Multivariate time delay analysis based local KPCA fault prognosis approach for nonlinear processes☆

Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in-cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal com-ponent analysis. In this approach, mutual information estimation and Bayesian information criterion (BIC) are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation (BP) network is applied whose input is multivar-iate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis (LKPCA) model for incipient fault prognosis. The new method has been exemplified in a sim-ple nonlinear process and the complicated Tennessee Eastman (TE) benchmark process. The results indicate that the new method has superiority in the fault prognosis sensitivity over other traditional fault prognosis methods. ? 2016 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. Al rights reserved.     

Measurment of gas-liquid two-phase slug flow with a Venturi meter based on blind source separation☆

We propose a novel flow measurement method for gas–liquid two-phase slug flow by using the blind source sep-aration technique. The flow measurement model is established based on the fluctuation characteristics of differ-ential pressure (DP) signals measured from a Venturi meter. It is demonstrated that DP signals of two-phase flow are a linear mixture of DP signals of single phase fluids. The measurement model is a combination of throttle re-lationship and blind source separation model. In addition, we estimate the mixture matrix using the independent component analysis (ICA) technique. The mixture matrix could be described using the variances of two DP sig-nals acquired from two Venturi meters. The validity of the proposed model was tested in the gas–liquid two-phase flow loop facility. Experimental results showed that for most slug flow the relative error is within 10%. We also find that the mixture matrix is beneficial to investigate the flow mechanism of gas–liquid two-phase flow.     

Development of a numerically efficient approach based on coupled CFD/FEM analysis for virtual fire resistance tests—Part B: Deformation process of a steel structure

In the present study, the structural analysis of a three-parted steel door during a fire resistance test was examined by FEM simulation. The structural analysis is part of a coupled CFD/FEM simulation approach developed for the prediction of fire resistance tests. The basis of this follow-up work was the calculated temperature in the test specimen from CFD to predict the thermal stresses, deformation and gap formation between the door parts. The spatial information of the temperature in the test specimen was exported. Subsequently, the thermal expansion of the door and the resulting stresses and gaps were calculated. To validate the FEM simulation, the deformation of the steel door was observed. It was found that the simulation predicted the deformation of the steel door in close accordance to the measurement. The maximum displacement was found in the centre of the construction with 141 mm, whereas the simulation predicted a value of 133 mm. In addition to the deformation of the door, also the prediction of the gap formation was validated against the flue gas leakage. The first flue gas exit occurred already after 120 seconds, which was in spatial and temporal conjunction with the maximum gap predicted in the simulation.     

Thermodynamic analysis on the direct preparation of metallic vanadium from NaVO3 by molten salt electrolysis☆

A novel and environmentally friendly route to directly prepare metallic vanadium from Na VO_3 by molten salt electrolysis is proposed.The feasibility about the direct electro-reduction of NaVO_3 to metallic vanadium is analyzed based on the thermodynamic calculations and experimental veri fications.The theoretical decomposition voltage of NaVO_3 to metallic vanadium is only 0.47 Vat 800°C and much lower than that of the alkali and alkali earth metal chloride salts.The value is slightly higher than that of low-valence vanadium oxides such as V_2O_3,V_3O_5 and VO.However,the low-valence vanadium oxides can be further electro-reduced to metallic vanadium thermodynamically.The thermodynamic analysis is veri fied by the experimental results.The direct preparation of metallic vanadium from NaVO_3 by molten salt electrolysis is feasible.     

