THE UNSTEADY-STATE SOLUTION BY AN OPERATOR THEORY FOR A DISPERSION-TYPE TUBULAR REACTOR WITH AN IMMOBILE ZONE

The analytical solution for an unsteady-state, dispersion-type, tubular reactor model with an immobile zone is obtained by an operator theory in a Hilbert space. The space is defined so as to make the operator positive and self-adjoint with a compact self-adjoint resolvent. A spectral representation is then applied to arrive at the analytical solution.     

THE UNSTEADY-STATE SOLUTION BY AN OPERATOR THEORY FOR A DISPERSION-TYPE TUBULAR REACTOR WITH AN IMMOBILE ZONE

The analytical solution for an unsteady-state, dispersion-type, tubular reactor model with an immobile zone is obtained by an operator theory in a Hilbert space. The space is defined so as to make the operator positive and self-adjoint with a compact self-adjoint resolvent. A spectral representation is then applied to arrive at the analytical solution.     

AN ANALYTICAL SOLUTION FOR A TUBULAR REACTOR MODEL WITH DISPERSION IN BOTH RADIAL AND AXIAL DIRECTIONS

An analytical solution for an unsteady-state tubular reactor model with dispersion in the radial as well as in the axial direction is presented. An arbitrary initial concentration profile and an arbitrary time-varying feed concentration are allowed; and the reaction occurs also on the interior surface wall of the reactor. The problem is recast into a more tractable form by an exponential transformation and then the method of Green's function combined with the orthonormal eigenfunction expansions based on the solution of the associated Helmholtz equation is used to arrive at the solution.     

乙氧基化管式反应器的数学模拟

建立了乙氧基化管式反应器的数学模型,考察了各参数对反应器温度分布的影响,认为反应器具有较强的参数敏感性,冷却剂进口温度是影响反应器温度分布的主导因素。分析了反应器的参数敏感性,得到了反应器的安全操作区域,对放大和生产操作提供了理论指导。     

START-UP TIME IN TUBULAR REACTORS WITH AXIAL DISPERSION

In the modeling of nonideal reactors the axial dispersion model is one of the most used (Butt, 1980). Boundary conditions for a tubular reactor with axial dispersion were extensively analyzed (Danckwerts, 1953, Wehner and Wilhelm, 1965, Van Cauwen-berghe, 1966, Choi and Perlmutter, 1976, Deckwer and Mahlmann, 1976) Similarly, the steady state behaviour of the reactor when simple or complex reactions take place was also studied by several authors (Deckwer et al. 1972, Wan and Ziegler, 1973). However, the transient behaviour was only analyzed for simple kinetics expressions (Fan and Ahn, 1963, Sawinsky artd Hunek, 1977, Godslave and Chang, 1980)

In the present work, the time necessary to reach the steady state or start-up time is determined for single and complex reversible reactions. The analysis presented is also valid in case there is a change in feed concentration (feed upset, etc.)     

START-UP TIME IN TUBULAR REACTORS WITH AXIAL DISPERSION

In the modeling of nonideal reactors the axial dispersion model is one of the most used (Butt, 1980). Boundary conditions for a tubular reactor with axial dispersion were extensively analyzed (Danckwerts, 1953, Wehner and Wilhelm, 1965, Van Cauwen-berghe, 1966, Choi and Perlmutter, 1976, Deckwer and Mahlmann, 1976) Similarly, the steady state behaviour of the reactor when simple or complex reactions take place was also studied by several authors (Deckwer et al. 1972, Wan and Ziegler, 1973). However, the transient behaviour was only analyzed for simple kinetics expressions (Fan and Ahn, 1963, Sawinsky artd Hunek, 1977, Godslave and Chang, 1980)

In the present work, the time necessary to reach the steady state or start-up time is determined for single and complex reversible reactions. The analysis presented is also valid in case there is a change in feed concentration (feed upset, etc.)     

超声协同三维电极处理染料废水

采用超声协同三维电极技术处理甲基橙模拟染料废水.通过对比试验,讨论了超声协同作用对降解效果的影响;考察了槽电压、原水浓度、pH、电解质浓度对去除效果的影响;通过中间产物的图谱分析,初步得出甲基橙在超声协同三维电极体系中的降解历程.试验表明,在最佳条件时,模拟废水中甲基橙的去除率接近100%,COD去除率超过80%.     

SIMULATION OF MICROMIXING IN A TURBULENT TUBULAR REACTOR WITH CONCENTRIC FEED

Turbulence on the axis of a pipe is isotropic and homogeneous and the rate of turbulent energy dissipation, ε, is known as a function of the velocity, pipe diameter and viscosity. When, however, a concentric feed pipe is introduced (as in a reactor), the ε field does not seem to be known. Evidence from fast, mixing-controlled reactions indicates a disturbance near to and downstream from the feed pipe with an increase in ε. Because of the lack of experimental information, the radial and axial distribution of ε has been modeled. One parameter—ε at the outlet of the feedpipe—is undetermined in this model. It is shown how the radial dispersion and especially the micromixing and reaction of fluid emerging isokinetically from the feed pipe can then be calculated, using a one-dimensional, radially averaged formulation. An application to four coupled, mixing-controlled reactions is included. Simulated and measured product distributions compared satisfactorily at various concentration levels and two solution viscosities. Whereas the new model is plausible, more work is needed to understand how a feed pipe modifies the flow in its vicinity.     

ON OPTIMIZATION IN TUBULAR REACTOR SYSTEMS

The Laguerre polynomial approximation technique is employed in obtaining optimal control variable profiles in distributed parameter systems. The classic problem posed by Denn et al. (1966) is presented and optimal cooling flux profiles obtained by several methods are compared.     

