Thermodynamic consistency of a pseudopotential lattice Boltzmann fluid with interface curvature

A Review of the Study of Fluid Phase Behavior at the Confined Scale of Shale Reservoirs: A Theoretical and Experimental Perspective

The fluids within the pores of shale reservoirs are influenced by nanoscale confinement effects, causing the phase behavior and flow characteristics of the oil and gas systems to deviate from bulk properties. Consequently, conventional phase theory and experimental methodologies are inadequate for studying such confined fluids. The phase characteristics and underlying microscopic mechanisms of oil and gas within confined spaces remain unclear, posing a substantial barrier to the efficient and rational development of shale reservoirs. This paper reviews current theoretical and experimental research on fluid phase behavior under nanoscale confinement in shale reservoirs. It provides a comprehensive discussion of four categories of research techniques, including mathematical models, numerical simulations, indirect measurement experiments, and direct observation experiments, detailing their principles, primary applications, and advantages and limitations. Furthermore, it compares the relationships and differences among these techniques and offers an outlook on the future development of research into the shale fluid phase behavior. Analyses indicate that various research methods can be employed to investigate the phase behavior of fluids at the confined scale of shale reservoirs. However, due to the influence of factors such as research techniques, target materials, and experimental conditions, there is no consensus on the critical pore size responsible for confinement effects, the shift in the critical properties, and the variations in bubble and dew points. The current research adopts the research idea of "theoretical exploration through mathematical modeling, mechanism revelation via numerical simulation, regularity reflection through indirect measurement experiments, and phenomenon demonstration through direct observation experiments" and forms a relatively complete research system of the confined fluid phase behavior of shale reservoir. However, the system still has some limitations and challenges, necessitating further optimization and refinement in future research.

Lattice Boltzmann simulation of deformable fluid-filled bodies: progress and perspectives

With the rapid development of studies involving droplet microfluidics, drug delivery, cell detection, and microparticle synthesis, among others, many scientists have invested significant efforts to model the flow of these fluid-filled bodies. Motivated by the intricate coupling between hydrodynamics and the interactions of fluid-filled bodies, several methods have been developed. The objective of this review is to present a compact foundation of the methods used in the literature in the context of lattice Boltzmann methods. For hydrodynamics, we focus on the lattice Boltzmann method due to its specific ability to treat time- and spatial-dependent boundary conditions and to incorporate new physical models in a computationally efficient way. We split the existing methods into two groups with regard to the interfacial boundary: fluid-structure and fluid-fluid methods. The fluid-structure methods are characterised by the coupling between fluid dynamics and mechanics of the flowing body, often used in applications involving membranes and similar flexible solid boundaries. We further divide fluid-structure-based methods into two subcategories, those which treat the fluid-structure boundary as a continuum medium and those that treat it as a discrete collection of individual springs and particles. Next, we discuss the fluid-fluid methods, particularly useful for the simulations of fluid-fluid interfaces. We focus on models for immiscible droplets and their interaction in a suspending fluid and describe benchmark tests to validate the models for fluid-filled bodies.

Force approach for the pseudopotential lattice Boltzmann method

One attractive feature of the original pseudopotential method consists on its simplicity of adding a force dependent on a nearest-neighbor potential function. In order to improve the method, regarding thermodynamic consistency and control of surface tension, different approaches were developed in the literature, such as multirange interactions potential and modified forcing schemes. In this work, a strategy to combine these enhancements with an appropriate interaction force field using only nearest-neighbor interactions is devised, starting from the desired pressure tensor. The final step of our procedure is implementing this external force by using the classical Guo forcing scheme. Numerical tests regarding static and dynamic flow conditions were performed. Static tests showed that current procedure is suitable to control the surface tension and phase densities. Based on thermodynamic principles, it is devised a solution for phase densities in a droplet, which states explicitly dependence on the surface tension and interface curvature. A comparison with numerical results suggest a physical inconsistency in the pseudopotential method. This fact is not commonly discussed in the literature, since most of studies are limited to the Maxwell equal area rule. However, this inconsistency is shown to be dependent on the equation of state (EOS), and its effects can be mitigated by an appropriate choice of Carnahan-Starling EOS parameters. Also, a droplet oscillation test was performed, and the most divergent solution under certain flow conditions deviated 7.5% from the expected analytical result. At the end, a droplet impact test against a solid wall was performed to verify the method stability, and it was possible to reach stable simulation results with density ratio of almost 2400 and Reynolds number of Re=373. The observed results corroborate that the proposed method is able to replicate the desired macroscopic multiphase behavior.