Energy-minimization Multi-scale Research Articles

The game theoretical approach for multi-phase complex systems in chemical engineering

This paper explores the application of noncooperative game theory together with the concept of Nash equilibrium to the investigation of some basic problems on multi-scale structure, especially the meso-scale structure in the multi-phase complex systems in chemical engineering. The basis of this work is the energy-minimization-multi-scale (EMMS) model proposed by Li and Kwauk (1994) and Li, et al. (2013) which identifies the multi-scale structure as a result of ‘compromise-in-competition between dominant mechanisms’ and tries to solve a multi-objective optimization problem. However, the existing methods often integrate it into a problem of single objective optimization, which does not clearly reflect the ‘compromise-in-competition’ mechanism and causes heavy computation burden as well as uncertainty in choosing suitable weighting factors. This paper will formulate the compromise in competition mechanism in EMMS model as a noncooperative game with constraints, and will describe the desired stable system state as a generalized Nash equilibrium. Then the authors will investigate the game theoretical approach for two typical systems in chemical engineering, the gas-solid fluidization (GSF) system and turbulent flow in pipe. Two different cases for generalized Nash equilibrium in such systems will be well defined and distinguished. The generalize Nash equilibrium will be solved accurately for the GSF system and a feasible method will be given for turbulent flow in pipe. These results coincide with the existing computational results and show the feasibility of this approach, which overcomes the disadvantages of the existing methods and provides deep insight into the mechanisms of multi-scale structure in the multi-phase complex systems in chemical engineering.

CFD simulation of gas-liquid-solid flow in slurry bubble columns with EMMS drag model

The drag models reflecting the complex phase interactions are of critical importance in the CFD simulation of gas-liquid or gas-liquid-solid flows. In this study, we demonstrate that the Dual-Bubble-Size (DBS) drag model based on the Energy-Minimization Multi-Scale (EMMS) concept, is capable of effectively predicting the distribution of gas holdup in slurry bubble columns. For solid-free or low solid loading systems, a thorough comparison of the DBS-Global and other drag models indicates that, without any fitting parameters, the DBS-Global drag model prediction on the radial distribution of gas holdup and solid hydrodynamics is in conformity with experiments over a wide range of superficial gas velocities. The three-fluid and two-fluid models are also compared in this work, indicating that the three-fluid model in combination with the DBS-Global drag model gives the best prediction. Previous experiments show that the effects of solid presence on hydrodynamics become pronounced at high solid loading conditions. The prediction of the original DBS-Global drag model deviates from the experiments at high solid loading conditions, and the solid effects need to be taken into account. This work then proposes a modified drag model for simulating three-phase systems at high solid concentration. The new model is capable of accurately predicting the local gas holdup for the systems of solid loading of 25% or 40%. Further fundamental study of the solid effect on the change of flow structure and dominant mechanisms in gas-liquid flow is required.

A simplified two-fluid model coupled with EMMS drag for gas-solid flows

A simplified two-fluid model (STFM) combined with energy-minimization multi-scale (EMMS) drag was proposed for accurate and fast simulation of gas-solid flows. In the proposed approach, the solid phase viscosity is neglected, the solid phase pressure is calculated with an empirical formulation, and the interphase momentum transfer is modeled with EMMS drag, which takes the effects of meso-scale structures into consideration. Three typical fluidization cases, namely, a 2D circulating fluidized bed, a 3D lab-scale bubbling fluidized bed, and a 3D lab-scale full-loop circulating fluidized bed, were successfully simulated with this approach. The numerical results are compared with those of full two-fluid model (FTFM, i.e., the two-fluid model using the kinetic theory for granular flow to close solid phase stress term), as well as experimental data. Predictions of STFM coupled with EMMS drag are comparable with those of FTFM coupled with EMMS drag, and both agree well with experimental data. However, computational cost of STFM is significantly reduced compared with that of FTFM. It is suggested that drag model has a dominant effect on gas-solid simulation, and the effect of solid phase stress term seems to play a minor role, demonstrating the feasibility and practicality of STFM with EMMS drag for describing the hydrodynamics of heterogeneous gas-solid flows.