RESIDENCE TIME DISTRIBUTION IN AN OPEN REACTOR:EFFECT OF BACKGROUND REACTANT ON TRACER DISPERSION

A new approach is presented for deriving the residence time distribution(RTD)in open-type reactors with exclusion of residence in the fore section.Inasmuch as failure to predict the con-version of chemical reactions has been evidenced in many occasions,numerical solution of tracerdispersion in the presence of background concentration gradient of reactant is given to demonstratethe strong effect of background reactant on the true RTD a reactant molecule experiences.Withinthe error of computation,the conversion of a first-order chemical reaction under steady state is shownto be equal in both closed and open reactors,despite difference in relevant RTDs     

AXIAL DISPERSION IN THE ANNULAR BED REACTOR

The objective of the present work was to study the effects of axial dispersion on the behavior of the annular bed reactor using the methanation of carbon monoxide as the test reaction. It was found that the reactor is nearly-isothermal with and without axial dispersion, but the concentration profiles differ significantly. The effects of dispersion on the behavior of the annular bed are similar to those in the conventional fixed bed reactor, but appear to be much stronger.     

ON THE INTEGRAL EVALUATION OF TUBULAR REACTOR DATA

An explicit method for evaluating the kinetics of data obtained in an integral tubular reactor has been developed. The method is demonstrated for n:th order irreversible reactions by using experimental data. The reaction order is obtained from the slope and the rate constant is calculated from the intercept in a straight line plot     

氯醇化管式反应器的设计计算方法

根据氯醇化反应的特点，利用气液反应的双膜理论，导出了宏观反应速率式，结合管式反应器的流动模型，提出了一个简便、有效的反应器的设计计算方法     

合成甲醇反应器流向变换强制周期操作特性

实验研究了合成甲醇固定床反应器流向变换强制周期操作的非定态特性 ,考查了流向变换周期、进料流速和进料组成对床层轴向温度分布、热波在床层内的爬行速度以及反应器流出物组成的影响 .研究发现 ,即使进料中∑CO_x 总浓度降低至 0 .33 % (mol) ,合成甲醇的非定态反应过程也能自热进行     

STUDY ON THE PERFORMANCE OF VERTICAL TUBULAR LEACHING REACTOR

Hydrodynamics in vertical tubular leaching reactor was studied in this work. Based on the observation of particle saltation in curved and square return bends, the inclined return bend was developed and examined. For the narrow and wide size distribution particle system, the method for calculating the particle holdup in upflow and downflow tubes was derived on the basis of generalized fluidization equation. The model of unit pressure drop was given and examined by experiments.     

列管式固定床F-T合成反应器的模拟及优化

针对列管式固定床F-T合成反应器的特点建立了一维拟均相数学模型。通过对模型计算与试验结果进行对比分析,表明该模型可以较好的描述反应过程。并从固定床反应器的操作热稳定性出发,对列管式固定床F-T合成反应器的最大允许管径和最大传热温差进行了计算。结合模型计算结果得出了合适的反应管直径与冷却介质温度范围,可以优化列管式固定床F-T合成反应器的设计。     

A STUDY OF THE HIGH PRESSURE POLYETHYLENE TUBULAR REACTOR

As an example of the free radical polymerization reactor we have conducted a theoretical study of the high pressure polyethylene tubular reactor with cooling from the jacket. The plug flow model including the axial dispersion is considered with as well as without the steady state assumption for the active intermediates. We observe that the axial dispersion has negligible effect on the reactor performance and that the steady slate assumption is quite reasonable. The performance of the reactor is characterized by the exit monomer conversion, the peak temperature and the number and weight average degrees of polymerization, and the effects of various operating conditions are extensively investigated. Finally, an optimal temperature policy that would maximize the exit monomer conversion is determined by means of the Maximum Principle.     

喷射式气,液反应器在空气—水系统中的传质特性

在对喷射式气、液反应器中复杂的流动行为进行简化和假定的基础上,导得了传质模型,并以空气-水系统进行实验研究。用光电毛细管法测定喷射管内气泡平均直径 d_(32)和比表面积 a,用氮气解吸水中溶解氧的方法获得体积传质系数 k_La,以确定传质模型中的有关参数。实验获得如下结果:α=9.18×10~2β~(0.74)e~(0.372),k_Lα=0.7206β~(0.88)e~(0.492)。其结果与理论分析较接近,可作为喷射式气、液反应器设计参数。     

MASS TRANSFER AND HYDRODYNAMICS IN AN AIRLIFT REACTOR WITH VISCOUS NON-NEWTONIAN FLUID

In an internal loop airlift reactor of 55L working volume,the gas-liquid volumetric oxygenmass transfer coefficient k_Lα,gas holdup ε_G and liquid circulation time t_c were measured with the sol-ution of carboxymethyl cellulose(CMC)to simulate the performance of a reactor with highly viscousbroth.Electric conductivity and oxygen probes were used to measure the local gas holdup,liquidcirculation time and oxygen mass transfer coefficient in the individual sections of the reactor(riser,downcomer and the gas-liquid separating section at the top of the reactor)and the total reactor,respectively.The values of k_Lα for the riser,downcomer and separation sections of the reactor were alsoestimated and compared with that for the total reactor.The results show that,both k_Lα and ε_G in-crease but t_c decreases with increasing gas velocity.Correlations and comparisons with works reportedin the literature are also presented.Data show that the methods developed for k_Lα measurements inthe individual section and