Multiplicity in Continuous Adiabatic MSMPR Reactive Precipitators

The possibility of both concentration and temperature multiplicities has bcen studied for the case of acontinuous adiabatic mixed suspension mixed product removal(MSMPR)reactive precipitaior.A Process in-volving homogeneous chemical reaction in first order reaction kinetics with respect to each of the reactive compo-nents and subsequent crystallization described by conventional power law growth and power law magma depen-dent nucleation models is considered.The temperature dependency of each of these kinetics is described by Ar-rhenius relations.Parameter regions are determined in which multiple steady states exist.The linear stability ofthese steady states is analyzed by using the Routh criterion approach.     

一种基于改进NLJ算法的对象辨识方法及其应用

The accurate model is the most important and basic condition for the application of advanced process control, but the conventional methods do not provide satisfactory results in the case of unstable processes. To effectively control these processes, a novel identification method （Model Parameters and Initial States Identification simultaneously in closed loop --MPISI） is proposed. The model parameters and initial states of state equation can be simultaneously identified using this method. The results of simulation and application show that this method has the advantageous of disturbance-rejection and robustness. This method proposes a novel way for the optimization and the advanced control of the process systems.     

Establishment of nucleation and growth model of silica nanostructured particles and comparison with experimental data

A mathematical model is developed for the calculation of the nucleation and growth process of silica nanostructured particles prepared by using the drop-by-drop method,and the calculation results of the proposed model is compared with the experimental value obtained from SAXS data.The model provides a non-ideal improvement in the supersaturation calculation and considers the impact of both mass transfer and surface reaction on the particle growth rate.The nucleation and growth rates are coupled ...     

STUDY ON LIQUID PHASE MIXING IN PACKED COLUMN (Ⅱ) A TWO-DIMENSIONAL MODEL

A two-dimensional model involving both radial and axial mixing under the condition of steady tracer injection from a point source is presented. The model parameters are estimated by the optimal method of nonlinear programming, using the two-dimensional RTD experimental data obtaincd in a 1m diameter packed column. Dimensionless equations for the evaluation of axial and radial Peeler numbers are regressed.     

A review of extractive distillation from an azeotropic phenomenon for dynamic control

Extractive distillation is an effective method for separating azeotropic or close boiling point mixtures by adding a third component. Various technologies for performing the extractive distillation process have been explored to protect the environment and save resources. This paper focuses on the improvement of these advanced technologies in recent years. Extractive distillation is retrieved and analyzed from the view of phase equilibrium, selection of solvent in extractive distillation, process design, energy conservation, and dynamic control. The quantitative structure–property relationship used in extractive distillation is discussed, and the future development of extractive distillation is proposed to determine how the solvent affects the relative volatility of the separated mixture. In the steady state design, the relationship between the curvature of the residue curve and parameters of the optimal steady state is also highlighted as another field worthy of further study to simplify the distillation process.     

STEADY STATE MULTIPLICITY FEATURES OF ETHYLENE OXIDATION ON PLATINUM FOIL

The catalytic oxidation of ethylene to carbon dioxide in excess air has been studied atsteady state.The catalyst temperature was measured for various feed temperature and concentration.The bifurcation diagrams Which describe the dependence of the catalyst temperature on the feed gastemperature were obtained for different ethylene concentrations in the feed gas.The ignition and ex-tinction temperatures were found out and the unique and multiple steady state regions could bedetermined from these diagrams.The experimental results can be satisfactorily explained by thecatastrophe theory and singularity theory.According to the steady state multiplicity features an at-tempt to discriminate the competitive kinetic models was made for the reaction.     

EQUATIONS OF STATE FOR HARD-SPHERE CHAIN FLUIDS AND SQUARE-WELL CHAIN FLUIDS

Based on the statistical theory for chemical association,equations of state for hard-spherechain fluids(HSCFs)and square-well chain fluids(SWCFs)can be derived through the n-particlecavity correlation function(CCF)of the corresponding reference system,where n is the chain lengthor the number of segments of a chain molecule.The reference system is a fluid composed of only cor-responding monomers.In this work,the n-particle CCF is approximated by a product of effectivetwo-particle CCFs which accounts for correlations in nearest-neighbour and next-to-nearest-neighboursegment pairs.The CCFs for SWCFs may be expressed by a product of the corresponding functionfor HSCFs and a perturbation term originated from the square-well attractive potential.All these ef-fective two-particle CCFs and perturbation terms are density dependent.The dependence is determinedmainly by using computer-simulation results.The obtained equations can excellently describecompressibility factors and second Virial coefficients for HSCFs     

Development of a bifurcation analysis approach based on gPROMS platform☆

A bifurcation analysis approach is developed based on the process simulator gPROMS platform, which can automatically trace a solution path, detect and pass the bifurcation points and check the stability of solutions. The arclength continuation algorithm is incorporated as a process entity in gPROMS to overcome the limit of turning points and get multiple solutions with respect to a user-defined parameter. The bifurcation points are detected through a bifurcation test function τ which is written in C ++ routine as a foreign object connected with gPROMS through Foreign Process Interface. The stability analysis is realized by evaluating eigenvalues of the Jacobian matrix of each steady state solution. Two reference cases of an adiabatic CSTR and a homogenous azeotropic distillation from literature are studied, which successfully validate the reliability of the proposed approach. Besides the multiple steady states and Hopf bifurcation points, a more complex homoclinic bifurcation behavior is found for the distillation case compared to literature.     

