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• The empirical cluster correlation can be replaced by a cluster evolution equation. • A general EMMS drag model is suggested for the overall fluidization regime. • The EMMS drag is used to simulate gas-solid turbulent beds and cocurrent downers. • The EMMS-based simulation shows better prediction than traditional CFD simulation. Eulerian-Eulerian models incorporated with the kinetic theory of granular flow were widely used in the simulation of gas-solid two-phase flow, while the effects of mesoscale structures such as particle clusters and gas bubbles could not be considered adequately if traditional homogeneous drag models were adopted in the coarse grid simulations. The energy minimization multiscale (EMMS) model has been proved to facilitate calculating a structure-dependent drag coefficient by considering particle clustering phenomena, which can be coupled with the two-fluid model (TFM) to improve the accuracy of coarse-grid simulation of gas-solid circulating fluidized beds. However, the original EMMS drag model cannot be further applied to the simulation of gas-solid fluidized beds with solids flow rate smaller than zero, e.g., turbulent fluidized beds and cocurrent downward flow, because the original cluster diameter correlation gives rise to a value smaller than single particle diameter or even negative value at extremely low solids fluxes or downward gas-solid flow. In this study, a new proposed cluster evolution equation is proposed by quantifying local clustering dynamics to replace the original cluster diameter correlation. The newly formulated EMMS drag model can be used to avoid a negative cluster diameter to be involved in calculating interphase drag force in the overall fluidization regime. The improved EMMS drag law is incorporated into the Eulerian-Eulerian model to simulate gas-solid turbulent fluidized beds and cocurrent downer reactors, since they both were widely used in many industrial processes. By analyzing local hydrodynamics as well as the axial and radial heterogeneous distributions in the two kinds of fluidized beds, it is clarified that the simulation using the improved EMMS drag model shows a better agreement with the experimental data than the computation using the homogeneous drag law. [ABSTRACT FROM AUTHOR]

• The EMMS drag was closed by the PBM to account for sub-grid corrections. • A CFD-PBM-EMMS model was formulated for bubbling fluidized beds. • The breakup and coalescence kernels were improved to achieve better versatility. • The bubble dynamics in 3D fluidized beds of Geldart A particles was captured. • The EQMOM was coupled with QMOM to reconstruct the NDF. The importance of bubble dynamics in fluidized beds is underscored by the efforts undertaken over the past decades through experimental and numerical studies. Nonetheless, the bubble dynamic evolution and its effects on sub-grid closures were neglected in previous coarse-grid CFD models, particularly for Geldart A particles. In this article, a population balance model with improved kernels was employed to describe the bubble dynamic evolution in three-dimensional bubbling beds, whereby the EMMS drag model was closedto be incorporated into an Eulerian continuum model. Furthermore, the Extended Quadrature Method of Moments (EQMOM) was utilized to reconstruct the number density function of bubble size once their lower moments were obtained. The simulation results showed that the hydrodynamics including bed expansion characteristics, solids concentration and bubble size distribution can be well predicted by the model, indicating its capability to capture the heterogeneous structures in three-dimensional bubbling beds of fine particles. [ABSTRACT FROM AUTHOR]

Abstract: Axial heterogeneity in circulating fluidized bed (CFB) risers is very important to the design of fluidized bed reactors, which is, however, still unable to be described in theory. Based on a successful description of local hydrodynamics in gas–solid flow, the Energy-Minimization Multi-Scale (EMMS) theory further relates axial hydrodynamics with local and global stability conditions in the system, providing a theoretical way to account for the axial heterogeneity in CFB risers. This research reveals that the interaction between particle clusters and the dilute phase as well as the surrounding dense phase has a significant effect on their dynamical evolution. Similar to cluster diameter in the EMMS theory, number density of particle clusters serving as a comprehensive indicator to the heterogeneity in gas–solid flow is constrained by both local and global stability conditions in the system. With the above cognition, a one-dimensional EMMS model is developed to perform steady-state modeling of the axial heterogeneity in CFB risers. The model successfully reproduces a complete transition zone and the parametric effects on it at the choking condition. The S-shaped axial voidage profile calculated by the one-dimensional EMMS model is in good agreement with the experimental results in gas–solid fast fluidization. This research is not only the first step toward implementing the three-scale computation in virtual process engineering (VPE), but also of referential significance to industrial chemical process development. [Copyright &y& Elsevier]

