Predicting cone-in-cone blender efficiencies from key material properties

Blending of powders and granular materials is a critical unit operation in many industries, yet the ability to predict blending effectiveness lags well behind our ability to create new and novel blenders. As a result of this, production plants must rely on vendor blending tests conducted on small scale model blenders to determine if their specific material will work in the proposed blender design. Once these blending tests are conducted, engineers must then use past experience and conservative design practices to scale-up to full scale units at process flow rates.The difficulty in predicting blending efficiencies arises from the fact that blending performance depends on basic material properties, blender geometry, blender flow rates, and blender operation parameters. These effects are convoluted during blending operation. Successful scale-up would require understanding how to separate the influence of these four effects. If this could be accomplished, blender performance could be determined by measuring simple material properties, predicting blender velocity profiles, and computing blender efficiencies from predicted velocity patterns. This method would allow separation of factors affecting blender performance and provide a means of reliable scale-up using simple material properties and specified blenders geometries.This paper presents a methodology of predicting blender performance in simple in-bin blenders using easily measured material properties. It discusses blender optimization and determines the influence of gas pressure gradients on blender flow and operation. The specific blender analyzed is the cone-in-cone blender and the analysis suggests that blender performance depends on wall friction parameters for conditions where input concentration fluctuations occupy much of the blender volume. However, blending action appears to be independent of friction angle for conditions where there are many concentration fluctuations within a blender volume. The analysis also shows that gas pressure gradients can lead to stagnant region formation.     

Impact of process parameters on critical performance attributes of a continuous blender—A DEM‐based study

A discrete element method‐based computational study carried out to study the effect of impeller design, speed, and input feed rate on the performance of a continuous powder blender is presented. The blender performance was characterized using the mean particle residence time, the residence time distribution, the number of blade passes experienced by the powder, and the mean centered variance. The powder residence time decreased with increasing impeller speed; however, the number of blade passes experienced a maximum at an intermediate speed. The effects of feed rate and impeller design were more prominent at lower speeds. Lower feed rate resulted in the powder experiencing higher number of blade passes. The number of blade passes was also higher for the alternate blade pattern when compared to the forward pattern. The computational findings were compared with an experimental study which showed that the model captured the essential flow dynamics well. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

The continuous mixing of segregating particles

Earlier work has shown that when non-segregating particles are fed to a continuous mixer the fluctuations in the output stream can be predicted if the input fluctuations and residence time distribution for the mixer are known. In this paper the work is extended to particles which segregate in the mixer. The amount of segregation occurring is characterised by a steady state variance, that is the variance of composition fluctuations in the exit stream when a mixture containing no fluctuations is fed to the mixer. It is shown that when known composition fluctuations are fed to the mixer the variance for the output stream can be predicted by adding together the steady state variance and the variance predicted for no segregation, using the residence time distribution. Predicted variances agree with the experimental results obtained for a continuous fluidized bed mixer.     

The thermodynamics of high shear blending

As a key constituent in many aerosol powder formulations, the properties of inhaled lactose greatly influence the overall performance of the pharmaceutical powder in inhalers. The interparticle forces defining pharmaceutical performance are markedly affected by the energy input during the high shear blending process. By conducting a number of lactose blending experiments in a small-scale pharmaceutical high shear blender, heat generation in lactose during blending was studied and shown to be consistently predictable. Experiments were then conducted in a larger high shear blender to quantify the energy input into powder using an energy balance equation. A set of relations were developed requiring only the powder temperature and jacket water temperature to approximate energy input into lactose at a given impeller speed and blend time in a high shear blending process. Additionally, this study sets out to substantiate the assumptions made in the proposed energy balance model. These experiments could not identify all possible sources of error; however, evidence is presented suggesting that energy input due to impeller shaft heating is negligible. As a result, the set of relations should be applicable for any high shear blender, given a constant blade size and shape. This analysis of powder heating with respect to blending parameters could be applied to tune blending parameters to minimize powder heating and the resulting change in powder properties. These experiments have provided the framework to understand power input in high shear blending for a range of blend parameters.     

