Multiphase Particle-in-cell Method Research Articles

Simulation of fallpipe rock dumping utilizing a multi-phase particle-in-cell (MPPIC)-Discrete Element Method (DEM) model. Part I: Concepts and formulation

Dumping blasted rock fragments into water bodies through vertical fallpipes can be a challenging engineering activity due to the concerns of dispersion of fine contents (suspended sediments). This study aims to provide better understanding of the fallpipe rock dumping processes through numerical simulation approaches. We propose a modified multiphase particle-in-cell (MPPIC) method to simulate the fluid–solid mixture flows, and an advection–diffusion model for handling the fine contents. The modifications to the MPPIC method include: (i) changing the pure Eulerian fluid model to a hybrid Eulerian–Lagrangian model for numerical flexibility in handling large free-surface deformations, and (ii) replacing the empirical interparticle stress model with the Discrete Element Method (DEM) for numerical stability when dealing with large-size solids. The numerical model is first validated via two physical experiments: (i) wave generation by a granular collapse and (ii) sand dumping from a split hopper. The simulations generally agree well with the experimental findings, reflecting both the fluid–solid interaction and propagation of suspended sediments. Fallpipe rock dumping is then simulated with a consideration of the effects of fallpipe size on the dynamic interactions between the DEM solid particles, the fluid, and, hence, the fine contents. The results show that long narrow fallpipes perform better in terms of containing the fine contents and limiting the spreading range of the DEM solid particles on the seabed. The time-varying distribution of the fines concentration and the fluid velocity within the fallpipe are also discussed based on the simulation results.

A volumetric-smoothed particle hydrodynamics based Eulerian-Lagrangian framework for simulating proppant transport

Different numerical methods have been applied to simulate the proppant transport in petroleum engineering, which can be roughly categorized as the Eulerian-Eulerian and Eulerian-Lagrangian models. Recently, a hybrid Eulerian-Lagrangian (E-L) approach, the multiphase particle-in-cell (MP-PIC) method, has been successfully applied to model large-scale proppant transport problems by introducing the concept of parcels (clusters of particle). In the MP-PIC method, particle-particle interaction force is expressed as the gradient of particle stress. The calculation of this gradient strongly depends on the interpolation between particle properties and Eulerian grids, which could lead to problems such as non-physical particle suspension, particle agglomeration and non-conserved interparticle interactions. In this study, a new method, the volumetric-smoothed particle hydrodynamics (V-SPH) method, is proposed to improve the calculation accuracy of the particle-particle interaction forces in the original MP-PIC method. In the V-SPH method, the calculation of the particle stress gradient no longer depends on the background Eulerian grids and the conservation of the interparticle stress is also guaranteed. In this paper, detailed introduction of the V-SPH based Eulerian-Lagrangian framework is provided. The reliability of the proposed V-SPH method is validated against both the numerical and experimental results in literature. By comparing with the original MP-PIC method, we observe that the non-physical particle agglomeration, as well as non-physical particle suspension problems can be well solved with the proposed new model. In addition, the impact of some key parameters in the V-SPH method on simulation results are also investigated. The choice of the PPP (number of particles per parcel) and the treatment of boundary particle deficiency are found to play important roles in model accuracy and efficiency. The V-SPH method proposed in this work can provide more accurate results than the original MP-PIC method, especially in the regions of dense proppant concentration, with comparable computing efficiency. With proper treatment of boundary deficiencies, it is promising to be used in more complex field-scale proppant transport problems.

MP-PIC simulation of dilute-phase pneumatic conveying in a horizontal pipe

Dilute gas-solid two-phase flows inside a pneumatic conveying pipe are simulated with the multiphase particle-in-cell (MP-PIC) method. To achieve high simulation accuracy, different particle-wall collision models, drag force models and turbulence modulation models have been tested. Simulation results including pressure drop, gas and solid mean velocities, fluctuating velocities are compared to experimental measurements. It is found that the particle-wall collision restitution coefficient, especially in the tangential direction, significantly influences the total pressure drop. The mean particle velocity and slip velocity are sensitive to the drag force and a much higher drag force can improve the simulation accuracy, whereas the mean gas velocity is not sensitive to the drag force. The fluctuating gas velocity is hard to be predicted with the currently available turbulence modulation modeling choices, implying more efforts are needed in understanding the turbulence in future. • Dilute-phase pneumatic conveying in a horizontal pipe was simulated by MP-PIC method. • Impact of different sub-models on simulation results has been investigated. • The sub-models include particle-wall collision, drag force and turbulence modulation models. • Special attention has been paid on the slip velocity prediction.

