Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution (RTD) in an impinging stream reactor, a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed. The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions. The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux, but is almost independent of gas flux. As the liquid flux and the gas flux increase, the liquid dispersion coefficient of center-to-wall decreases. The axial liquid dispersion coefficient is much larger than that of center-to-wall, which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.     

用于青霉素裂解的反冲式中空纤维膜反应器

给出了反冲式中空纤维膜反应器进行复杂生物催化反应的操作特性方程.以青霉素酶法裂解生成六氨基青霉烷酸体系进行了实验验证.底物浓度和催化剂负载密度对反应器生产能力的影响存在着最佳值,且催化剂负载的最佳密度随操作压力和膜的固有透量的增加而增大,随底物浓度的增加而减小.     

STEP COVERAGE PREDICTIONS USING COMBINED REACTOR SCALE AND FEATURE SCALE MODELS FOR BLANKET TUNGSTEN LPCVD

A reactor scale model (RSM) for a stagnation point, single wafer reactor for blanket tungsten LPCVD is used to calculate concentrations at the wafer surface. These concentrations and the wafer temperature, which is assumed to be measurable, are needed to determine the local tungsten deposition rate on the wafer and local film conformality (step coverage) in features on patterned wafers. Two feature scale models (FSMs) are used to determine step coverages in infinite trenches which have rectangular initial cross sections and an aspect ratio of five, as a function of reactor operating conditions; 1. a continuum-like diffusion-reaction model (DRM) for simultaneous Knudsen diffusion and heterogeneous surface reactions, and 2. a flux based model which includes ballistic transport of molecules and heterogeneous surface reactions (BTRM).|The RSM establishes “boundary conditions” for the feature scale models, by providing the flux of each species to the local wafer surface. Step coverages predicted using the FSMs with the reactant partial pressures at the wafer surface can be significantly lower than those predicted using reactant partial pressures at the reactor inlet, due to depletion of reactants. The flux based BTRM predicts higher step coverages than the DRM for the same wafer surface conditions.     

Assessment of the role of thermally induced gas flow inhomogeneities in fixed bed reactors

The paper presents results of a numerical solution of the equation of motion of gas in a fixed bed catalytic reactor. The equation was formulated so as to reflect the effects on the velocity field of variable local temperature in the bed through the temperature dependences of density and viscosity of the flowing gas. The temperature field used for the calculation was obtained from experiments with catalytic oxidation of ethane in a laboratory fixed bed reactor, 4 cm in diameter, packed with 0.4 cm catalyst particles.

The computed velocity field in the reactor is thus only approximate as, rigorously, the equation of motion is coupled with the heat and mass balances of the reacting species. Nevertheless, the estimated velocity field induced by the inhomogeneous temperature field indicated severe inhomogeneities of the axial velocity component which in the wall region exceeded the value on the reactor axis by about 50%. Additional convective heat fluxes induced by the temperature field amounted to as much as 20% of the radial heat dispersion flux. This contribution, however, must be expected to be substantially larger in reactors with larger reactor to particle diameter ratio and at higher gas velocities.

Rigorous forms of the model equations are suggested, accounting simultaneously for the thermally induced and variable void fraction induced flow inhomogeneities in the reactor as well as corresponding forms of heat and mass balances to be solved simultaneously.     

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution (RTD) in an impinging stream reactor, a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed. The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions. The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux, but is almost independent of gas flux. As the liquid flux and the gas flux increase, the liquid dispersion coefficient of center-to-wall decreases. The axial liquid dispersion coefficient is much larger than that of center-to-wall, which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.     

大型乙苯脱氢轴径向反应器的研究与开发(Ⅰ) 流体力学特性

乙苯脱氢轴径向反应器是一种催化床上部采用催化剂自封结构的新颖径向反应器 ,其催化床中的流体流动是复杂的二维流动 .在催化床的表征体积元上应用连续性方程和Ergen方程描述了其流动 ,应用有限差分法通过数学模拟得出了轴径向反应器流场 ,其结果在Φ30 0 0× 10 0 0 0的冷模装置得到了验证 .以大型乙苯脱氢轴径向反应器为背景 ,讨论了流向和触媒封高对流场的影响 ,得出径向段主要以径向流动为主 ,在催化剂封区以轴向、径向二维流动为主 ;催化剂封高是影响流场的主要因素 ,对于向心流动δ在 0 .7附近是Q_a/Q与Q_r/Q相同的等比流量点 ,对于离心流动在δ为 1.1处 ,是Q_a/Q和Q_r/Q相同的等比流量点 .δ小于此值 ,是以轴向流动为主径向流动为次的二维流动区 ;δ大于此值 ,是轴向流动为次径向流动为主的二维流动区 ;与离心流动型相比 ,向心流动型轴径向床有明显的限流作用     

