Lattice Boltzmann Methods for Particulate Flows with Medical and Technical Applications

Particulate flows appear in numerous medical and technical applications. The main aim of this thesis is to contribute models and numerical schemes towards an accurate as well as efficient simulation of a huge number of arbitrarily shaped particles. We therefore develop holistic mesoscopic models and simulation approaches using the Lattice Boltzmann Method, that on massively parallel machines efficiently solve a variety of problems of particulate flows

( )Pore-scale dissolution mechanisms in calcite-CO2-brine systems: The impact of non-linear reaction kinetics and coupled ion transport

We simulate two sets of dissolution experiments in which CO2-saturated solutions are injected into calcite formations. We explore the impact of non-linear reaction kinetics and charge-coupled ion transport in systems representing different levels of flow and mineralogical complexity. First, we flow CO2-saturated water and brine through cylindrical channels drilled through solid calcite cores and compare directly with experimental dissolution rates. We find that simulations using a linear saturation model match experimental results much better than the batch-reactor-derived non-linear saturation model. The use of a coupled diffusion model causes only a very small increase in the overall dissolution rate compared to a single diffusion coefficient, due to the increase in transport rates of reaction products, particularly the highly charged Ca2+ ion. We also determine the relative importance of the two calcite dissolution pathways, with H+ and H2CO3, and conclude that the H2CO3 – calcite reaction is by far the more dominant, in contrast with common assumptions in the literature. Then, we compare to the experiments of Menke et al. (2015) in which CO2-saturated brine was injected into a microporous Ketton carbonate, and compare dissolution rates over time. We find that including non-linear saturation behaviour markedly changes the simulated dissolution rate, by up to a factor of 0.7 in the case of the experimentally derived saturation model of Anabaraonye (2017), however neither case matches the experimental result which is several times slower than the simulation. Including the effects of coupled ion transport lead to virtually no change in overall dissolution rate due to the convection dominated behaviour. The model also shows differences in the trend of the dissolution rate over time observed in Menke et al, with an approximately linear relationship with time compared to the experimental square-root dependence on time. We conclude that the geochemical model may need to include other effects such as dissolution inside microporous regions

Development of lattice Boltzmann CO2 dissolution model

In this study, a novel lattice Boltzmann model (LBM) of CO2 dissolution at porous scale is proposed and developed to predict the CO2 dispersion and dissolution in geo-formations. The developed LBM dissolution model consists of an interfacial momentum interaction model, a mass transfer model and a convection (advection) model. Shen-Chen’s pseudopotential model using Equation of State (EOS) of real fluids is tested for momentum interaction model. It is found that a sharp interface can be maintained by optimizing the interaction strengths of two fluids with minimum numerical diffusion in the interfacial momentum interaction model. This makes it possible to model physical diffusion and interfacial tension individually. A new diffusion force, describing the particle diffusion driving by chemical potential at given solubility, is proposed for mass transfer model by applying the interparticle interaction pseudopotential concept. The dissolution is governed by coupling mechanism of diffusion and convection. The interface between the solute of CO2 and solvent water is monitored by the solubility, which changes and indicates the moving of interface as CO2 dissolving. The solution is considered as the mixture of dissolved CO2 and water. Instead of using an additional Lattice that is requested by the existed LBM, the further dispersion of dissolved solutes is attached to the Lattice of water, by which the cost of computing memory size and time is significantly reduced. The developed LBM dissolution model is calibrated by the data from Lab experiment of dissolution of CO2 droplet in water at a state of CO2 geological storage about 1000m depth. The calibration is made by comparison of simulation results with the data, in terms of the shrinking rate of CO2 droplet and the concentration distribution of dissolved CO2 in the solution layer. As the whole, the numerical predictions are well agreement with those of lab experiment. The developed model is then applied to investigate the mechanism of dispersion and dissolution of CO2 droplet in channels at pore scale, in terms of the effects of the Eo number, channel width and channel tilt angle. It is found under the state at 1000m depth that it is difficult for a dissolving CO2 droplet, unlike that of an immiscible droplet, to reach to a ’terminal velocity’. Because of the shrinking, dissolving CO2 droplets accelerate from a quiescent state to a maximum velocity and then decelerate in the channels. The ratio of droplet diameter (Do) to channel width (Lx), M=Do/Lx, and the inclination are the parameters that significantly affect the dynamics of dissolving CO2 droplets. The smaller the channel width or the tilt angle of the pores of the geoformation, the slower of stored CO2 can penetrate vertically and dissolve out. While, as the channel width increases to provide enough space, M<1, the shrinking rate is independent of the channel width and wobbling of droplets is observed at the region with the Re number of 300-600 and the Eo number of 20-43. The interactions of droplets in the channels (M=1 and M=0.3) are investigated by simulating of a pair of droplets dispersion and dissolution, with an initial distance of 4.5 times of droplet diameter. Comparison is made to that of single droplet in terms of the rising velocity and shrinking rate. It is found that the shrinking rate of the upper droplet is larger than that of the following droplet when the following droplet moves into the solution field of the upper droplet. The following droplet rises, when M=1 and M=0.3, faster than that of the upper droplet and also than that of the single droplet under the same conditions. The coalescence of two droplets is observed in the channel at M=0.3, which is due to the action of tail vortex of the upper droplet on the following droplet. The following droplet accelerates at a different wobbling frequency with that of the upper droplet. As the implication in model development, in term of numerical stability, the so called ’non-linear implicit trapezoidal lattice Boltzmann scheme’, proposed by Nourgaliev et al. [1], is re-examined in order to simulate the large density ratio of two-fluid flows. It is found from the re-derivation that the scheme is a linear scheme in nature. Therefore, the re-derived scheme is more efficient and the CPU time can be reduced. The test cases of the simulation of a steady state droplet using SC EOS show that re-derived scheme improves the numerical stability by reducing the spurious velocity about 21.7% and extending the density ratio 53.4% as relaxation time of the improved scheme is 0.25, in comparison to those from the traditional explicit scheme. Meanwhile, in the multicomponent simulation, with the same density distribution at steady state, the improved scheme reduces both the magnitude and spreading region of the spurious velocity. The spurious velocity of the improved method reduces approximate 4 times than that of the explicit scheme