A scaled MP-PIC method for bubbling fluidized beds

Coarse-graining is widely used in simulations of gas-solid fluidization. However, as a key parameter, the coarse-graining ratio, and its relevant scaling law is still far from reaching a consensus. In this work, a scaling law is developed based on a similarity analysis, and then it is used to scale the multi-phase particle-in-cell (MP-PIC) method. The approach is then validated by simulating two bubbling fluidized beds. The simulation results show that scaled MP-PIC reduces the errors of solids volume fraction and velocity distributions over a wide range of coarse-graining ratios for simulated conditions. In future, a scaling law with consideration of the heterogeneity inside a parcel or numerical particle will be developed which is expected to further improve the performance of coarse-grained modeling in simulation of fluidized beds.

CPFD simulation of a dual fluidized bed cold flow model

The present work was carried out to simulate a cold flow model of a biomass gasification plant. For the simulation, a Eulerian-Lagrangian approach, more specifically the multi-phase particle in cell (MP-PIC) method, was used to simulate particles with a defined particle size distribution. Therefore, Barracuda VR, a software tool with an implemented MP-PIC method specifically designed for computational particle fluid dynamics simulations, was the software of choice. The simulation results were verified with data from previous experiments conducted on a physical cold flow model. The cold flow model was operated with air and bronze particles. The simulations were conducted with different drag laws: an energy-minimization multi-scale (EMMS) approach, a blended Wen-Yu and Ergun drag law, and a drag law of Ganser. The fluid dynamic behavior depends heavily on the particles’ properties like the particle size distribution. Furthermore, a focus was placed on the normal particle stress (PS value variation), which is significant in close-packed regions, and the loop seals’ fluidization rate was varied to influence the particle circulation rate. The settings of the simulation were optimized, flooding behavior did not occur in advanced simulations, and the simulations reached a stable steady state behavior. The Ganser drag law combined with an adjusted PS value with (PS = 30 Pa) or without (PS = 50 Pa) increased loop seal fluidization rates provided the best simulation results.

Effect of particle concentration on turbulent modulation inside hydrocyclone using coupled MPPIC-VOF method

We discuss the implementation of a coupled Multi-phase particle in cell method (MPPIC) and Volume of Fluid (VOF) flow solver to simulate particles in a fluid flow field having a free surface. Using the solver developed using OpenFOAM 4.1 library, we study the flow of particles inside a highly anisotropic turbulent flow field of a hydrocyclone. The free surface from the air-core inside the hydrocyclone is resolved using the VOF method coupled with the LES turbulence model. We test multiple sub-grid scale model and find the dynamic k-equation model to have the best-predicting capability of the mean and turbulent flow field as well as the air-core shape. Using the established flow field, we study the particle flow properties and its effect on the fluid flow field using a four-way coupled description between MPPIC and VOF. Important flow properties such as the particle flow field velocity and turbulence modulation with varying particle concentration were studied. It was found that even with low solid concentration (0.3–1.5% by volume) there is a quite substantial increase in the fluctuating flow field (around 12%) and with a further increase (1.8%) we observe a decrease in the turbulent levels by approximately 6%.

