DIFFUSION AND REACTION OF BENZENE HYDROGENATION OVER POROUS Ni/γ-Al_2O_3 CATALYST

The macro-kinetics of benzene hydrogenation over porous Ni/γ-Al_2O_3 catalyst was measured with asingle-pellet diffusion reactor.Based on the dusty-gas model,the differential equations by taking into account ofthe variation of effective diffusivities with the composition were derived to describe the diffusion and reactionprocesses of reacting species over porous catalyst.Using the tortuosity factors determined under the condition ofsteady physical diffusion,the global reaction rates were calculated by solving the equations,and the results are ingood agreement with the experimental data obtained.     

Fourth-Order Runge–Kutta Schemes for Fluid Mechanics Applications

Multiple high-order time-integration schemes are used to solve stiff test problems related to the Navier–Stokes (NS) equations. The primary objective is to determine whether high-order schemes can displace currently used second-order schemes on stiff NS and Reynolds averaged NS (RANS) problems, for a meaningful portion of the work-precision spectrum. Implicit–Explicit (IMEX) schemes are used on separable problems that naturally partition into stiff and nonstiff components. Non-separable problems are solved with fully implicit schemes, oftentimes the implicit portion of an IMEX scheme. The convection–diffusion-reaction (CDR) equations allow a term by term stiff/nonstiff partition that is often well suited for IMEX methods. Major variables in CDR converge at near design-order rates with all formulations, including the fourth-order IMEX additive Runge–Kutta (ARK₂) schemes that are susceptible to order reduction. The semi-implicit backward differentiation formulae and IMEX ARK₂ schemes are of comparable efficiency. Laminar and turbulent aerodynamic applications require fully implicit schemes, as they are not profitably partitioned. All schemes achieve design-order convergence rates on the laminar problem. The fourth-order explicit singly diagonally implicit Runge–Kutta (ESDIRK4) scheme is more efficient than the popular second-order backward differentiation formulae (BDF2) method. The BDF2 and fourth-order modified extended backward differentiation formulae (MEBDF4) schemes are of comparable efficiency on the turbulent problem. High precision requirements slightly favor the MEBDF4 scheme (greater than three significant digits). Significant order reduction plagues the ESDIRK4 scheme in the turbulent case. The magnitude of the order reduction varies with Reynolds number. Poor performance of the high-order methods can partially be attributed to poor solver performance. Huge time steps allowed by high-order formulations challenge the capabilities of algebraic solver technology.     

Three-dimensional numerical study of heat and mass transfer in fluidized beds with spray nozzle

The numerical computations of temperature and concentration distributions inside a fluidized bed with spray injection in three-dimensions are presented. A continuum model, based on rigorous mass and energy balance equations developed from Nagaiah et al., is used for the three-dimensional simulations. The three-dimensional model equation for nozzle spray is reformulated in comparison to Heinrich. For solving the non-linear partial differential equations with boundary conditions a finite element method is used for space discretization and an implicit Euler method is used for time discretization.The time-dependent behavior of the air humidity, air temperature, degree of wetting, liquid film temperature and particle temperature is presented using two different sets of experimental data. The presented numerical results are validated with the experimental results. Finally, the parallel numerical results are presented using the domain decomposition methods.     

Parametric uncertainty quantification using proper generalized decomposition applied to neutron diffusion

In this paper, a proper generalized decomposition (PGD) approach is employed for uncertainty quantification purposes. The neutron diffusion equation with external sources, a diffusion-reaction problem, is used as the parametric model. The uncertainty parameters include the zone-wise constant material diffusion and reaction coefficients as well as the source strengths, yielding a large uncertain space in highly heterogeneous geometries. The PGD solution, parameterized in all uncertain variables, can then be used to compute mean, variance, and more generally probability distributions of various quantities of interest. In addition to parameterized properties, parameterized geometrical variations of three-dimensional models are also considered in this paper. To achieve and analyze a parametric PGD solution, algorithms are developed to decompose the model's parametric space and semianalytically integrate solutions for evaluating statistical moments. Varying dimensional problems are evaluated to showcase PGD's ability to solve high-dimensional problems and analyze its convergence.     

