Evaluation of hydrodynamic behavior of the perforated gas distributor of industrial gas phase polymerization reactor using CFD-PBM coupled model

A 2D computational fluid dynamics (Eulerian–Eulerian) multiphase flow model coupled with a population balance model (CFD-PBM) was implemented to investigate the fluidization structure in terms of entrance region in an industrial-scale gas phase fluidized bed reactor. The simulation results were compared with the industrial data, and good agreement was observed. Two cases including perforated distributor and complete sparger were applied to examine the flow structure through the bed. The parametric sensitivity analysis of time step, number of node, drag coefficient, and specularity coefficient was carried out. It was found that the results were more sensitive to the drag model. The results showed that the entrance configuration has significant effect on the flow structure. While the dead zones are created in both corners of the distributors, the perforated distributor generates more startup bubbles, heterogeneous flow field, and better gas–solid interaction above the entrance region due to jet formation.     

Relationships between urbanization and the oak resource of the Minneapolis/St. Paul Metropolitan area from 1991 to 1998

Urbanization was associated with loss and transformation of the oak forest in the Twin Cities (Minneapolis and St. Paul) metropolitan area (TCMA) over a recent 7-year interval. Between 1991 and 1998, urbanization increased based on several indicators: population density, area of developed land, and area of impervious surface—total impervious area and area within three classes of increasing degree of imperviousness (protected, affected, and degraded). We quantified relationships between changes in urbanization and changes in several parameters describing the oak forest at the scale of ecological subsection. Increased total and affected impervious area were strongly correlated with decreased area of oak forest when changes of the urbanization indicators and oak were expressed as percentages of the subsection area. Relationships were reversed when changes were expressed as percentages of the 1991 values. Increased population density was strongly correlated with increased loss in numbers and increased isolation of oak patches, but weakly correlated with loss of oak forest area. This is the first study to quantify relationships between changes in urbanization and changes in a specific forest cover type. Our results demonstrate complexities of urbanization impacts on a metropolitan forest resource, and highlight the importance of selected variables, spatial and temporal scales, and expressions of change when quantifying these relationships.     

Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique

A new discretization method for aggregation equations is developed. It is compared to the fixed pivot technique proposed by Kumar and Ramkrishna (1996a. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science 51, 1311-1332). The numerical results for aggregation problems by discretized population balances are consistently overpredicting and diverge before the gelling point in the case of a gelling kernel. The present work establishes a new technique which assigns the particles within the cells more precisely. This is achieved by taking first the average of the newborn particles within the cell and then assigning them to the neighboring nodes such that pre-chosen properties are exactly preserved. The new technique preserves all the advantages of the conventional discretized methods and provides a significant improvement in predicting the particle size distribution (PSD). In addition, it is found that the technique is a powerful tool for the computation of gelling problems. The effectiveness of the technique is illustrated by application to several aggregation problems for suitably selected aggregation kernels including physically relevant kernels.     

Optimal control and operation of drum granulation processes

Process optimisation and optimal control of batch and continuous drum granulation processes are studied in this paper. The main focus of the current research has been: (i) construction of optimisation and control relevant, population balance models through the incorporation of moisture content, drum rotation rate and bed depth into the coalescence kernels; (ii) investigation of optimal operational conditions using constrained optimisation techniques; (iii) development of optimal control algorithms based on discretized population balance equations; and (iv) comprehensive simulation studies on optimal control of both batch and continuous granulation processes. The objective of steady state optimisation is to minimise the recycle rate with minimum cost for continuous processes. It has been identified that the drum rotation-rate, bed depth (material charge), and moisture content of solids are practical decision (design) parameters for system optimisation. The objective for the optimal control of batch granulation processes is to maximize the mass of product-sized particles with minimum time and binder consumption. The objective for the optimal control of the continuous process is to drive the process from one steady state to another in a minimum time with minimum binder consumption, which is also known as the state-driving problem. It has been known for some time that the binder spray-rate is the most effective control (manipulative) variable. Although other possible manipulative variables, such as feed flow-rate and additional powder flow-rate have been investigated in the complete research project, only the single input problem with the binder spray rate as the manipulative variable is addressed in the paper to demonstrate the methodology. It can be shown from simulation results that the proposed models are suitable for control and optimisation studies, and the optimisation algorithms connected with either steady state or dynamic models are successful for the determination of optimal operational conditions and dynamic trajectories with good convergence properties.     