Effect of Nano-Pore Wall Confinements on Non-Ideal Gas Dynamics in Organic Rich Shale Reservoirs

The advancements in horizontal well drilling and multistage hydraulic fracturing technology enabled us to unfold major sources of hydrocarbon trapped in ultra-tight formations such as tight sands and organic rich shales. Tremendous gas production from these reservoirs has transformed today\u27s energy landscape. To effectively optimize the hydrocarbon production from these ultra-tight formations, it is essential to study and model the fluid transport and storage sealed in multiscale pore structure of these formations, i.e. micro-, meso- and macro-pores. In shale gas reservoirs, Kerogen, the finely dispersed organic nano-porous material with an average pore size of less than 10 nm holds bulk of the total gas in place (GIP) in an adsorbed state. The molecular level interactions between fluid-fluid and fluid-solid organic pore walls govern the transport and storage in these organic nano-pores. Among different methods used to model gas dynamics in organic nano-pores such as the multi-continuum, molecular dynamics and Monte Carlo, the lattice Boltzmann method (LBM) is a more effective method with much less computational cost relative to other techniques. This is due to the applicability of this technique in wide range of flow regimes and ease of handling complex boundary conditions such as incorporation of the molecular interactions in porous media.;The objective of this research is to develop a two-dimensional LBM of organic rich shales that can be used to quantify the effect of organic pore wall confinement on non-ideal gas flow and storage in organic nano-pores of the shale reservoirs. This method incorporates the involvement of molecular forces between fluid particles such as, adsorptive and cohesive forces. Using the Langmuir-slip boundary condition at capillary walls, slippage of free gas molecules and surface transport of adsorbed molecules are studied. This effect is investigated in a large range of Knudsen numbers from continuum flow to transition flow regime with varying capillary width sizes from 100 nm to 5 nm.;Simulation results concentrates on the molecular phenomena like- adsorptive/cohesive forces, and the kinetic energy of the fluid molecules at different pressures, and reservoir temperatures. The LBM model results displays a clear indication that the gas transport in the capillary tube is depends on the pore width size. A critical Knudsen number exists with changing reservoir conditions, where the anticipated fluid velocity profile in organic nano-pores alters showing higher flow rate as capillary widths reduces due to the underlying effect of molecular phenomena of double slippage and wall confinement, introduced earlier by Fathi et al. These results are compared with traditional continuum Hagen-Poiseuille law, Klinkenberg slip theory, and recent modified version of Klinkenberg slip flow equation. This work is not only important for the advancement of shale gas flow simulator, but also for organic rich shale characterization