Abstract: Effect of particle acceleration/deceleration on particle clustering behavior in dilute gas–solid flow was studied by experimental measurements and mathematical modeling. Calculation results of the model are in good agreement with experimental data from Phase Doppler Particle Analyzer (PDPA) measurements. The variation of voidage inside particle clusters is strongly dependent upon the change of the number of particles within the clusters. During acceleration, particle clusters are gradually disaggregated into smaller clusters with increasing voidage, while during deceleration, particle clusters are aggregated into larger clusters with decreasing voidage. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Understanding the hydrodynamics of gas–solid flows is a grand challenge in mechanical and chemical engineering. The continuum-based two-fluid models (TFM) are currently not accurate enough to describe the multi-scale heterogeneity, while the discrete particle method (DPM) following the trajectory of each particle is computationally infeasible for industrial systems. Following our previous work, we report in this article a coarse-grained DPM considering the meso-scale structure based on the energy-minimization multi-scale (EMMS) model, which can be orders of magnitude faster than the traditional DPM and can take full advantage of CPU–GPU (graphics processing unit) hybrid supercomputing. The size and solids concentration of the coarse-grained particles (CGP), as well as their interactions with the gas flow (the drag) are determined by the EMMS model with a two-phase decomposition. The interactions between CGPs are determined according to the kinetic theory of granular flows (KTGF). The method is tested by simulating the onset of fluidization and the steady state flow in lab-scale circulating fluidized bed (CFB) risers with different geometries and operating conditions both in 2D and 3D. The results agree well with experiments and traditional DPM based on single particles. The prospect of this method as a higher-resolution alternative to TFM for engineering applications and even for virtual process engineering is discussed finally. [ABSTRACT FROM AUTHOR]

Abstract: With the dramatic development of computational science and technology, computer simulation is playing an increasingly important role in scientific research and engineering practice, and is believed to bring about a profound revolution to the mode and means of these activities. For chemical engineering, it will promote the transition from an experience-and-experiment-based research and development mode to the one based on virtual process engineering (VPE). However, such a revolution still requires tremendous improvements in the Accuracy of physical modeling and numerical methods, the Capability of the computing hardware and software, and the Efficiency of the simulation activities, or in short, ACE. This article will systematically review the 3-decade endeavors at IPE, CAS (Institute of Process Engineering, Chinese Academy of Sciences) on upgrading ACE by establishing a multi-scale computing paradigm focusing on meso-scale structures. We also report recent developments in this direction with projections on future work. Meso-scales refer to the intermediate scales at which the discrete elements in a system interact to shape the global behavior of the system. Reasonable description of the structures at such scales is a bottleneck for reliable and accurate modeling of global behaviors. To address this problem, we started from gas–solid flow by proposing the energy minimization multi-scale (EMMS) model to quantify the hydrodynamics of meso-scale structures in gas–solid fluidization. This model, that is, its stability condition, was thoroughly analyzed and verified with the pseudo-particle modeling (PPM) method. Other systems, such as turbulence and gas–liquid flow, were then studied following the same strategy, revealing the ubiquity of stability conditions for meso-scale structures as a result of the compromise among different dominant mechanisms, and leading to a generalized model mathematically formulated as a multi-objective variational (MOV) problem. Meanwhile, along with wider industrial applications of the EMMS-based simulation methods, common features were recognized that ACE requires structural consistency among the simulated system, the physical model, the numerical software and the computing hardware under the umbrella of MOV, which we have named as the EMMS Paradigm. The EMMS Paradigm was first implemented from the software level using traditional computing hardware to achieve Accuracy. Since 2007, with the development of general-purpose GPU (graphic processing unit) computing, CPU (central processing unit)–GPU hybrid computing was deployed to implement the Paradigm from the hardware level, boosting the Capability to Petaflops range. In applying the Paradigm to the development of an industrial petro-chemical process (maximizing iso-paraffins, MIP), enabling technologies such as pre- and post-processing, error-tolerance, network-based computing and seamless integration of different simulation methods are now under development, which will greatly improve the Efficiency. A demonstration virtual laboratory featuring the comparison and interaction of online measurement and real-time computing is under construction. With these endeavors, an industrial process could be simulated globally in almost real-time, and different levels of details could be traced from the global distribution of flow parameters in a reactor to the inner-channels of catalytic particles at a perceivable evolution speed. The realization of VPE is, therefore, in the foreseeable future. [Copyright &y& Elsevier]

This paper reviews the development of the multi-scale methodology in complexity science, and elucidates the importance of understanding complex systems in chemical engineering by discussing the relevance between complex systems and a few challenging problems in this field. Multi-scale structure is considered to be the focus in studying complex systems, particularly, the following four critical issues: correlation between phenomena at different scales, compromise between different dominant mechanisms, coupling between spatial and temporal structural changes and critical phenomena occurring in complex systems. It is considered that complex systems can be formulated as a multi-objective variational problem. The multi-scale methodology is promising in coping with complex systems, which can be descriptive, correlative or variational. It will be reviewed in particular by analyzing the above four critical issues and by showing its 20-year development at IPE from a rough idea to modeling approaches, softwares and finally to industrial applications as well as its extension to a number of chemical and physical systems. The strategy of “from the particular to the general” in developing the variational multi-scale methodology is emphasized, and challenges for mathematicians and physicists are identified to show the necessity of transdisciplinary cooperations. The paper will be concluded by prospects and suggestions. [Copyright &y& Elsevier]