反应精馏过程中的多稳态分析

Reactive distillation processes for synthesis of ethylene glycol （EG） and ethyl tert-butyl ether （ETBE） were modeled with the simulation package ASPEN PLUS. The input multiplicity and output multiplicity were discussed with the method of sensitivity analysis for both cases. In EG production process, steady state multiplicities were studied in terms of effective liquid holdup volume and boil-up ratio. In ETBE synthesis process, the user kinetic subroutine was supplied into ASPEN PLUS firstly, and then the composition, temperature and reaction-rate profiles within the reactive distillation column were presented in detail. A set of stable solution branches based on distinct initial guesses for a range of boil-up ratio were found in EG synthesis. Input multiplicities were observed for a range of reboiler duty at several values of reflux ratio for ETBE synthesis process. These results can be used to avoid excessive energy consumption and achieve optimum design of reactive distillation column.     

工业醋酸脱水系统多稳态模拟与分析(英文)

In this work, an industrial acetic acid dehydration system via heterogeneous azeotropic distillation is simulated by Aspen Plus software. Residue curves are used to analyze the distillating behavior, and appropriate operating region of the system is determined. Based on steady states simulation, a sensitivity analysis is carried out to detect the output multiple steady states in the system. Different solution branches are observered when the flow rates of the feed stream and the organic reflux stream are selected as manipulated variables. The performance of the column under different steady states is different. A method is proposed to achieve the desired steady state.     

等温CMSMPR结晶器定态及瞬态特性分析(Ⅰ)存在多定态及发生持续振荡的条件

运用分岔理论 ,对同时发生初级成核和二次成核的等温连续混合悬浮混合排料 (CMSMPR)结晶器的定态特性进行了分析 ,推导了系统存在多定态及发生持续振荡的参数条件 .以结晶过程的物性参数、动力学参数以及操作参数为基础 ,应用非线性方程组的延拓方法分别求解极限点条件方程组及Hopf分岔点条件方程组 ,确定了系统存在多定态及发生持续振荡的参数边界     

等温CMSMPR结晶器定态及瞬态特性分析(Ⅱ)分岔行为及瞬态特性

应用非线性方程组的延拓解法 ,对同时发生初级成核和二次成核的等温连续混合悬浮混合排料(CMSMPR)结晶器的定态方程组进行了求解 ,考察了结晶过程的定态在不同参数区域之间的分岔行为 ,确定了各参数区域内结晶过程的定态数目 ,并应用Routh -Hurwitz准则对各定态的稳定性进行了分析 .采用四阶Runge -Kutta法求解CMSMPR结晶器的动态方程组 ,分析了在多定态区域以及持续振荡区域中结晶过程的瞬态特性     

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     

MULTIPLICITY IN CONTINUOUS CRYSTALLIZERS: ADIABATIC REACTIVE PRECIPITATION

The application of the theory of both concentration and temperature multiplicities is extended to the case of a reactive precipitation system in a continuous mixed suspension mixed product removal (MSMPR) crystallizer. A process involving elementary homogeneous chemical reaction with first order reaction kinetics with respect to each of the reactive components and subsequent crystallization described by conventional power law growth and power law magma dependent nucleation models is considered; the temperature dependency of each of these kinetics is described by Arrhenius relations. Exact uniqueness and multiplicity (i.e. multiple steady states) criteria are developed. The stability of these steady states is analysed using small perturbations around the steady state     

Steady states of a biotechnological process for producing lactic acid at a given dilution rate

Conditions are determined that ensure the presence of steady states in a continuous biotechnological process for producing lactic acid. The possibility of implementing multiplicity depending on the kinetic parameters and the inlet values of the characteristics of the synthesis process is shown. An algorithm is developed for evaluating the multiplicity of steady states and calculating the characteristics of the process under the conditions of multiplicity.     

Multiplicity of steady states in an isothermal batch fluidized bed reactor

An investigation of uniqueness and multiplicity of the steady states in an isothermal fluidized bed reactor and continuous stirred tank reactor is presented. Material balance equations for the two phase model of Davidson and Harrison and the modified Partridge and Rowe model, are transformed into a single equation which is of the same form as the material balance equation for an isothermal continuous stirred tank reactor. Exact uniqueness and multiplicity criteria are derived, and numerical examples illustrating the influence of some parameters on the steady state multiplicity are presented.     

Steady state multiplicity of chemically reacting systems. The method of computation

To analyse the steady state multiplicity of chemically reacting systems of different types it is necessary to find all roots of systems of non-linear equations describing steady states of the systems. This can be solved rather simply in the case of a reducible system to a single equation. We present a numerical method of nonlocal solution for systems of non-linear equations which does not require computing with the Jacobian matrix. The method is illustrated by joint equilibrium absorption of two species for a semi-empirical model of induced inhomogeneity of the catalyst surface and by computation of the steady states of the stirred tank reactor in which the reaction A → B → C occurs.