Two methods for sensitivity analysis of coagulation processes in population balances by a Monte Carlo method

We consider two stochastic simulation algorithms for the calculation of parametric derivatives of solutions of a population balance equation, namely, forward and adjoint sensitivity methods. The dispersed system is approximated by an N-particle stochastic weighted ensemble. The infinitesimal deviations of the solution are accounted for through infinitesimal deviation of the statistical weights that are recalculated at each coagulation. In the forward method these deviations of the statistical weights immediately give parametric derivatives of the solution. In the second method the deviations of the statistical weights are used to calculate a finite-mode approximation of the linearized version of the population balance equation. The linearized equation allows for the calculation of the eigenmodes and eigenvalues of the process, while the parametric derivatives of the solution are given by a Lagrange formalism.     

A probabilistic simulator for population dynamics of quasispecies

We constructed a probabilistic simulator that allows all the events in population dynamics such as death, birth, mutation, and suppression/stimulation to be described by probabilistic rules. The simulator also facilitates a lattice used for expressing distribution and diversity (number of distinct strains) of quasispecies. The simulator is used to investigate the diversity threshold in HIV and T-cell interaction. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Efficient solution of population balance equations with discontinuities by finite elements

Two refinements of Galerkin's method on finite elements were evaluated for the solution of population balance equations for precipitation systems. The traditional drawbacks of this approach have been the time required for computation of the two-dimensional integrals arising from the aggregation integrals and the difficulty in handling discontinuities that often arise in simulations of seeded reactors. The careful arrangement of invariant integrals for separable aggregation models allows for a thousandfold reduction in the computational costs. Discontinuities that may be present due to the hyperbolic nature of the system may be specifically tracked by the method of characteristics. These discontinuities will arise only from the initial distribution or nucleation and are readily identified. A combination of these techniques can be used that is intermediate in computational cost while still allowing discontinuous number densities. In a case study of calcium carbonate precipitation, it is found that the accuracy improvement gained by tracking the slope discontinuity may not be significant and that the computation speed may be sufficient for dynamic online optimization.     

用于多峰函数优化的小生境差分演化算法

针对监控视频图像的特点,提出了一种有效的实时视频降噪算法。首先结合多帧图像采用基于Non—localmeans的运动检测方法自适应地区分图像的运动区域和静止区域,对静止区域采用时域加权均值滤波,对运动区域采用空域ANL滤波。充分利用了视频的时域、空域信息,在去除视频序列噪声的同时很好地保护了图像的细节。实验结果表明,提出的算法在不造成运动拖影的前提下,能够显著提高视频的信噪比和图像的主观质量。     

Run(n=2～7)金属团簇与氧反应的DFT研究

采用密度泛函理论的广义梯度近似(DFT／GGA)，对Run簇(n=2～7)与氧相互作用的几何结构与电子结构及吸附能之间的关系进行讨论。对氧原子及氧分子在Run金属簇上的吸附研究表明：电荷主要是从Ru的5s、4d轨道向O的2p轨道迁移，并使得金属．金属之间的键减弱。比较特殊的是当氧分子在桥位吸附时，Ru与吸附的O2会发生化学反应，并且由于Ru金属轨道的电子向O2的反键πg轨道转移，导致Ru-O之间的键的生成以及O-O之间的键发生断裂。同时，作者也观察到Ru．Ru之间的化学键发生断裂，形成具有原子活性的自由Ru原子，这可以部分解释一旦氧化物种形成，经过一诱导期后，氧化反应会加速进行的实验事实。     

Coupling granule properties and granulation rates in high-shear granulation

It is possible to link granulation rates to granule properties. The linkage is by multiple dimension population balance equations that, by means of simplifying assumptions, can be reduced to multiple one-dimensional (1-D) population balance equations (PBEs). Using simple physically based models, this paper demonstrates how multiple one-dimensional population balance equations can describe the results of high-shear granulation experiments of two different materials, calcium carbonate and lactose. Good agreement between experimental and simulated results was achieved enabling the granulation rates to be defined by two model parameters: the critical binder volume fraction and the aggregation rate constant. The modelling framework presented in this paper also provides a basis for the kinetic analysis of granulation experiments so that with further work, it is possible to determine the effect of process conditions and material properties on the model parameters.