Quantifying cluster dynamics to improve EMMS drag law and radial heterogeneity description in coupling with gas-solid two-fluid method

Quantification of multiscale heterogeneity is the key to the simulation of gas-solid two-phase flow. The energy-minimization multiscale (EMMS) model can be used at different scales to describe local and global heterogeneities as well as steady-state fluid dynamics of gas-solid fluidization. However, the same cluster diameter correlation based on energy dissipation was used in all cases, which may give a smaller cluster diameter than single particle diameter at low solids fluxes. In this paper, a description of the solids mass transfer between the dilute and dense phases in heterogeneous gas-solid flow is proposed to replace the correlation of cluster diameter to avoid some problems associated with the empirical calculation of the cluster diameter. This cluster description can facilitate the prediction of the drag coefficient at the scale of numerical cells in computational fluid dynamics (CFD) at extremely low solids fluxes and the radial heterogeneity in large-scale circulating fluidized bed (CFB) risers with downward particle velocities near the wall. It is integrated with two-fluid model (TFM) to simulate the fluid dynamics in an industrial-scale CFB riser accurately, which is also accelerated significantly by using the predicted radial voidage distribution as the initial condition of CFD.

Computer virtual experiment on fluidized beds using a coarse-grained discrete particle method—EMMS-DPM

Virtual process engineering (VPE) aims to redefine the roadmap for process scaling-up and optimization, from stepwise experiments to high-performance computer simulations. This is a long-cherished dream of chemical engineers, but requires high standards of Accuracy (the agreement between the simulation and the real process), Capability (the computational speed, scale, and resolution of the simulation), and Efficiency (cost-effective and easy to use), in short, ACE. For complex processes such as gas–solid fluidization, the gap between state-of-the-art simulations and VPE is still huge in terms of ACE. However, the work reported in this paper narrows this gap significantly. In this study, a coarse-grained discrete particle method (DPM) defined by the energy-minimization multi-scale (EMMS) model is deployed for high-resolution simulations of fluidized beds, with the gas- and solid-phase equations solved concurrently by CPUs and GPUs in a heterogeneous supercomputing system. With systematic optimization of the model, numerical method, software, and hardware, we are able to simulate lab- to pilot-scale fluidized beds at quasi-realtime speed, and conduct virtual experiments on such systems. This enables very-long-time simulations to obtain important engineering parameters such as the particle residence time distribution, attrition and deactivation indexes. This work demonstrates that the industrial application of VPE is almost on the horizon.

CFD-PBM simulation of droplets size distribution in rotor-stator mixing devices

Rotor-Stator mixing devices (RS) have found widespread application in mixing, dispersion and emulsification processes to acquire the desirable droplet size distribution (DSD) which is critical to the function and quality of products. Thus the precise control of DSD through the rational design and optimization of process or formulation is highly demanded. Computational fluid dynamics (CFD) becomes increasingly important to simulate the complex turbulence flow in RS devices which has significant impact on the final DSD. CFD can also be integrated with population balance equations (PBE) to predict the DSD as long as the droplet breakage and coalescence rates could be accurately modeled by the kernel functions. However, the underlying physics of droplet breakage and coalescence is complex and far from being well understood. We simulated the liquid–liquid two-phase flow and DSD for a weak coalescence emulsification system in a Megatron RS mixer with the CFD-PBM approach, then tentatively proposed a novel approach for correcting the breakage kernels based on the Energy-Minimization Multi-Scale (EMMS) concept. This method features the multi-scale resolution of energy dissipation, and utilizes the so-called meso-scale energy dissipation to derive a correction factor for the breakage rate for PBE. The results show that the new model can greatly improve the CFD-PBM simulation, and the DSD predicted is in good agreement with experiments, demonstrating the rationality and potential of this new approach.