制备工艺对微乳化柴油稳定性能的影响

为了考察制备工艺对微乳化柴油稳定性能的影响,采用单因素变化试验和正交试验设计安排试验,系统分析了制备微乳化柴油时的温度、搅拌速度、搅拌方式、试剂的添加顺序以及各工序搅拌时间对其稳定性能的影响。结果表明:温度为25～35℃,搅拌速度为300～500r/m in,添加顺序为乳化剂和柴油先混合,再加入水,最后加入助乳剂,各工序搅拌时间均为5m in时所制备的微乳化柴油稳定性好。结论为制备微乳化柴油时温度、搅拌速度、搅拌时间以及添加顺序对其稳定性能影响较大,搅拌方式对其稳定性能影响较小。     

An input/output approach to the optimal transition control of a class of distributed chemical reactors

An input/output approach to the optimal concentration transition control problem of a certain type of distributed chemical reactors is proposed based on the concept of residence time distribution, which can be determined in practice by using data from experimental measurements or computer simulations. The main assumptions for the proposed control method to apply are that the thermal and fluid flow fields in the reactor are at pseudo-steady-state during transition and that the component whose concentration is to be controlled participates only in first-order reactions. Using the concept of cumulative residence time distribution, the output variable is expressed as the weighted sum of discretized inputs or input gradients in order to construct an input/output model, on the basis of which a constrained optimal control problem, penalizing a quadratic control energy functional in the presence of input constraints, is formulated and solved as a standard least squares problem with inequality constraints. The effectiveness of the proposed optimal control scheme is demonstrated through a continuous-stirred-tank-reactor (CSTR) network and a tubular reactor with axial dispersion and a first-order reaction. It is demonstrated through computer simulations that the proposed control method is advantageous over linear quadratic regulator (LQR) and proportional-integral (PI) control in terms of control cost minimization and input constraint satisfaction.     

System Identification and Feedback Control of an Aerosol Production Process

ABSTRACT

A method for determining the relationship between the input (generator output rate) and output (chamber aerosol concentration) of an aerosol generating system is discussed. This relationship is modeled in terms of discrete transfer functions that separate the input that results from the physical aspects of the generating system from the input that is a result of the noise inherent to the process. A computer-aided design (CAD) software package was used to estimate these transfer functions and simulate the response of the modeled system to step-changes in generator output rate. The estimated transfer functions were then used to design a feedback control system that incorporated a proportional-integral-derivative (PID) control algorithm. This algorithm effectively established new concentration levels after step-changes in generator output rate of various magnitudes were made.     

An analysis of chemical reactor stability and control—XVI: The stochastic stirred pot

A continuous stirred tank reactor subject to random fluctuations in flow rate and inlet temperature was simulated on a hybrid computer. The stochastic response of the reactor about unique stable deterministic steady states was studied as a function of the damping coefficient and response time of the deterministic system and the power spectrum of the stochastic input. It was found that the stochastic response could be classified into categories similar to those used for forced periodic systems according to the relationship between the deterministic system response time and the 90% cut-off frequency of the stachastic input. The nature of the stochastic response is predictable for relatively low frequency inputs but unexpected results may occur at intermediate frequencies. The magnitude of reactor state fluctuations was seen to be dependent on the deterministic damping coefficient. The distribution of reactor states was studied as a function of input process variance and it was found that the distribution can become bimodal even when the associated deterministic steady state is unique.The concept of stochastic stability is discussed and several practical stochastic stability definitions are proposed. The stochastic stability of the random systems was seen to be well described by the stochastic regions of operation predicted by the input process power spectrum and the deterministic system response time. The input variance levels necessary to produce stochastic instability can be estimated in the Quasi Steady region of operation. It was found that exposure of an autonomous limit cycle about a unique unstable deterministic steady state to high frequency random inputs may lead to effective stabilization.     