Field-Scale Numerical Investigation of Proppant Transport among Multicluster Hydraulic Fractures

Summary Plug-and-perforation (P-n-P) completion has been widely used in horizontal wells for the development of unconventional reservoirs. In the field, uneven proppant distribution among different fractures within a fracturing stage has been frequently observed in P-n-P treatments, leaving a large portion of reservoir volume understimulated. In this paper, an efficient 3D multiphase particle-in-cell (MP-PIC) method has been used to simulate proppant transport among multiple fractures (fracture near the heel, middle fracture, fracture near the toe) at the field scale. This work studies the fundamental physics of the proppant transport process and reveals the mechanisms of uneven proppant placement, giving strategies to improve the proppant placement. Before applying the MP-PIC method to field-scale problems, we conducted indoor experiments to validate the model. The simulation results show an excellent agreement with the vertical slot experimental results. After model validation, we used the MP-PIC method to directly simulate the field process of proppant transport, involving slurry transport from the wellbore through perforation holes and finally into fractures. A base case with three fractures in a stage was first established to calculate the percentage of proppant mass distribution in each fracture. Then, we performed the sensitivity analysis of both proppant size and injection rate to investigate their effects on proppant placement. The results reveal that all the cases tend to have a heel-biased proppant distribution among three fractures, which agrees with the field observations. There are two reasons for the heel-biased proppant distribution. First, at the very beginning of the injection, more proppants tend to flow toward the toe side because of large momentum. As more and more proppants move to the toe side, the concentration near the toe side gradually increases, which adds flow resistance to the newly injected proppants. Therefore, most newly injected proppants will go to the first fracture. The second reason comes from the fracture geometry. Because the first fracture has the largest fracture width among three fractures, it has the smallest flow resistance for proppant transport. More slurry will flow into the first fracture. Apart from giving explanations for the heel-biased distribution, we also suggest some strategies to improve the proppant distribution. The sensitivity analysis shows that the strong heel-biased proppant distribution can be mitigated by optimizing the proppant size and injection rate. Our study for the first time conducts a field-scale numerical investigation of proppant transport in the wellbore-fracture system during P-n-P treatments. The results can provide us with more insights into the optimization of fracture design in field practice.

Eulerian-Lagrangian simulation of the full-loop gas-solid hydrodynamics in a pilot-scale circulating fluidized bed

The full-loop gas-solid hydrodynamics in a pilot-scale circulating fluidized bed (CFB) is numerically investigated by using multi-phase particle-in-cell (MP-PIC) method. In this method, fluid motion is resolved under Eulerian framework while particle motion is tackled under Lagrangian framework. The numerical results agree well with experimental data, demonstrating the reasonability of the MP-PIC method in simulating dense gas-solid systems. The main features of gas-solid flows in the full-loop CFB are qualitatively predicted, with a typical core-annulus flow structure in the riser. A large pressure gradient of gas phase in the bottom region and top region of riser reflects the turbulent and chaotic gas-solid flows in these two regions. Enlarging superficial gas velocity leads to a more non-symmetrical pattern of axial gas velocity, indicating the enhanced influence of recycle structure on gas-sold uniformity under the higher superficial gas velocity. The solid residence time (SRT) distribution in the riser exhibits a feature of early peak and a long tail, which can be well fitted by a lognormal probability distribution function. Enlarging superficial gas velocity gives rise to a decreased mean value and narrower distribution of the solid residence time in the riser, reflecting the depressed solid back-mixing intensity in this condition.

CFD Modelling Based on MP-PIC of Low Rank Pulverized Coal Pyrolysis in Pyrolysis Furnace

The multi-phase particle in cell (MP-PIC) method through defining the concept of ‘parcel of particles’ has been applied to study the simulation of gas-solid fluidized bed. In this paper, in order to reveal the pyrolysis behaviors with low-rank pulverized coal, the three-dimensional gas-solids flow, heat transfer and chemical reaction in a pilot-scale descending pyrolysis furnace was simulated by adopting the MP-PIC method coupled with a distributed activation energy model (DAEM) reaction model. First, the MP-PIC method was validated by comparing the experimental data and simulation results of the furnace temperature at four different pyrolysis reaction regions in a vertical square descending pyrolysis furnace with the throughput of 1.2 t/h, respectively. Then this MP-PIC method was further extended for analyzing the effects of handling capacity with the throughput of 1.2, 1.5, 2.0, 2.5, 3.0 t/h.

