CONTRIBUTIONS TO EVOLUTIONARY SPECTRAL THEORY

Abstract. The purpose of this paper is to discuss several fundamental issues in the theory of time-dependent spectra for univariate and multivariate non-stationary processes. The general framework is provided by Priestley's evolutionary spectral theory which is based on a family of stochastic integral representations. A particular spectral density function can be obtained from the Wold—Cramér decomposition, as illustrated by several examples. It is shown why the coherence is time invariant in the evolutionary theory and how the theory can be generalized so that the coherence becomes time dependent. Statistical estimation of the spectrum is also considered. An improved upper bound for the bias due to non-stationarity is obtained which does not rely on the characteristic width of the process. The results obtained in the paper are illustrated using time series simulated from an evolving bivariate autoregressive moving-average process of order (1, 1) with a highly time-varying coherence.     

Coupled simulation of the flue gas and process gas side of a steam cracker convection section

A coupled simulation of the flue gas and process gas side of the convection section of a steam cracker is performed, making use of the CFD software package Fluent. A detailed overview of the operating mode of the different heat exchangers suspended in the convection section is obtained. The asymmetric inlet flow field of the flue gas in the convection section, and the radiation from the convection section walls leads to large differences in outlet temperatures of the tubes located in the same row. The flow fields and temperature fields in the tubes of a single heat exchanger differ significantly with e.g., outlet temperatures of the hydrocarbon‐steam mixture ranging from 820 K to 852 K. Moreover, the simulations reveal the presence of hot spots on the lowest tube row, possibly causing fouling. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

In situ active chlorine generation for the treatment of dye-containing effluents

This study examined the possibility to remove colour causing-compounds from synthetic effluent by indirect electrochemical oxidation using iridium oxide anode electrodes. Using a high concentration of chloride ions (17.1 mM) and various current densities, it was possible to produce high concentration of active chlorine with a specific production rate of 2.8 mg min⁻¹ A⁻¹. The best performance for acid methyl violet 2B dye (MV2B) decomposition was obtained using Ti/IrO₂ anodes operated at a current density of 15 mA cm⁻² during 40 min of treatment in the presence of 3.42 mM of chloride ions. Under these conditions, more than 99% of MV2B was removed (with a reaction rate apparent constant of 0.20 min⁻¹), whereas COD and TOC removal were 51% and 75%, respectively. The electrolytic cell was then used for the degradation of three other synthetic dye solutions: Eosin yellowish (EOY), Trypan Blue (TRB), Acridine Orange (ACO). TRB was the most difficult dye to remove from solution with a value reaction rate constant of 0.12 min⁻¹, compared to 0.19 min⁻¹ and 0.24 min⁻¹ recorded for ACO and EOY dyes, respectively. More than 99% of these dyes were removed by electrochemical oxidation.     

Cavern formation in pulp suspensions using side-entering axial-flow impellers

Pulp fibre suspensions display non-Newtonian rheology, including a yield stress. In mixing operations, this creates regions of active motion around the impellers with the cavern size affecting the quality of mixing attained. Due to the opacity of the suspensions, two non-invasive techniques were evaluated for determining cavern dimensions: electrical resistance tomography (ERT) and ultrasonic Doppler velocimetry (UDV), with ERT chosen for most tests due to the speed of data acquisition. Cavern volume as a function of impeller speed is reported for a range of mixing conditions (hardwood and softwood pulp, suspension mass concentrations from one to five percent, two impeller offsets from the wall, and three suspension height-to-chest diameter ratios). A scaled version of a commercial axial flow impeller was used in a standard side-entering configuration. Measured cavern diameters were compared against model predictions available in the literature. The discrepancy between experimental data and model predictions were significant and were attributed to interaction between the developing cavern and the vessel walls. An alternative model was developed for predicting cavern volume taking this interaction into account.     

Compared imbibitions of ordinary and high performance concrete with null or positive water pressure head

A method to simultaneously measure the moisture diffusion coefficient, D_θ, of unsaturated concrete, and the saturated concrete hydraulic conductivity, K_l, was developed for cylindrical specimens placed on a container filled with water that could be maintained at a given hydraulic pressure. Ordinary Portland cement Concrete (OPC) with a moderate and High Performance Concrete (HPC) with a low water to cement ratio were tested. The time dependent distribution of water content in the specimens was measured using a non-intrusive method based on gamma-ray attenuation. The measurements were conducted with varying hydraulic head (positive or null). Boltzmann's transformation was used to analyze the experimental results obtained at different hydraulic pressures and the difference between the null (or atmospheric) and positive pressure results is used to accurately determine K_l and also D_θ . This paper will present the results obtained using this original method, possible interpretations and future research.     

