同时发生初次和二次成核且为聚结控制的沉淀过程多定态及稳定性分析

The possibility of multiplicity in an isothermal continuous mixed suspension-mixed product removal crystallizer is explored using the bifurcation theory.A process involving agglomeration controlled precipitation is considered in which secondary nucleation occurs simultaneously with primary nucleation.The determinant equations for the existence of multiple steady states are developed and the multiplicity boundaries dependent on the physical and kinetic properties and operational parameters of the process are obtained by resolving these determinant equations.The number of steady states in the precipitator for various multiplicity regions is determined and the linear stability of these steady states is analyzed by using the Routh criterion.     

A Two-step Design Method for Shaft Work Targeting on Low-temperature Process

In low-temperature processes, there are interactions between heat exchanger network （HEN） and refrig-eration system. The modification on HEN of the chilling train for increasing energy recovery does not always coor-dinate with the minimum shaft work consumption of the corresponding refrigeration system. In this paper, a sys-tematic approach for optimizing low-temperature system is presented through mathematical method and exergy analysis. The possibility of＂pockets＂, which appears as right nose section in the grand composite curve （EGCC） of the process, is first optimized. The EGCC with the pockets cutting down is designed as a separate part. A case study is used to illustrate the application of the approach for a HEN of a chilling train with propylene and ethylene refrig-erant system in an ethylene production process.     

基于时段过渡分析的多时段间歇过程质量预测(英文)

Batch processes are usually involved with multiple phases in the time domain and many researches on process monitoring as well as quality prediction have been done using phase information. However, few of them consider phase transitions, though they exit widely in batch processes and have non-ignorable impacts on product qualities. In the present work, a phase-based partial least squares (PLS) method utilizing transition information is proposed to give both online and offline quality predictions. First, batch processes are divided into several phases using regression parameters other than prior process knowledge. Then both steady phases and transitions which have great influences on qualities are identified as critical-to-quality phases using statistical methods. Finally, based on the analysis of different characteristics of transitions and steady phases, an integrated algorithm is developed for quality prediction. The application to an injection molding process shows the effectiveness of the proposed algorithm in comparison with the traditional MPLS method and the phase-based PLS method.     

压力保持系统中一口井的压力恢复分析

The development and application of a new solution is demonstrated for the type-curve analysis and interpretation of well test data from a multiwell reservoir system of both production and injection wells with two-phase flow. The buildup type curves or buildup behavior could be obtained through the solution by using superposition. But a new outer boundary condition for variable pressure boundary must be introduced to obtain the correct pressure buildup solutions by superposition. A technique is shown to determine the deviation time from the infinite-acting semilog radial flow stabilization in the derivatives of pressure, which is calculated with respect to and plotted vs. shut-in time.
Field examples are given to illustrate the use of the proposed method for analyzing transient pressure data from a well located in a multi-well water-injection reservoir. An adaptive genetic algorithm-based method is used to match the pressure and pressure derivative data to estimate reservoir parameters. The validity and applicability of the proposed method are also demonstrated through the examples.     

采用同步策略的化工动态优化求解(英文)

An approach of simultaneous strategies with two novel techniques is proposed to improve the solution accuracy of chemical dynamic optimization problems. The first technique is to handle constraints on control variables based on the finite-element collocation so as to control the approximation error for discrete optimal problems, where a set of control constraints at element knots are integrated with the procedure for optimization leading to a significant gain in the accuracy of the simultaneous strategies. The second technique is to make the mesh refinement more feasible and reliable by introducing length constraints and guideline in designing appropriate element length boundaries, so that the proposed approach becomes more efficient in adjusting elements to track optimal control profile breakpoints and ensure accurate state and control profiles. Four classic benchmarks of dynamic optimization problems are used as illustrations, and the proposed approach is compared with literature reports. The research results reveal that the proposed approach is preferable in improving the solution accuracy of chemical dynamic optimization problem.     