CFD optimization of feedstock injection angle in a FCC riser

Feedstock injection zone is a key section for fluid catalytic cracking (FCC) riser reactor. In conventional design of commercial FCC risers, the injection angle of the feedstock is 30° upward with the riser axis, which is found to easily cause nonuniform oil-catalyst contact and severe back-mixing in the feedstock injection zone. In this work, the effect of feedstock injection angle is investigated by performing 3-D simulations with seven injection configurations including three inclined upward, one horizontally and three inclined downward. The two-fluid model (TFM) and the energy-minimization multi-scale (EMMS) drag is combined in simulations. Comparison with experimental data is conducted in terms of the profiles of solids and feed volume fractions. Several variables including the backflow ratio, the radial nonuniformity index and the mean residence time of feed, are further introduced to quantify the hydrodynamic dependence of flow and mixing on the injection settings. It is found that the downward injection schemes are better to realize uniform mixing and matching between catalysts and feed than the upward injection schemes. A 30° downward injection angle is desired to improve the distributions of catalysts and feed, reduce the catalyst-feed contacting time and eliminate the effect of secondary flow on severe back-mixing near the riser wall.

Análisis numérico de la hidrodinámica y la transferencia de calor del flujo gas-sólidos en dos configuraciones de salida de un riser industrial usando la teoría meso-escala para predecir el arrastre interfacial

In the FCC process two configurations riser are numerically analyzed varying the upper outlet orientation using a 2D CFD model which includes the Two Fluid Model (TFM), Kinetic Theory of Granular Flow (KTGF), and Energy Minimization Multi-Scale (EMMS) theory as drag model. This model is solved using the ANSYS Fluent® 14.5 software, solving the governing equations of mass, momentum, and energy balance; and the constitutive equations to calculate interfacial interaction, wall-solid phase interaction, and granular phase properties. The model proposed in this work properly predicts the gas-solid flow behavior, predicting different solid flow patterns in radial and axial riser directions, as well as concentrated and diluted zones at riser's top and bottom respectively. The radial and axial solids concentration and velocities profiles fluctuations observed are produced by the high radial solid mix which is higher near the riser walls due to drag force considered by the model used. On the other hand, a rapid radial and axial thermal stabilization is observed reaching the steady state rapidly. The profiles obtained from riser configurations analyzed are very similar, so in future works other riser outlets configurations will be analyzed to try to improve the solid concentration and velocity profiles.

Modeling the hydrodynamics of cocurrent gas–solid downers according to energy-minimization multi-scale theory

Cocurrent gas–solid downer reactors have many applications in industry because they possess the technological advantages of a lower pressure drop, shorter residence time, and less solid backmixing when compared with traditional circulating fluidized bed risers. By introducing the concept of particle clusters explicitly, a one-dimensional model with consideration of the interphase interactions between the fluid and particles at both microscale and mesoscale is formulated for concurrent downward gas–solid flow according to energy-minimization multi-scale (EMMS) theory. A unified stability condition is proposed for the differently developed sections of gas–solid flow according to the principle of the compromise in competition between dominant mechanisms. By optimizing the number density of particle clusters with respect to the stability condition, the formulated model can be numerically solved without introducing cluster-specific empirical correlations. The EMMS-based model predicts well the axial hydrodynamics of cocurrent gas–solid downers and is expected to have a wider range of applications than the existing cluster-based models.

Turbulence originating from the compromise-in-competition between viscosity and inertia

Fluid flows in chemical engineering are mainly characterized by the coexistence of turbulent and non-turbulent fluids. Nonetheless, in traditional turbulence models, the laminar portion of the fluid flow is often neglected and constitutive laws are expressed to describe fully turbulent states within computational grids. We perceived this situation is a source of inaccuracies in modeling practical engineering flows. In this work, a stability criterion for turbulent flows, originating from the principle of compromise-in-competition between viscosity and inertia, is used to obtain closure in the turbulence model, which defines the energy-minimization multi-scale (EMMS)-based turbulence model. Analogous to two-phase flow, the model regards single-phase complex flows as a mixture of turbulent and non-turbulent fluids, and the effect of meso-scale eddy structure on the effective coefficient of viscosity is also considered. The EMMS-based turbulence model is tested against three benchmark problems, namely, the lid-driven cavity problem, flow through a conical diffuser, and flow over an airfoil using experimental and direct numerical simulation (DNS) data. Numerical results show that the EMMS-based turbulence model improves the accuracy of turbulence modeling, demonstrating its feasibility and practicality for accurate simulations of engineering complex flows.

