MSMPR连续结晶器的多定态

对混合悬浮混合排料(MSMPR)连续结晶器的定态方程组进行了剖析,应用非线性方程组的延拓求解法,求得了定态方程组的分岔图,即MSMPR连续结晶器状态参数与操作参数的依赖关系.利用分岔理论对MSMPR连续结晶过程的定态数目及相应的参数范围进行了预测,导出了连续结晶过程存在多定态或唯一定态的判据。该判据仅与过程的动力学参数和操作参数有关,而与过程的状态参数无关。最后应用Routh-Hurwitz准则,确定了连续结晶过程各定态的稳定性。     

MULTIPLICITY AND STABILITY ANALYSIS OF AGGLOMERATION CONTROLLED PRECIPITATION

The possibility of multiplicity in continuous isothermal MSMPR precipitators has been explored for agglomeration controlled conditions and general criteria, independent of nucleation kinetics, are developed for stability and multiplicity of the steady states. For the Volmer model of primary nucleation and the magma dependent power law model of secondary nucleation, parameter regions are determined in which multiple steady states exist, and their linear stability is analyzed. The analysis holds in general for all types of agglomeration kernel. For the Volmer nucleation kinetics three steady states exist in the region of multiplicity with the “middle” one always being unstable. The analysis for magma dependent power law model showed multiplicity regions having as many as four steady states, the number depending on magma and kinetic order. Unlike the case of molecular growth control, limit cycle behaviour is not possible, and the approach to the steady state is always asymptotic     

MULTIPLICITY AND STABILITY ANALYSIS OF AGGLOMERATION CONTROLLED PRECIPITATION

The possibility of multiplicity in continuous isothermal MSMPR precipitators has been explored for agglomeration controlled conditions and general criteria, independent of nucleation kinetics, are developed for stability and multiplicity of the steady states. For the Volmer model of primary nucleation and the magma dependent power law model of secondary nucleation, parameter regions are determined in which multiple steady states exist, and their linear stability is analyzed. The analysis holds in general for all types of agglomeration kernel. For the Volmer nucleation kinetics three steady states exist in the region of multiplicity with the “middle” one always being unstable. The analysis for magma dependent power law model showed multiplicity regions having as many as four steady states, the number depending on magma and kinetic order. Unlike the case of molecular growth control, limit cycle behaviour is not possible, and the approach to the steady state is always asymptotic     

THE INFLUENCE OF PROCESS PARAMETERS ON STRUVITE CONTINUOUS CRYSTALLIZATION KINETICS

Experimental data concerning the kinetics of mass crystallization of struvite during the process of magnesium ion removal from water with the use of ammonium dihydrogenphosphate, NH₄H₂PO₄, addition under alkaline conditions are presented. The tests were carried out in a continuous laboratory DTM MSMPR crystallizer with internal circulation of suspension (T = 298 K). The influence of concentration of Mg^2 +  ions in the raw material, pH of the process environment, and residence time of suspension on the nucleation and growth rates of struvite crystals was established. Kinetic parameters were evaluated from the crystal size distributions using selected size-dependent growth (SDG) models.     

NUMERICAL TECHNIQUE FOR SOLVING POPULATION BALANCES IN PRECIPITATION PROCESSES

A simple, accurate and efficient numerical technique for solving the dynamic population balance associated with precipitation/crystallization reactors is presented. The basic approach is to determine the solute concentration dynamics first using the method of moments and an efficient ordinary differential equation solver, and then to solve the dynamic population balance, a partial differential equation having coefficients which depend on the known solute concentration, by standard finite difference techniques. The method is illustrated by simulating the dynamics of MSMPR and semi-batch reactors for BaSO₄ precipitation. The technique should be applicable to a wide range of population balance models.     

THE NARROWING OF CRYSTAL SIZE DISTRIBUTIONS IN A SONICATOR-MSMPR CRYSTALLIZER SYSTEM

Obtaining small crystals of a narrow crystal size distribution is an important problem in many pharmaceutical, biotechnological, and ceramic processing applications. This paper describes the use of a two-stage system to reproducibly produce pilot-scale quantities of a ceramic precursor powder.

