Equation of State’s Crossover Enhancement of Pseudopotential Lattice Boltzmann Modeling of CO2 Flow in Homogeneous Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 434
Author(s):  
Assetbek Ashirbekov ◽  
Bagdagul Kabdenova ◽  
Ernesto Monaco ◽  
Luis R. Rojas-Solórzano
Keyword(s):  
Porous Medium ◽  
Lattice Boltzmann ◽  
Multiphase Flows ◽  
Equations Of State ◽  
Density Ratio ◽  
Narrow Channel ◽  
Lattice Boltzmann Model ◽  
High Density Ratio ◽  
Homogeneous Porous Medium ◽  
Density Ratios

The original Shan-Chen’s pseudopotential Lattice Boltzmann Model (LBM) has continuously evolved during the past two decades. However, despite its capability to simulate multiphase flows, the model still faces challenges when applied to multicomponent-multiphase flows in complex geometries with a moderately high-density ratio. Furthermore, classical cubic equations of state usually incorporated into the model cannot accurately predict fluid thermodynamics in the near-critical region. This paper addresses these issues by incorporating a crossover Peng–Robinson equation of state into LBM and further improving the model to consider the density and the critical temperature differences between the CO2 and water during the injection of the CO2 in a water-saturated 2D homogeneous porous medium. The numerical model is first validated by analyzing the supercritical CO2 penetration into a single narrow channel initially filled with H2O, depicting the fundamental role of the driving pressure gradient to overcome the capillary resistance in near one and higher density ratios. Significant differences are observed by extending the model to the injection of CO2 into a 2D homogeneous porous medium when using a flat versus a curved inlet velocity profile.

The Lattice Boltzmann Equation Method for Complex Flows

2012 ◽  
Author(s):  
Laura Schaefer ◽  
Michael Ikeda ◽  
Jie Bao
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann ◽  
Thermal Effects ◽  
Multiphase Flows ◽  
Density Ratio ◽  
Kinetic Equations ◽  
High Density ◽  
Lattice Boltzmann Equation ◽  
High Density Ratio ◽  
Density Ratios

The lattice Boltzmann equation (LBE) method is a promising technique for simulating fluid flows and modeling complex physics. Because the LBE model is based on microscopic models and mesoscopic kinetic equations, it offers many advantages for the study of multi-component or multiphase flows. However, there are still challenges encountered when dealing with thermal effects and multiphase flows, particularly at small scales or in varying geometries. In this paper, we discuss some techniques to overcome these challenges. First, we present an overview of the LBE method, and show how it can be extended to model multiple phases and thermal effects. Next, we describe our multi-component and multiphase (MCMP) LBE method for high density ratios. While the original formulation of Shan and Chen’s (SC) model can incorporate some multiphase and component scenarios, the density ratio of the different components is restricted (less than approximately 2.0), which limits the applications. Hence, based on the SC model and improvements in the single-component multiphase (SCMP) flow model reported by Yuan and Schaefer, we have developed a new model that can simulate a MCMP system with a high density ratio. An example of that system is shown. Finally, we have developed a parallel computation LBE method based on the Compute Unified Device Architecture for NVIDIA GPUs. Using this method, we are able to efficiently model a number of phases and length scales, examples of which are presented.

Study on C–S and P–R EOS in pseudo-potential lattice Boltzmann model for two-phase flows

2017 ◽  
Vol 28 (09) ◽  
pp. 1750120 ◽  
Author(s):  
Yong Peng ◽  
Yun Fei Mao ◽  
Bo Wang ◽  
Bo Xie
Keyword(s):  
Surface Tension ◽  
Lattice Boltzmann ◽  
Equations Of State ◽  
Density Ratio ◽  
Maximum Density ◽  
Lattice Boltzmann Model ◽  
Two Phase Flows ◽  
Two Phase ◽  
Spurious Currents ◽  
Pseudo Potential

Equations of State (EOS) is crucial in simulating multiphase flows by the pseudo-potential lattice Boltzmann method (LBM). In the present study, the Peng and Robinson (P–R) and Carnahan and Starling (C–S) EOS in the pseudo-potential LBM with Exact Difference Method (EDM) scheme for two-phase flows have been compared. Both of P–R and C–S EOS have been used to study the two-phase separation, surface tension, the maximum two-phase density ratio and spurious currents. The study shows that both of P–R and C–S EOS agree with the analytical solutions although P–R EOS may perform better. The prediction of liquid phase by P–R EOS is more accurate than that of air phase and the contrary is true for C–S EOS. Predictions by both of EOS conform with the Laplace’s law. Besides, adjustment of surface tension is achieved by adjusting [Formula: see text]. The P–R EOS can achieve larger maximum density ratio than C–S EOS under the same [Formula: see text]. Besides, no matter the C–S EOS or the P–R EOS, if [Formula: see text] tends to 0.5, the computation is prone to numerical instability. The maximum spurious current for P–R is larger than that of C–S. The multiple-relaxation-time LBM still can improve obviously the numerical stability and can achieve larger maximum density ratio.

A New Lattice Boltzmann Model for Phase Transition Process

2009 ◽  
Author(s):  
Longjian Li ◽  
Jianbang Zeng ◽  
Quan Liao ◽  
Wenzhi Cui
Keyword(s):  
Phase Transition ◽  
Lattice Boltzmann ◽  
Equations Of State ◽  
Density Ratio ◽  
Transition Process ◽  
Lattice Boltzmann Model ◽  
New Model ◽  
Phase Transition Process ◽  
Simulation Results ◽  
Boltzmann Model

A new lattice Boltzmann model, which is based on Shan-Chen (SC) model, is proposed to describe liquid-vapor phase transitions. The new model is validated through simulation of the one-component phase transition process. Compared with the simulation results of van der Waals fluid and the Maxwell equal-area construction, the results of new model are closer to the analytical solutions than those of SC model and Zhang model. Since the range of temperature and the maximum density ratio are increased, and the value of maximum spurious current is between those of SC and Zhang models, it is believed that this new model has better stability than SC and Zhang models. Therefore, the application scope of this new model is expanded. According to the principle of corresponding states in Engineering Thermodynamics, the simulations of water and ammonia phase transition process are implemented by using this new model with different equations of state. Compared to the experimental data of water and ammonia, the results show that the Peng-Robinson equation of state is more suitable to describe the water, ammonia and other substances phase transition process. Therefore, these simulation results have great significance for the real engineering applications.

Efficient GPGPU implementation of a lattice Boltzmann model for multiphase flows with high density ratios

2014 ◽  
Vol 93 ◽  
pp. 1-17 ◽  
Author(s):  
Amir Banari ◽  
Christian Janßen ◽  
Stephan T. Grilli ◽  
Manfred Krafczyk
Keyword(s):  
Lattice Boltzmann ◽  
Multiphase Flows ◽  
High Density ◽  
Lattice Boltzmann Model ◽  
Density Ratios ◽  
Boltzmann Model
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