in a capillary tube, and multiphase species transport in the porous media. This CST-LB model can also be coupled with other multiphase LBMs since the model depends on the phase fraction field, which is not explicitly limited to specified multiphase models.

Mixed bounce-back boundary scheme of the general propagation lattice Boltzmann method for advection-diffusion equations

In this work, a mixed bounce-back boundary scheme of general propagation lattice Boltzmann (GPLB) model is proposed for isotropic advection-diffusion equations (ADEs) with Robin boundary condition, and a detailed asymptotic analysis is also conducted to show that the present boundary scheme for the straight walls has a second-order accuracy in space. In addition, several numerical examples, including the Helmholtz equation in a square domain, the diffusion equation with sinusoidal concentration gradient, one-dimensional transient ADE with Robin boundary and an ADE with a source term, are also considered. The results indicate that the numerical solutions agree well with the analytical ones, and the convergence rate is close to 2.0. Furthermore, through adjusting the two parameters in the GPLB model properly, the present boundary scheme can be more accurate than some existing lattice Boltzmann boundary schemes.

Numerical Study of Droplet Dynamics on a Solid Surface with Insoluble Surfactants

Surfactants are widely used in many industrial processes, where the presence of surfactants not only reduces the interfacial tension between fluids but also alters the wetting properties of solid surfaces. To understand how the surfactants influence the droplet motion on a solid surface, a hybrid method for interfacial flows with insoluble surfactants and contact-line dynamics is developed. This method solves immiscible two-phase flows through a lattice Boltzmann color-gradient model and simultaneously solves the convection-diffusion equation for surfactant concentration through a finite difference method. In addition, a dynamic contact angle formulation that describes the dependence of the local contact angle on the surfactant concentration is derived, and the resulting contact angle is enforced by a geometrical wetting condition. Our method is first used to simulate static contact angles for a droplet resting on a solid surface, and the results show that the presence of surfactants can significantly modify surface wettability, especially when the surface is more hydrophilic or more hydrophobic. This is then applied to simulate a surfactant-laden droplet moving on a substrate subject to a linear shear flow for varying effective capillary number ( Ca_e), Reynolds number ( Re), and surface wettability, where the results are often compared with those of a clean droplet. For varying Ca_e, the simulations are conducted by considering a neutral surface. At low values of Ca_e, the droplet eventually reaches a steady deformation and moves at a constant velocity. In either a clean or surfactant-laden case, the moving velocity of the droplet linearly increases with the moving wall velocity, but the slope is always higher (i.e., the droplet moves faster) in the surfactant-laden case where the droplet exhibits a bigger deformation. When Ca_e is increased beyond a critical value ( Ca_e,c), the droplet breakup would happen. The presence of surfactants is found to decrease the value of Ca_e,c, but it shows a non-monotonic effect on the droplet breakup. An increase in Re is able to increase not only droplet deformation but also surfactant dilution. The role of surfactants in the droplet behavior is found to greatly depend upon the surface wettability. For a hydrophilic surface, the presence of surfactants can decrease the wetting length and enables the droplet to reach a steady state faster; while for a hydrophobic surface, it increases the wetting length and delays the departure of the droplet from the solid surface.

Separate-phase model and its lattice Boltzmann algorithm for liquid-vapor two-phase flows in porous media

In this article, we formulate a set of the separate-phase governing equations at the representative-elementary-volume scale and develop its double-distribution function lattice Boltzmann (LB) algorithm to describe liquid-vapor two-phase flows with or without phase change in porous media. Different from those previous studies, the mathematical description in this article involves the Darcy force, viscous force, and pressure gradient, and the resulting LB simulations can well describe two-phase flows and mass transfer throughout porous media under the compounding effects of these forces. The LB algorithm was validated by simulating single-phase flows in porous media. Its results are in good agreement with those available analytical solutions. We also applied it to model water flows through a semi-infinite porous region bounded by a heated solid wall, where liquid-vapor phase change takes place. The numerical simulations recover the previous results in the limit of the zero Darcy number. Significantly, it reveals much richer two-phase flow and mass transfer characteristics in porous media adjacent to solid walls. The separate-phase model and its lattice Boltzmann algorithm in this article are effective means to gain more profound and clearer understandings of complex two-phase transport processes in a porous system.