The population balance is used to determine the crystal size distributions obtained from a staged crystallization system. The staged crystallization system consists of two units, a mininucleator (sonicator) and an MSMPR crystallizer. Experimental and theoretical studies of this system showed that the use of the mininucleator leads to narrowing of the crystal size distribution obtained from the MSMPR crystallizer. The resulting expression for the population density distribution allows direct fitting of experimental log population density data from the second stage to determine the growth and nucleation kinetics for both the mininucleator and the MSMPR crystallizer     

THE NARROWING OF CRYSTAL SIZE DISTRIBUTIONS IN A SONICATOR-MSMPR CRYSTALLIZER SYSTEM

Obtaining small crystals of a narrow crystal size distribution is an important problem in many pharmaceutical, biotechnological, and ceramic processing applications. This paper describes the use of a two-stage system to reproducibly produce pilot-scale quantities of a ceramic precursor powder.

The population balance is used to determine the crystal size distributions obtained from a staged crystallization system. The staged crystallization system consists of two units, a mininucleator (sonicator) and an MSMPR crystallizer. Experimental and theoretical studies of this system showed that the use of the mininucleator leads to narrowing of the crystal size distribution obtained from the MSMPR crystallizer. The resulting expression for the population density distribution allows direct fitting of experimental log population density data from the second stage to determine the growth and nucleation kinetics for both the mininucleator and the MSMPR crystallizer     

THE DYNAMIC BEHAVIOR AND CHAOS FOR TWO PARALLEL REACTIONS IN A CONTINUOUS STIRRED TANK REACTOR

The dynamical behavior for two parallel reactions in a continuous stirred tank reactor (CSTR) is considered. The global maximum number of steady states is five. Stability conditions are obtained. When the steady state is unique and unstable, a circulating attractor is proven to exist. The orbit structure is numerically found to consist of periodic orbits and chaotic behavior.     

丙烯腈连续水相沉淀聚合动力学数模

本文研究了丙烯腈（AN）、丙烯酸甲酯（MA）和甲基丙基烯磺酸钾（MAS）在水介质中的沉淀聚合反应。从基本反应和速率方程出发，应用连续搅拌釜（CSTR）的设计方程和聚合物颗粒表面的吸附方程，导出了丙烯腈连续水相沉积聚合的数模。结果表明，由模型算得的反应器出口处单体转化率和产品的平均分子量与实验值相吻合。     

MULTIPLICITY OF STATES IN SYSTEMS OF INTERACTING CATALYST PARTICLES

Presented here are several case studies, both theoretical and experimental, of the steady-state features of an assembly of interacting catalyst particles in a CSTR. Ostensibly, the results of these studies, though bused on simple string arrangements of two and three particles in a uniform environment, have meaning in terms of the behavioral characteristics of more complicated situations, including fixed-bed reactors.

Theoretical results exhibit complex bifurcation patterns and multiplicity features for steady-state curves when the particles are described as individual interacting entities. The complexity increases when the catalytic activities of the particles are not all alike.

Observations from experiments with the oxidation of hydrogen on spherical pellets of supported platinum resemble the theoretical cases. Individual pellet states in the laboratory work are depicted by their temperature maps obtained by means of a thermal infrared imaging system.     

MULTIPLICITY OF STATES IN SYSTEMS OF INTERACTING CATALYST PARTICLES

Presented here are several case studies, both theoretical and experimental, of the steady-state features of an assembly of interacting catalyst particles in a CSTR. Ostensibly, the results of these studies, though bused on simple string arrangements of two and three particles in a uniform environment, have meaning in terms of the behavioral characteristics of more complicated situations, including fixed-bed reactors.

Theoretical results exhibit complex bifurcation patterns and multiplicity features for steady-state curves when the particles are described as individual interacting entities. The complexity increases when the catalytic activities of the particles are not all alike.

Observations from experiments with the oxidation of hydrogen on spherical pellets of supported platinum resemble the theoretical cases. Individual pellet states in the laboratory work are depicted by their temperature maps obtained by means of a thermal infrared imaging system.     

EFFECT OF GAS-SIDE RESISTANCE ON STEADY STATE MULTIPLICITY IN GAS-LIQUID CSTRs

The effect of gas-side resistance to mass transfer on the existence and uniqueness of steady states in gas-liquid CSTRs is analyzed. It is shown that there exists an upper bound on gas-side resistance beyond which multiplicity cannot arise.     