TURBULENT TRANSITION SIMULATION AND PARTICULATE CAPTURE MODELING WITH AN INCOMPRESSIBLE LATTICE BOLTZMANN METHOD

Derivation of an unambiguous incompressible form of the lattice Boltzmann equation is pursued in this dissertation. Further, parallelized implementation in developing application areas is researched. In order to achieve a unique incompressible form which clarifies the algorithm implementation, appropriate ansatzes are utilized. Through the Chapman-Enskog expansion, the exact incompressible Navier-Stokes equations are recovered. In initial studies, fundamental 2D and 3D canonical simulations are used to evaluate the validity and application, and test the required boundary condition modifications. Several unique advantages over the standard equation and alternative forms found in literature are found, including faster convergence, greater stability, and higher fidelity for relevant flows. Direct numerical simulation and large eddy simulation of transitional and chaotic flows are one application area explored with the derived incompressible form. A multiple relaxation time derivation is performed and implemented in a 2D cavity (direct simulation) and a 3D cavity (large eddy simulation). The Kolmogorov length scale, a function of Reynolds number, determines grid resolution in the 2D case. Comparison is made to the extensive literature on laminar flows and the Hopf bifurcation, and final transition to chaos is predicted. Steady and statistical properties in all cases are in good agreement with literature. In the 3D case the relatively new Vreman subgrid model provides eddy viscosity modeling. By comparing the center plane to the direct numerical simulation case, both steady and unsteady flows are found to be in good agreement, with a coarse grid, including prediction of the Hopf bifurcation. Multiphysics pore scale flow is the other main application researched here. In order to provide the substrate geometry, a straightforward algorithm is developed to generate random blockages producing realistic porosities and passages. Combined with advection-diffusion equations for conjugate heat transfer and soot particle transport, critical diesel particulate filtration phenomena are simulated. To introduce additional fidelity, a model is added which accounts for deposition caused by a variety of molecular and atomic forces. Detailed conclusions are presented to lay the groundwork for future extensions and improvements. Predominantly, higher lattice velocity large eddy simulation, improved parallelization, and filter regeneration

Extending a Gray Lattice Boltzmann Model for Simulating Fluid Flow in Multi-Scale Porous Media

Abstract A gray lattice Boltzmann model has previously been developed by the authors of this article to simulate fluid flow in porous media that contain both resolved pores and grains as well as aggregates of unresolved smaller pores and grains. In this model, a single parameter is introduced to prescribe the amount of fluid to be bounced back at each aggregate cell. This model has been shown to recover Darcy-Brinkman flow but with effective viscosity and permeability correlated through the model parameter. In this paper, we prove that the model parameter relates to the fraction of the solid phase of a sub-pore system for a specific set of bounce-back conditions. We introduce an additional parameter to the model, and this enables flow simulation in which cases with variable effective viscosity and permeability can be specified by selecting the two parameters independently. We verify and validate the model for layered channel cases and mathematically analyze fluid momentum and energy losses for the single- and two-parameter models to explain the roles of the parameters in their conservation. We introduce a strategy to upgrade our model to an isotropic version. We discuss the fundamental differences between our model and the Brinkman body-force LBM scheme

A simplified mesoscale 3D model for characterizing fibrinolysis under flow conditions

One of the routine clinical treatments to eliminate ischemic stroke thrombi is injecting a biochemical product into the patient’s bloodstream, which breaks down the thrombi’s fibrin fibers: intravenous or intravascular thrombolysis. However, this procedure is not without risk for the patient; the worst circumstances can cause a brain hemorrhage or embolism that can be fatal. Improvement in patient management drastically reduced these risks, and patients who benefited from thrombolysis soon after the onset of the stroke have a significantly better 3-month prognosis, but treatment success is highly variable. The causes of this variability remain unclear, and it is likely that some fundamental aspects still require thorough investigations. For that reason, we conducted in vitro flow-driven fibrinolysis experiments to study pure fibrin thrombi breakdown in controlled conditions and observed that the lysis front evolved non-linearly in time. To understand these results, we developed an analytical 1D lysis model in which the thrombus is considered a porous medium. The lytic cascade is reduced to a second-order reaction involving fibrin and a surrogate pro-fibrinolytic agent. The model was able to reproduce the observed lysis evolution under the assumptions of constant fluid velocity and lysis occurring only at the front. For adding complexity, such as clot heterogeneity or complex flow conditions, we propose a 3-dimensional mesoscopic numerical model of blood flow and fibrinolysis, which validates the analytical model’s results. Such a numerical model could help us better understand the spatial evolution of the thrombi breakdown, extract the most relevant physiological parameters to lysis efficiency, and possibly explain the failure of the clinical treatment. These findings suggest that even though real-world fibrinolysis is a complex biological process, a simplified model can recover the main features of lysis evolution.</p

Homogenized lattice Boltzmann model for simulating multi-phase flows in heterogeneous porous media

A homogenization approach for the simulation of multi-phase flows in heterogeneous porous media is presented. It is based on the lattice Boltzmann method and combines the grayscale with the multi-component Shan–Chen method. Thus, it mimics fluid–fluid and solid–fluid interactions also within pores that are smaller than the numerical discretization. The model is successfully tested for a broad variety of single- and two-phase flow problems. Additionally, its application to multi-scale and multi-phase flow problems in porous media is demonstrated using the electrolyte filling process of realistic 3D lithium-ion battery electrode microstructures as an example. The approach presented here shows advantages over comparable methods from literature. The interfacial tension and wetting conditions are independent and not affected by the homogenization. Moreover, all physical properties studied here are continuous even across interfaces of porous media. The method is consistent with the original multi-component Shan–Chen method (MCSC). It is as stable as the MCSC, easy to implement, and can be applied to many research fields, especially where multi-phase fluid flow occurs in heterogeneous and multi-scale porous media