Modelling of fluidized bed reactors—VI(a): An isothermal bed with stochastic bubbles

A two-phase stochastic isothermal fluidized bed reactor model with first order reaction in the dense phase is developed to investigate the significance of the fluctuating nature of fluidized beds on reactor performance. Several stochastic processes are employed as the overall mass transfer coefficient between phases. Analytical moment solutions are obtained for white noise coefficients while hybrid computer simulation was used for correlated stochastic coefficients. Results indicate that a gamma distributed coefficient is preferred over white noise and Gaussian correlated coefficients. When compared with the deterministic model, randomness in the mass transfer coefficient is seen to lead to a decrease in reactor performance. Deviation from the deterministic model increases with increasing variance and decreasing fluctuation frequency of the correlated stochastic coefficients.     

GROUP DELAY AND THE TIME-LAG RELATIONSHIP BETWEEN STOCHASTIC PROCESSES

Abstract. A time-lag interpretation is given for the group delay between continuous-time weakly-stationary stochastic processes, and a corresponding time-lag relationship between stochastic processes is revealed. The group delay for discrete-time processes and its relationship to time leakage are also discussed.     

Zur Bewegung feiner Partikeln,die in turbulent strömenden Medien suspendiert sind

Motion of fine grained particles, suspended in turbulent flow . This article considers the motion of particles, suspended in turbulent flow. If the particles are sufficiently small to respond to turbulence, their motion includes stochastic components. Concerning processes like air classification or separation of fine powders the stochastic contribution – characterized by the conception of a particle diffusivity – the particle motion exhibits a detrimental influence. Sharpness of cut and separation efficiency are reduced. The paper aims to present the state of the art in particle diffusion. First, theoretical investigations are reported, attention being focused on the equation of motion of the particle which is the link between the motion of the fluid and the motion of the particle. Then, experimental results are reviewed. The following tendencies can be seen: Particles which response to turbulence of fluid flow show increasing diffusivity with increasing inertia. Field forces like gravity or electrical field forces exhibit a damping effect on diffusivity.     

Stochastic models of the grinding of disperse materials

A unified methodology for constructing stochastic models of the processes of the grinding of disperse materials is proposed. Using the fundamental relationships of the theory of stochastic Markovian processes, the integrodifferential and diffusion equations of the kinetics of grinding are rigorously derived. Particular solutions of these equations are obtained and their analysis is performed.     

Modeling and theoretical development in controlled radical polymerization

Controlled radical polymerization (CRP) systems have gained increasing interests for the past two decades. Numerous publications may be found in the literature reporting experimental and modeling work on various CRP processes, including their use in surface modification through grafting. Knowledge of underlying mechanism behind polymerization systems is valuable for product design and process optimization. This information may be obtained through the combination of modeling and experimental studies. In this review, published studies on kinetic and stochastic based modeling for CRP systems are summarized. Their relevance in model discrimination of proposed mechanisms is discussed. This review also includes various parameter estimation studies, that is crucial to obtain accurate simulation predictions. Existing issues on the fundamental mechanism in CRP processes are also addressed.     

ON VECTOR AUTOCORRELATIONS AND GENERALIZED SECOND-ORDER FUNCTIONS FOR TIME SERIES

Abstract. Some structural properties of certain vector generalizations of second-order functions of a stationary stochastic process based on determinantial functions of autocovariances are discussed. In particular, a generalized autocovariance function which retains all properties of the ordinary autocovariance function is considered and the linear dependence structure of certain scalar stochastic processes associated with this function is investigated. Properties of the normalized function are discussed and a duality property is found, according to which this function also generalizes in a natural way the ordinary partial autocorrelation function of stochastic processes.     

The simulation of turbulent mixing with simultaneous reaction of miscible reactant streams

The use of stochastic models to predict chemical conversion in turbulent tubular reactors with separate but miscible reaction feed streams has been limited by the inefficiency of the computational processes. This is despite the advantages of the stochastic approach when compared to the more popular diffusional based techniques. Mathematic analysis of the stochastic process leading to direct algabraic representation of the stochastic model is presented which considerably reduces the computational time requirement of the stochastic approach.     