Dual-radiation-chamber coordinated overall energy efficiency scheduling solution for ethylene cracking process regarding multi-parameter setting and multi-flow allocation

Ethylene cracking process is the core production process in ethylene industry, and is paid more attention to reduce high energy consumption. Because of the interdependent relationships between multi-flow allocation and multi-parameter setting in cracking process, it is difficult to find the overall energy efficiency scheduling for the purpose of saving energy. The traditional scheduling solutions with optimal economic benefit are not applicable for energy efficiency scheduling issue due to the neglecting of recycle and lost energy, as well as critical operation parameters as coil outlet pressure(COP) and dilution ratio. In addition, the scheduling solutions mostly regard each cracking furnace as an elementary unit, regardless of the coordinated operation of internal dual radiation chambers(DRC). Therefore, to improve energy utilization and production operation, a novel energy efficiency scheduling solution for ethylene cracking process is proposed in this paper. Specifically, steam heat recycle and exhaust heat loss are considered in cracking process based on 6 types of extreme learning machine(ELM) based cracking models incorporating DRC operation and three operation parameters as coil outlet temperature(COT), COP, and dilution ratio according to semi-mechanism analysis. Then to provide long-term decision-making basis for energy efficiency scheduling, overall energy efficiency indexes, including overall output per unit net energy input(OONE), output-input ratio per unit net energy input(ORNE), exhaust gas heat loss ratio(EGHL), are designed based on input–output analysis in terms of material and energy flows. Finally, a multiobjective evolutionary algorithm based on decomposition(MOEA/D) is employed to solve the formulated multi-objective mixed-integer nonlinear programming(MOMINLP) model. The validities of the proposed scheduling solution are illustrated through a case study. The scheduling results demonstrate that an optimal balance between multi-flow allocation, multi-parameter setting, and DRC coordinated operation is reached, which achieves 3.37% and 2.63% decreases in net energy input for same product output and conversion ratio, as well as the 1.56% decrease in energy loss ratio.     

用于吸附过程开发的从分子水平级开始的多尺度模拟

This article presents a multiscale simulation approach starting at the molecular level for the adsorption process development. A grand canonical Monte Carlo method is used for the prediction of adsorption isotherms of methanol on an activated carbon at the molecular level. The adsorption isotherms obtained in the linear region （or adsorption constant） are exploited as a model parameter required for the adsorption process simulation. The adsorption process model described by a set of partial differential equations （PDEs） is solved by using the conservation element and solution element method, which produces a fast and an accurate numerical solution to PDEs. The simulation results obtained from the adsorption constant estimated at the molecular level are in good agreement with the experimental results of the pulse response. The systematical multiscale simulation approach addressed in this study may be useful to accelerate the adsorption process development by reducing the number of experiments.     

Using hot-vapor bypass for pressure control in distillation columns

Distillation column control is widely explored in literature due to its complexity and importance in chemical and petrochemical industries.In this process,pressure represents one of the most important variables to be controlled.However,there are few studies about how pressure affects the dynamic behavior of distillation columns and most research on distillation column control involve direct manipulation of cooling fluid through the condenser.Nevertheless,such an approach demands constant changes in cooling fluid flowrates that are commonly by the order of tons per hour,which can be difficult to work or even unfeasible in a real plant.Furthermore,this strategy is usually avoided,as it can cause fouling and corrosion acceleration.The hot-vapor bypass strategy fits well as a solution for these issues,eliminating the need to dynamically manipulate cooling fluid flowrates in the condensation unit.This work presents the modeling and simulation of a conventional distillation column for the separation of water and ethanol,in which a comparative study between a conventional pressure control and a control using hot-vapor bypass was performed.The main results were obtained through dynamic simulations which considered various disturbances in the feed stream,and demonstrated superior performance by the hot-vapor bypass system over the usual scheme proposed in literature,while evaluating the Integral Absolute Error (IAE) norm as the control performance index.     

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.     

一种新颖的面向化工过程的实时优化方法(英文)

In this paper, a novel approach termed process goose queue (PGQ) is suggested to deal with real-time optimization (RTO) of chemical plants. Taking advantage of the ad-hoc structure of PGQ which imitates biologic nature of flying wild geese, a chemical plant optimization problem can be re-formulated as a combination of a multi-layer PGQ and a PGQ-Objective according to the relationship among process variables involved in the objective and constraints. Subsequently, chemical plant RTO solutions are converted into coordination issues among PGQs which could be dealt with in a novel way. Accordingly, theoretical definitions, adjustment rule and implementing procedures associated with the approach are explicitly introduced together with corresponding enabling algorithms. Finally, an exemplary chemical plant is employed to demonstrate the feasibility and validity of the contribution.     