Kinetics and reaction engineering of penicillin G hydrolysis

A general diffusion reaction model for immobilised biocatalysis has been developed. The model has been used to study the deacylation of penicillin G to 6-aminopenicillanic acid using two commercially available immobilised Penicillin acylases. The values of D_e/R² for the enzyme pellets have been estimated using data on uptake of 6-aminopenicillanic acid and phenylacetic acid by the enzyme pellets. The kinetic parameters of the model were individually estimated from a suitably designed set of experiments. The values of the Thiele modulus from the kinetic parameters so calculated have been found to be in the range 1·67 to 9·8 for the two enzymes studied, implying that diffusional effects cannot be ignored. The effect of such diffusional limitations on the overall rates and hence on the utilisation of the intrinsic kinetic ability of the enzyme has been demonstrated. This paper also reports on the implementation of the fed-batch strategy for this system. The proposed strategy, which involves maintaining the substrate concentration at the optimum value for a large part of the conversion, results in higher product concentrations than in batch operation, thereby reducing downstream procesing costs. The productivity was also shown to be considerably higher than for batch operation. Further, the ease of implementation of this mode of operation has been demonstrated.     

Diffusion-Reaction in the Au-Rich Ternary Au-Pt-Sn System as a Basis for Ternary Diffusion Soldering

Basic thermodynamic considerations indicate nonequilibrium between gold-tin intermetallic phases and platinum. Therefore, diffusion and reactions in the Au-Pt-Sn(-Ti) thin-film system have been investigated, and a mechanism of reaction is proposed based on experimental results and thermodynamic considerations. The present paper may also help researchers understand previous results that could be interpreted differently based on the new results of this work and basic thermodynamic considerations. A ternary diffusion soldering concept has been proposed, and its application on up to 4-inch wafer-scale bonding was successful. Generalizations of the present approach to other bonding systems appears promising.     

混凝土硫酸盐侵蚀理论模型的研究现状及展望

综合评述了混凝土硫酸盐侵蚀理论模型的研究进展。首先总结了混凝土受硫酸盐侵蚀的劣化机理及存在的争议问题,着重介绍了两类硫酸盐侵蚀理论模型的最新研究进展,包括离子扩散反应,材料初始裂缝的影响,水泥石微观结构改变以及材料损伤演化等问题。对各模型的理论基础、适用条件及存在的不足进行了分析,并提出了硫酸盐侵蚀建模中需要考虑的关键问题。最后,对硫酸盐侵蚀理论模型今后的研究重点进行了展望。     

Processing efficiency of immobilized non-growing bacteria: Biocatalytic modeling and experimental analysis

Modeling methods used to optimize the biocatalytic efficiency of freely suspended cells have been applied to non-growing microbial cells entrapped within a macro-porous carrier. The catalytic rate, which is dependent on cell concentration inside the biocatalyst beads, coincided with catalytic parameters for freely suspended cells. Immobilized non-growing cell systems could be optimized utilizing the characteristics of freely suspended cells without requiring extensive experimentation to define catalytic behaviour inside the biocatalyst. A dynamic diffusion–reaction model was developed and validated using experimental data for thiodiglycol degradation by Alcaligenes xylosoxidans subsp. xylosoxidans immobilized within macro-porous poly(vinyl alcohol) cryogel in a completely mixed batch bioreactor.     

计算多孔催化剂有效因子的区域分割法

提出了计算多孔催化剂颗粒有效因子的区域分割法,将整个一维区间划分为几个子区间,然后在每个子区间内用一点配置法求解非线性扩散-反应问题.采用区域分割法,针对三种不同形状的催化剂颗粒,对幂函数型动力学方程和双曲型动力学方程进行了大量的计算.所得的计算结果与正交配置解吻合.区域分割法的优点是使用简便、计算快速.采用区域分割法还可以计算催化剂颗粒死区半径,所得计算结果合理.