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.     

采用粒数衡算模型研究沉淀过程中粒子的聚结和破裂

通过采用MSMPR反应沉淀器,研究了普鲁卡因青霉素反应沉淀过程中粒子的聚结和破裂对过程的影响机理,并对用生死函数表征聚结和破裂的粒数衡算模型采用新的分析方法。结果表明,将二元破裂模型应用于该粒数衡算模型是可行的。     

采用粒数衡算模型研究沉淀过程中粒子的聚结和破裂

通过采用MSMPR反应沉淀器,研究了普鲁卡因青霉素反应沉淀过程中粒子的聚结和破裂对过程的影响机理,并对用生死函数表征聚结和破裂的粒数衡算模型采用新的分析方法。结果表明,将二元破裂模型应用于该粒数衡算模型是可行的。     

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     

MODELLING AND ANALYSIS OF PARTICLE FORMATION DURING AGGLOMERATIVE CRYSTAL PRECIPITATION PROCESSES

While nucleation and crystal growth are normally considered to be the primary particle formation processes during industrial crystallization, secondary processes including crystal agglomeration and breakage can have a determining effect on product form, especially of precipitates. In addition to the usual overall size distribution, primary and secondary particle size, particle structure and morphology then become important characteristics affecting both product quality and downstream processing performanc

In this paper, the kinetics of processes which determine the formation of both primary particles and crystal agglomerates are briefly reviewed together with established and recent population balance and simulation techniques for analysing and predicting primary and secondary particle size distributions and total specific surface area. These approaches are then illustrated by some experimental and modelling studies of agglomerative precipitation reported recently in the literature.     

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 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.     

Agglomeration and breakage of nanoparticles in stirred media mills—a comparison of different methods and models

The increasing industrial demand for nanoparticles challenges the application of stirred media mills to grind in the sub-micron size range. It was shown recently [Mende et al., 2003. Mechanical production and stabilization of submicron particles in stirred media mills. Powder Technology 132, 64-73] that the grinding behavior of particles in the sub-micron size range in stirred media mills and the minimum achievable particle size is strongly influenced by the suspension stability and thus the agglomeration behavior of the suspension. Therefore, an appropriate modeling of the process must include a superposition of the two opposing processes in the mill i.e., breakage and agglomeration which can be done by means of population balance models. Modeling must now include the influence of colloidal surface forces and hydrodynamic forces on particle aggregation and breakup. The superposition of the population balance models for agglomeration and grinding with the appropriate kernels leads to a system of partial differential equations, which can be solved in various ways numerically. Here a modified h-p Galerkin algorithm which is implemented in the commercially available software package PARSIVAL developed by CiT (CiT GmbH, Rastede, Germany) and the moment methodology according to [Diemer and Olsen, 2002a. A moment methodology for coagulation and breakage problems: Part I—analytical solution of the steady-state population balance. Chemical Engineering Science 57 (12), 2193-2209; Diemer and Olsen, 2002b. A moment methodology for coagulation and breakage problems: Part II—moment models and distribution reconstruction. Chemical Engineering Science 57 (12), 2211-2288] are used and compared to explicit data on alumina. This includes a comparison of the derived particle size distributions, moments and its accuracy depending on the starting particle size distribution and the used agglomeration and breakage kernels. Finally, the computational effort of both methods in comparison to the prior mentioned parameters is evaluated in terms of practical application.     

黄原胶发酵的动力学模型及过程模拟

在5L 通气式搅拌发酵罐中,非溶氧限制的条件下,实验测定了间歇黄原胶发酵的过程数据,并建立了描述这一过程的动力学方程。菌体生长动力学方程(dC_b)/(dt)=0.2675C_b(1(-C_b/1.75))底物(碳源)消耗的动力学方程-(dC_s)/(dt)=0.14C_b(1-(C_b/1.75))+0.5806C_b~2/(1+0.06326C_p)产物(黄原胶)生成动力学方程(dC_p)/(dt)=0.4452C_b~2/(1+0.06326C_p)利用上述动力学方程能较好地描述生长期和稳定期的黄原胶发酵行为。     