UV enhanced gas-solid synthesis of chlorinated poly vinyl chloride characterized by a UV-Vis online analysis method☆

Dynamic characteristics of UV enhanced gas–solid PVC chlorination process were revealed by a UV–Vis spectral online analysis method. Experimental results showed an instantaneous increase of the chlorination rate as soon as UV lightwas affiliated, which demonstrated the intensified effect of UV radiation on PVC chlorination directly. Different affiliationmethods of UV light were then studied, proving that continuous UV radiation could enhance the chlorination process significantly while intermittent UV radiation was able to initiate the chlorination reaction once it was conducted. Besides, experiments were carried out to study the influences of parameters on the chlorination process such as UV wavelength, chlorination temperature, partial pressure of chlorine gas and PVC raw materials. Among all the parameters, chlorination temperature and partial pressure of chlorine gas were testified as two key factors to determine the chlorination performance. Thermal analysis of CPVC products showed that their corresponding properties such as the glass transition temperature (T_g) and the homogeneity of chlorine distribution in polymer phase were improved with the increase of chlorine content.     

Experimental research on breakup of 2D power law liquid film☆

On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict the breakup characteristics of the power law film. The predicting formulas of stripping breakup length and diameter of ligament were put forward presently. Through high-speed photography and laser light sheet illumination, different breakup characteristics of flat power law film under different conditions were derived. The characteristic dimension of breakup regimes were defined and extracted. The effects of several parameters (injection pressure, ambient pressure, nozzle structure and fluid property) on the stripping breakup length and spray angle were investigated. The results revealed that increasing both the velocity of liquid film and the ambient pressure facilitated the breakup of film, reduced the stripping breakup length and enlarged the spray angle in different extents. The comparison between theoretical and experimental results was conducted to validate the feasibility of the linear stability theory.     

Development of a filtered interphase heat transfer model based on fine-grid simulations of gas–solid flows

The filtered interphase heat-transfer coefficient for coarse-grid simulations of gas–solid flows can be obtained via a correction (Q) to its microscopic counterpart. The numerical results show that a good linear correlation between Q and the subgrid drift temperature exists at various filtered solid volume fractions, filter sizes and Reynolds numbers, where the subgrid drift temperature is the correlation between the fluctuating temperature of the gas phase and the fluctuation of the gas volume fraction. Since Q can be determined solely by one subgrid quantity, closure for Q is directly pursued. It is found that Q correlates surprisingly well with the product of the filtered solid volume fraction and the filtered temperature difference between the two phases normalized by the filtered heat transfer at a larger scale than the considered coarse grid. A fitting correlation is formulated based on this observation, and its predictability is evaluated in an a priori test.     

Economic analysis in product design——A case study of a TCM dietary supplement

An approach for the economic analysis of chemical product design is proposed. It takes into account of customers' preference on product quality and economic considerations such as pricing, profit, market share, capital investment, and operating cost. The activities needed to support business decision making – identifying product quality, estimating product cost, calculating financial metrics, and performing make–buy analysis – are discussed.The design of a Ganoderma lucidum dietary supplement, a traditional Chinese medicinal(TCM) product, is used to illustrate all the activities in this approach.     

Development of a filtered reaction rate model for reactive gas–solid flows based on fine-grid simulations

The filtered reaction rate for the coarse-grid simulations of reactive gas–solid flows can be obtained via a correction to its microscopic reaction rate. The correction term is defined as the mesoscale effectiveness factor η_Δ , which is the ratio of the reaction rate obtained from the fine-grid simulations to that obtained from the coarse-grid simulations. The considered reaction is an isothermal, solid-catalyzed surface reaction with a power law reaction rate model. The simulation results show that the mean η_Δ is almost invariant with the reaction orders at the same Damköhler number. A closure correlation for the mean η_Δ is formulated. However, the standard deviation of η_Δ is found to be quite large. A presumed probability density function model is proposed to capture the fluctuating properties of η_Δ . The predictability of the closure correlations are evaluated via performing the filtered two fluid model simulations in circulating fluidized beds of ozone decomposition.     