Dynamics of a CSTR for styrene polymerization initiated by a binary initiator system

The steady state and dynamic behavior of a continuous stirred tank reactor has been analyzed for free radical solution polymerization of styrene initiated by a mixture of two initiators having different thermal stabilities. From the steady state analysis of the reactor model with a mean residence time as a bifurcation parameter, four unique regions of steady state solutions are identified in an operating parameter space for a given initiator feed composition. A variety of complex bifurcation behavior such as multiple steady states, Hopf bifurcation and limit cycles have been observed and their stability characteristics have been analyzed. The effects of feed initiator composition and the concentration of the initiator in the feed stream on the reactor dynamics are also presented.     

Steady‐state process optimization with guaranteed robust stability under parametric uncertainty

Interest in chemical processes that perform well in dynamic environments has led to the development of design methodologies that account for operational aspects of processes, including flexibility, operability, and controllability. In this article, we address the problem of identifying process designs that optimize an economic objective function and are guaranteed to be stable under parametric uncertainties. The underlying mathematical problem is difficult to solve as it involves infinitely many constraints, nonconvexities and multiple local optima. We develop a methodology that embeds robust stability constraints to steady‐state process optimization formulations without any a priori bifurcation analysis. We propose a successive row and column generation algorithm to solve the resulting generalized semi‐infinite programming problem to global optimality. The proposed methodology allows modeling different levels of robustness, handles uncertainty regions without overestimating them, and works for both unique and multiple steady states. We apply the proposed approach to a number of steady‐state optimization problems and obtain the least conservative solutions that guarantee robust stability. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

Periodic solutions in a porous catalyst pellet—homoclinic orbits

The analysis performed as well as extensive numerical simulations have revealed the possibility of the generation of homoclinic orbits as a result of homoclinic bifurcation in the model which describes transport phenomena and chemical reaction in a porous catalyst pellet. A method has been proposed for the development of a special type of diagrams—the so-called bifurcation diagrams. These diagrams comprise the locus of homoclinic orbits together with the lines of limit points bounding the region of multiple steady states as well as the locus of the points of Hopf bifurcation. Thus, they define a set of parameters for which homoclinic bifurcation can take place. They also make it possible to determine conditions under which homoclinic orbits are generated.Two kinds of homoclinic orbits have been observed, namely semistable and unstable orbits. It is found that the character of the homoclinic orbit depends on the stability features of the limit cycle which is linked with the saddle point.Very interesting dynamic phenomena are associated with the two kinds of homoclinic orbits; these phenomena have been illustrated in the solution diagrams and phase diagrams.     

气相法聚乙烯工艺冷凝态操作模式的稳定性和动态行为

气相法聚乙烯工艺冷凝态操作模式由于显著提高了循环气移热能力和反应器时空产率,已成为流化床乙烯聚合工艺的主流操作模式。建立了气相法聚乙烯工艺冷凝态操作模式的数学模型,包括流化床反应器模型,多级换热器模型和反应温度、压力以及循环气组成的控制模型。基于此,采用流程模拟方法,计算了系统在反应器温度采用闭环控制时的稳态解;根据系统对小扰动的动态响应特点,定性判断了反应器温度采用开环控制和闭环控制时聚合反应系统的稳定性;考察了系统对1-己烯分压和催化剂进料速率的阶跃响应特性。结果表明,反应器温度采用闭环控制时,聚合反应系统在所考察操作条件下均是稳定的,而采用开环控制时,解曲线被分叉点分割为稳定区域和不稳定区域。反应器温度对1-己烯分压阶跃变化的动态响应表明聚合反应系统存在长、短周期两类振荡,表明冷凝态操作模式下乙烯聚合反应过程是一个多控制回路耦合的复杂过程。     

Global solution approaches in equilibrium and stability analysis using homotopy continuation in the complex domain

Recently, significant attention has been shown to physical and chemical equilibrium and stability analysis in the real and complex domains. In this work, a new procedure involving the continuation method in the complex domain using bifurcation theory is propounded. Based on this method, homotopy branches in real and complex space are connected to each other through bifurcation branches. Thus, by just one initial guess, multiple solution branches are found. When calculations are only made in the real domain, multiple solutions are not always found from an arbitrary initial guess. Examples are presented to show the application of the method to nonlinear sets of equations in phase equilibrium, chemical and phase equilibrium, and stability analysis. These types of problems are believed to contain significant nonlinearities in process simulations. The results can be applied to flowsheet calculations.     

