Multiphase lattice Boltzmann simulations for porous media applications -- a review (1404.7523v2)

Abstract: Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.

• The paper presents an extensive review of multiphase LBM models, highlighting their capabilities and limitations in simulating porous media flows.
• It details diverse interface models, including color gradient, inter-particle potential, and free-energy approaches, and evaluates their effectiveness for interfacial dynamics.
• The paper discusses advanced boundary condition strategies and computational implementations that enhance simulation accuracy and efficiency in porous media applications.

Overview of "Multiphase Lattice Boltzmann Simulations for Porous Media Applications"

The paper "Multiphase lattice Boltzmann simulations for porous media applications" by Liu et al. provides an exhaustive review of lattice Boltzmann methods (LBM) tailored for the simulation of multiphase flows in porous media. Over recent decades, LBM has become increasingly prominent due to its capacity to efficiently handle complex geometries and intricate flow dynamics at the pore-scale level in porous media. This paper reviews the different interface models used within LBM, discussing the strengths and weaknesses of each, while also exploring the computational intricacies that underpin these models.

Lattice Boltzmann Method (LBM) for Porous Media

1. LBM Fundamentals: The LBM is grounded in kinetic theory and utilizes a lattice structure to simulate fluid flow through complex geometrical configurations. Rather than solving Navier-Stokes equations directly, LBM computes fluid dynamics by tracking the evolution of the particle distribution function, which calculates macroscopic properties via moment integration. This approach inherently supports parallel computation, making it suitable for simulations in porous media with complex interconnectivity and morphology.
2. Multiphase Flow and Models: The paper offers an extensive overview of five primary multiphase models within the LBM framework:
   • Color Gradient Model: Originating from lattice-gas models, this approach distinguishes between different fluid phases using distinct color functions, facilitating the modeling of interfacial tension and wettability effects.
   • Inter-Particle Potential Model: Introduces forces between neighboring particles, allowing for the simulation of fluids that interact with different wetting properties.
   • Free-Energy Model: Utilizes a free-energy functional to ensure thermodynamic consistency, simulating interface dynamics without explicitly tracking the interface.
   • Mean-Field Theory Model: Accounts for molecular interactions on a mean-field level, thus facilitating simulations with phase segregation and interfacial tension.
   • Stabilized Diffuse-Interface Model: Capable of handling large density ratios with enhanced numerics to minimize spurious currents, suitable for high-fidelity simulations of multiphase flows.
3. Boundary Conditions and Implementation: The adaption of LBM to porous media requires careful attention to boundary conditions and implementation strategies:
   • Boundary Conditions: The paper discusses several strategies for handling fluid-solid interactions and multiphase boundaries, such as bounce-back, fluid-solid interaction tuning, and surface wettability treatment.
   • Numerical Implementation: Different parallel computing approaches—ranging from shared-memory architectures to GPUs—are evaluated for their effectiveness in handling the computational demands of LBM, especially as applied to large-scale porous media simulations.

Practical and Theoretical Implications

The review highlights the significant capabilities of LBM in capturing detailed pore-scale phenomena, enhancing our understanding of multiphase flow dynamics in porous structures. Practically, this advances applications such as enhanced oil recovery, CO2 sequestration, fuel cell design, and groundwater contamination prediction. Theoretically, the diverse array of models suggests rich avenues for refining simulation fidelity and addressing computational bottlenecks.

Future Directions

The paper suggests that future developments in LBM for porous media should aim at improving computational efficiency and accuracy, particularly through adaptive mesh refinement and more robust treatment of flow physics at material interfaces. Moreover, the integration of machine learning algorithms could revolutionize the predictive capability of LBM simulations, potentially providing real-time insights into fluid behaviors within increasingly complex porous structures.

This detailed review by Liu et al. lays foundational knowledge for researchers engaged in high-performance computational modeling of multiphase flows, with implications that stretch across both academic and industrial applications.