Analysis of the nonlinear dynamic characteristics of two-phase flow based on an improved matrix pencil method☆

Gas–liquid two-phase flow is complex and has uncertainty in phase interfaces, which make the two-phase flow look very complicated. Even though the flow behavior(e.g. coalescence, crushing and separation) of single bubble or bubble groups in the liquid phase looks random, combining some established characteristics and methodologies can find regularities among the randomness. In order to excavate the nonlinear dynamic characteristics of gas–liquid two-phase flow, the authors developed an improved matrix pencil(IMP) method to analyze the pressure difference signals of the two-phase flow. This paper elucidates the influence of signal length on MP calculation results and the anti-noise-interference ability of the MP method. An IMP algorithm was applied to the fluctuation signals of gas–liquid two-phase flow to extract the mode frequency and damping ratio, which were combined with the component energy index(CEI) entropy to identify the different flow patterns. It is also found that frequency, damping ratio, CEI entropy and stability diagram together not only identify flow patterns, but also provide a new way to examine and understand the evolution mechanism of physical dynamics embedded in flow patterns. Combining these characteristics and methods, the evolution of the nonlinear dynamic physical behavior of gas bubbles is revealed.     

Dynamics of liquid-liquid systems based on linear thermodynamics of irreversible processes

The use of non-equilibrium models for integrated processes involving liquid-liquid systems has increased in recent years. These processes often exhibit complex dynamic behavior. These dynamical systems still pose many open questions, e.g. with regard to the sources of multiple steady states (MSS). This article analyzes the effect of mass transfer on the MSS of these systems. A generalized non-equilibrium modeling approach based on linear thermodynamics of irreversible processes (LTIP) is presented, and the dynamics of the system is studied systematically. It is shown that the non-linearity present in even the simplest non-ideal activity model acts as a source for MSS. The parameters that affect the solubility, e.g. temperature, can play a critical role on the existence of MSS in the system. A geometrical visualization of the MSS is also illustrated.     

ON THE PARAMETER-SPACE CLASSIFICATION OF THE DYNAMIC BEHAVIOR OF A CONTINUOUS MICROBIAL FLOW REACTOR

Recently Agrawal et al.¹ classified the dynamic behavior of continuous stirred tank fermentor for the Monod's model and the two parameter hump function model with variable yield coefficient in the parameter space. We employed the more general three parameter substrate inhibition model which includes the Monod's model as a limiting case, derived the boundary equations which rigorously divide the parameter space of different dynamic behavior, and showed the interesting phenomenon that a limit cycle suddenly vanished for the slight change in the Damköhler number by computer simulation.     

Multiplicity Regions in a Moving‐Bed Reactor: Bifurcation Analysis,Model Extension,and Application for the High‐Temperature Pyrolysis of Methane

This paper reports studies on the bifurcation analysis and the generation of regions of multiplicity in the operation of moving‐bed reactors. The studies were first carried out for a generalized model, which allows the investigation of the effect of various scenarios, such as changes in heat capacity or the number of moles with reaction, as well as the previously unstudied equilibrium and allothermic reactions. The insights gained from this extension were then applied to an actual reaction, namely the high temperature pyrolysis of methane.     

A bifurcation approach to understanding instabilities in gas-fluidized beds using a single phase compressible flow model

It has been shown that the equations of motion and continuity for the particles in a fluidized bed can be related to those of a compressible fluid acted upon by a density-dependent force. In the previous work on the compressible flow equations, the solution structure of fully developed plane (one-dimensional) waves was computed. It was shown that the plane waves can lose stability in the lateral direction. In this work we study the two-dimensional solutions which reveal that bubble-like solutions can evolve both from the plane waves as well as from the uniform state. A representative value of the lateral wavenumber is chosen and the global bifurcation diagram is explored, which consists of a number of distinct one- and two-dimensional branches. The existence of mixed mode and double humped solutions is demonstrated and transient simulations are used to examine the mechanism of density wave development and coalescence.     

Application of Lyapunov's Methods for Analyzing the Stability of a Tubular Chemical Reactor with Recycle

The first and second Lyapunov methods were adapted to analyze the stability of a tubular chemical reactor with recycle. The criterion of local stability in the form of inequalities was derived using Lyapunov's first method. It is an explicit algebraic form, despite the fact that the mathematical model of the reactor is a partial differential problem with a boundary condition. As part of the second Lyapunov method, a mathematical criterion for non-local stability was derived in the form of an increase of Lyapunov's function. Both criteria are presented on graphs.     