Numerical Simulation of a Small-Scale Cyclone Separator using MP-PIC Method

This paper presents a numerical study of a small-scale cyclone separator performance by means of computational fluid dynamics (CFD). The family of Euler-Lagrange approach named multiphase particle-in-cell (MP-PIC) is employed for modelling gas-solid interaction. The three-dimensional small-scale cyclone separator geometry was discretized with hexahedral-dominant mesh. The gas phase is assumed to be a flue gas which density is 0.363 kg/m3 and dynamic viscosity is 7.47E-5 Pa s. The solid particles are catalyst used in a small-scale fluid catalytic cracking (FCC) unit which are having 2400 kg/m3 of density and diameters vary from 90 µm to 130 µm. Large Eddy Simulation (LES) turbulence model was used to accurately predict turbulent flow behaviour of flue gas inside the cyclone. The simulation was performed for 7.82 m/s inlet velocity for both flue gas and catalyst. The pressure drop and catalyst collection efficiency were the variables of interest to be analysed, which were compared to the analytical solutions. It was found that the results generated from numerical simulation using MP-PIC method reflect a good agreement with the analytical solutions.

Impacts of solid stress model on MP-PIC simulation of a CFB riser with EMMS drag

The cluster-based EMMS (energy minimization multi-scale) drag model in combination with MP-PIC (multi-phase particle in cell) method can successfully simulate the fluidization behavior in CFBs (circulating fluidized beds). The solid normal stress model is very important to MP-PIC simulations, but still lacks thoroughly investigation, especially in CFB riser simulation. In this work, the effects of parameters from the solid normal stress model have been investigated by using 2D simulations of a laboratory-scale CFB riser with MFIX (Multiphase Flow with Interphase eXchanges) open-source code. The results show that the role of the solid stress parameters is more significant when the solid approaches close packing state. Based on the comparison between simulation results and experimental data and the elapsed simulation time, optimal values for the solid stress model parameters were obtained. The thickness of the third direction for 2D simulations has also been investigated. Increase of the thickness entails additional computational costs with little effect on the accuracy and the recommended value of thickness is the diameter of one single particle.

Numerical simulation of proppant transport in propagating fractures with the multi-phase particle-in-cell method

In this work, the proppant transport process in large-scale propagating fractures is simulated using an Eulerian–Lagrangian method. Fracture propagation is solved using the Perkins–Kern–Nordgren(PKN) model, while the fluid-particle system is solved with the multi-phase particle-in-cell (MP-PIC) method. The fluid motion is governed by volume-averaged Navier–Stokes equations, and solved using the finite volume method, and the particle motion is solved by applying Newton’s second law in a Lagrangian manner. Based on the original MP-PIC method, an extended 2D system of governing equations for fluid-particle flow is derived to solve the moving boundary problems associated with fracture propagation. By means of this method, the fluid-particle interaction is fully coupled, and the propagating fracture is considered as a prior-known boundary for the fluid and particle phases. Several numerical experiments are performed to validate the method for simulating fluid motion and proppant settling behaviors in a fracture through comparison with results in the literature. The simulation results of the 2D framework are also compared with those of 3D framework and show a good agreement. Large-scale problems of proppant transport in propagating fractures for different proppant and fracturing fluid properties, including the leak-off effect, are then simulated using this method. The Lagrangian feature of the MP-PIC method allows for flexible design of proppant injection, such as injection of proppant with multi-densities and/or multi-sizes.