R&D OF LARGE AXIAL-RADIAL REACTOR FOR ETHYLBENZENE DEHYDROGENATION(Ⅰ) HYDRODYNAMICS STUDY

乙苯脱氢轴径向反应器是一种催化床上部采用催化剂自封结构的新颖径向反应器 ,其催化床中的流体流动是复杂的二维流动 .在催化床的表征体积元上应用连续性方程和Ergen方程描述了其流动 ,应用有限差分法通过数学模拟得出了轴径向反应器流场 ,其结果在Φ30 0 0× 10 0 0 0的冷模装置得到了验证 .以大型乙苯脱氢轴径向反应器为背景 ,讨论了流向和触媒封高对流场的影响 ,得出径向段主要以径向流动为主 ,在催化剂封区以轴向、径向二维流动为主 ;催化剂封高是影响流场的主要因素 ,对于向心流动δ在 0 .7附近是Q_a/Q与Q_r/Q相同的等比流量点 ,对于离心流动在δ为 1.1处 ,是Q_a/Q和Q_r/Q相同的等比流量点 .δ小于此值 ,是以轴向流动为主径向流动为次的二维流动区 ;δ大于此值 ,是轴向流动为次径向流动为主的二维流动区 ;与离心流动型相比 ,向心流动型轴径向床有明显的限流作用     

环隙气提式环流反应器中的气含率和液相循环流动

在筒体直径310mm、高2000mm的环隙气提式环流反应器实验装置中,对上流区的气含率、液相循环流动等流体力学特性作了研究.用漂流通量模型描述了上流区的气含率;通过对体系的能量耗散机理进行分析,基于体系总能耗最小的原理推导出液相循环流动方程,结果表明:用此方程能较好地模拟这种反应器内的液相循环状况.     

Model predictive control of a second-order hyperbolic transport-reaction process

The model predictive controller (MPC) design is developed for a tubular chemical reactor, considering a second-order hyperbolic partial differential equation as the model of the transport-reaction process with boundary actuation. Without loss of generality, closed–closed boundary conditions and relaxed total flux are assumed. At the same time, the model is discretized in time by the Cayley–Tustin method, and, under the assumption that only the reactor's output is measurable, the observer design for the state reconstruction is addressed and integrated with the MPC design. The Luenberger observer gain is obtained by solving the operator Ricatti equation in the discrete-time setting, while the MPC accounts for constrained and optimal control. The simulations show that the output-based MPC design stabilizes the system under the input and output constraints satisfaction. In addition, to address the models' disparities, the results for both parabolic and hyperbolic equations are presented and discussed.     

The moment method for one-dimensional dynamic reactor models with axial dispersion

A polynomial approximation method for calculating state profiles for plug-flow reactors is extended to one-dimensional reactor models that include axial dispersion. The method is based on the conservation of reactor state profile moments along the spatial dimension. The moments are then transformed analytically into a polynomial approximation at each timestep. The boundary conditions of the parabolic partial differential equation are given special attention. It is shown that the Danckwerts boundary conditions are an appropriate set of boundary conditions for flow problems with axial dispersion in closed-closed geometries. A significant feature of the present method is that boundary conditions of the partial differential equation model to be solved are implicitly satisfied via the moment transformation, while the polynomial profile in the numerical approximation does not have to satisfy the boundary conditions exactly. The method is tested in two cases: startup of a tubular reactor and fixed-bed adsorber involving axial dispersion.     