A Novel Stochastic Model of the Photo-Thermoelasticity Theory of the Non-Local Excited Semiconductor Medium

Silicon - A novel technique under the effect of stochastic heating due to the thermal effect of the photothermal theory is investigated. Realistically, stochastic processes are taken on the...     

The dispersion of material in slowly moving fluids

The dispersing action of a mass of slowly moving fluid is modelled by a stochastic partial differential equation. The separate components of the fluid velocity are represented as stochastic processes and appear as coefficients in that equation. These processes can take one of two forms: Markov processes with finite state-space, or independent Ornstein-Uhlenbeck processes. To confirm the predictions of the model they were compared with the mean response to a pulse-like injection of tracer and with the observed cross-correlation between tracer concentration at two points in the fluid. The statistical properties of the velocity processes, as estimated from these tracer studies, were confirmed by direct measurement with a hot-film anemometer probe.     

Deterministic vs. stochastic performance assessment of iterative learning control for batch processes

The performance assessment of linear time‐invariant batch processes when iterative learning control (ILC) is implemented has been discussed. Previous literatures show that conventional performance assessment cannot be directly applied to batch processes due to the nature of batch operations. Chen and Kong have suggested a new method to assess the control performance of batch processes using optimal ILC as the benchmark. In their work, ILC controllers are assumed to affect either stochastic or deterministic performance but without considering their interaction. This work elaborates the controllers effects on both stochastic and deterministic control performance of batch processes. It is shown that the optimal solution based on the minimum variance control law has a trade‐off between deterministic and stochastic performance, which can be shown by a trade‐off curve. Furthermore, a method is proposed to estimate this curve from routine operating data, against which the performance of ILC controllers can be assessed. Simulation studies are conducted to verify the proposed method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 457–464, 2013     

An online change detection test for parametric discrete-time stochastic processes

Detecting a change as fast as possible in an observed stochastic process is an important task. In this article, an online procedure is presented to detect changes in the parameter of general discrete-time parametric stochastic processes. As examples, regression models, autoregressive processes, and Galton–Watson processes are investigated. The test is called cumulative sum (CUSUM) type because it is based on the cumulated sums of the estimates of certain martingale difference sequences belonging to the process. In case of a single change alternative hypothesis, the procedure is examined in terms of consistency. Due to the online manner, the time of change can also be estimated.     

A flexible design framework for process systems under demand-side management

Demand response (DR) has been an appealing strategy for both residential and commercial/industrial customers of electricity due to the increasing penetration of renewable energy resources into the power grid and the deregulation of the energy markets. For industrial DR participants, the management of energy consumption along with the satisfaction of production expectations is generally referred to as demand-side management. Recent research in this area has focused mostly on process scheduling and capacity planning, especially for energy-intensive processes. This article presents a new direction through an optimization-based process design paradigm that allows for the potential reconfiguration of the process flow sheet in real time. Based on a case study of pump network design, a network superstructure is first defined, followed by a two-stage stochastic optimization model. The method of progressive hedging is used to solve the resulting mixed-integer stochastic programming problem. The results demonstrate that, under various scenarios, the reconfigurable design offers significant benefits compared to a fixed network structure in terms of total design cost and expected operating cost.     

A Note on Modelling Seasonal Processes in Continuous Time

It is shown that stochastic differential equations are capable of handling stationary seasonal processes but not processes that are integrated of order 1 at frequency π. Such seasonally integrated processes can be modelled in continuous time but require the use of mixed differential--difference equations.     

INFINITE VARIANCE STABLE ARMA PROCESSES

Abstract. The asymptotic dependence structure of autoregressive moving-average processes with stable innovations is analyzed. The analysis is carried out by means of a measure of dependence which extends the covariance function and is applicable to stochastic processes with infinite variance.     