Numerically accelerated pore-scale equilibrium dissolution

Simulation of dissolution processes with a pore-scale reactive transport model increases insight in coupled chemical-physical-transport processes. However, modelling of dissolution process often requires a large number of time steps especially when the buffering capacity of solid phases is high. In this work we analyze the interplay between solid buffering on one hand and transport on the other. Based on this analysis we propose an approach to reduce the number of required time steps for simulating equilibrium dissolution processes. The underlying idea is that the number of time step iterations can be reduced if the buffering is sufficient to bring the system to a steady state, i.e. that the concentration field around solid is time-invariant. If this condition is satisfied, then it is possible to reduce the physical (and thus also computational) time by adjusting the chemical system appropriately. First we derived a dimensionless value - called buffering number - to determine under which conditions reduction in time can be made. Several examples illustrate that below a certain buffering number, the physical time can be reduced without significant effect on result (e.g. dissolution front) as long as the solid volume fraction is sufficient. This means that for a given solid-liquid system, the calculation time can be reduced either by the reduction of mass in solid or by the increase of equilibrium concentration (solubility). We also show that the calculation time for calcium leaching in cementitious systems can be reduced by 50 times with a negligible error.

Liquid membrane catalytic model of hydrolyzing cellulose into 5-hydroxymethylfurfural based on the lattice Boltzmann method

Conversion of cellulose to 5-hydroxymethylfurfural (HMF) is an important means of biomass utilization.

Prediction of the moments in advection-diffusion lattice Boltzmann method. II. Attenuation of the boundary layers via double-Λ bounce-back flux scheme

Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order to vanish or attenuate the disparity of the modeled transport coefficients with the equilibrium weights without any modification of the BB rule, we propose to use the two-relaxation-times collision operator with free-tunable product of two eigenfunctions Λ. Two different values Λ_{v} and Λ_{b} are assigned for bulk and boundary nodes, respectively. The rationale behind this is that Λ_{v} is adjustable for stability, accuracy, or other purposes, while the corresponding Λ_{b}(Λ_{v}) controls the primary accommodation effects. Two distinguished but similar functional relations Λ_{b}(Λ_{v}) are constructed analytically: they preserve advection velocity in parabolic profile, exactly in the two-dimensional channel and very accurately in a three-dimensional cylindrical capillary. For any velocity-weight stencil, the (local) double-Λ BB scheme produces quasi-identical solutions with the (nonlocal) specular-forward reflection for first four moments in a channel. In a capillary, this strategy allows for the accurate modeling of the Taylor-dispersion and non-Gaussian effects. As illustrative example, it is shown that in the flow around a circular obstacle, the double-Λ scheme may also vanish the dependency of mean velocity on the velocity weight; the required value for Λ_{b}(Λ_{v}) can be identified in a few bisection iterations in given geometry. A positive solution for Λ_{b}(Λ_{v}) may not exist in pure diffusion, but a sufficiently small value of Λ_{b} significantly reduces the disparity in diffusion coefficient with the mass weight in ducts and in the presence of rectangular obstacles. Although Λ_{b} also controls the effective position of straight or curved boundaries, the double-Λ scheme deals with the lower-order effects. Its idea and construction may help understanding and amelioration of the anomalous, zero- and first-order behavior of the macroscopic solution in the presence of the bulk and boundary or interface discontinuities, commonly found in multiphase flow and heterogeneous transport.