Synthesis of α‐Carbolines Starting from 2,3‐Dichloropyridines and Substituted Anilines

9H‐α‐Carbolines have been prepared via consecutive intermolecular Buchwald–Hartwig reaction and Pd‐catalyzed intramolecular direct arylation from commercially available 2,3‐dichloropyridines and substituted anilines. The combination of a high reaction temperature (180 °C) and the use of DBU were found to be crucial for the intramolecular direct arylation reactions of the 3‐chloro‐N‐phenylpyridin‐2‐amines as no reaction was observed at 120 °C and 180 °C using different inorganic and other organic bases. On the other hand, nitrogen‐methylated pyridine analogues of these substrates {N‐[3‐chloro‐1‐methylpyridin‐2(1H)‐ylidene]anilines} do undergo ring closure at 120 °C, with K₃PO₄ as base, affording the respective 1‐methyl‐1H‐α‐carbolines in good yields.     

Enlèvement du phosphore des eaux usées par traitement à base de tourbe dopée aux boues rouges

The addition of an aluminium and iron doping agent, bauxite red mud, has been tested with a commercial peat for thetreatment of a secondary municipal wastewater. Based on a column study, phosphorus (P) removal was raised from about17% to 21% on peat alone to over 95% with red mud treatment of peat. By this mean, the use of red muds allowed areduction of P, concentration effluent to below 0.15 mg/L. The boosting effect of red mud seemed to decrease with timeand especially with the hydraulic loading. For a hydraulic loading of 30 cm/j, P removal met govermental guidelines (_t effluent < 1 mg/L) for a period of 50 days. Other classic efficiency parameters such as BOD₅, COD and coliforms werenot altered by the use of the doping agent.     

Improvement of the stoichiometric network analysis for determination of instability conditions of complex nonlinear reaction systems

Stoichiometric network analysis (SNA), a known method for analyzing complex reaction systems including biochemical ones, is improved and applied to a nonlinear process studied far from equilibrium in a continuously fed, well stirred tank reactor (CSTR). A particular attention is focused on the determination of the narrow range of the control parameter values where the main steady state is unstable and where different dynamic states can be simulated numerically. The instability region, the most important feature of nonlinear reaction systems, is calculated as a function of the SNA parameters (current rates and reciprocal concentrations of intermediate species in the steady state) and simplified by retaining only the dominant terms. Since the number of the current rates is usually larger than the number of linearly independent equations to be used for their calculation, it is shown here that the current rates can be replaced with a smaller number of reaction rates at the steady state. These rates are related to the experimental data in a simple manner. The instability condition is also written as a function of dimensionless parameters derived from the SNA. This general approach is applied to a model of the Bray–Liebhafsky (BL) reaction having seven reactions without direct autocatalysis or autoinhibition, studied under CSTR conditions. Since the model has six intermediate species, it would be very difficult to analyze its instability condition by the conventional procedure, where a sixth order characteristic equation would have to be solved. On the other hand, the instability condition, obtained easily by the improved SNA, locates correctly the oscillatory region using numerical integration. Other dynamic states found earlier with a larger model of the BL reaction, such as mixed-mode oscillations, period doubling and chaos, are also obtained within the theoretically predicted oscillatory region. Thus, besides the general advantages of the improved stoichiometric network analysis as a method appropriate for the examination of complex nonlinear reactions, we show that the various mentioned dynamic states can be obtained by a very simple variant of the model of the BL reaction realized under CSTR conditions.     

Rotating fluidized bed with a static geometry: Guidelines for design and operating conditions

Computational fluid dynamics (CFD) simulations of the hydrodynamic behavior of rotating fluidized beds in static geometry (RFB-SG) are carried out for gas–solid flows. The rotating motion of the reactor bed is induced by the tangential injection of the gas along the circumference of the fluidization chamber. Steep gradients in the gas velocity fields both in radial and tangential direction generate turbulence. The radial and tangential drag forces fluidize the particle bed in both radial and tangential direction.An Eulerian two-fluid model is used. Gas phase turbulence is accounted for by a k–ε model adapted for rotational flows. The RFB-SG simulations provide guidelines for a design and operation with a high efficiency in gas–solid momentum transfer, excellent gas–solid separation and limited solids losses. Hydrodynamic variables like the centrifugal force, the injection pressure, the radial and tangential slip velocities, solids hold-up are calculated for both polymer particles (300 μm, 950 kg/m³, Geldart Group B) and glass beads (70 μm, 2500 kg/m³, Geldart Group A) to allow for a comparison among different fluidization chamber designs. Unstable bed behavior, like slugging and channeling, is also numerically predicted.