SOLUTION OF POPULATION BALANCE EQUATIONS IN EMULSION POLYMERIZATION USING METHOD OF MOMENTS

In this work, the method of moments is used for solution of population balance equations appearing in modeling of emulsion polymerization (EP). The zero-one model without coagulation effect and the pseudo-bulk model including coagulation effect are investigated as two common approaches for modeling EP processes. The fixed quadrature method is used to close the set of moment equations, and the maximum entropy approach is applied to reconstruct the particle size distribution from a finite number of its moments. Comparing the results with those obtained by the high-precision finite volume technique indicates that, despite the low computational load of the moment method, it has an acceptable accuracy. These features support use of the moment technique for other applications such as on-line control or optimization in particulate processes.     

布朗工艺蒸汽系统分析与研究

对乌石化二化肥蒸汽系统进行全面、系统的分析和研究,以为天然气为原料的合成氨装置蒸汽平衡的优化设计提供依据。     

SIMULATION AND CONTROL OF MULTIDIMENSIONAL CRYSTALLIZATION PROCESSES

In this article, solving the population balance equation (PBE) and controlling the final particle size for crystallization problems have been addressed. For solving the general form of multidimensional PBE, a numerical method called conservation element and solution element (CE/SE) has been used. By applying this method to one- and two-dimensional crystallization problems, it has been shown that this technique can handle all types of source terms in the PBE. Model accuracy has been checked with experimental data reported in the literature and also with the analytical solution of PB-type equations. Control of final particle size was formulated in an optimization framework. To obtain a desired final size distribution for one-dimensional crystallization, the optimal temperature trajectory was achieved for size-dependent growth rate case with the agglomeration effect. For the two-dimensional case, the aspect ratio was controlled and the crystallization batch time minimized. To track the optimal temperature trajectories, PI controllers were used. Simulation results indicate that the desired final size distribution for the one-dimensional case and the aspect ratio for the two-dimensional case were approached very closely.     

水平衡及水解操作对二氧化碳汽提工艺系统的影响

通过对１６２０ｔ／ｄ尿素装置中水平衡的估算、分析并讨论水解蒸馏塔（Ｃ－１）出汽温度控制对优化合成塔的水碳比影响,为系统的稳定运行和优化操作提供借鉴依据。     

A FUNDAMENTAL ANALYSIS OF CONTINUOUS FLOW BIOREACTOR AND MEMBRANE REACTOR MODELS WITH TESSIER KINETICS

In this research we analyze the steady-state operation of a continuous flow bioreactor, with or without recycle, and an idealized or nonidealized continuous flow membrane reactor. The model extends to include a fixed bed reactor where a fraction of the biomass is detached by the flow. The reaction is assumed to be governed by Tessier growth kinetics. We show that a flow reactor with idealized recycle has the same performance as an idealized membrane reactor and that the performance of a nonidealized membrane reactor is identical to that of an appropriately defined continuous flow bioreactor with nonidealized recycle. The performance of all three reactor types can therefore be obtained by analyzing a flow reactor with recycle. The steady states of the recycle model are found and their stability determined as a function of the residence time. The performance of the reactor at large residence times is obtained.     

改良A~2O工艺中MLSS的影响及物料衡算

通过对两级污泥体积回流比的设置,实现了混合液污泥浓质量度(MLSS)对改良A2O工艺效果影响的研究。当二沉池污泥体积回流比40%,浓缩池污泥体积回流比20%时,MLSS可保持在2 100～2 500 mg/L范围内,COD污泥负荷为0.17 kg/(kg.d),COD、TP、TN以及NH3-N的去除率分别达到78.3%、74.1%、76.2%和100%。适当选取MLSS可同时提高改良A2O工艺对氮和磷的去除效果。由物料衡算发现,厌氧池出水中60.2%的TP和72.9%的TN均通过两级缺氧池去除。尽管只有35.6%的厌氧池出水TP在两级好氧池中继续得到去除,但两级好氧池对上级缺氧池流入的TP去除效率分别高达84.7%和75.0%,对提高TP去除率十分重要。此外,两级好氧池对TN的去除作用不明显,仅为厌氧池出水TN的6.7%。     