Influence of phase connectivity on the relationship among capillary pressure, fluid saturation, and interfacial area in two-fluid-phase porous medium systems

Multiphase flows in porous medium systems are typically modeled at the macroscale by applying the principles of continuum mechanics to develop models that describe the behavior of averaged quantities, such as fluid pressure and saturation. These models require closure relations to produce solvable forms. One of these required closure relations is an expression relating the capillary pressure to fluid saturation and, in some cases, other topological invariants such as interfacial area and the Euler characteristic (or average Gaussian curvature). The forms that are used in traditional models, which typically consider only the relationship between capillary pressure and saturation, are hysteretic. An unresolved question is whether the inclusion of additional morphological and topological measures can lead to a nonhysteretic closure relation. Relying on the lattice Boltzmann (LB) method, we develop an approach to investigate equilibrium states for a two-fluid-phase porous medium system, which includes disconnected nonwetting phase features. A set of simulations are performed within a random close pack of 1964 spheres to produce a total of 42 908 distinct equilibrium configurations. This information is evaluated using generalized additive models to quantitatively assess the degree to which functional relationships can explain the behavior of the equilibrium data. The variance of various model estimates is computed, and we conclude that, except for the limiting behavior close to a single fluid regime, capillary pressure can be expressed as a deterministic and nonhysteretic function of fluid saturation, interfacial area between the fluid phases, and the Euler characteristic. To our knowledge, this work is unique in the methods employed, the size of the data set, the resolution in space and time, the true equilibrium nature of the data, the parametrizations investigated, and the broad set of functions examined. The conclusion of essentially nonhysteretic behavior provides support for an evolving class of two-fluid-phase flow in porous medium systems models.

Lattice Boltzmann method for convection-diffusion equations with general interfacial conditions

In this work, we propose an interfacial scheme accompanying the lattice Boltzmann method for convection-diffusion equations with general interfacial conditions, including conjugate conditions with or without jumps in heat and mass transfer, continuity of macroscopic variables and normal fluxes in ion diffusion in porous media with different porosity, and the Kapitza resistance in heat transfer. The construction of this scheme is based on our boundary schemes [Huang and Yong, J. Comput. Phys. 300, 70 (2015)JCTPAH0021-999110.1016/j.jcp.2015.07.045] for Robin boundary conditions on straight or curved boundaries. It gives second-order accuracy for straight interfaces and first-order accuracy for curved ones. In addition, the new scheme inherits the advantage of the boundary schemes in which only the current lattice nodes are involved. Such an interfacial scheme is highly desirable for problems with complex geometries or in porous media. The interfacial scheme is numerically validated with several examples. The results show the utility of the constructed scheme and very well support our theoretical predications.

Discrete effect on the halfway bounce-back boundary condition of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations

In this paper, we will focus on the multiple-relaxation-time (MRT) lattice Boltzmann model for two-dimensional convection-diffusion equations (CDEs), and analyze the discrete effect on the halfway bounce-back (HBB) boundary condition (or sometimes called bounce-back boundary condition) of the MRT model where three different discrete velocity models are considered. We first present a theoretical analysis on the discrete effect of the HBB boundary condition for the simple problems with a parabolic distribution in the x or y direction, and a numerical slip proportional to the second-order of lattice spacing is observed at the boundary, which means that the MRT model has a second-order convergence rate in space. The theoretical analysis also shows that the numerical slip can be eliminated in the MRT model through tuning the free relaxation parameter corresponding to the second-order moment, while it cannot be removed in the single-relaxation-time model or the Bhatnagar-Gross-Krook model unless the relaxation parameter related to the diffusion coefficient is set to be a special value. We then perform some simulations to confirm our theoretical results, and find that the numerical results are consistent with our theoretical analysis. Finally, we would also like to point out the present analysis can be extended to other boundary conditions of lattice Boltzmann models for CDEs.

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.