New Analytical Method for Maximum Temperature Assessment in an Exothermic Tubular Chemical Reactor

This paper deals with an analytical method to assess the maximum temperature value along a tubular chemical reactor at steady state. This reactor is provided with a jacket in which a counter current cooling liquid flows. The thermal behavior of the chemical reactor is calculated with the McCormack numerical method. Comparison of the exothermic reaction generated flux with the removed flux from the separating wall leads to a two-part reactor subdivision. In the first part, the reactor behaves as an adiabatic reactor followed by a zone in which the flux removed from the wall is not negligible and remains constant. In the second part, the reactor behaves like a simple heat exchanger without internal energy source. Analytical integration of mass and energy balance equations in each subsystem was used to determine the analytical expression of maximum temperature.     

化学法测定转鼓反应器气液相界面积

采用化学法对转鼓反应器内气液相界面积进行测定,考察了转鼓表面超重力因子、气体通量、液体通量对转鼓反应器内气液相界面积的影响。结果表明:反应器气液相界面积分别随超重力因子和液体通量的增大,先增大后趋于平缓;随着气体通量的增加,转鼓反应器内气液相界面积先增大然后减小;在液体通量为5 m3/(m2.h)、转鼓表面超重力因子为77、气体通量为398 m3/(m2.h)时,可获得最大的气液相界面积为0.058 m2,比相界面积为137 m2/m3,约为鼓泡反应器比相界面积的6.8倍。研究结果为转鼓反应器的优化设计和操作条件的选择提供了依据。     

卧式双轴圆盘反应器功率特性研究

以聚酯生产为应用背景 ,用中、高粘糖浆作模拟物料 ,通过扭矩法测量了卧式双轴圆盘反应器的搅拌功率 P0 回归出 P与搅拌转速、物料粘度、装料量、圆盘桨数量 ,以及在圆盘桨边缘设置横向刮刀等诸多因素之间的定量影响关系 ,得到了统一的功率关联式。     

A hybrid membrane-emulsion reactor for the enzymatic hydrolysis of lipids

A hybrid reactor, consisting of a stirred vessel, a hydrophilic membrane loop and a hydrophobic membrane loop, is presented for the continuous enzymatic hydrolysis of soybean oil in an emulsion. The permeates of the hydrophilic and the hydrophobic membrane consist of a single water phase and a single lipid phase, respectively. No lipase activity could be detected in the permeates of both membranes, which implies that all enzyme is retained in the system. An important advantage of this system is that it combines the high surface area in an emulsion with the containment of lipase in a membrane reactor. It is further shown that the stability of the system can be improved considerably by the addition of CaCl₂ to the water phase. Under comparable conditions the enzyme stability in the hybrid reactor is lower than the stability in a stirred vessel. The composition of the emulsion appears to influence the flux of the membranes. The flux of the hydrophobic membrane increases with an increasing oil fraction of the emulsion while the flux of the hydrophilic membrane has an optimum for two different oil fractions—0 and 0.55 (v/v).     

Multicomponent mass diffusion in porous pellets: Effects of flux models on the pellet level and impacts on the reactor level. Application to methanol synthesis

A heterogeneous model has been derived for a fixed packed‐bed reactor producing methanol. Several closures for the intra‐particle mass diffusion fluxes; Maxwell–Stefan, Wilke, dusty gas and Wilke–Bosanquet, have been compared on the level of the catalyst pellet and the impacts of the different particle flux closures on the reactor performance are investigated. A preparatory study of the transport phenomena on the pellet level is recommended prior to any large‐scale reactor simulation to determine what are the rate determining transport mechanisms. Hence, if Knudsen diffusion is apparent on the level of the pellet, a combined bulk and Knudsen diffusion model should naturally be used in the reactor simulations as well, because Knudsen diffusion can influence significantly on the reactor conversion. Minor differences are observed between the diffusion flux models on both pellet and reactor level. Hence, for the reactor operation conditions applied in this study, the Wilke model is a good approximation to the rigorous Maxwell–Stefan model, and similarly, the Wilke–Bosanquet model is an appropriate model to use in replacement for the dusty gas model. Moreover, variable pressure and viscous flow can be neglected in the pellet model, as the effect of these contributions are not visible at neither pellet or reactor level. © 2011 Canadian Society for Chemical Engineering     

Low Dissipation with Normalized Flux Surfaces in 2-Dimensional Coordinate for IR-T1 Tokamak Using Grad–Shafranov Equation Solution