AGGLOMERATION, BREAKAGE, POPULATION BALANCE, AND CRYSTALLIZATION KINETICS OF REACTIVE PRECIPITATION PROCESS

The agglomeration and breakage of particles play a significant role in determining final particle size distribution (PSD) and other qualities such as filtering characteristics and impurity content. In reactive precipitation processes, especially during the precipitation of fine particles, the agglomeration and breakage of particles normally cannot be neglected. In this study, the agglomeration and breakage of particles during the reactive precipitation process of procaine penicillin has been investigated experimentally through a continuous steady MSMPR crystallizer. Based on the population balance theory, a crystallization kinetics model including agglomeration and breakage is established, in which the breakage of particles is expressed by a two-body equal-volume birth function and a two-body power-law death function. The crystallization kinetics model is shown to be more suitable than size-dependent growth models as ASL and MJ2.     

AGGLOMERATION,BREAKAGE, POPULATION BALANCE,AND CRYSTALLIZATION KINETICS OF REACTIVE PRECIPITATION PROCESS

The agglomeration and breakage of particles play a significant role in determining final particle size distribution (PSD) and other qualities such as filtering characteristics and impurity content. In reactive precipitation processes, especially during the precipitation of fine particles, the agglomeration and breakage of particles normally cannot be neglected. In this study, the agglomeration and breakage of particles during the reactive precipitation process of procaine penicillin has been investigated experimentally through a continuous steady MSMPR crystallizer. Based on the population balance theory, a crystallization kinetics model including agglomeration and breakage is established, in which the breakage of particles is expressed by a two-body equal-volume birth function and a two-body power-law death function. The crystallization kinetics model is shown to be more suitable than size-dependent growth models as ASL and MJ2.     

MULTIPLICITY OF STATES IN CONTINUOUS STIRRED COPOLYMERIZATION REACTORS: ITS EXISTENCE AND CONSEQUENCES*

The dynamic behaviour of a continuous copolymerization stirred tank reactor is analyzed. The evolution of multiple steady states due to Trommsdorf or gel effect in free radical bulk copolymerization systems is illustrated for the first time taking into consideration the changes in the cross termination rate constant [or the φ factor] at high extent of reaction. The effect of concentration multiplicity on cumulative copolymer composition is illustrated. The consequences of the results of the present analysis in copolymerisation reactor operation and design have been discussed.     

TRANSIENT ANALYSIS OF CRYSTALLIZATION: EFFECT OF THE INITIAL SIZE DISTRIBUTION

The effect of seed size distribution on the transient and steady-state crystal size distribution in a continuous mixed suspension, mixed product removal crystallizer has been analyzed and simulated from a stochastic point of view. The resultant stochastic model provides an easier way of obtaining the dynamic information on the performance of the crystallizer under consideration than the conventional population balance techniques. Moreover, the moments of the number of crystals at each size can be evaluated. Simulation results indicate that the seed size distribution gives rise to a maximum in the crystal size distribution. The steady-state representation can be recovered from the resultant dynamic model; it reduces to the conventional deterministic population balance model under the condition of no random variation.     

MICROMIXING EFFECTS ON BARIUM SULFATE PRECIPITATION IN AN MSMPR REACTOR

The Effects of non-ideal and nonhomogeneous mixing on barium sulfate precipitation in an MSMPR reactor were observed experimentally and analyzed theoretically. To generate nonhomogeneous mixing the unmixed feed streams were fed to the reactor at the same location (joint feeding mode) or a plug flow reactor was connected to the MSMPR reactor. These nonhomogeneous mixing conditions resulted in significant reductions in particle size and increases in particle numbers. These non ideal mixing effects were dependent on the impeller speed, feed stream velocity and residence time in the connected plug flow reactor and are believed to result from elevated supersaturation levels in a premixing zone which are controlled by turbulent micromixing

To model the effect of nonhomogeneous mixing (premixing) in the MSM PR reactor a plug flow-stirred lank reactor series model was developed. The plug flow reactor represents the premixing region of the MSMPR reactor in which turbulent micromixing is important, and the stirred tank reactor describes the homogeneous mixing region of the MSMPR reactor where particle growth is important. The model predicts that the premixing effect is strongly dependent on micromixing of the feeds in the premixing region, and thus, as the turbulent mixing intensity in this region is increased, the particle size in the product suspension is reduced and the particle population is increased. These predictions of the model arc in good agreement with the experimental data. An interesting prediction of the model is that as the impeller speed increases, the precipitation of barium sulfate in an MSMPR reactor deviates increasingly from the precipitation in a perfectly mixed (ideal) reactor.