Steady-state multiplicity analysis of two-stage-riser catalytic pyrolysis processes

New two-stage-riser fluidized catalytic pyrolysis (TSRFCP) for maximizing propylene yield technology is considered as an efficient route to moderate the propylene demand/supply gap and to lower the propylene price. The possibility of existence of complex nonlinear behavior associated with the TSRFCP process puts limitations on the supervision of this system. Based on the developed and validated model for the TSRFCP process, this paper focuses on the elucidation of multiple steady states and relevant (in) stability characteristic over a wide range of operating condition. First, graphic analysis of heat generation/removal curves demonstrates that the TSRFCP process has at least one steady state and a maximum of three output steady states under the considered operating conditions and uncertainties such as cooling water flow rates and Conradson carbon residue. Then, operating maps revealing topologies between important input and output variables can disclose detailed nonlinear behavior (input/output multiplicity). Moreover, depending on the choice of the input variable and the relevant operating/design condition, input multiplicity may exist. In short, these results can guide the succeeding control structure selection for realistic TSRFCP processes.     

A numerical bifurcation analysis of nonlinear oscillations in crystallization processes

The main aim of this work is the theoretical prediction and analysis of the nonlinear behavior of crystallization processes. As a first step towards the theoretical analysis a fairly simple population balance model including fines dissolution and classified product removal has been considered. By means of numerical bifurcation and stability analysis, regions in the parameter space of the operating conditions and the physical properties with periodic behavior have been predicted. Due to the simplicity of the underlying model the results are only of qualitative nature. Future work will focus on a quantitative prediction of the nonlinear behavior with more detailed models and an experimental verification.     

Numerical strategies for the bifurcation analysis of perfectly stirred reactors with detailed combustion mechanisms

The paper introduces a numerical tool based on a predictor–corrector continuation algorithm to obtain the bifurcation analysis of a perfectly stirred reactor with detailed reaction mechanisms.Each step of the continuation algorithm is reviewed and adapted to handle reaction mechanisms with hundreds of species and thousands of reactions. Particularly, the adoption of a Broyden solver in the predictor–corrector algorithm and a new formulation of the test functions are proposed. The implementation in Matlab and the adoption of the CANTERA Toolbox, make the tool easily applicable to reaction mechanisms available in CHEMKIN format.To validate and demonstrate the capability of the tool, the full equilibrium curves have been obtained for three different cases, having increasing number of species and reactions: methane–air (GRIMech.1.2), simple surrogates of Jet-A in air (JetSurF2.0) and a ternary surrogate of Jet-A in air (CRECK). The tool gets performances that make affordable the computations even with desktop computers.     

Design of a Dividing‐Wall Column Considering its Multiple Steady State Characteristic

A dividing‐wall column (DWC) may have more than one solution of liquid and vapor split ratio for the same feed and product streams under a fixed number of stages and reflux ratio, so the multiple steady states (MSS) of a DWC in the design stage should be considered. An improved design method of a DWC is proposed by studying its MSS characteristics. Additional steps are inserted after optimization to check if MSS exist for the obtained optimal solution of vapor and liquid split ratio, and further to select the best candidate. Finally, two cases of three‐product DWCs are described to verify this method. The results indicate that multiple solutions exist for these cases, which confirm the necessity of this method and provide an important guidance for the flowing design of a DWC.     

The bifurcation behavior of a polyurethane continuous stirred tank reactor

In this work the open-loop nonlinear bifurcation analysis of a continuous stirred tank reactor where polyurethane polymerization reactions take place is carried out. The effect of potential manipulated, disturbance and design variables on the reactor nonlinear behavior is addressed. Moreover, the impact of cascade feedback control on the steady-state multiplicity pattern is also discussed. It is shown that cascade control introduces new nonlinearity patterns increasing closed-loop sensitivity.