Toward a mesoscale‐structure‐based kinetic theory for heterogeneous gas‐solid flow: Particle velocity distribution function

Mesoscience has recently been proposed as a possible general concept for describing complex systems far from equilibrium, however, concrete formulations are needed, and particularly, a statistical mechanics foundation of mesoscience remains to be explored. To this end, the mathematical theory of stochastic geometry is combined with the energy minimization multi‐scale (EMMS) principle under the concept of mesoscience to propose a statistical mechanics framework. An EMMS‐based particle velocity distribution function is then derived as an example to show how the proposed framework works, and more importantly, as a first key step toward a generalized kinetic theory for heterogeneous gas‐solid flow. It was shown that the resultant EMMS‐based distribution is bimodal, instead of the widely‐used Maxwellian distribution, but it reduces to the Maxwellian distribution when the gas‐solid system is homogeneous. The EMMS‐based distribution is finally validated by comparing its prediction of the variance of solid concentration fluctuation and granular temperature with experimental data available in literature. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2649–2657, 2016

CFD simulation of a fluidized bed using the EMMS approach for the gas-solid drag force

Drag force is one of the main contributing factors in describing the hydrodynamics of gas-solid flow systems. In fact, the drag force is the primary coupling force between the fluid and particulate phases. Therefore, accurate prediction of the drag is the goal of the present study. Flow of particulate solids in gas-solid flow systems is inherently heterogeneous due to different attraction and repulsion forces between the particles. The assumption of a homogeneous system leads to unrealistic predictions of system characteristics for different gas-solid regimes, e.g., bubbling fluidized beds and circulating fluidized beds. In the literature, several approaches have been developed to encounter the effect of heterogeneities inside the system, e.g., EMMS (Energy Minimization Multi-Scale) and subgrid filtering approaches. In this study, an EMMS approach was applied to a fluidized bed operating at the ranges between the bubbling regime and packed bed. The result of 2D simulations in a fluidized bed was compared with both experimental data and homogeneous models. Simulation results using the EMMS approach showed very good agreement with the Krishna [20] bed expansion experimental data, while the modeling using homogeneous drag force diverged considerably from the experimental data.

CFD simulation of gas–solid two-phase flow and mixing in a FCC riser with feedstock injection

The feedstock injection zone is a key section for Fluid Catalytic Cracking riser reactor. A 3-D Computational Fluid Dynamics simulation is performed by coupling the two-fluid model and the energy-minimization multi-scale (EMMS) drag. The prediction agrees well with the available data and the secondary flow phenomenon is captured. The simulation reveals that the M-shape distributed feed sprays interact with the W-shape distributed solid particles and then cause the undesirable W-shape distribution of the matching ratio of catalysts to feed. The transformation of such uneven distribution to the finally core-annular distribution heavily depends on the secondary flow, whereas its mechanism can be explained by using the Kutta–Joukowski lift theorem. The increase of the feed spray velocity facilitates the feed diffusion and reduces the transition region. However, excessively high jet velocity may intensify the back-mixing near the wall and causes intense attrition or breakage of catalysts and thereby an increase of costs.

Correction to “Hydrodynamic Modeling of Gas–Solid Bubbling Fluidization Based on Energy-Minimization Multiscale (EMMS) Theory”

ADVERTISEMENT RETURN TO ISSUEPREVAddition/CorrectionORIGINAL ARTICLEThis notice is a correctionCorrection to “Hydrodynamic Modeling of Gas–Solid Bubbling Fluidization Based on Energy-Minimization Multiscale (EMMS) Theory”Xinhua Liu*†, Yuefang Jiang†‡, Cenfan Liu†, Wei Wang†, and Jinghai Li*†View Author Information† State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China‡ State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao 266555, People’s Republic of ChinaCite this: Ind. Eng. Chem. Res. 2015, 54, 32, 7998Publication Date (Web):August 6, 2015Publication History Published online6 August 2015Published inissue 19 August 2015https://doi.org/10.1021/acs.iecr.5b02797Copyright © 2015 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views343Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (256 KB) Get e-Alerts Get e-Alerts