Multiplicity and stability of premixed laminar flames: an application of bifurcation theory

Numerical bifurcation techniques are used to describe multiple steady states for a premixed, laminar flame stabilized on a flat flame burner. The flame is assumed to be adiabatic, and the kinetic mechanism is approximated by a single reaction. The numerical methods make it possible to determine all steady states and eliminate computational difficulties near singular points. The possibility of defining solutions near singularities is particularly important in flame modeling for it is near such points that ignition and burn-out may occur. Three steady states are identified: a stable upper state corresponding to a flame burning at or near the adiabatic flame temperature, a lower solution representing an extinguished stable state, and an unstable intermediate state. Sensitivity of the solutions to changes in kinetic parameters is enhanced near burn-out. It is expected that the ability to predict flame behavior near such singular points will be particularly useful in the determination of flame kinetics.     

旋转弯曲管内流动的数值模拟

为了分析弯曲管内流动的稳定性、解的分支产生以及流动类型的变化,对正方形断面弯曲管内的流动进行了数值模拟计算。这个流动除了外墙以外的其他墙壁随着弯曲管中心轴旋转,沿着管的轴向具有压力梯度。使用波谱分析法对内圆筒旋转和由压力综合作用下所产生的流动进行了计算。流动是以螺旋泵为模型的。获得了断面二次流动的变化规律,相对于断面中心线得到了2涡流,4涡流,8涡流以及非对称的流动类型,并获得了多重解。对得到的解,进行了线性稳定性分析,并且求解了流量的变化特性。     

Linear stability analysis of high- and low-dimensional models for describing mixing-limited pattern formation in homogeneous autocatalytic reactors

In this paper, we perform linear stability analysis of high- and low-dimensional models for describing mixing-limited pattern formation in fast, homogeneous autocatalytic reactions occurring in isothermal tubular reactors. We consider three different models of varying dimensionality—the 3D convection-diffusion-reaction (CDR) model is the high dimensional one, and the Liapunov–Schmidt reduction based spatially averaged two-dimensional CDR model and its regularized form are the two low-dimensional ones. For each of these three models, steady state bifurcation diagrams that show the presence of multiple steady states were obtained and the stability of these multiple steady states to transverse perturbations was analyzed using linear stability analysis. Parametric analysis of the steady state bifurcation diagrams shows that for sufficiently large values of transverse Péclet number p, mixing-limited patterns may emerge from the unstable middle branch that connects the ignition and extinction points of an S-shaped bifurcation curve. Comparison of the bifurcation diagrams and the stability boundaries of the two low-dimensional models with that of the 3D CDR model reveals that the regularized form of the low-dimensional model has higher accuracy and a larger region of validity than the averaged form and is therefore recommended over the latter.     

Bifurcation analysis of two continuous bioreactors operated in series with recycle

In this paper, bifurcation analysis has been carried out for two continuous bioreactors operated in series with recycle from the second reactor. The existence of multiplicity of steady states is analyzed by considering Contois growth kinetics in the process model. It was observed that there exist two possible steady states of which one is trivial (wash out condition). Stability analysis is carried out to determine the stability of these steady states and it was observed that both these steady states are unstable in nature. Bifurcation analysis has been carried out for substrate and biomass concentration with dilution rate as the bifurcation parameter. Effect of recycle ratio, substrate separation factor and biomass separation factor is studied and analyzed. It was observed that Hopf bifurcation occurs at a dilution rate of 1.0208 with purely imaginary Eigen values which showed that sustained oscillatory behavior exists in the substrate concentration of the second reactor. The significance of different bifurcation points and the operating conditions by considering biomass and substrate concentrations in each reactor is studied and it was observed that the bioreactors need to be operated at intermediate dilution rates to obtain improved conversion and yield.     

GLOBAL STABILIZATION OF A BIOLOGICAL REACTOR BY LINEAR FEEDBACK CONTROL

A classical substrate inhibition model for biological reactors with PI controllers is subjected to a rigorous nonlinear analysis. The operating conditions and control settings that ensure global stability of the set-point are derived from bifurcation studies of the solution branches with the controller gains as the bifurcation parameters. The global stability of the set-point can be destroyed by co-existing extraneous attracting states, both steady and time-dependent, which may be introduced by the controllers that are designed to stabilize the set-point locally.