Parameter estimation in models with hidden variables : An application to a biotech process

Biological processes are often characterised by significant nonlinearities, noisy measurements and hidden process variables. The dynamic behaviour of such processes can be represented by stochastic differential equations obtained from physical laws. We propose a Bayesian algorithm for parameter estimation in stochastic nonlinear biological processes with unmeasured (or hidden) variables. The proposed algorithm, involves drawing random samples iteratively from a posterior density functions of the parameters and the hidden variables. A Bayesian sampling techniques is used to approximate these posterior density functions. Both Metropolis–Hastings algorithm and Gibbs sampling are used for sample generation. The algorithm is extended to handle multiple data sets and missing observations. The algorithm is applied to an experimental data set collected from an algal bioreactor system. © 2011 Canadian Society for Chemical Engineering     

On the Worth of Perfect Information in Bandits with Random Discounting

Abstract

A discrete-time bandit process is a sequential decision problem in which one selects from a finite number of stochastic processes at each stage, and receives as a reward the product of the value of the observed process and a discount factor. In the classical formulation of the problem, the sequence of discount factors is known in advance, but the distributions governing the observations on the stochastic processes are not known. In this paper we consider the case in which the discount sequence is random and compare the reward of observers who have information about the discount sequence from the start with those who do not. In particular, we obtain bounds on the expected rewards for processes in which the discount sequence is random.     

Demand response potential of industrial processes considering uncertain short-term electricity prices

Time-varying electricity prices on the day-ahead and intraday market incentivize demand response of industrial processes. In prior work (Schäfer et al. AIChE J. 2020;66:1-14), we studied the demand response potential with a generalized process model, but neglected the intraday market. Extending our prior investigation, we account for uncertain intraday prices in a mixed-integer linear stochastic programming-based scheduling, that is, we minimize expected cost and conditional value-at-risk in a bi-objective optimization. We find that for very broad variations of the generalized process parameters, the conditional value-at-risk can be reduced significantly without drastically increasing the expected cost. Furthermore, simultaneously improving multiple process parameter leads to synergetic benefits. Moreover, the savings of three electrolysis processes can be more than doubled by marketing flexibility on the intraday market in addition to the day-ahead market. Overall, our model allows for a rapid early assessment of the demand response potential considering the two markets.     

A multi-compartment population balance model for high shear granulation

This work extends the granulation model published by Braumann et al. (2007) to include multiple compartments in order to account for mixture heterogeneity encountered in powder mixing processes. A stochastic weighted algorithm is adapted to solve the granulation model which includes simultaneous coalescence and breakage. Then, a new numerical method to solve stochastic reactor networks is devised. The numerical behaviour of the adapted stochastic weighted algorithm is compared against the existing direct simulation algorithm. Lastly, the performance of the new compartmental model is then investigated by comparing the predicted particle size distribution against an experimentally measured size distribution. It is found that the adapted stochastic weighted algorithm exhibits superior performance compared to the direct simulation algorithm and the multi-compartment model produces results with better agreement with the experimental results compared to the original single-compartment model.     

Dynamic characteristics of binary mixtures in a two-jet fluidized bed

Aiming to understand biomass-related pyrolysis and gasification processes, which have received particular interests recently due to increasing concerns over fossil fuels and carbon emissions, this work conducts a detailed experimental study of the fluidization characteristics and jet dynamics of biomass mixtures in a fluidized bed. Both single jet and two jets dynamics are investigated, and a parametric study of the influence of particle properties and operational conditions on the dynamic performance of the bed, especially on the jet penetration depth and jet frequency of the binary mixtures, is conducted. Detailed frame-by-frame image analysis coupled with physical parameters reveals many interesting phenomena, which includes multistage flow pattern development and a stochastic nature of jet dynamics, as well as a strong dependence of the jet penetration depth and jet frequency on the bed materials.     

Inference on Multivariate Heteroscedastic Time Varying Random Coefficient Models

In this article, we introduce the general setting of a multivariate time series autoregressive model with stochastic time‐varying coefficients and time‐varying conditional variance of the error process. This allows modelling VAR dynamics for non‐stationary time series and estimation of time‐varying parameter processes by the well‐known rolling regression estimation techniques. We establish consistency, convergence rates, and asymptotic normality for kernel estimators of the paths of coefficient processes and provide pointwise valid standard errors. The method is applied to a popular seven‐variable dataset to analyse evidence of time variation in empirical objects of interest for the DSGE (dynamic stochastic general equilibrium) literature.