MP-PIC modeling of CFB risers with homogeneous and heterogeneous drag models

In this paper, the MP-PIC (multiphase particle-in-cell) approach is used for three-dimensional (3D) modeling of the gas-solid flows in two types of circulating fluidized bed (CFB) risers with Geldart group A and B particles by incorporating the homogeneous and heterogeneous drag force models in the MP-PIC method, respectively. First, the effects of the three important simulation parameters, namely, the grid cell number, numerical particle-parcel size and time step, are investigated. Having determined the appropriate values for the three parameters, the hydrodynamic characteristics predicted by different drag force models are rigorously analyzed. The homogeneous drag models considered are the six models, the Wen-Yu, Wenyu-Ergun, Syamlal-O’Brien, Gidaspow, HKL, and BVK models, while the four heterogeneous models considered are Sarkar and EMMS-based models (EMMS-Yang, EMMS-Matrix and EMMS-QL). For the riser 1 with the Geldart A particles, all the six homogeneous models predict extremely high solid fluxes and inconsistent void fraction distributions compared with experimental results. The heterogeneous Sarkar and EMMS-based models can effectively improve the simulation accuracy and predict a typical core-annulus flow structure. The lately-developed EMMS-QL model produces the most accurate solid flux. For the riser 2 with the Geldart B particles, both the heterogeneous and homogeneous drag force models can predict a reasonable flow structure. Further, there are no significant differences in the void fraction and velocity profiles due to the choice of a drag force model over the other. These drag force models also successfully capture the meso-scale local particle clusters. Of these drag-force models, the Wenyu-Ergun drag-forec model predicts comparatively accurate solid flux. Generally, MP-PIC combined with heterogeneous Sarkar and EMMS-based drag force models reasonably improve the simulation accuracy for the Geldart A particles, while these heterogeneous models have no superiority over the homogeneous drag models for the Geldart B particles.

Assessment of Different Discrete Particle Methods Ability To Predict Gas-Particle Flow in a Small-Scale Fluidized Bed

Several discrete particle methods exist in the open literature to simulate fluidized bed systems, such as discrete element method (DEM), time-driven hard sphere (TDHS), coarse-grained particle method (CGPM), coarse grained hard sphere (CGHS), and multiphase particle-in-cell (MP-PIC). The main difference between these methods is in the treatment of particle–particle interactions: by calculating collision forces (DEM and CGPM), using momentum conservation laws (TDHS and CGHS), or based on the particle stress model (MP-PIC). Here, these methods are compared by simulating the same small-scale fluidized bed with the same open-source code MFIX. The results indicate that both modeling the particle–particle collision by TDHS and lumping a few particles in a parcel increase the computation speed with little loss in accuracy. However, the MP-PIC method predicts an unphysical particle–particle overlap, which results in incorrect overall bed hydrodynamics. These results suggest using the CGHS method for fluidized bed...

Application of the MP-PIC method for predicting pneumatic conveying characteristics of dilute phase flows

This study investigated the applicability of the multiphase particle-in-cell (MP-PIC) method for predicting pneumatic conveying characteristics. Three-dimensional computational particle fluid dynamics (CPFD) simulations were performed to assess the dilute-phase pneumatic conveying of plastic pellets in a horizontal circular pipe. The pellets were 80–500μm in diameter and 1000kgm−3 in density. The air velocities ranged from 6 to 15ms−1, and the solids-to-air mass flow ratios (solids loading ratios) ranged from 1 to 3. The predicted pressure drops and solids and air velocity profiles were compared with experimental data from the existing literature. A parametric study was carried out to investigate the effects of model collision parameters on pneumatic conveying characteristics. Moreover, the importance of including new collision terms developed by other researchers in the MP-PIC method for the prediction of dilute phase flows was emphasized.

Operating parameter effects on the solids circulation rate in the CFD simulation of a dual fluidized-bed gasification system

The solids circulation is crucial for sustaining biomass gasification within dual fluidized-bed gasification systems, because the heat utilization between the gasifier and combustor is mainly implemented through the circulation of bed material. In this work, a three-dimensional model was established to simulate the hydrodynamics of a dual fluidized-bed gasification system. The purpose of this work was to find effective ways to improve the solids circulation. In this CFD (computational fluid dynamics) model, the MP-PIC (multiphase particle-in-cell) method was applied to simulate the gas-solid flows in the dual fluidized-bed system. This model simulated the hydrodynamics of the bubbling fluidized-bed gasifier, chute, pneumatic-riser combustor, cyclone separator, and loop-seal in the dual fluidized-bed system. Studies of grid resolution and numerical parcel were conducted to examine the model accuracy. A series of case studies were implemented to investigate the impact of operating parameters on the solids circulation rate, such as particle diameter, solid inventory, steam supply to gasifier, and air supplies to combustor.