Numerical simulation of loop seal for a circulating fluidized bed based on an improved EMMS bubbling model

A typical loop seal consists of a supply chamber and a recycle chamber as well as a bottom connection slit in between. The supply chamber is generally operated in the minimum fluidization state, while the recycle chamber in the bubbling fluidization regime. The energy-minimization multi-scale (EMMS) model, as generally used to calculate interphase drag coefficient in previous simulations of the loop seal, is still open to discussion since it is based on the concept of particle clusters. So an EMMS bubbling model was developed to model dense gas–solid flow by taking into account the interphase interaction between the emulsion and bubble phases. In this article, a heterogeneity index is calculated from an improved EMMS bubbling model to measure the interphase drag coefficient and further integrated into the two-fluid-model (TFM) approach to simulate the loop seal for a circulating fluidized bed (CFB) system. This index is dependent on superficial gas velocity in bubbling fluidization, so a region-specific drag correction scheme is proposed to allow the application of various heterogeneity index correlations to different zones of the loop seal, since superficial gas velocity may differ much from the recycle to supply chamber. Several typical cases of drag correction are comparatively investigated by applying various gas velocities and/or drag models in the recycle and supply chambers, and the optimal one is proven to be able to reasonably simulate the parametric effects on gas inverse flow in the loop seal.

Fine-grid two-fluid modeling of fluidization of Geldart A particles

A series of fine-grid simulation with two-fluid model (TFM) is performed for bubbling, turbulent and circulating fluidized beds (CFB) with Geldart A particles. The results show that the fine-grid TFM with homogeneous drag seems feasible for simulation of low-velocity, bubbling fluidized beds. However, the fidelity of fine-grid TFM declines with the increase of gas velocity. In particular, the solids flux predicted deviates much from the experimental data of CFB though the clustering phenomenon can be captured with refinement of grid. In contrast, the structure-dependent approach as exemplified by the energy-minimization multi-scale (EMMS)-based multi-fluid model gives better agreement with experimental data. This discrepancy raises the question of the applicability of the local equilibrium assumption underlying the TFM. It also sheds light to the necessity of meso-scale modeling and the critical role of solids flux to evaluate the simulation of CFB.

Effect of Different Gas-Solid Drag Models in a High-Flux Circulating Fluidized Bed Riser

Circulating fluidized beds (CFBs) have applications in many industrial processes like fluid catalytic cracking, coal gasification, coal combustion, biomass gasification and chemical looping. Consequently, the process have been studied intensively for many researchers seeking to understand the complex gas-solid flow encountered in circulating fluidized beds. In this sense, the Computational Fluid Dynamics (CFD) tools are very useful to study gas-solid flows, but this approach directly depends on the correct choice of the mathematical models. There are many numerical studies on CFBs at low solids fluxes and only a few studies for high solids flux, which is very common in many applications, therefore, this regime was chosen to conduct the simulations in this work. The results were compared with experimental data on a riser with an internal diameter of 76 mm and a height of 10 m. Radial and axial profiles were computed using a two-phase 3-D computational fluid dynamics model, with four different correlations for the drag between the phases, Gidaspow, Syamlal-O’Brien, and other two models that account for particle clusters, the energy-minimization multi-scale (EMMS) and the Four-Zone model. The results indicates that all the correlations predicts the solids concentration, found experimentally, in the dilute and developed flow regions but, in the region of highest solids concentration, especially at the level close to the inlet, the Gidaspow and Syamlal-O’Brien correlations not properly represented the solids concentration. The EMMS and Four-Zone models improved the results on these regions showing the influence of these models especially at the bottom of the riser, where the solids concentration is higher.