Relative time‐averaged gain array (RTAGA) for distributed control‐oriented network decomposition

Input‐output partitioning for decentralized control has been studied extensively using various methods, including those based on relative gains and those based on relative degrees and sensitivities. These two concepts are characterizations of long‐time and short‐time input‐output response, respectively. A unifying new input‐output interaction measure, called relative time‐averaged gain, which characterizes the input‐output interactions during a time scale of interest for linear time‐invariant systems is proposed. This measure is used as a basis for community detection in the input‐output bipartite graph of a process network to produce subnetworks whose responses are weakly coupled in the time scale of interest. As such, the resulting decomposition accounts for both response characteristics and the network topology, and can be used efficiently for distributed control architecture design. In a case study, the proposed decomposition is applied to the distributed model predictive control of a reactor‐separator benchmark process. © 2018 American Institute of Chemical Engineers AIChE J, 64: 1682–1690, 2018     

Evaluating the mixing performance of a ribbon blender

This paper investigates the effects of processing and equipment parameters of a ribbon blender (i.e. loading method of lubricant, fill level, blade speed and blade design) on magnesium stearate homogeneity. A core sampling technique is used to obtain at least one hundred samples per sampling event, which are extracted throughout the blender and yield a thorough characterization of the entire bed. The results presented here can be used as a guideline to develop appropriate blending processes and characterization protocols for ribbon blenders.     

Evaluation of Performance of Periodically Operated Reactors for Single Input Modulations of General Waveforms

The nonlinear frequency response (NFR) method is used for evaluating the time‐average performance of a chemical reactor subjected to single input modulations of general waveforms, by using Fourier series for representing the input and Volterra series for representing the output. Both the input and the output are approximated by finite sums. The obtained results are applied for the case of a square‐wave input modulation. As a case study, the improvement of an isothermal continuous stirred‐tank reactor with simple reaction mechanism with modulation of the inlet reactant concentration is used and the results are tested on a numerical example.     

Estimating short-run operating costs for a reverse osmosis desalting plant

This paper uses an engineering-economic approach to estimate operating costs for a reverse osmosis desalting plant. The emphasis is on developing long-run costs for operating at design capacity and associated costs (penalties) for outputs that deviate from this design capacity. This information is important in determining optimal capacity expansion planning over time. Pertinent costs considered include membrane replacement, chemicals, energy and labor. Using a basic RO membrane model, local concentration effects and other mechanical-chemical processes are simulated in a digital computer program. This program was used to compute the appropriate long-run and short-run costs. Results show that while long-run operating costs are approximately constant with scale, the cost per unit output of operating below or above design output is greater than unit cost at design output.     

Dynamic modelling of a gas phase catalytic fixed bed reactor—III: Identification using binary pulse sequence test signals

The dynamics of a gas phase catalytic reactor is identified experimentally using broad bandwidth Walsh-Hadamard sequences as test signals.The binary test signals are designed from Walsh functions as they appear in Hadamard matrices. Each element of the matrix is multiplied with a fundamental signal with zero mean.The input and output time series are Fourier analysed to give local frequency responses. The reliabilities of the estimated gain and phase angels are evaluated and provide a useful guide for experimental design and interpretation. Results from a Walsh-Hadamard sequence are compared to results from a square wave signal and found to give similar accuracy.Good agreement between experimental values and theoretical predictions is obtained. The test signal period should be at least three times the thermal residence time or generally the dominating time delay.     

A COMPOSITE LINEAR MODEL GENERATING A STATIONARY STOCHASTIC PROCESS WITH GIVEN THIRD-ORDER AUTOCORRELATION FUNCTION

Abstract. A composite linear model is proposed which generates a non-Gaussian stationary stochastic process with a given third-order autocorrelation function and a white power spectrum. The design of the model is based on the fact that a type of finite-impulse-response linear system with a non-Gaussian white input series produces an output process whose third-order correlations exist only for special time lags. An arbitrary third-order autocorrelation function can be constructed by superposing output processes of this type. The model requires at most 2 L² + 4 L + 1 independent identically distributed (i.i.d.) input processes for the third-order autocorrelation function with the largest time lag L . Results of numerical experiments confirm the validity of the model.     

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.     