Numerical simulation of particulate flows in CFB riser with drag corrections based on particle distribution characterization

A heterogeneous drag force model was developed using a Eulerian-Lagrangian scheme for multiphase flow modeling. The model is based on an idea called particle distribution characterization (PDC), in which transient distribution of particle position is analyzed with an intuitive method to quantify the local heterogeneity of gas-solid flow for drag force correction. The model was implemented into the multiphase particle-in-cell (MP-PIC) method and applied to particulate flow simulation in circulating fluidized bed (CFB) risers. Whereas traditional homogeneous drag models tend to over-estimate gas-particle interactions and present homogeneous flow fields, the developed PDC model successfully predicts the heterogeneous gas-solid flow structures. The PDC predictions on time-averaged distributions and solid fluxes also correspond better with experimental measurements. Effects of the statistical parcel weight, an important parameter in computational parcel assumption in MP-PIC method (wherein parcels are employed to represent real particles), were investigated with both traditional and the PDC drag models. Results show defects of the assumption that agree with literature. It is proved that the PDC drag model is applicable to particulate flow modeling in CFB riser, and considerable for simulation of other industrial processes.

CFD studies on biomass gasification in a pilot-scale dual fluidized-bed system

A comprehensive CFD (Computational Fluid Dynamics) model using the MP-PIC (Multiphase Particle-In-Cell) method was developed to simulate a pilot-scale (6 tons/day, 1 MW th) dual fluidized-bed biomass gasification system. In this model the particulate phase was described with the blended acceleration model. The momentum, mass, and energy transport equations were integrated with the kinetics of heterogeneous biomass and char reactions and homogeneous gas-phase reactions to predict the particle circulation, producer gas composition, and reactor temperature. The simulation results were compared with experimental data from the pilot-scale gasification system to validate the model at different operating conditions. Parametric studies were conducted to investigate the impact of gasifier temperature, steam to biomass ratio (S/B), and air supply to the combustor on the producer gas composition. The studies showed that increasing gasifier temperature and steam to biomass ratio (S/B) promoted syngas (CO + H2) production and increased hydrogen content in producer gas. The effect of air supply was minor, because for the dual fluidized-bed system air was not directly involved in biomass gasification.

Numerical approach to predict particle breakage in dense flows by coupling multiphase particle-in-cell and Monte Carlo methods

A hybrid numerical approach coupling the multiphase particle-in-cell (MP-PIC) method for multiphase flows and the Monte Carlo method for population balances is proposed to simulate particle breakage in dense particulate flows. When the computational time step is short enough, the particle motion and breakage can be decoupled approximately into separate processes. With this assumption, the MP-PIC method is firstly employed to solve the current multiphase flow dynamics, and then breakage events that might have occurred during the time step are predicted by the Monte Carlo method. Basic models and implementation of the coupling algorithm are described. Four test problems are presented for accuracy and capability demonstration. A kinetic breakage kernel is applied with a parabolic fragment distribution to the simulation of particle abrasion in a fluidized bed. Results suggest the approach an effective method for particle breakage modeling in dense particulate flows.

Simulation of an internally circulating fluidized bed using a multiphase particle-in-cell method

This paper investigates the use of the multiphase particle in cell method (MP-PIC) in modelling the gas–solid flow in a laboratory-scale isothermal internally circulating fluidized bed (ICFB), and compares results with experimental observations previously published by Hadley et al. (“Experimental quantification of the solids flux in an internally circulating fluidised bed”, Fluidization XIII, 2010, pp. 885–892). Glass ballotini (140μm mean diameter) were fluidized with room temperature air, and fluidisation velocities in both the central reaction chamber and two heat exchange chambers were varied to provide nine different chamber velocity ratio conditions for investigation. The model reliably predicted the overall bed dynamics of both gas and solid flow. Predicted solid recirculation rates were generally within one standard deviation of the mean experimental values, although under-prediction tended to occur at lower fluidisation rates. It was concluded that the MP-PIC method was a reliable tool for modelling bubbling fluidized bed behaviour of non-cohesive particles.