Together with the problem of confinement, plasma–wall interactions present the major constraints toward a magnetic fusion reactor. The solutions of Grad–Shafranov equation (GSE) analytically can be used for theoretical studies of plasma equilibrium, transport and magneto-hydrodynamic stability. Here we introduce specific choices for source functions, kinetic pressure and poloidal plasma current, to be quadratic in poloidal magnetic flux and derive an analytical solution for GS equation. With applying this solution to IR-T1 tokamak, we have calculated the poloidal magnetic flux, toroidal current density and normalized pressure profiles for this tokamak. Toroidal and poloidal flows can considerably change the equilibrium parameters of tokamak. These effects on the equilibrium of tokamak plasmas are numerically investigated using a code FLOW. As a comparative approach to equilibrium problem, the code is used to model equilibrium of IR-T1 tokamak for case pure toroidal flow.     

EFFECT OF EQUATION OF STATE ON PREDICTION OF TRICKLE BED REACTOR MODEL PERFORMANCE

Trickle bed reactors are widely employed in hydrotreating pocesses that operate at conditions where a significant portion of the liquid phase will flash. This partial vaporization of the feed affects the reactor performance. In order to determine the extent of liquid flashing and its effect on reactor performance, an equation of state is needed. In this study we used seven cubic equations of state to determine their effect in predicting reactor performance as well as parameter estimation

Two important variables that are calculated from the equation of state are the vapor liquid equilibrium and the molar density of the liquid phase. It was observed that although the distribution coefficients calculated by each equation of state are significantly different from each other, they do not affect the reactor model appreciably. However, molar density determination has a large effect both on modelling of reactor performance and the parameter estimation.     

On Danckwerts’ Boundary Conditions for the Plug-Flow with Dispersion/Reaction Model

Accurate predictions of oxygen utilization with position in plug-flow like (aka serpentine) reactors employed for aerobic activated-sludge treatment of municipal and industrial wastewaters are desired. Three non-ideal reactor models—completely-mixed flow reactors (CMFRs) in series, segregated flow, and plug-flow with dispersion (PFD)—and the ideal plug-flow model were investigated considering typical reaction kinetics and a typical reactor configuration to perform such predictions. Significant differences arose between predictions from the PFD model relative to those from the CMFR in series and segregated flow models. These differences led to re-examination of the PFD model and the inlet/outlet boundary conditions postulated more than six decades ago by P. V. Danckwerts. Major criticisms are found in the literature addressing the PFD model arising from the concentration “jump” at the inlet boundary necessitated by specification of conservation of reactant flux at the expense of continuity of target reactant concentration. A fresh theoretical examination of the dispersive/reactive processes within a closed reactor with particular attention paid to the inlet and outlet boundary planes led to alternative statements for the inlet and outlet boundary conditions. Revisions proposed herein to Danckwerts’ boundary conditions for the PFD/reaction model preserve both continuity of reactant concentration and conservation of reactant flux at both inlet and outlet boundaries. Hypothetical computations based on pseudo-first-order kinetics for a reaction carried out within a serpentine reactor of typical configuration illustrate the differences between concentration profiles through the reactor predicted using the proposed and Danckwerts’ boundary conditions.     

Optimization of polymer synthesis through distributed control of polymerization conditions

An optimal control methodology is applied to the goal of lowering polydispersity while increasing conversion in polymerization reactions. An illustration using initiator, heat, and monomer flux control profiles for free‐radical polymerization of styrene in a plug flow reactor is provided and compared with available experimental data. The design calculations use a kinetic model that includes the gel effect. The reactor designs show that distributed initiator, heat, and monomer fluxes along the length of the reactor lower the polydispersity of the styrene polymers and increase conversion for a given reaction time. The monomer flux maintains a nearly constant monomer concentration in the reactor. The initiator and heat fluxes are highly correlated. The temperature rises as a result the heat flux; but the initiator flux results in a lower initiator concentration relative to the initiator cofeed case. At a reaction time of 120 min, a conversion of 44% and a polydispersity of 1.73 have been achieved. The theoretical designs, although not proven to be globally optimal, are of high quality. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2922–2928, 2002