Model predictive control of a second-order hyperbolic transport-reaction process

The model predictive controller (MPC) design is developed for a tubular chemical reactor, considering a second-order hyperbolic partial differential equation as the model of the transport-reaction process with boundary actuation. Without loss of generality, closed–closed boundary conditions and relaxed total flux are assumed. At the same time, the model is discretized in time by the Cayley–Tustin method, and, under the assumption that only the reactor's output is measurable, the observer design for the state reconstruction is addressed and integrated with the MPC design. The Luenberger observer gain is obtained by solving the operator Ricatti equation in the discrete-time setting, while the MPC accounts for constrained and optimal control. The simulations show that the output-based MPC design stabilizes the system under the input and output constraints satisfaction. In addition, to address the models' disparities, the results for both parabolic and hyperbolic equations are presented and discussed.     

基于人工神经网络的电力负荷预测算法研究

电力负荷数据管理系统是电力营销技术支持系统的组成部分,对电力系统运行有着重要的辅助作用。采用神经网络预测模型．设计输入变量和确定神经网络结构的方法和算法．可以使得从历史样本知识数据到最终预测模型的建模过程变得简单明了,便于实际应用。预测方法是使用MATLAB建立模型,对24个负荷点预测,采用多输入单输出的神经网络预测每天的整点负荷值。因为电力负荷与环境因素有关,在输入、输出向量设计中输入变量加入天气特征值。根据输入、输出向量对BP网络设计。该算法结构简单,最后进行短期负荷预测仿真,仿真结果表明其有较好的预测精度。该模型具有网络结构较小,训练时间短的优点,并考虑不同小时负荷差异,易于实现,具有较高的预测精度．预测误差在15％以下,一定程度上克服传统算法收敛速度慢,容易陷入局部积小的缺点。     

Melt flow indexer evidence of high‐temperature transitions in molten high‐density polyethylenes

A melt flow indexer (MFI) was used to investigate high‐temperature transitions in melts of high‐density polyethylene (HDPE). The MFI data were obtained in the range 190–230°C. These transitions were found in the MFI at about 210 and 225°C and reproduced in a Haake melt blender. Polystyrene was used in the blender experiment to demonstrate typical amorphous behavior. For HDPE melts, the MFI–temperature behavior and the torque–temperature data of the blender were found to be alternative images of the same anomalous temperature dependency in the range 210–225°C. Also, the Haake melt blender was able to reproduce the 150°C transition observed by Kolnaar and Keller in the extrusion of HDPE. Regardless of the simplicity of the MFI device, results are in agreement with our previous DSC findings. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1309–1313, 2004     

Studies on the Applicability of Artificial Neural Network (ANN) in Continuous Stirred Ultrafiltration

An artificial neural network model of a continuous stirred ultrafiltration process, is proposed in the present study, which is able to predict permeate volumetric flux and permeate concentration at different bulk concentration, stirrer speed, pressure and time. Because of the complexity in generalization of the phenomenon of ultrafiltration by any mathematical model, the neural network proves to be a very promising method for the purpose of process simulation. The network uses the Back‐propagation Algorithm for evaluating the connection strengths, representing the correlations between inputs (bulk concentration, stirrer speed, pressure and time) and output (permeate concentration and flux). The network employed in the present study uses four input nodes corresponding to the operating variables, and two output nodes corresponding to the measurement of the performance of the network (flux and permeate concentration). Experiments were performed to constitute the learning databases for the continuous stirred ultrafiltration process using PEG‐6000 solute, and cellulose acetate membrane of 5000 MWCO. The network employed in the present study uses two hidden layers, with the optimum number of nodes being thirty and twenty. A leaning rate of 0.3, and momentum factor of 0.4 was used. The results predicted by the model were in good agreement with the experimental data, and the average deviations for all the cases are found to be well within ±10 %.     

烷氧基化釜式反应器设计探讨

合理地进行烷氧基化釜式反应器的设计,对于提高非离子表面活性剂和聚氨酯聚醚生产能力和产品质量具有显著意义。因此本文从流程设计、反应器的结构尺寸、搅拌器的型式选择、搅拌器的功率计算、反应器的传质以及反应器的传热等方面详细论述了烷氧基化釜式反应器的设计过程。