Changes in pore geometry and relative permeability caused by carbonate precipitation in porous media

The CO_{2} behavior within the reservoirs of carbon capture and storage projects is usually predicted from large-scale simulations of the reservoir. A key parameter in reservoir simulation is relative permeability. However, mineral precipitation alters the pore structure over time, and leads correspondingly to permeability changing with time. In this study, we numerically investigate the influence of carbonate precipitation on relative permeability during CO_{2} storage. The pore spaces in rock samples were extracted by high-resolution microcomputed tomography (CT) scanned images. The fluid velocity field within the three-dimensional pore spaces was calculated by the lattice Boltzmann method, while reactive transport with calcite deposition was modeled by an advection-reaction formulation solved by the finite volume method. To increase the computational efficiency and reduce the processing time, we adopted a graphics processing unit parallel computing technique. The relative permeability of the sample rock was then calculated by a highly optimized two-phase lattice Boltzmann model. We also proposed two pore clogging models. In the first model, the clogging processes are modeled by transforming fluid nodes to solid nodes based on their precipitated mass level. In the second model, the porosity is artificially reduced by adjusting the gray scale threshold of the CT images. The developed method accurately simulates the mineralization process observed in laboratory experiment. Precipitation-induced evolution of pore structure significantly influenced the absolute permeability. The relative permeability, however, was much more influenced by pore reduction in the nonwetting phase than in the wetting phase. The output of the structural changes in pore geometry by this model could be input to CO_{2} reservoir simulators to investigate the outcome of sequestered CO_{2}.

Boundary conditions for surface reactions in lattice Boltzmann simulations

A surface reaction boundary condition in multicomponent lattice Boltzmann simulations is developed. The method is applied to a test case with nonlinear reaction rates and nonlinear density profiles. The results are compared to the corresponding analytical solution, which shows that the error of the method scales with the square of the lattice spacing.

Single-relaxation-time lattice Boltzmann scheme for advection-diffusion problems with large diffusion-coefficient heterogeneities and high-advection transport

The paper presents an approach that extends the flexibility of the standard lattice Boltzmann single relaxation time scheme in terms of spatial variation of dissipative terms (e.g., diffusion coefficient) and stability for high Péclet mass transfer problems. Spatial variability of diffusion coefficient in SRT is typically accommodated through the variation of relaxation time during the collision step. This method is effective but cannot deal with large diffusion coefficient variations, which can span over several orders of magnitude in some natural systems. The approach explores an alternative way of dealing with large diffusion coefficient variations in advection-diffusion transport systems by introducing so-called diffusion velocity. The diffusion velocity is essentially an additional convective term that replaces variations in diffusion coefficients vis-à-vis a chosen reference diffusion coefficient which defines the simulation time step. Special attention is paid to the main idea behind the diffusion velocity formulation and its implementation into the lattice Boltzmann framework. Finally, the performance, stability, and accuracy of the diffusion velocity formulation are discussed via several advection-diffusion transport benchmark examples. These examples demonstrate improved stability and flexibility of the proposed scheme with marginal consequences on the numerical performance.

Improved treatments for general boundary conditions in the lattice Boltzmann method for convection-diffusion and heat transfer processes

In spite of the increasing applications of the lattice Boltzmann method (LBM) in simulating various flow and transport systems in recent years, complex boundary conditions for the convection-diffusion and heat transfer processes in LBM have not been well addressed. In this paper, we propose an improved bounce-back method by using the midpoint concentration value to modify the bounced-back density distribution for LBM simulations of the concentration field. An accurate finite-difference scheme in the normal boundary direction has also been introduced for gradient boundary conditions. Compared with existing boundary methods, our method has a simple algorithm and can easily deal with boundaries with general geometries, motions, and surface conditions (the Dirichlet, Neumann, and mixed conditions). Carefully designed simulations are performed to examine the capacity and accuracy of this proposed boundary method. Simulation results are compared with those from theory and a representative boundary method, and an improved performance is observed. We have also simulated the effect of reference velocity on global accuracy to examine the performance of our model in preserving the fundamental Galilean invariance. These boundary treatments for concentration boundary conditions can be readily applied to other processes such as heat transfer systems.