CFD modeling of gas–solids flow in a large scale circulating fluidized bed furnace

A Eulerian multiphase model was used to study the hydrodynamics of the gas–solids flow in a circulating fluidized bed (CFB) furnace. Alternative modeling approaches were tried to evaluate their effects on the predicted solids distribution in the furnace. Due to high computational costs, large scale calculations are commonly performed by using a coarse mesh, which leads to too uniform solids flow field and an overestimated gas–solid drag force. Thus, a suitable form of correction of the gas–solid drag is needed for coarse mesh simulations. This study presents fluid dynamics simulations of a 235MWe CFB furnace by two sets of interphase momentum exchange coefficients: the model based on the homogeneous flow condition and the model based on the energy-minimization multi-scale (EMMS) approach. The calculations with one solid phase included studies with two mesh resolutions and different particle sizes. Additional simulations were performed using two solid phases and four solid phases to analyze the effect of polydispersity of particles. The model results were compared with the measured vertical pressure profile of the furnace and the locally measured solid concentration and velocity profiles. The results show that with a homogeneous model, the model matches better with measurements if the mesh resolution is finer. The EMMS approach can be used to improve the calculations in a coarse mesh if the average particle size can be determined correctly for the model. With multiple solid phases, the vertical and horizontal segregation could be simulated. However, increasing the number of solid phases did not change the total solid concentration and pressure profiles if the Sauter mean diameter of the total system was constant. The results indicate that with a coarse mesh, similar drag corrections would be necessary between the solid phases that have been developed for gas–solid drag.

Extension and application of energy-minimization multi-scale (EMMS) theory for full-loop hydrodynamic modeling of complex gas–solid reactors

Virtual reality in chemical engineering features real-time simulation of complex industrial processes by utilizing multi-scale computation paradigm, and its realization is premised on global hydrodynamic modeling of the processes. Initial energy-minimization multi-scale (EMMS) model, though originally proposed for gas–solid fast fluidization, is extended to bubbling fluidization and in both axial and radial directions, so as to enable unified modeling of the entire gas–solid fluidization regime and theoretical computation of axial and radial heterogeneities in gas–solid flow. By applying the EMMS and its extension models to the segments divided from complex gas–solid reactors, an EMMS-based general method is proposed for global hydrodynamic calculation of the complex systems. Compared with traditional empirical schemes, the EMMS-based method avoids pre-separating the complex systems into various reaction zones until each has a single and simple flow state. And its feasibility is demonstrated by performing full-loop computation of an industrial-scale circulating fluidized bed, but its flexibility to the complexities of industrial processes in configuration and hydrodynamics still needs to be increased further in order to develop a software package for chemical process and virtual reality technology development.

CFD study of mixing and segregation in CFB risers: Extension of EMMS drag model to binary gas–solid flow

The Energy Minimization Multi-Scale (EMMS) drag model, using Sauter mean particle diameter to represent real particle size distribution, has proven to be effective in improving the accuracy of continuum modeling of gas–solid flow. Nevertheless, mixing and segregation characteristics in circulating fluidized bed (CFB) risers are very important in many situations, which necessitates the explicit consideration of the effects of particle size distribution on the bed hydrodynamics. To this end, an attempt is made to extend the EMMS drag model to binary gas–solid system, where four input parameters that can be obtained from computational fluid dynamics (CFD) simulation, including two slip velocities between gas and each particle phase and two particle concentrations of each phase, are used to solve the proposed EMMS drag model. Heterogeneous indexes, which are used to modify the drag correlation obtained from homogeneous fluidization, are then predicted and fed into multifluid model (MFM) to predict the dynamical behavior of mixing and segregation of binary gas–solid flow in a CFB riser. The effects of different drag force models, kinetic theories and particle–particle drag force models are also systematically evaluated. It was shown that (i) MFM with the proposed EMMS drag model and the kinetic theory developed by Chao et al. (Chemical Engineering Science 2011, 66: 3605–3616) is able to correctly predict the mixing and segregation pattern in the studied riser, while MFM with homogenous drag forces and the simplified kinetic theory available in commercial software FLUENT completely fails; and (ii) with or without particle–particle drag force has a substantial influence upon the particle behavior.