RELIABLE ON-LINE KINETICS IDENTIFICATION FOR A SEMI-BATCH PROCESS BY PARALLEL USE OF SHORT-CUT TRANSFER OF INFORMATION RULE AND RECURSIVE ESTIMATORS

On-line concentration measurements from an isothermal semi-batch system, i.e. the liquidphase acetoacetylation of pyrrole with diketene, are used for identification of a kinetic model. An integrated expert system, containing coupled estimation procedures and statistical analysis tools as well as a kinetic model data bank, chooses the most suitable structure for the kinetic model and subsequently identifies model parameters. With the increased availability of data during the run, refinements or structural changes in the kinetic model are performed automatically and parameter estimates are updated. A recently developed short-cut procedure (the Modified Integral transformation Procedure, MIP, Maria and Rippin, 1995, 1996; Maria, 1995), is compared against classical direct methods. Interactive use of a kinetic model-data bank through a numerical transfer of information strategy allows adaption of the mechanism-based kinetic model structure. Multiple nonlinear state estimators of the Extended Kalman Filter (EKF) type are operated in parallel, while the MIP/kinetic data-bank provides information for switching between the EKFs and concerning mechanism and model structure. This on-line use of parallel direct (short-cut) estimation procedures is particularly suitable for real-time process supervision, control and optimisation purposes.     

REACTIVE EXTRACTION OF LEVULINIC ACID FROM AQUEOUS SOLUTIONS WITH TRI-n-OCTYLAMINE (TOA) IN 1-OCTANOL: EQUILIBRIA,KINETICS, AND MODEL DEVELOPMENT

Levulinic acid, a carboxylic acid containing a ketone structure, can be used as an acidulant in foods and beverages. Reactive extraction is a promising alternative for the recovery of carboxylic acids from aqueous streams. The design of an amine extraction process requires kinetic data for the acid-amine + solvent system used. In this study, equilibrium and kinetic data on the extraction of levulinic acid from aqueous solutions using tri-n-octylamine (TOA) in 1-octanol have been determined. The mass transfer coefficients of levulinic acid, TOA, and 2:1 levulinic acid-amine complex in 1-octanol were calculated from the acetic acid mass transfer coefficient, which was determined by measuring its fluxes of simple diffusion from kerosene to water. Based on the Hatta number and the criterion given by Doraiswamy and Sharma, the reaction regime has been found to be instantaneous reaction regime occurring at the interface on the organic phase side. An extraction model comprising equilibrium complexation constant w.r.t 2:1 levulinic acid-TOA complex formation, K_E2i (14.794 (m³ kmol^?1)²), and complex mass transfer coefficient, k_B2A (2.193 × 10^?6 m s^?1), has been developed.     

Investigation of aggregation, breakage and restructuring kinetics of colloidal dispersions in turbulent flows by population balance modeling and static light scattering

Quantitative modeling of aggregating colloidal systems is the underlying problem in many industrial processes, such as micro and nanoparticle processing, crystallization or flocculation. Population balance models with various aggregation and breakage kernels have been proposed in order to describe aggregating systems, but they have been rarely validated against appropriate experimental data. Typically, model parameters are fitted against a single measured moment of the cluster distribution which can usually be equivalently described using several variations of the set of parameters underlying the relevant aggregation, breakage and restructuring kernels. In order to discriminate among alternative models we propose an approach based on measurement and quantitative modeling of multiple moments of the cluster mass distribution, such as those obtained from static light scattering measurements. This approach is applied to aggregation processes in turbulent conditions in order to test alternative kernels for aggregation, breakage, and restructuring kinetics. We present a detailed study on the sensitivity of measurables from static light scattering with respect to commonly used aggregation and breakage kinetic models. In particular, we analyze the dynamic and steady state behavior of two measurables: the average radius of gyration and the average zero angle intensity which represent two independent moments of the cluster mass distribution. In addition, we discuss the effect of cluster structure and mass distribution on the average structure factor and the apparent fractal dimension measured by static light scattering, in order to assess what structural information can be reliably extracted from such measurements.